DECENTRALISED CONTROL FOR DAMPING MULTI- MODAL OSCILLATIONS THROUGH CSC/VSC BASED HVDC TRANSMISSION TECHNOLOGIES Y.Pipelzadeh, B.Chaudhuri, T.C.Green Control and Power Research Group, Imperial College London, U.K., {y.pipelzadeh08, b.chaudhuri, t.green}@imperial.ac.uk Keywords: High Voltage Direct Current (HVDC), Power Oscillation Damping (POD), Decentralised Control, Multi-Input-Multi-Output (MIMO) System Identification, Wide-area Signals Abstract The damping of multi-modal oscillations through supplementary control of multiple HVDC systems is presented. The resulting controller produced is a fixed low- order decentralised controller, capable of providing adequate damping towards the low-frequency power oscillations. Linear analysis is substantiated with non-linear simulations in DIgSILENT PowerFactory with detailed representation of HVDC links. 1 Introduction With major reinforcements worth approximately £4.7 billion by 2020 to accommodate 45 GWs of new generation, of which 34 GWs anticipated from wind to meet EU target of ‘15% energy from renewables’ [1], the application of HVDC transmission technologies within the existing GB network as a means of enhancing the transfer capacity and improving the system dynamics is becoming more evident. In recent years there has been vast interest into the application of decentralised control techniques to design damping control devices in power systems. A number of approaches to decentralised control have been proposed [2-5]. However, the focus of most of them are on decentralised design of low-order PSS in a SISO or MIMO framework; or otherwise, on the robust control design techniques which evidently result in high order controllers and thus proving a practical limitation amongst the network operators. Ramos et al. [4] used dynamic output feedback for decentralised design using LMIs considering multiple operating conditions. The controller order, however, is at least, as high as the open-loop plant. Messina et al. used a decentralised approach to co-ordinate multiple FACTs devices using classical control approach; however, it may lack robustness with varying operating conditions [5]. Modulation of the active power order of an HVDC link could be extremely effective for damping low-frequency power oscillations [6], thereby increasing the transfer capacity of an AC transmission system. This paper examines the application of decentralised controllers through supplementary control of combined CSC/VSC HVDC systems for the damping of low-frequency electromechanical modes of oscillations which are inherent in large interconnected power systems. Subspace-based, MIMO system identification is used to estimate and validate linearised state-space models through pseudo random binary sequence (PRBS) probing in DIgSILENT. The impact of both current source converter (CSC) and voltage source converter (VSC) based HVDC with only their primary control on the system stability is examined. VSC stations offer damping services at both ends of the line which could raise the stability limit of the remaining AC routes through modulation of either the active or reactive powers, or both, at each converter station. Hence, offering more flexibility than CSC systems where only the active power can be modulated. There are tremendous potential for VSC-HVDC systems to contribute towards improvement in AC system dynamics. Here, secondary control among the available control variables in both CSC-HVDC and VSC- HVDC is demonstrated. The objective here is to establish by how much transmission system capacity might be improved by raising the AC stability limits through a series of DC upgrades with secondary control action. The contributions of this paper are as follows: Development of detailed HVDC models in DIgSILENT PowerFactory MIMO system identification and validation using sub-space state-space system identification ( N4SID) The design of a decentralised controller to damp multiple swing modes through CSC/VSC HVDC devices Validate the findings through linear and non-linear simulations in DIgSILENT PowerFactory
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DECENTRALISED CONTROL FOR DAMPING MULTI-
MODAL OSCILLATIONS THROUGH CSC/VSC BASED
HVDC TRANSMISSION TECHNOLOGIES
Y.Pipelzadeh, B.Chaudhuri, T.C.Green
Control and Power Research Group,
Imperial College London, U.K., {y.pipelzadeh08, b.chaudhuri, t.green}@imperial.ac.uk
Keywords: High Voltage Direct Current (HVDC), Power
Oscillation Damping (POD), Decentralised Control,
Multi-Input-Multi-Output (MIMO) System Identification,
Wide-area Signals
Abstract
The damping of multi-modal oscillations through supplementary control of multiple HVDC systems is presented. The resulting controller produced is a fixed low-
order decentralised controller, capable of providing adequate damping towards the low-frequency power oscillations. Linear analysis is substantiated with non-linear simulations in DIgSILENT PowerFactory with detailed representation of HVDC links.
1 Introduction
With major reinforcements worth approximately £4.7 billion by 2020 to accommodate 45 GWs of new generation, of which 34 GWs anticipated from wind to meet EU target of ‘15% energy from renewables’ [1], the application of HVDC transmission technologies within the existing GB network as a means of enhancing the transfer capacity and improving the
system dynamics is becoming more evident. In recent years there has been vast interest into the application of decentralised control techniques to design damping control devices in power systems.
A number of approaches to decentralised control have been proposed [2-5]. However, the focus of most of them are on decentralised design of low-order PSS in a SISO or MIMO framework; or otherwise, on the robust control design techniques which evidently result in high order controllers and thus proving a practical limitation amongst the network
operators. Ramos et al. [4] used dynamic output feedback for decentralised design using LMIs considering multiple operating conditions. The controller order, however, is at least, as high as the open-loop plant. Messina et al. used a
decentralised approach to co-ordinate multiple FACTs devices using classical control approach; however, it may lack robustness with varying operating conditions [5].
Modulation of the active power order of an HVDC link could be extremely effective for damping low-frequency power
oscillations [6], thereby increasing the transfer capacity of an AC transmission system. This paper examines the application of decentralised controllers through supplementary control of combined CSC/VSC HVDC systems for the damping of low-frequency
electromechanical modes of oscillations which are inherent in large interconnected power systems. Subspace-based, MIMO system identification is used to estimate and validate linearised state-space models through pseudo random binary sequence (PRBS) probing in
DIgSILENT. The impact of both current source converter (CSC) and voltage source converter (VSC) based HVDC with only their primary control on the system stability is examined. VSC stations offer damping services at both ends of the line which could raise the stability limit of the remaining AC routes through modulation of either the active or reactive
powers, or both, at each converter station. Hence, offering more flexibility than CSC systems where only the active power can be modulated. There are tremendous potential for VSC-HVDC systems to contribute towards improvement in AC system dynamics. Here, secondary control among the available control variables in both CSC-HVDC and VSC-
HVDC is demonstrated. The objective here is to establish by how much transmission system capacity might be improved by raising the AC stability limits through a series of DC upgrades with secondary control action. The contributions of this paper are as follows:
Development of detailed HVDC models in DIgSILENT PowerFactory
MIMO system identification and validation using
sub-space state-space system identification ( N4SID)
The design of a decentralised controller to damp
multiple swing modes through CSC/VSC HVDC devices
Validate the findings through linear and non-linear simulations in DIgSILENT PowerFactory
2 Test Cases in DIgSILENT
2.1 Test System
A 14-machine, 59-bus study system, shown in Fig.1, was
considered for the case study. This system has been recently adopted as an IEEE benchmark for stability studies [7].
Figure 1 Simplified 14-machine equivalent of Australian system modelled in DIgSILENT
The detailed description of the study system including network data and dynamics data for the generators, excitation systems, PSSs and SVCs can be obtained from [7]. The network constitutes of 5 areas in which areas 1 and 2 are more closely coupled electrically. Therefore, in essence the power
system is made of 4 main regions and has 3 inter-area modes, as well as 10 local-area modes. The machines are equipped with either IEEE type AC1A, AC4A or ST5B excitation system models. All generators are supplied with speed-input power system stabilizers of second and fourth order transfer functions. Five Static VAr Compensators (SVCs), set in
voltage control mode, are installed at nominated bus terminals (1 in each area), to improve the voltage profile of the system. The loads are all assumed to be of Constant Impedance (CI) type for all operating conditions.
2.2 Problem Formulation
The power system shown in Fig.1 was modelled and
benchmarked against standard results [7] in DIgSILENT PowerFactory. To investigate power oscillation damping (POD) control through HVDC, 6 of the 14 PSSs were placed
out of service to create a more oscillatory behaviour (see Table 1 for relative damping and frequency of inter-area modes). A point-to-point VSC- HVDC link was added in parallel to the AC corridors between area 2 and area 4 and a CSC- HVDC link was added in parallel to the AC corridors in area 1 and area 2 (see Figure 2).
Area 1
Area 4
Area 2
VS
C-H
VD
C
P =
50
0 M
W
MWP
MWP
L
Gen
450
317
MWP
MWP
L
Gen
9550
10550
MWP
MWP
L
Gen
4500
5187
Vd
cr
Vd
ci
Pi
Qi
Pr Q
r
Vdcr
Pi Pr
CSC-HVDC
AC
tran
sm
iss
ion
line
AC
tra
ns
mis
sio
n
lin
es
P = 1134 MW
P =
10
00
MW
Phasor Data
Concemtrator (PDC)
Qr m
od
P
r mo
d
Qi m
od
Co
ntro
l
ce
nte
r
Co
ntro
l
ce
nte
r
Area 3
MWP
MWP
L
Gen
2300
1836
Area 5
MWP
MWP
L
Gen
5500
5140
P =
50
0 M
W
Control
center
AC transmission lines
Pr mod
PMU at
bus 507PMU at
bus 405
bus angles 507 bus angles 405
AC
tra
ns
mis
sio
n
lin
es
Figure 2 14-machine, 5-area test system with CSC-HVDC and VSC-HVDC link. Secondary control loops with PMU signals are shown
Both CSC and VSC based HVDC systems are modelled in detail in DIgSILENT Power Factory. The primary controls for CSC-HVDC is based on the CIGRE benchmark model [8] with rating of +/- 500kV, 1000MW link. The VSC link has rating of +/- 150kV, 350MW.
The DC links accommodate 50% of the total inter-area flows (originally accounted by the AC lines but now placed out of service - see grey transmission lines in Fig.1). Out of several scenarios considered the heavy loading scenario is presented here. In steady-state operation the active power order for CSC-HVDC was set to 50% of 1134MW and VSC-HVDC
accommodating 50% of 500MW. The reactive power order was set to maintain close to unity power factor at the AC bus terminals. The problem is then formulated as the ability of the converter stations to provide services that enable optimised power flow and stabilising services (through control centres) for
extending the stability limit of the AC network.
Grids
Area 1Area 2Area 3CSC-HVDCArea 4Area 5Complete GridVSC Grid
VSC HVDC
CSC HVDC
MPS_2
Area 1
CP
S_4
TP
S_4
EPS_2
BPS_2
TPS_5
PPS_5
YPS_3
SP
S_4
Area 3
Area 2
Area 4
Area 5
HPS_1
BPS_2
LPS_3
242.6501.055
241.0071.048
240.9631.048
339.3260.984
345.7301.048
324.5730.984
20.0001.000
279.1251.015
348.1501.055
343.3261.040
20
.00
01
.00
0
20
.00
01
.00
0
20
.00
01
.00
0
20
.00
01
.00
0
281.0661.022
280.6181.020
277.8681.010
283.2501.030
15.0001.000
15.0001.000
288.1581.048
20.0001.000
22
8.4
26
1.0
38
51
8.3
32
1.0
37
34
1.8
44
1.0
36
285.4931.038
22
3.5
39
1.0
16
22
3.3
00
1.0
15
33
5.6
18
1.0
17
33
6.5
54
1.0
20
50
9.6
31
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19
50
8.5
05
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17
50
8.7
17
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50
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39
1.0
10
52
1.0
42
1.0
42
20
.00
01
.00
0
345.7931.048
345.2491.046
15.0001.000
344.3841.044
286.7881.043
275.0001.000
272.0850.989
28
5.1
44
1.0
37
270.7770.985
345.2901.046
28
7.7
95
1.0
47
28
7.2
42
1.0
45
286.2071.041
331.6751.005
336.1461.019
518.6021.037
331.2281.004
331.2521.004
288.4001.049
527.8771.056
341.9001.036
340.0581.030
33
6.7
08
1.0
20
20.0001.000
20.0001.000
20.0001.000
20.0001.000
199.07..-0.000..0.474 kA
-199.0..0.000 ..0.330 kA
-200.0..-0.000..0.479 kA
200.00..0.000 ..0.334 kA
-592.9..-37.21..0.992 kA
592.96..37.218..1.424 kA
-600.0..-0.699..1.021 kA
600.00..0.699 ..1.067 kA
249.86..-13.58..0.506 kA
-245.8..22.236..0.503 kA
450.00..45.000..0.755 kA
-313.5..-197.3..0.619 kA
313.56..208.64..
14.497 kA
1260.0..126.00..2.252 kA
279.08..-147.5..0.562 kA
-271.8..126.85..0.501 kA
279.71..-147.7..0.563 kA
-272.4..127.13..0.502 kA
292.79..8.699 ..0.510 kA
-288.4..-22.89..0.515 kA
743.68..124.97..1.268 kA
-705.1..110.36..1.270 kA
743.68..124.97..1.268 kA
-705.1..110.36..1.270 kA
303.40..-10.54..0.529 kA
-296.9..-5.690..0.528 kA
432.23..47.743..0.747 kA
-423.1..-23.54..0.754 kA
G~
2950.2..811.99..
88.332 kA
2950.2..811.99..
88.332 kA
-2950...-481.7..5.027 kA
-800.0..-61.65..1.648 kA
800.00..160.26..
31.404 kA
SVS
-0.000..-22.64..0.047 kA
SVS
-0.000..-8.288..0.017 kA
SVS
0.000 ..-41.99..0.088 kA
SV
S
-0.0
00
..-6
0.1
6..
0.1
56
kA
SVS
0.000 ..32.891..0.055 kA
840.73..169.99..1.448 kA
-83
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35
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1.4
51
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721.39..47.172..1.209 kA
-69
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-0.000..65.673..0.110 kA
0.000 ..32.672..0.055 kA
-0.000..-29.36..0.062 kA
0.000 ..-58.17..0.124 kA
1255.0..126.00..2.648 kA
575.00..58.000..1.226 kA
53
0.0
0..
53
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0..
1.0
78
kA 260.00..
26.000..0.557 kA
15
0.0
0..
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0.3
02
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740.00..74.000..1.500 kA
990.00..99.000..1.992 kA
254.62..-50.44..0.434 kA
-252.4..-2.287..0.421 kA
254.62..-50.44..0.434 kA
-252.4..-2.287..0.421 kA
255.83..-45.03..0.435 kA
-254.6..17.612..0.427 kA
255.83..-45.03..0.435 kA
-254.6..17.612..0.427 kA
-209.0..83.732..0.473 kA
209.63..-87.93..0.482 kA
-209.0..83.732..0.473 kA
209.63..-87.93..0.482 kA
-255.8..27.059..0.518 kA
25
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21
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21
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21
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-209.2..-62.86..0.459 kA
-209.2..-62.86..0.459 kA
21
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33
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3 k
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15
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62
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-145.7..-92.35..0.366 kA
14
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62
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23
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445.35..-19.56..0.950 kA
-424.2..119.79..0.935 kA
445.35..-19.56..0.950 kA
-424.2..119.79..0.935 kA
33
0.3
2..
-10
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62
3.7
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411.59..-86.50..0.842 kA
-383.5..23.766..0.819 kA
411.59..-86.50..0.842 kA
-383.5..23.766..0.819 kA
411.59..-86.50..0.842 kA
-383.5..23.766..0.819 kA
-176.4..20.652..0.356 kA
17
8.0
2..
-26
.80
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.36
1 k
A
251.57..-44.72..0.515 kA
-249.2..31.147..0.503 kA
251.57..-44.72..0.515 kA
-249.2..31.147..0.503 kA
255.83..-27.05..0.518 kA
-255.8..28.702..0.432 kA
255.83..-27.05..0.518 kA
-255.8..28.702..0.432 kA
14
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42
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0 k
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44.848 kA
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44.848 kA
200.00..40.000..0.416 kA
800.00..160.00..1.695 kA
1000.0..200.00..2.109 kA
300.00..60.000..0.613 kA
161.62..15.281..0.334 kA
-160.8..-22.55..0.337 kA
274.37..39.221..0.570 kA
-273.7..-39.14..0.572 kA
-244.6..-20.74..0.510 kA
246.16..19.652..0.507 kA
553.83..42.006..1.141 kA
-551.4..-23.10..1.142 kA
600.00..50.693..
17.382 kA
-600.0..33.170..1.204 kA
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31.404 kA
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17.382 kA
-436.0..-54.50..0.904 kA
436.00..100.85..
17.225 kA
144.80..-37.99..0.300 kA
-139.8..-50.53..0.309 kA
144.80..-37.99..0.300 kA
-139.8..-50.53..0.309 kA
-5.085..-50.29..0.105 kA
5.194 ..-8.591..0.020 kA
-5.085..-50.29..0.105 kA
5.194 ..-8.591..0.020 kA
-114.8..-15.62..0.241 kA
115.07..8.872 ..0.239 kA
145.86..-38.09..0.307 kA
-139.8..-11.69..0.290 kA
145.86..-38.09..0.307 kA
-139.8..-11.69..0.290 kA
249.97..-13.57..0.506 kA
-245.9..22.231..0.503 kA
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415.19..-13.55..0.694 kA
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88
1.8
6..
-10
6.1
..1
.00
8 k
A
-87
9.5
..9
3.8
97
..1
.00
2 k
A
88
1.8
6..
-10
6.1
..1
.00
8 k
A
-87
9.5
..9
3.8
97
..1
.00
2 k
A
12
94
.1..
-64
.01
..1
.47
1 k
A
-12
90
...
79
.50
3..
1.4
68
kA
60
.93
2..
-20
2.5
..0
.24
0 k
A
-60
.89
..1
89
.82
..0
.22
6 k
A
14
39
.1..
19
0.3
5..
1.6
09
kA
-14
19
...
-69
.75
..1
.62
5 k
A
43
7.6
2..
-23
6.2
..0
.56
9 k
A
-43
6.9
..2
01
.94
..0
.54
6 k
A
93
9.9
0..
15
4.5
7..
27
.49
7 k
A
-93
9.9
..-6
1.8
5..
2.3
81
kA
13
80
.4..
11
5.6
8..
1.5
35
kA
-13
60
...
-8.8
43
..1
.54
4 k
A
13
80
.4..
11
5.6
8..
1.5
35
kA
-13
60
...
-8.8
43
..1
.54
4 k
A
42
00
.0..
98
4.2
7..
12
4.5
2..
-42
00
...
-42
1.7
..4
.67
7 k
A
G ~
93
9.9
0..
15
4.5
7..
27
.49
7 k
A
G ~
42
00
.0..
98
4.2
7..
12
4.5
2..
G~
14
00
.0..
42
9.0
6..
42
.27
0 k
A
G~
313.56..208.64..
14.497 kA
304.85..-61.30..0.519 kA
-301.7..19.606..0.501 kA
1840.0..184.00..3.219 kA
480.00..48.000..0.811 kA
1660.0..166.00..2.908 kA
1700.0..170.00..2.978 kA
210.00..21.000..0.358 kA
18
80
.0..
18
8.0
0..
3.2
40
kA
130.00..13.000..0.218 kA
390.00..39.000..0.650 kA
0.000 ..-303.0..0.528 kA
0.000 ..-402.9..0.702 kA
-570.2..16.064..0.994 kA
584.86..53.899..0.992 kA
774.85..101.84..1.307 kA
-737.5..128.31..1.305 kA
774.85..101.84..1.307 kA
-737.5..128.31..1.305 kA
17
7.4
1..
-10
3.3
..0
.35
2 k
A
-176.7..90.751..0.337 kA
17
7.4
1..
-10
3.3
..0
.35
2 k
A
-176.7..90.751..0.337 kA
721.39..47.172..1.209 kA
-69
9.7
..7
7.0
25
..1
.20
7 k
A
-534.4..-160.1..0.621 kA
537.20..30.751..0.589 kA
-534.4..-160.1..0.621 kA
537.20..30.751..0.589 kA
-1.500..-105.4..0.184 kA
1.673 ..87.416..0.150 kA
40.958..-12.58..0.075 kA
-40.93..-0.633..0.071 kA
40.958..-12.58..
0.075 kA
-40.93..-0.633..0.071 kA
780.08..81.461..1.319 kA
-750.8..97.783..1.318 kA
780.08..81.461..1.319 kA
-750.8..97.783..1.318 kA
635.07..106.33..1.106 kA
-631.0..-85.21..1.108 kA
547.81..61.126..0.936 kA
-538.8..-21.10..0.940 kA
547.81..61.126..0.936 kA
-538.8..-21.10..0.940 kA
547.81..61.126..0.936 kA
-538.8..-21.10..0.940 kA
293.65..-39.27..0.495 kA
-288.4..10.468..0.485 kA
294.10..-39.23..0.496 kA
-288.9..10.434..0.486 kA
-55.12..-54.90..0.130 kA
55.394..-45.74..0.119 kA
55.394..-45.74..0.119 kA
-55.12..-54.90..0.130 kA
1068.9..320.20..1.242 kA
-1068...-241.4..1.882 kA
2500.0..698.22..
74.931 kA
-2500...-356.0..4.264 kA
1500.0..558.70..
46.207 kA
-1500...-385.8..2.630 kA
3600.0..596.78..105.34..
-3600...-122.7..6.023 kA
G~
1500.0..558.70..
46.207 kA
G~
2500.0..698.22..
74.931 kA
G~
3600.0..596.78..105.34..
-0.000..65.880..0.110 kA
3 Design Approach
3.1 Linear Model Estimation and Validation
Since it is not possible to directly obtain the linearised system models from DIgSILENT then system identification technique was used to estimate the linear model from the
simulated outputs in response to appropriate probing signals at the inputs. Here, the linear model has 3 control inputs - Pr, Qr and Qi for the VSC HVDC and 1 control inputs – Pr for the CSC HVDC and 16 possible phase angle measurements available from the PMUs. Identification of such MIMO systems is quite challenging and gets further complicated with
increase in number of output signals [9]
The amplitude of the PRBS was chosen to be high enough to sufficiently excite the critical modes without pushing the responses into nonlinear zone. Persistent excitation of at least the model order of interest was provided. Moreover, the
probing sequence for different inputs was ensured to be uncorrelated [10]. Typical PRBS injection signals used for probing the test system is shown in Fig. 3. The process for model identification and validation is illustrated in Fig.4. Using the input probing signal
and output responses
the matrices
were calculated such that the simulated
data resembled the responses from the estimated linear model. Numerical algorithm for subspace state space system identification (N4SID) [11] was used to estimate the above matrices. A model order of 35 was found to be appropriate. To validate the model an input pulse signal was applied to the identified and full model (see Fig.4).
Figure 3 Typical PRBS injection used for system identification
Actual Power System
SV
C
SV
C
SV
CS
VC
SV
CS
VC
C S C H V D C L i n k
Gri
ds
Are
a 1
Are
a 2
Are
a 3
Are
a 4
Are
a 5
Co
mp
lete
Gri
d
HV
DC
Gri
d
HV
dc
I
nt
er
-t
ie
VP
S_
2
PP
S_
5
GP
S_
4
CPS_4
TPS_4
EP
S_
2
BP
S_
2
NP
S_
5
TP
S_
5
PP
S_
5
YP
S_
3
SPS_4
Are
a 3
Are
a 1
Are
a 2
Are
a 4
Are
a
5
HP
S_
1
TP
S_
5
BP
S_
2
LP
S_
3
SV
S
SV
S
SV
S
SVS
SV
S
G~
G~
G ~
G~
G~
G~
G~G~
G~
G ~
G ~
G~
G~G~
DIgSILENT
14-machine, 5-area power system
( 163rd
order)
System Identification (N4SID)
Validation
Full Model
SV
C
SV
C
SV
CS
VC
SV
CS
VC
C S C H V D C L i n k
Gri
ds
Are
a 1
Are
a 2
Are
a 3
Are
a 4
Are
a 5
Co
mp
lete
Gri
d
HV
DC
Gri
d
HV
dc
In
ter-
tie
VP
S_
2
PP
S_
5
GP
S_
4
CPS_4
TPS_4
EP
S_
2
BP
S_
2
NP
S_
5
TP
S_
5
PP
S_
5
YP
S_
3
SPS_4
Are
a 3
Are
a 1
Are
a 2
Are
a 4
Are
a
5
HP
S_
1
TP
S_
5
BP
S_
2
LP
S_
3
SV
S
SV
S
SV
S
SVS
SV
S
G~
G~
G ~
G~
G~
G~
G~G~
G~
G ~
G ~
G~
G~G~
DIgSILENT
163rd
Order
Identified Model
Linear Model ( 35th Order)
nnnDuCxy
nnnBuAxx
1
Input Output
HVDC
Intertie
Simulated Outputs
Measured Outputs
VSC
Intertie
Pr
Qr
Qi
Pr
CSC
Intertie
1 51 29630 [s ]
-3 0 .9
-3 1 .2
-3 1 .5
-3 1 .8
-3 2 .1
-3 2 .4
Bu s 9 : Vo lta g e a n g le , d e g
1 51 29630 [s ]
0 .0
-0 .2
-0 .4
-0 .6
-0 .8
-1 .0
Bu s 5 : Vo lta g e a n g le , d e g
1 51 29630 [s ]
-9 .8-1 0 .0-1 0 .2-1 0 .4-1 0 .6-1 0 .8-1 1 .0
Bu s 6 : Vo lta g e a n g le , d e g
1 51 29630 [s ]
-1 E+ 1-1 E+ 1-1 E+ 1-1 E+ 1-1 E+ 1-1 E+ 1-1 E+ 1
Bu s 1 1 : Vo lta g e a n g le , d e g
Bus Angle, degPRBS probing signal
15.012.09.06.03.00.0 [s]
1.00
0.60
0.20
-0.20
-0.60
-1.00
Identified Model A: bus1 - bus3, deg
Actual Model A: bus1 - bus3, deg
15.012.09.06.03.00.0 [s]
0.60
0.36
0.12
-0.12
-0.36
-0.60
Identified Model B: bus8 - bus3, deg
Actual Model B: bus8 - bus3, deg
15.012.09.06.03.00.0 [s]
0.30
0.18
0.06
-0.06
-0.18
-0.30
Identified Model B: bus9 - bus3, deg
Actual Model B: bus9 - bus3, deg
15.012.09.06.03.00.0 [s]
0.70
0.46
0.22
-0.02
-0.26
-0.50
Identified Model A: bus2 - bus3, deg
Actual Model A: bus2 - bus3, deg
15.012.09.06.03.00.0 [s]
1.40
0.84
0.28
-0.28
-0.84
-1.40
Identified Model A: bus6 - bus3, deg
Actual Model A: bus6 - bus3, deg
15.012.09.06.03.00.0 [s]
2.00
1.20
0.40
-0.40
-1.20
-2.00
Identified Model B: bus1 - bus3, deg
Actual Model B: bus1 - bus3, deg
15.012.09.06.03.00.0 [s]
1.50
1.00
0.50
0.00
-0.50
-1.00
Identified Model B: bus 2- bus3, deg
Actual Model B: bus2 - bus3, deg
15.012.09.06.03.00.0 [s]
0.30
0.18
0.06
-0.06
-0.18
-0.30
Identified Model A: bus7 - bus3, deg
Actual Model A: bus7 - bus3, deg
Pr Pr
Pr-Qr-Qi-UiQr-Qi
Pr-Qi Pr-Qi
Qr Qr
400MW 600MW
86420 [s ]
2
1
0
-1
-2
Prm o d _ CSC: M W (a )
86420 [s ]
2
1
0
-1
-2
Qrm o d _ VSC: M VAr
86420 [s ]
2
1
0
-1
-2
Prm o d _ VSC: M W
Identification
15129630 [s]
0.2
0.1
0.0
-0.1
-0.2
Vdcimod: kV
15129630 [s]
2
1
0
-1
-2
Prmod: MW
15129630 [s]
2
1
0
-1
-2
Qrmod: MVAr
15129630 [s]
2
1
0
-1
-2
Qimod: MVAr
3210 [s ]
0 .0 1
0 .0 1
0 .0 1
0 .0 0
0 .0 0
-0 .0 0
Ea s t Sid e : In p u t Sig n a l
Input pulse signal
Figure 4 Model identification and validation process
3.2 Signal Selection Product of modal controllability and observability gives the Residue which indicates the extent to
which mode can be observed and controlled through input and output . The elements of an eigenvector are complex
numbers, in general, and as such modal controllability ,
modal observability and residue are all complex
numbers with a magnitude and a phase angle component. Once the residues corresponding to all possible input-output combinations are calculated and sorted in descending order of
magnitude, the appropriate ones are chosen from the top (with highest residues) to ensure minimum control effort. Bus angles 405 and 507 (from area 4 and 5 respectively) yielded the highest residues and are subsequently chosen as the feedback signals for the damping controller.
3.3 Controller Design
In this work a decentralised control framework is used at the rectifier and inverter end control centres of the HVDC transmission systems (see Fig. 2). There are 4 possible control (modulation) inputs Prmod, Qrmod, Qimod (for VSC-HVDC) and Prmod (for CSC-HVDC), and 16 pre-selected outputs -
the phase angles measured by the PMUs installed at 16 buses. Residues were calculated for all possible input-output combinations. For the case study presented, it was found from modal residues that modulating the CSC-HVDC active power and reactive power on rectifier side of VSC-HVDC would effectively meet the design objective of 10.0 s settling.
Further control centres can obviously be used to possibly provide improved results. The conceptual representation of a decentralised control system for MIMO systems is shown in Fig. 5.
Power System
with Multiple
HVDC links
G(s)
Qrmod
Qimod
Prmod
Prmodr1r1 r1
r2
r3
r4
)(2 sK
y1
y2
y3
y4
)( sK
)(4 sK
)(1 sK
)(3 sK
-
-
-
-Decentralised
controller
Figure 5 Conceptual representation of a decentralised control system
for damping control
A control system is referred to as decentralised if the off-
diagonal elements of the controller transfer function matrices are zero, as shown in the equation below.
86420 [s]
2
1
0
-1
-2
Prmod_CSC: MW (a)
86420 [s]
2
1
0
-1
-2
Qrmod_VSC: MVAr
86420 [s]
2
1
0
-1
-2
Prmod_VSC: MW
It follows that each control centre can be designed for
individual HVDC converter station without any loss of performance or interacting with other control loops [12]. It is important to structurally decompose the decentralised control system into individual SISO loops to reduce the problems of interaction [5].The system consists of a set of SISO loops as shown in Fig.6.
4
3
1
1
sT
sT
2
1
1
1
sT
sTK
sTw
sTw
1
bus angle, degHVDC modulation
signal
ControllerWashout
limX
limX
8
7
1
1
sT
sT
6
5
1
1
sT
sT
Figure 6 Control centres composed of individual decentralised control,
The use of decentralised structure can result in performance degradation compared to a full feedback system. However, it leads to reduction in the number of tuning parameters, simplified hardware and is vastly used by industry compared to a centralised approach.
3.4 Controller Synthesis
The decentralised damping controller is required to ensure a settling time of 10.0 s for all operating conditions considered during the design stage whilst ensuring optimum control effort is achieved. An objective function is minimised such that that the poles of the closed loop system are properly placed under each scenario. The objective function is as
follows:
Subject to the following constraints,
Any evolutionary technique can be used to solve this multi-objective constrained optimisation problem (i.e. genetic algorithm, particle swarm optimisation). The resulting controller is a 2-input, 2-outputs, with each channel of 4
th
order (see Fig.6). The controller was obtained using a PSO technique. The interested reader is referred to [13].
4 Simulation Results
4.1 Linear Analysis The location of the open-loop (blue) and closed-loop (black) poles (dominant modes of interest) are shown in Fig.7 for the nominal operating condition. A direct left shift for the three critical poles beyond the respective reference damping ratio
lines can be observed with minimal frequency variation (shown by the arrow).
The robustness of the designed controller is evaluated in terms of damping ratio ( ), frequency of oscillation ( and
the settling time ( for each individual modal oscillations across a range of operating conditions. Due to limited space the results presented here are for the nominal operating point.
Figure 7 Location of open-loop and closed-loop poles (not including the higher frequency and fast settling modes) under nominal
operating condition
Figure 8 Open-loop and closed-loop settling times (in sec) for the
three modal oscillations under the nominal operating condition.
The closed-loop settling times for the critical inter-area modes, shown in Fig.8, are within the target settling time of 10.0 s. This indicates that the original design specification (specified by the horizontal solid line) is achieved.
The impact of both VSC and CSC based HVDC systems within the AC system on the relative damping ratio (ζ) and modal frequency (ƒ) with only their primary control is shown in Table 1. Referring to Table 1, in closed-loop, c), it can be seen that the
damping ratios are significantly improved from those in b) to achieve the minimum settling time (see bold-faced). The range of frequency variation is not too significant; 0.03 Hz (0.27 – 0.30Hz), 0.1Hz (0.35-0.45Hz) and 0.01Hz (0.52-0.53Hz) for modes 1, 2 and 3, respectively. A constraint on
-1.5 -1 -0.5 0-10
-8
-6
-4
-2
0
2
4
6
8
10
10
8
6
4
2
10
8
6
4
2
0.4
0.2
0.13 0.09 0.062 0.042 0.026 0.012
0.4
0.2
0.13 0.09 0.062 0.042 0.026 0.012
Real Axis
Imagin
ary
Axis
the frequency can be considered in the design stage to minimise the variation but the impact is not considerable.
Mode a) AC system only
b) with multiple HVDC
c) Multiple HVDC + POD
no. ζ, % ƒ, Hz ζ, % ƒ, Hz ζ, % ƒ, Hz
1 10.1 0.29 10.2 0.27 20.7 0.30
2 11.1 0.35 12.9 0.35 18.0 0.45
3 6.5 0.55 5.5 0.52 14.6 0.53
Table 1 Relative damping ratio, ζ, and modal frequency, ƒ, of multiple HVDC with primary controls (b) and with POD control (c) against AC system only (a) for the nominal operating condition.
The performance in presence of nonlinearities is presented in the next section through time domain simulations.
4.2 Nonlinear Simulation
Nonlinear simulations are conducted in DIgSILENT PowerFactory to demonstrate the performance of the designed
controller. A severe three-phase solid fault at a critical bus (Inverter-side of CSC) for 5 cycles (100ms) followed by outage of one of the adjacent lines between area 1 and area 2 is simulated. The top two subplots (a, b) show the angular separation
between G503, G301 with the slack generator G101; the power flow in the AC corridor between areas 2- 4 is exhibited in (c) and the HVDC modulation signals required to damp out the oscillation’s is shown in (d). The CSC-HVDC bus voltage ends are shown in (e, f) and finally the VSC-HVDC Inverter d-axis and q-axis currents ( ) are plotted in (g and h)
respectively.
Figure 9 Dynamic behaviour of the system following a fault at bus 102 for 5 cycles and subsequent outage of line 102_207
Figure 9 (a, b, c) show that oscillations settle slightly beyond 10.0 s. This is due to the severity of the fault which has violated the limits of the VSC-HVDC, as is evident from (d). It is also clear from (d) that a considerably higher control effort is demanded from reactive power VSC modulation signal Qrmod as compared to the modulation signal required
from the CSC Pr mod. During the fault, the dc bus voltages at both HVDC ends drop sharply due to reduction of ac side power transfer. This is followed by oscillations in Vdcr due to the dc link dynamics while the Vdci is regulated to a constant
value, see subplots (e, f). Because of the magnitude of the fault close to inverter bus, Idi is seen to violate its respective limits, see subplot (g).
5 Summary
The damping of multi-modal oscillations through supplementary control of multiple HVDC systems is
presented. It was found that active power modulation through CSC and reactive power modulation through VSC provided adequate damping through an 8
th order (2input- 2output)
decentralised controller.
Acknowledgements
Support from the EPSRC UK under grant EP/F037686
(Power Networks Research Academy) is gratefully acknowledged.
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Trans. Power Syst., 2001
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[4] RAMOS R., ALBERTO L., BRETAS N.: ‘ A new methodology for the coordinated design of robust decentralized power system damping controllers’, IEEE Trans. Power Syst., 2004, 19, (1), pp. 444-454
[5] MESSINA A. R., BEGOVICH O.: ‘Design of multiple FACTs controllers for damping inter-area oscillations: a decentralized control approach, Elsevier, 2004, pp.19-29
[6] ARRILLAGA J., LIU Y.U., WATSON N.R.: ‘Flexible
Power Transmission: the HVDC options’ Wiley, 2007 [7] GIBBARD M., VOWLES D.: "Simplified 14-Generator
Model of the SE Australian Power System," 2007. [8] SOOD V.K.: ‘HVDC and FACTS Controllers:
Applications of Static Converters in Power Systems’ Kluwer Power Electronics Series, 2004.
[9] WELLSTEAD P. E., ZARROP M. B.: ‘Self-tuning Systems Control and Signal Processing’, Wiley, 1991.
[10] HSIA T. C.: ‘System identification: least-squares method’
linear systems: theory, implementation, applications’,
Boston, London: Kluwer, 1996. [12] SKOGESTAD S, and POSTETHWAITE I, ‘Multivariable
Feedback Control: Analysis and Design,’ Wiley, 2007. [13] CHAUDHURI B., RAY S., MAJMUMDER R., ‘Robust
low-order controller design for multi-modal power oscillation damping using flexible AC transmission system devices, IET Gen, Trans & Distr, Vol.3, (5), pp.448-459, 2009