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Analytical Investigation of Factors Influencing Controllability of MMC-VSC-HVDC on Inter-area and
Local Oscillations in Interconnected Power Systems Ngoc Tuan Trinh
Network Consulting Siemens AG
Erlangen, Germany [email protected]
Istvan Erlich Institute of Power Systems
University of Duisburg-Essen Duisburg, Germany
Abstract –This paper investigates various factors influencing the capability of MMC-VSC-HVDC systems to enhance damping of system oscillations. The investigation is done in the frequency-domain using a detail model of a MMC-VSC-HVDC system. Simulation results demonstrating the controllability of MMC-VSC-HVDC systems on inter-area and local oscillations in interconnected power systems are described. It is revealed that voltage-dependency characteristics of system loads, inertia and impedance of interconnected AC systems are significant factors influencing the damping support ability of a MMC-VSC-HVDC system. The influencing tendencies of the factors are different to different oscillation types (inter-area and local) and on different modulation channels (active & reactive powers).
Index Terms – Controllability, Inter-Area Oscillations, Modular Multilevel Converter, Power Oscillation Damping, Voltage-Sourced Converter
I. INTRODUCTION
The VSC-based HVDC systems are recently reported to possess a promising capability in improving the damping of system oscillations [1-6]. Analyses have been done in time domain and frequency domain simulations. Different POD controllers are used, such as the PSS-based POD controller [1], the modal linear quadratic Gaussian (MLQG) [4] or model predictive control (MPC) controllers [5]. The benefits of applying POD controllers on both the active and reactive (P&Q) modulation channels are also reported. However, main influencing factors on the capability of MMC-VSC-HVDC systems in enhancing damping of system oscillations cannot be easily recognized due to either the complex oscillations in the investigated large systems or the various designs of the applied POD controllers.
The paper focuses on investigating the several potential influencing factors on the damping capability of a MMC-VSC-HVDC system. They are voltage-dependency characteristics of system loads, inertia and impedance of interconnected AC systems. To assess the investigated factors, the controllability of the MMC-VSC-HVDC system of the oscillation modes is used. The variations of the
controllability under various study cases are observed and analyzed to discover influencing tendencies of the factors to the damping capability of a MMC-VSC-HVDC system.
The analysis in this paper is done using a two-area system for much of the results presented. The small system enables us to concentrate on factors which particularly influence the effect of the MMC-VSC-HVDC system on system oscillations. It is ideally proved suitable for studies related to the stability and control of local and inter-area modes, without the overwhelming complexity of actual interconnected power systems. However, results of simulations on the small system still reveals the key phenomena obtained from simulations in large systems.
The paper is aimed to demonstrate a methodology to investigate the damping capability of a MMC-VSC-HVDC system and derive general influencing tendencies of the investigated factors basing on the investigation results using the test system.
II. CHARACTERISTICS OF THE TEST SYSTEM
The test network used in this study is shown in Fig. 1. The test system is a 50 Hz system with three generators located in two areas. The two areas are interconnected via a high voltage AC transmission line and a point-to-point MMC-VSC-HVDC connection. The generators are modeled by a sixth-order model, and are equipped with speed governors
Fig. 1. Two-Area Test System.
1
G1 G3~= ~
=VSC1 VSC2
C9
50 km500 km
1380 MW 684 MW
2400 + j750 MVA
C7
Area 1 Area 2
300 + j70 MVA
7 9
10 4
377 MW
700 MW
100 km
6
G2720 MW
3
11
150 km
Line param.
R’ (O/km) 0.0278 0.01200.2550 -14.127 210.0
L’C’
(O/km)(nF/km)
AC DCPI - modelPGi
(MW)
1380720684
Gen. i1
TAi
(s)13
2 103 10
SGNi
(MVA)
1800900900
vGi (pu)
1.031.031.01 Uk: 16%
UDC: ±320 kVSN: 900 MVA
UN: 400/350 kVSN: 900 MVA
TransformerConverter
LC: 50 mH
151515
500 km
ukTi
(%)
978-1-5090-4168-8/16/$31.00 ©2016 IEEE
(GOV), automatic voltage regulators (AVR) and power system stabilizers (PSS). There are two load centers LOAD7 and LOAD9 that are represented as constant impedances. The power transferred from area 1 to area 2 is also denoted in Fig. 1. The AC system is created by modifying the 10-bus-4-generator network used in [7]. The generator controller data are given in appendix. The other parameters of the modeled generators, VSC stations, lines and loads can be found in Fig. 1. This is the base case of this study.
A. Linearized model of the test system
The complete state-space representation of the entire system can be obtained by combining the state-space models of individual devices and the AC network. In this study, synchronous generators including AVR and GOV are in form of the current injection model derived following the description in [7]. The MMC-VSC-HVDC system is represented by a linearized model, developed in [8]. The validation of the linearized model against the established EMT model can be found in [8]. Figure 2 illustrates the model schematic diagram for the MMC-VSC-HVDC system. The figure also reveals the linkage between linearized modules and between the MMC-VSC-HVDC system and the interconnected AC system. The linearized model of the MMC-VSC-HVDC system is also represented in form of the current injection model. Therefore, the state equation for the MMC-VSC-HVDC system and synchronous generators in the system may be combined into the form:
⎥⎥⎦
⎤
⎢⎢⎣
⎡
Δ⎥⎦
⎤⎢⎣
⎡=
⎥⎥⎦
⎤
⎢⎢⎣
⎡
Δ v
x
DC
BAi
x
DD
DD&
(2.1)
where x is the state vector of the complete system; i is the current injection into the network from the devices; v is the vector of the system bus voltage; AD and CD are the block
diagonal matrices composed of Ai and Ci associated with individual generators and MMC-VSC-HVDC systems.
In this work, the AC network is represented by the node equation with the admittance matrix YN:
vYi Δ=Δ N (2.2)
Substituting equation (2.2) in Equation (2.1) yields the overall system state equation:
AxxCDYBAx =−+= ))(( D-1
DNDD& (2.3)
B. Modal analysis
The analysis of the state matrix of the complete system reveals two interesting low frequency oscillation modes (see Table I). The test system contains two weakly damped oscillatory modes. The first oscillation mode M1 at 1.24 Hz is a local mode characterizing the swinging of G2 against G3. The second mode M2 is a weakly damped inter-area oscillation mode between generator G1 and generator group G2/G3 at 0.71 Hz. The controllability of the VSC-HVDC system to these modes will be analyzed in the next section.
III. CONTROLLABILITY MEASURE
The capability of the MMC-VSC-HVDC system in improving system oscillation damping depends on many influencing factors. Input/output signals and the design of POD controllers equipped to the MMC-VSC-HVDC system are among the most important. The input signals are associated to the observability of oscillation modes. They are
Fig. 2. Linearized model structure of a point-to-point MMC-VSC-HVDC system [8]
AC interconnected system
ordAC,1qΔ
ordDC,1pΔ
DC,1pΔ
DC,1pΔ
DC,1vΔ
RI,1vΔ
dq,1iΔ
Tiq,id,idq, )( ii ΔΔ=Δi
TiI,iR,iRI, )( vv ΔΔ=Δv
AC-side linearized model
DC-side linearized model DC-grid linearized model
ordAC,2qΔ
ordDC,2pΔ
DC,2pΔ
DC,2pΔ
DC,2vΔ
RI,2vΔ
dq,2iΔ
AC-side linearized model
DC-side linearized model
Direct and quadrature terminal current vector
Real and imagine terminal voltage vector
DCNDCNDCN xAx =&DC,1DCI,1dq,1DCI,1 vΔ+Δ+ DiCRI,1DCI,1DCI,1DCI,1 vBxA Δ+=iDCI,x&
ordDC,1DCI,1 pΔ+ F
=ACV,1x& RI,1ACV,1ACV,1ACV,1 vBxA Δ+ordAC,1ACV,1DC,1ACV,1 qp Δ+Δ+ EC
DCNDCN pB Δ+DC,2DCI,2dq,2DCI,2 vΔ+Δ+ DiCRI,2DCI,2DCI,2DCI,2 vBxA Δ+=DCI,2x&
ordDC,2DCI,2 pΔ+ F
=ACV,2x& RI,2ACV,2ACV,2ACV,2 vBxA Δ+
TiDC,iDCI,iDCI, )...(... px Δ=x
TDC,2DC,1DCN )( vv ΔΔ=x
TDC,2DC,1DCN )( pp ΔΔ=Δp
ordAC,2ACV,2DC,2ACV,2 qp Δ+Δ+ EC
the superscript T denotes the transposition
TiACV,iq,id,iACV, ...)...( xii ΔΔ=x State variable vector including terminal
current and ac control module state variables
State variable vector including dc control module state variables and an algebraic variable pDC,i
State variable vector associated with capacitor voltages of the dc grid model
Algebraic variable vector of dc power
MMC-VSC 1
MMC-VSC 1
MMC-VSC 2
MMC-VSC 2
Δ
TABLE I EIGEN VALUE ANALYSIS RESULTS
Mode Mode type
Eigen value analysis result Oscillating generator group Freq. (Hz) Damp. (%)
M1 Local 1.24 +5.6 G2 vs. G3 M2 Inter-area 0.71 +1.8 G1 vs. G2/G3
978-1-5090-4168-8/16/$31.00 ©2016 IEEE
selected from signals measured locally or globally and provided through wide-area measurement systems. The output signals refers to VSC stations and modulation channels in which the POD controllers are incorporated. They are linked to the controllability of oscillation modes. The POD controller designs are to realize the capability provided by the inputs and outputs. There are several controller designs, such as PSS-based, MPC based, MSLQ based, Fuzzy –based designs. This study focuses on analysis the factors influencing the controllability of the MMC-VSC-HVDC system of the oscillation modes.
To access the controllability of the MMC-VSC-HVDC, a controllability measure is defined according to the geometric approach [9]. The controllability measure is defined as:
Let us consider a power system in which a POD controller is to be applied. The linearized model of the entire system is described by:
⎩⎨⎧
=+=
Cxy
BuAxx& (3.1)
where x is the state vector; y is the output vector; u is the input vector; A, B, C are state, input, and output matrices, respectively. Let the eigenvalue λi, i = 1,2,…,n, of A assumed to be distinct.
Let ei and fi be respectively the right and left eigenvectors associated with the distinct eigenvalue λi, i.e., Aei = λiei, fi
*A = λifi
* where fi* is the conjugate transpose of fi and the pairs
(ei, fi*) have been scaled so that fi
*ei = 1. The right and left eigenvectors ei and fi are orthogonal and normalized.
The controllability measures mci associated with mode i following the geometric approach is defined, as follows [9]:
iTk
iTk
kici )),(cos((k)fb
fbbfm == θ (3.2)
where bk is the kth column of B; the superscript T denotes the transposition; |z| and ||z|| are respectively, the modulus and the Euclidian norm of z; θ (fi, bk) is the acute angle between the input vector bk and the left eigenvector fi.
IV. INVESTIGATION RESULTS
The controllability of the modulation channels (denoted by P or Q) of VSC stations (denoted by 1 or 2) of system oscillations (M1, M2) are studied with the considerations of the following influencing factors: voltage-dependency characteristic of load, loading level and impedance of the parallel AC line L7-9, impedance of series AC line L9-10, and inertia of the area 2 (receiving end area). The variations of the investigated factors are created in such the way that the load flow and the two oscillation modes of the test system are not dramatically changed.
A. Effect of voltage-dependency characteristics of system load
To investigate the effect of the load characteristics on the controllability, three models of the system load are
investigated: the constant impedance model (const. Z), the constant current model (const. I) and the constant active/reactive power model (const. PQ). With these load models, the controllability measures for these modes are calculated and shown in Fig. 3.
For the P channel, the controllability measures of VSC1 and VSC2 are almost identical for the both modes. The controllability measures of the inter-area mode are higher than the local mode. As Fig. 3 shows, the controllability measure of the inter-area mode increases with the reduction the voltage-dependent level of the system loads, while the controllability measure of the local mode slightly decreases.
For the Q channel, the controllability measures are strongly influenced by the VSC station location and the voltage-dependent level of the system loads. If the system load is highly voltage-dependent (i.e. const. Z load), the closer VSC station to the load center is, the greater influence on modulating the system load the Q channel has. Therefore the controllability measure is the higher. When the voltage-dependency level decreases, different tendencies are observed. For the local mode, the controllability measures increases at both VSC stations. For the inter-area mode, the controllability measures increase at the VSC 1 (located away from to the biggest load center) but decrease at VSC2 (located close to the biggest load center).
B. Effect of impedance of parallel line
In this investigation, the impedance of the parallel line L7-9 is reduced to electrically bring the area 1 closed to the area 2. By doing so, the impact of the area 1 on the load center LOAD09 increases. The simulation results are shown in Fig. 4. Due to the greater impact of the area 1 on the system loads, and the stronger relation with the area 2, the controllability of the VSC-HVDC connection on both channels reduces for both modes. The reduction for inter-area mode is stronger than the local mode. There is an exception to the Q channel of VSC1. When the impedance of the parallel line is reduced, the VSC1 is also electrically located closer to the load center. It has the greater influence on modulating the system load. Therefore, the controllability measures of the local mode slightly increase.
C. Effect of loading level of the parallel line
The variations of the loading level of the parallel line L7-9 are studied and the simulation results are plotted in Fig. 5. The results show that, the loading level has insignificant influences on the controllability of the VSC-HVDC.
D. Effect of impedance of receiving-end area
In this investigation, the impedance of the series line L9-10 is reduced to bring the area 2 electrically closed to the VSC 2. The calculations show that, the controllability measures of the MMC-VSC-HVDC system on the P channel for both modes increases. In contrast, the controllability measures of Q channel insignificantly vary. The simulation results are shown in Fig. 6.
978-1-5090-4168-8/16/$31.00 ©2016 IEEE
Active power modulation channel
Reactive power modulation channel
Fig. 3. Effect of voltage-dependency character of system loads.
Active power modulation channel
Reactive power modulation channel
Fig. 4. Effect of impedance of parallel AC line
Active power modulation channel
Reactive power modulation channel
Fig. 5. Effect of loading level of parallel AC line
Active power modulation channel
Reactive power modulation channel
Fig. 6. Effect of impedance of receiving-end area
Active power modulation channel
Reactive power modulation channel
Fig. 7. Effect of inertia of receiving-end area
0,0
0,4
0,8
1,2
1,6
2,0
Z load I load PQ const.
Cont
rola
bilit
y m
easu
re (1
0-4)
Load typeM1-P1 M1-P2 M2-P1 M2-P2
0,0
0,2
0,4
0,6
0,8
1,0
Z load I load PQ const.
Cont
rola
bilit
y m
easu
re (1
0-4)
Load typeM1-Q1 M1-Q2 M2-Q1 M2-Q2
0,0
0,4
0,8
1,2
1,6
2,0
500km 350km 200kmCont
rola
bilit
y m
easu
re (1
0-4)
L7-9(km)
M1-P1 M1-P2 M2-P1 M2-P2
0,0
0,2
0,4
0,6
0,8
1,0
500km 350km 200kmCont
rola
bilit
y m
easu
re (1
0-4)
L7-9 (km)
M1-Q1 M1-Q2 M2-Q1 M2-Q2
0,0
0,4
0,8
1,2
1,6
2,0
Low (377MW) Medium (467MW) High (557MW)
Cont
rola
bilit
y m
easu
re (1
0-4)
Loading levelon L7-9M1-P1 M1-P2 M2-P1 M2-P2
0,0
0,2
0,4
0,6
0,8
1,0
Low (377MW) Medium (467MW) High (557MW)
Cont
rola
bilit
y m
easu
re (1
0-4)
Loading levelon L7-9M1-Q1 M1-Q2 M2-Q1 M2-Q2
0,0
0,4
0,8
1,2
1,6
2,0
90km 50km 10km
Cont
rola
bilit
y m
easu
re (1
0-4)
L9-10(km)
M1-P1 M1-P2 M2-P1 M2-P2
0,0
0,2
0,4
0,6
0,8
1,0
90km 50km 10km
Cont
rola
bilit
y m
easu
re (1
0-4)
L9-10(km)
M1-Q1 M1-Q2 M2-Q1 M2-Q2
0,0
0,4
0,8
1,2
1,6
2,0
10s 8s 6s
Cont
rola
bilit
y m
easu
re (1
0-4)
TA(s)
M1-P1 M1-P2 M2-P1 M2-P2
0,0
0,4
0,8
1,2
1,6
2,0
10s 8s 6s
Cont
rola
bilit
y m
easu
re (1
0-4)
TA(s)
M1-Q1 M1-Q2 M2-Q1 M2-Q2
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E. Effect of inertia of receiving-end area
The purpose of this analysis is to see how the controllability of the oscillations of the VSC-HVDC system is affected when the inertia of the sending-end area (area 2) reduces. The simulation results show that the controllability measures notably increase for both types of the modes and on both modulations channels (see Fig. 7).
V. RELATIVE COMPARISON WITH THE CONTROLLABILITY
OF THE VOLTAGE REFERENCE OF THE AVRS
One of the most effective solutions to improve the damping of the system oscillations is the use of PSS equipped to the voltage reference of the AVRs. Such control activity through the AVR of the generators which are deeply involved in the system oscillation modes provides a high possibility to influence the modes. In this section, an impression about the numerical values of the controllability measures of the MMC-VSC-HVDC system is relatively made by a comparison with the controllability of the voltage reference of the AVR.
The table II provides the resulted controllability measures of the voltage reference of the AVR of the three generators for each oscillation mode. The results shows that the controllability measures of the MMC-VSC-HVDC system are considerably lower than that of the voltage reference of the AVR at all the modes.
VI. SUMMARY AND CONCLUSION
The MMC-VSC-HVDC connection has a moderate controllability of the system oscillations. The controllability on the P channel of the inter-area oscillation is higher than one of the local oscillation. Whereas the controllability for the Q channel of both the inter-area oscillation and the local oscillation depends very much on the electric distance to load centers. Comparison between VSC1 and VSC2 shows that, the more closely to load centers the VSC station locates the more controllability of the both oscillation modes it has.
For the VSC station located near to the load center (VSC2), the controllability of both channels for both modes increases when: the electric distance to the sending end area increases (weaker area 1); the electric distance to the receiving end area decreases (stronger area 2).
The investigation results show that the controllability of the modulation channels of both the oscillation modes is quite sensitive to the voltage-dependency level of the system loads. The voltage-dependency level has different influences on the controllability of the modulation channels. When the voltage-dependency level reduces, the controllability measures of the P channel of inter-area oscillations increase while of the local
oscillations decrease. Whereas, the controllability measures of the P channel of the inter-area oscillations and of the local oscillations vary in the reversed direction, correspondingly.
The investigation results also show that the inertia of the generators in the receiving-end area has significantly influences on the controllabilities of the modulation channels of both the oscillation. If the inertia of the generators decreases, the controllability measures increase.
APPENDIX
All parameters of the generator controllers in per unit are in basic of power and voltage ratings of the generator.
A. Governor for G3
B. AVR+PSS for G1, G2, G3
REFERENCES [1] N.T. Trinh, I. Erlich, S. P. Teeuwsen, "Methods for Utilization of
MMC-VSC-HVDC for Power Oscillation Damping," IEEE PES General Meeting, Washington DC, 27-31 July 2014, pp. 1-5.
[2] Chunye Li, Sheng Li, Fuchun Han, Jingfu Shang, Ermin Qiao, "A VSC-HVDC fuzzy controller to damp oscillation of AC/DC power system," IEEE International Conference on Sustainable Energy Technologies, Singapore, 24-27 Nov. 2008, pp.816 - 819
[3] H.F. Latorre, M. Ghandhari, L. Soder, "Use of local and remote information in POD control of a VSC-HVdc," IEEE Bucharest PowerTech, Bucharest, 28 June-02 July 2009, pp.1 - 6
[4] R. Preece, A.M. Almutairi, O. Marjanovic, J.V. Milanovic, "Damping of electromechanical oscillations by VSC-HVDC active power modulation with supplementary wams based modal LQG controller," IEEE PES General Meeting, San Diego, CA, 24-29 July 2011, pp. 1– 7.
[5] A. Fuchs, M., Imhof, T. Demiray, M. Morari, "Stabilization of Large Power Systems Using VSC–HVDC and Model Predictive Control," IEEE Transactions on Power Delivery, vol. 29, issue 1, pp. 480 – 488.
[6] L. Zeni, R. Eriksson, S. Goumalatsos, M. Altin, P. Sorensen, A. Hansen, P. Kjaer, B. Hesselbaek, "Power Oscillation Damping from VSC-HVDC connected Offshore Wind Power Plants," IEEE Transactions on Power Delivery, published on30 April 2015 (DOI: 10.1109/TPWRD.2015.2427878)
[7] P. Kundur, "Power system stability and control," New York: McGraw-Hill, 1994, ch. 12, pp. 835.
[8] N.T. Trinh, I. Erlich, M. Zeller, K. Wuerflinger, "Generic Model of MMC-VSC-HVDC for Interaction Study with AC Power System," IEEE Transactions on Power Systems, vol. 31, no. 1, pp. 27-34, Jan. 2016
[9] H. M. A. Hamdan and A. M. A. Hamdan, “On the coupling measures between modes and state variables and subsynchronous resonance,” Elect. Power Syst. Res., vol. 13, pp. 165–171, 1987.
s311
+
s+1
1s101
1
+∑
20.0
1
2.0 ∑∑
MinpMECH
0.90
-0.05
0.9
Load reference
-
-ωΔ
s
s
101
10
+20
s
s
02.01
05.01
++
0.1
-0.1s
s
4.51
0.31
++ωΔ
s01.01
1
+ B1
)1(250
sT
s
++
∑
Reference
-tv
EFD
kONkON = 0 for G2 kON = 1 for G1 and G3TB = 5s for G1; TB = 3s for G2 TB = 7s for G3
TABLE II CONTROLLABILITY MEASURES OF THE VOLTAGE REFERENCE OF THE AVRS
Mode Mode type
Controllability measure (x10-4)
G1 G2 G3
M1 Local 1.50 19.5 27.6 M2 Inter-area 16.0 17.4 13.6
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