Stability Analysis of Power Transmission of Offshore Wind Farms Fed to Onshore Power Grids Using a

Multi-Terminal VSC-HVDC System

Mi Sa --- Nguyen Thi Department of Electrical Engineering

National Cheng Kung University Tainan City, Taiwan

E-mail: dalat1984@yahoo.com

Li Wang Department of Electrical Engineering

National Cheng Kung University Tainan City, Taiwan

E-mail: liwang@mail.ncku.edu.tw

Abstract This paper presents the analyzed results of a novel power transmission scheme for delivering large generated active power of doubly-fed induction generator (DFIG)-based offshore wind farms (OWFs) fed to onshore AC grids using a multi-terminal HVDC (MT-HVDC) system based on voltage-source converter (VSC). Control scheme for the MT-HVDC system is proposed and designed to transmit total generated active power to two AC grids under various operating conditions. A frequency-domain approach based on a linearized system model using eigenvalue technique and a time-domain scheme based on a nonlinear system model subject to normal and disturbance conditions are both proposed. The modeling and simulations of this paper have been carried out to validate the stability of the proposed control scheme on power transmission of the MT-HVDC system using Matlab/Simulink.

I. INTRODUCTION

HVDC system with multiple points of connection, which is referred to as multi-terminal HVDC (MT-HVDC), is one of the hottest research issues in the whole world today. Linking more than two HVDC terminals to form a MT-HVDC system may have several advantages. Firstly, a meshed grid can be created, which is desirable to provide high power transfer capability combined with operational flexibility and the necessary levels of redundancy and security. Secondly, the outage of one DC line will not interrupt the power flow at any terminal, each terminal can be operated at a different power and current, and the power exchange with all AC connection points can be fully controlled.

The first parallel MT-HVDC system based on line-commutated converter (LCC) was proposed in [1] while a series MT-HVDC system was discussed in [2]. The VSC-

HVDC systems are more suitable to the multi-terminal configuration than the LCC-HVDC systems. The reasons of using the VSC-HVDC system include independent control of reactive power and active power, black-start capability, no commutation failure, and no voltage polarity reversal needed to reverse power [3-4]. The control of VSC-based MT-HVDC transmission for offshore wind power was examined in [5]. A detailed analysis of different MT-HVDC system topologies was discussed in [6]. The steady-state models of converters in VSC-based MT-HVDC systems were investigated for power flow analysis [7].

This paper presents both steady-state and transient analyzed results of large OWFs connected to onshore power grids via a MT-HVDC system. The control schemes using VSC-based MT-HVDC system are also proposed. A systematic analysis using a frequency-domain approach based on both eigenvalue analysis and a time-domain scheme based on nonlinear model simulations are performed to demonstrate the effectiveness of the proposed control scheme.

II. SYSTEM CONFIGURATION AND MATHEMATICAL MODELS

Fig. 1 shows the configuration of the studied three OWFs fed to two AC grids through a five-terminal VSC-based HVDC system. The 80-MW DFIG-based OWFs (OWF #1, OWF #2, and OWF #3) are connected to the studied MT VSC-HVDC system through Converter #A, Converter #B, and Converter #C, respectively. Each OWF is represented by a large equivalent aggregated DFIG driven by an equivalent aggregated variable-speed WT through an equivalent gearbox (GB). An AC network, a capacitor bank, and a local load are connected between each OWF and the corresponding converter. The output terminals of these three converters are connected to the DC lines and fed to AC grids Grid #1 and Grid #2 through Converter #D and Converter #E,

This work is supported by National Science of Council (NSC) ofTaiwan under Grant NSC 100-3113-P-006-014, Grant NSC 100-3113-E-006-013, and Grant NSC 100-ET-E-006-005-ET.

575978-1-4577-1729-1/12/$26.00 2012 IEEE.

respectively. The employed mathematical models of the studied system are described as below.

A. Wind Turbine The captured mechanical power (in W) by a WT can be

written by

31 ( , )2mw w rw W pw w w

P A V C= (1) where w is the air density (kg/m3), Arw is the blade impact area (m2), VW is the wind speed (m/s), and Cpw is the dimensionless power coefficient of the WT, w is the tip speed ratio and w is blade pitch angle (degrees) of the studied WT. B. Mass-Spring-Damper Systems for OWF

The two-inertia reduced-order equivalent mass-spring-damper model of the WT directly coupled to the rotor shaft of the wind DFIG is proposed in [8-9]. The effect of gearbox between WT and DFIG has been included in this model. C. DFIG -based OWFs

The corresponding per-unit (p.u) q- and d-axis voltage-current equations of the DFIG model as well as the detail operation of the converters can be referred to [10].

D. Multi-Terminal VSC-HVDC System Fig. 2 shows a simplified steady-state DC-equivalent

circuit where R1-R6 represent the equivalent DC resistances of the six DC cables. The p.u voltage-current equations of the DC lines between the Converters #A-#C and the Converters #D of the proposed multi-terminal VSC-HVDC system shown in Fig. 1 can be expressed by

(Xi/b)p(Idci) = VdcK Ri Idci V41 (2)

(Xj/b)p(Idcj) = V42 Rj Idcj VdcN (3)

where subscript i=1, 2, 3 represents the order of the three offshore DC cables, K = A, B, C is corresponding to Converter #A, Converter #B, and Converter #C, respectively; subscript j=1, 2 represents the order of the three offshore DC cables, N = D, E is corresponding to Converter #D, and Converter #E, respectively. The relationship between the sending and receiving ends voltages and currents are shown in Fig. 2 can be given as

44 41 4 4 42( )dc dc

b

X p I V R I V

=

(4)

4 1 2 3 5 6dc dc dc dc dc dcI I I I I I= + + = +

(5)

The proposed control block diagrams of VSCs of multi-terminal VSC-HVDC system in this paper are shown in Fig. 3. The corresponding p.u differential equations for controlling the modulation index and phase angle of Converters #A-#E of the studied multi-terminal VSC-HVDC are described as below.

Fig. 2. Steady-state DC equivalent circuit of the five-terminal system

Fig. 1. Configuration of the studied two OWFs and one MCF fed to power grid through a five-terminal VSC-HVDC system

576

( ) ( )_MK K MK stK ref stK KT p M K P P M = (6) ( ) ( )_K K K WFK ref WFK KT p K V V = (7) ( ) ( )_MN N MN stN ref stN NT p M K Q Q M = (8) ( ) ( )0N N N dc dcN dcN dcN NT p K V k I V = + (9)

where subscript st denotes the quantities of converter station, Idc is the dc current of the grid-side converters, Vdc0 is the dc voltage when the dc current is zero, kdc is the slope of the droop characteristic. The power is shared between the two grid-side converters as [4]

1 6

2 5

22

grid dcD dcE

grid dcE dcD

P I k RP I k R

+= =

+ (10)

where R5 and R6 are the equivalent resistances of the cables connected to GSVSC1 and GSVSC2.

(a)

(b)

Fig. 3. The control diagrams of (a) VSC connecting to OWF (b) VSC connecting to an AC network of multi-terminal VSC-HVDC system

III. EIGENVALUES ANALYSIS

The nonlinear system equations developed in Section II can be linearized around a nominal operating point to obtain a set of linearized system equations in matrix form of

pX = AX (11)

where X is the state vector and A is the system matrix with appropriate dimensions. The eigenvalues of the studied system can be obtained by solving the following characteri-stic equation

det(I A) = 0 (12)

where I is an identify matrix having the same dimensions as A and is one of the system eigenvalues. Table I lists the system eigevalues of the studied system under the wind speed Vw of 12 m/s. It is discovered from the eigenvalue results listed in Table I that all eigenvalues are located on the left-hand side of the complex plane and, hence, the studied five-terminal VSC-HVDC system is stable.

IV. TIME-DOMAIN SIMULATIONS This section uses the nonlinear system model developed

in Section II to demonstrate the effectiveness of control scheme on power dispatch performance of the studied five-terminal VSC-HVDC system under different wind speeds. Fig. 4 shows transient responses of the studied system with the proposed MT-HVDC link under different wind speeds and power dispatch between Grid 1 and Grid #2. The wind speed is modeled as the algebraic sum of base wind speed, gust wind speed, ramp wind speed, and noise wind speed [11]. Fig. 4(a) shows the wind-speed responses of different OWFs. When the wind speeds are different, the quantities of the three OWFs such as active power and terminal voltage shown in Figs. 4(b) and 4(c), respectively will be different. Fig. 4(d) plots the all DC-link currents and it is obviously seen that the changes of the DC currents of Converter #D and #E conform to the power sharing between the two AC grids. Fig. 4(e) draws the active power of the two AC grids according to a

TABLE I SYSTEM EIGENVALUES (RAD/S) OF THE STUDIED SYSTEMS

No. Subsystem Eigenvalues No. Subsystem Eigenvalues

1-6 7-12 13-18 19-24 25-30 31-36 37-42 43-48 49-51 52-54 55-57 58-60 61-66 67-72

WT-DFIG Systems

(-4.055 j37383)3 ( -4.0751 j36629)3

( -23.673 j482.21)3 (-6.5538 j375.53)3

( -75.387 j263.72)3 (-57.302 j228.75)3 (-48.266 j73.588)3 (-106.8 j1.4413)3

(-84.7)3 (-10.9 )3 (-0.606)3 (-135)3

(-1.9272 j5.9548)3 (-10.048 j0.0080278)3

73-74 75-76 77-78 79-80 81-82 83 84 85 86 87-91

Multi-HVDC Link

-18.85 j98390 -15.901 j693.34 -48.322 j642.47 -59.433 j580.16 -38.419 j202.45

-100 -12.6 -0.997 -0.999 (-1)5

92-93 Local load -562.27 j4.5077

577

predefined ratio, and it can be seen that it is not significantly affected by wind-speed disturbances.

V. CONCLUSION

This paper has presented the analyzed results of a configuration containing three OWFs fed to two power grids through a five-terminal VSC-HVDC system. Control strategies for the voltage-source converters of the multi-terminal VSC-HVDC system have been proposed. Eigenvalue results of the studied system under steady-state condition have also been carried out. Through the simulation results of power dispatch under different wind speeds, it is found that the dynamic responses of the studied system under different power sharing conditions are stable.

REFERENCES [1] U. Lamm, E. Uhlmann, and P. Danfors, Some aspects of tapping of

H.V.D.C. transmission systems, Direct Current, vol. 8, no. 5, pp. 124-129, May 1963.

[2] J. Reeve and J. Arrillaga, Series connection of converter stations in an HVDC transmission system, Direct Current, vol. 10, no. 2, pp. 72-78, 1965.

[3] V. F. Lescale, A. Kumar, L.-E. Juhlin, H. Bjorklund, and K. Nyberg, Challenges with multi-terminal UHVDC transmissions, in Proc. IEEE Power India Conference and Powercon 2008, New Delhi, India, Oct. 2008.

[4] J. Liang, T. Jing, O. Gomis-Bellmunt, J. Ekanayake, and N. Jenkins, Operation and control of multiterminal HVDC transmission for offshore wind farms, IEEE Trans. Power Delivery, vol. 26, no. 4, pp. 2596-2604, Oct. 2011.

[5] J. Liang, O. Gomis-Bellmunt, J. Ekanayake, and N. Jenkins, Control of multi-terminal VSC-HVDC transmission for offshore wind power, presented at the 13th Int. Eur. Power Electron. Conf. Exhibit., Barcelona, Spain, Sep. 8-10, 2009.

[6] O. Gomis-Bellmunt, J. Liang, R. King, J. Ekanayake, and N. Jenkins, Topologies of multiterminal HVDC-VSC transmission for large offshore wind farms, Elect. Power Syst. Res., vol. 81, no. 2, pp. 271-281, Feb. 2011.

[7] X.-P. Zhang, Multiterminal voltage-sourced converter based HVDC models for power flow analysis, IEEE Trans. Power Systems, vol. 18, no. 4, pp. 1877-1884, Nov. 2004.

[8] D. J. Trudnowski, A. Gentile, J. M. Khan, and E. M. Petritz, Fixed-speed wind-generator and wind-park modeling for transient stability studies, IEEE Trans. Power Systems, vol. 19, no. 4, pp. 1911-1917, Nov. 2004.

[9] S. M. Muyeen, M. H. Ali, R. Takahashi, T. Murata, J. Tamura, Y. Tomaki, A. Sakahara, and E. Sasano, Transient stability analysis of wind generator system with the consideration of multi-mass shaft model, International Conference on Power Electronics and Drives Systems, vol. 1, pp. 511-516, 16-18 Jan. 2006.

[10] L. Wang and K.-H. Wang, Dynamic stability analysis of a DFIG-based offshore wind farm connected to a power grid through an HVDC link, IEEE Trans. Power Systems, vol. 26, no. 3, pp. 1501-1510, Aug. 2011.

[11] L. Wang, K. Wang, W. Lee, and Z. Chen, Power-Flow control and stability enhancement of four paralleloperated offshore wind farms using a linecommutated HVDC link, IEEE Trans. Power Del., vol. 25, no. 2, pp. 1190-1202, Apr. 2010.

a) Wind Speed

b) Pw

c) Vw

d) Idc

e) Pgrid

Fig. 4. Transient responses of studied system under different wind speeds and power dispatch sharing between two grids

0 5 10 15 20 25 30 35 40 45 5010

12

14

16

t (s)

Win

dspe

ed(m

/s)

Wsp3 Wsp2 Wsp1

0 5 10 15 20 25 30 35 40 45 50

0.7

0.8

0.9

1

t (s)

Pw(p.

u.)

Pw1 Pw2 Pw3

0 5 10 15 20 25 30 35 40 45 501.36

1.38

1.4

t (s)

Vw(p.

u.)

Vw1 Vw2 Vw3

0 10 20 30 40 50-1

0

1

2

t (s)

Idc(p

.u.)

Idc1Idc2Idc3Idc5Idc6Idc4

0 5 10 15 20 25 30 35 40 45 500

0.5

1

1.5

t (s)

Pgrid

(p.u.

)

Pg.1

Pg.2

578

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