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Enhancement of voltage quality in a passive network supplied by a VSC-HVDC transmission under disturbances
Electrical Power and Energy Systems 54 (2014) 45–54
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Enhancement of voltage quality in a passive network supplied by a VSC-HVDC transmission under disturbances Xin Tang a,⇑, Dylan Dah-Chuan Lu b a b
Department of Electrical Engineering, The Changsha University of Science & Technology, Changsha 410076, China School of Electrical and Information Engineering, The University of Sydney, NSW 2006, Australia
a r t i c l e
i n f o
Article history: Received 22 February 2013 Received in revised form 18 June 2013 Accepted 28 June 2013
Keywords: AC voltage control Voltage quality Nonlinearity compensation VSC-HVDC
a b s t r a c t When a VSC-HVDC transmission is connected to a passive network, the receiving AC system is weak and is subject to power quality problems such as voltage sag and swell. Dynamic performance of voltage control would affect the voltage quality in the receiving AC system directly. The direct voltage control (DVC) method is simple but fails to quickly eliminate voltage fluctuation caused by load current change. One solution is to add a feed-forward controller to the DVC. The inverter nonlinearities, however, degrade the performance of the feed-forward controller. This paper presents a modified direct voltage control to enhance control dynamics in the receiving AC system by overcoming the effect of inverter nonlinearities. In the proposed control scheme, the influence of inverter nonlinearities on the performance of the feed-forward controller is first discussed. A compensation method for nonlinearities of the inverter is then designed in the d–q rotating axis. Moreover, to overcome parameter sensitivity of the feed-forward controller, a feed-back loop with a PI controller is implemented. Simulation results from PSCAD/EMTDC showed that the VSC-HVDC system using the proposed control scheme, as compared to that with the conventional control methods, has a better capability to mitigate voltage fluctuation during system disturbances. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction POWER supply from onshore utility grid to offshore drill platforms or islands has advantages of cost effectiveness and less emission of greenhouse gas. Due to the capacitive charging currents of AC cables, DC transmission offers a feasible solution for subsea transmission. There are two categories of high-voltage directcurrent (HVDC) schemes currently available – conventional HVDC [1] and voltage-source converter (VSC)-HVDC [2]. The conventional HVDC has several limitations and undesirable characteristics including being physically large and requiring the ac network with sufficient short-circuit ratio. The VSC-HVDC, which uses modern semiconductors with self-commuted ability, overcomes the disadvantages of conventional HVDC and is therefore more suitable for a weak ac network [3] or a passive network without any power sources. A passive network supplied by VSC-HVDC transmission is a relatively isolated power system for the reactive power supply is not from utility grid but mainly from the inverter station of VSC-HVDC transmission. The inverter station often possesses a relatively large phase reactor, the receiving AC system is therefore considerably ⇑ Corresponding author. E-mail addresses: [email protected] (X. Tang), [email protected] (D.D.-C. Lu). 0142-0615/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.06.030
weak and subject to power quality problems such as voltage sag and swell due to load changes [4,5]. Network voltage control becomes a challenging task as a result. However, existing literature mainly focuses on topologies [6–8] and control strategies for ride-through disturbances [9–11] and, to the best knowledge of the authors, rarely discusses voltage quality problem under disturbances. The root-mean-square voltage of AC bus at inverter station is usually expected to be constant in a passive network which is supplied by VSC-HVDC transmission. The inverter station then operates in constant AC voltage control mode. Since the short-circuit capacity of AC bus at the inverter station in a passive network is smaller than that in a grid, larger fluctuation of voltage at the AC bus in the passive network can occur under disturbances. An example of disturbances that causes voltage sag and swell is switching on and off of load. To improve voltage quality, voltage control of inverter station connecting to a passive network is required to have a faster response to disturbances than that connecting to a large AC system [12–16]. There are mainly two categories of constant voltage control methods, namely, direct voltage control (DVC) [6,17,18] and cascade vector control (CVC) [9,11]. The DVC method uses the deviation between the reference value and the measured value by means of a PI-controller to provide a suitable value for modulation index. The DVC method is simple but does not compensate load current disturbance. Consequently, it fails
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X. Tang, D.D.-C. Lu / Electrical Power and Energy Systems 54 (2014) 45–54
used to transform the abc-axis signals to a d–q rotating frame is expressed as
to eliminate quickly the voltage fluctuation caused by load current change. The CVC method with an outer voltage control loop and an inner current control loop has been proposed to control the inverter station which can independently control active and reactive powers. Normally, the control bandwidth of the outer voltage loop is designed to be five or ten times narrower than that of the inner current control loop. Hence, the cascaded vector controller has poorer dynamics response to voltage sag/swell. The aim of this paper is hence to improve voltage quality during disturbances through a modified direct voltage control in the receiving AC system (i.e. a passive network) which is supplied by a VSC-HVDC transmission. Firstly, a feed-forward controller is designed in rotating d–q frame. The influence of inverter nonlinearity on the control dynamic is further analyzed. Based on this analysis, a nonlinearity compensation method is proposed. In addition, a PI regulator is applied to overcome parameter sensitivity of the feedforward compensation. Simulation results using PSCAD/EMTDC are reported to confirm the designed control scheme under different operation conditions.
3 cos h cos h 23p cos h þ 23p 7 26 p ¼ 4 sin h sin h 23p sin h 23p 5 3 1=2 1=2 1=2 2
3. voltage control scheme 3.1. Feed-forward control The control goal is to regulate the voltage at PCC2 so that high quality power is fed to the loads. In other words, the d-axis voltage component us2D is expected to keep constant and the q-axis voltage component us2Q is expected to be zero when d-axis is fixed to the PCC2 voltage space vector. The control system will be able to not only regulate the output voltage according to the reference voltage but also reject properly disturbances from the load current. From (1) and (2), to the d–q voltage component us2D and us2Q, the disturbances from the load currents are (R + sL)is2D xLis2Q and (R + sL)is2Q + xLis2D respectively. When the inverter nonlinearities is not considered, the feed-forward compensation can be designed as (R + sL)is2D + xLis2Q and (R + sL)is2Q xLis2D to the respective voltage component us2D and us2Q. The feed-forward controller is shown in Fig. 2.
2. System description Fig. 1 shows the main circuit diagram of a VSC-HVDC transmission connected to a passive network in which the converter transformer and phase reactor between VSC and point of common-coupling (PCC) are represented as a series combination of an inductor L and a resistor R. The inverter station connects to a rectifier station, which is connected to a strong grid, through DC cables. The reactors are used for controlling the active and reactive power flow by regulating the current through them and for reducing the high frequency content of the AC line current caused by the switching of the VSC. Shunt AC filters are also implemented to reduce the switching ripple on AC voltage and current. The capacitor provides an energy buffer to keep the power balance during transients and for reducing the voltage ripple on the DC side. The rectifier station contains both DC voltage control and reactive power control. The inverter station regulates the voltage at PCC2. In Fig. 1, us1, uc1, udc1, us2, uc2 and udc2 denote PCC voltage, output voltage of VSC station and DC voltage on rectifier and inverter sides respectively. The dynamic voltage equations in the rotating dq frame can be written as follows:
L
dis2D ¼ Ris2D xLis2Q þ uc2D us2D dt
ð1Þ
L
dis2Q ¼ Ris2Q þ xLis2D þ uc2Q us2Q dt
ð2Þ
3.2. Influence analysis and compensation of inverter nonlinearities The abc-axis voltage references supply to the inverter station can be expressed as
uc2a ðtÞ ¼ U C cosðh þ dÞ
ð4Þ
2 uc2b ðtÞ ¼ U C cos h p þ d 3
ð5Þ
2 uc2c ðtÞ ¼ U C cos h þ p þ d 3
ð6Þ
where Uc is the magnitude of the voltage and d is the angular displacement of the voltage reference. The abc-axis voltage references can be transformed to the d–q rotating frame using (3) as
uc2D ¼
2 2 2 cos huc2a þ cos h p uc2b þ cos h þ p uc2c 3 3 3
¼ U C cos d uc2Q ¼
where uc2D, uc2Q and us2D, us2Q are the d–q components of the inverter output voltage and PCC2 voltage, respectively. is2D and iS2Q are the d–q components of currents in the phase reactor. The matrix
ð7Þ
2 2 2 sin huc2a þ sin h p uc2b þ sin h þ p uc2c 3 3 3
¼ U C sin d
ð8Þ M
idc
AC1
R + jω L
PCC1
uc1
u dc1
is 2 u dc 2
Rectifier AC filter
K1
2C dc
i s1
u s1
ð3Þ
us2
M1
M
M2
u c 2 R + jω L Inverter
Resistive Load
Dc cable
PCC2 Fig. 1. The main-circuit diagram of a VSC-HVDC transmission connected to a passive network.
AC filter
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X. Tang, D.D.-C. Lu / Electrical Power and Energy Systems 54 (2014) 45–54
u *s 2 D
+ +
1 R+sL
is 2 D
ωL
is 2Q
ωL
Feed-forward control
0
u s*2Q
+ +
I N V E R T E R
u c*2 D
R+sL
+ +
−
u *c2Q
−
− R+sL
uc 2 D
u c2Q +
+
frequency is usually set to around 1 kHz. The delay increases undesired damping and cross-coupling effects on the above feed-forward control when the switching frequency is down to around 1 kHz as sin u and cos u are approximately 0.31 and 0.95 in this situation respectively. Considering the influence of inverter nonlinearies, the transfer functions of us2D and us2Q versus is2Q are respectively
us 2 D ωL
is 2 D
ωL
is 2 Q
R+sL
−
Plant
us 2Q
Fig. 2. The block diagram of the feed-forward controller.
The delay introduced by the PWM inverter including the turnon and turn-off time of devices and digital signal process are approximately equal to a switching period [19,20]. So the abc-axis voltage outputs of the inverter can be expressed as
uc2a ðtÞ ¼ K w U C cosðh þ d uÞ
ð9Þ
2 uc2b ðtÞ ¼ K w U C cos h p þ d u 3
ð10Þ
2 uc2c ðtÞ ¼ K w U C cos h þ p þ d u 3
ð11Þ
where u = xT, x is the angular frequency, T is a switching period and Kw = udc2(t)/2UT, udc2(t) is the DC voltage on inverter side and UT is the peak value of carrier signal. The abc-axis voltage outputs of the inverter can be transformed to the d–q rotating frame using (3) as
uc2D
2 2 2 cos huc2a þ cos h p uc2b þ cos h þ p uc2c ¼ 3 3 3 ¼ K w cos uuc2D sin uuc2Q ð12Þ 2 2 2 sin huc2a þ sin h p uc2b þ sin h þ p uc2c 3 3 3 ¼ K w cos uuc2Q þ sin uuc2D
uc2Q ¼
ð13Þ
Fig. 3 shows the transfer function of the inverter in d–q rotating frame. Eqs. (12) and (13) show that the coefficient Kw and phase angle u are parameters causing the nonlinearities of the inverter. The gain of the inverter can be regarded as unity if UT is designed to be udc2/2 and the switching frequency fs is high enough (up to several kHz). However, to restrain the switching loss of the power semiconductor devices in the VSC-HVDC system, the switching
* usd 1
+ + R+sL
isd
ωL
isq
ωL
Feed-forward control
0 * u sq
U s2D ðsÞ ¼ sLK w sin u þ ðK w cos u 1ÞxL RK w sin u Is2Q ðsÞ
ð14Þ
U s2Q ðsÞ ¼ sLðK w cos u 1Þ þ RðK w cos u 1Þ þ xLK w sin u Is2Q ðsÞ
ð15Þ
where Us2D(s), Us2Q(s) and Is2Q(s) are the Laplace transforms of the respective us2D, us2Q and is2Q. From (14) and (15), we can see that in the ideal condition with Kw = 1 and u = 0, there will be no voltage fluctuation in the presence of load changes. However, there is always a time delay in the inverter and meanwhile Kw varies along with the change of DC voltage under disturbances. The performance of the feed-forward controller considering inverter nonlinearities is illustrated in Fig. 4. Fig. 4 shows that 30% load current change may cause a voltage dip of 0.67 p.u. when Kw = 0.9, fs = 1 kHz, L = 0.726 mH and R = 0.0076 X. This means that the inverter nonlinearities degrade the performances of the feed-forward controller and thus deteriorate voltage quality. In order to eliminate the influence of the inverter nonlinearities, the compensation in the d–q rotating frame is proposed and expressed as
uc2D ðtÞ ¼
1 u þ uc2Q K w sin u K w cos u c2D
ð16Þ
uc2Q ðtÞ ¼
1 u c2Q uc2D K w sin u K w cos u
ð17Þ
where u c2D and uc2Q are outputs of the feed-forward controller. The compensation method for the inverter nonlinearities is shown in Fig. 5. It is should be mentioned that ucd and ucq replace uc2D and uc2Q in the compensation method respectively for uc2Q is not available to the calculation of uc2D and vice versa.
3.3. Feed-back control In order to overcome the sensitivity of the feed-forward control to parameters, a feed-back control with a PI controller is designed for each d–q voltage component and shown in Fig. 6. The PI controller takes the form
GPI ðsÞ ¼ K P þ K I =s
where KP and KI are the proportional and integral gain respectively.
+ + * ucd
KW cos ϕ + KW sin ϕ KW sin ϕ
R+sL
+ +
ð18Þ
−
* ucq
KW cos ϕ
−
++ Inverter
−
R+sL
u cd
u cq +
−
u sd
−
ωL
isd
ωL
isq
R+sL +
Fig. 3. The transfer function of the inverter in d–q rotating frame.
u sq Plant
X. Tang, D.D.-C. Lu / Electrical Power and Energy Systems 54 (2014) 45–54
Voltage response
48
0 -0.1 -0.2 -0.3 -0.4 -0.5
Us2D Us2Q
-0.6 -0.7 0.099
0.0995
0.1
0.1005
0.101
0.1015
0.102
0.1025
Time Fig. 4. us2D and us2Q responds to 30% current is2Q change with Kw = 0.9 and fs = 1 kHz.
u c 2Q u
* s2 D
+ +
1 R+sL
is2 D
ωL
is 2Q
ωL
Feed-forward control
u
+
+
1 KW cos ϕ
u*c*2Q + +
* s 2Q
+
u*c*2 D
R+sL
0
KW sin ϕ
−
+
KW cos ϕ + KW sin ϕ
uc*2Q
1 KW cos ϕ
−
uc*2 D
KW sin ϕ KW cos ϕ
+
u c2 D −
u s2 D
+
u c2 Q
P L A N T u s 2Q
Inverter
KW sin ϕ Nonlinearity
u c2 D compensation Fig. 5. The block diagram of the feed-forward control with the nonlinearity compensation.
u
* s2D
1
uc 2Q
u s2D +
−
PI
+ +
R+sL
is 2 D
ωL
is 2 Q
ωL
Feed-forward control
0
u s*2Q
+
R+sL PI
−
KW sin ϕ
+
+
+
u *c*2 D
+ +
u s 2Q
Table 1 System parameters.
−
u *c2*Q +
−
1 KW cos ϕ
1 KW cos ϕ
u c*2 D
uc*2Q
uc 2 D
I N V E R T E uc 2Q R
us2D
P L A N T u s 2Q
KW sin ϕ
Us Udc L R f 2Cdc DC cable
Rated voltage of inverter and rectifier DC voltage Reactor inductance Reactor resistance System frequency DC capacitor Pi line Rdc, Ldc, Cdc
SRload VBAC VBDC SB
Resistive load AC based voltage DC based voltage Based power
4.16 kV 10 kV 0.000726 H 0.0076 X 50 Hz 5600 lF 1.39 X 15.9 mH 23.1 lF 0.526 MW 4.16 kV 10 kV 170 MV A
Nonlinearity u c 2 D compensation
Fig. 6. The block diagram of the proposed control scheme Table 1 system parameters.
4. Simulation results To evaluate the proposed control scheme, a model of a VSCHVDC supplying a passive network shown Fig. 1 is simulated in PSCAD/EMTDC. The rectifier station of the VSC-HVDC transmission under study is assumed to be connecting to a strong grid. Induction motors are considered as the dominant loads in a passive network. The simulation model consists of a resistive load, an induction motor M1 and an induction motor M2 which represents all other induction motors. All loads are connected to the PCC. The HVDC converter is based on two-level bridges with mid-point of the capacitor connected to ground. Sine-triangle modulation technique
Table 2 Induction motor data. Motor
M1
M2
Rs + jXs (p.u.) Xm (p.u.) Rr + jXr (p.u.) s (%) H (s) S (kV A) V (kV)
0.0163 + j0.0816 2.250 0.0287 + j0.0836 2.209 0.5 1260 4.16
0.0022 + j0.0759 2.620 0.0288 + j0.1037 2.147 0.33 10,260 4.16
is used for PWM generation. The parameters of the VSC-HVDC transmission and the induction motors are shown in Tables 1 and 2 [6].
X. Tang, D.D.-C. Lu / Electrical Power and Energy Systems 54 (2014) 45–54
In this simulation model, a cascaded vector control scheme with an outer voltage loop for constant DC voltage and reactive power control and an inner current loop for active and reactive current
49
control is implemented to control the rectifier station. The inverter station uses the proposed control scheme. The switching frequency is set to 1 kHz and parameters sin u and cos u are then set to 0.31
Fig. 7. Performance comparison of three controllers during M1 start.
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X. Tang, D.D.-C. Lu / Electrical Power and Energy Systems 54 (2014) 45–54
and 0.95 in the nonlinearity compensation respectively. The proportional and integral gains are 3 and 0.2 respectively.
The voltage quality of the passive network, which is supplied by the VSC-HVDC, is simulated. The simulation compares three meth-
Fig. 8. Effect of voltage regulation margin on voltage quality.
X. Tang, D.D.-C. Lu / Electrical Power and Energy Systems 54 (2014) 45–54
ods, namely, the proposed modified direct voltage control (MDVC), direct voltage control (DVC), PI control with feed-forward control (PI-FFC) and cascaded control for the inverter station. In compari-
51
son with the PI-FFC, the DVC does have not the feed-forward control part. In comparison with the MDVC, the PI-FFC does not have the nonlinearity compensation part. For fair comparison, the afore-
Fig. 9. Performance comparison of three controllers during load shedding.
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X. Tang, D.D.-C. Lu / Electrical Power and Energy Systems 54 (2014) 45–54
mentioned three methods used the same PI parameters. The performance comparison is evaluated under various operating condi-
tions in a wide neighborhood of the initial operating point. The subscripts ‘r’ and ‘i’ of curve legends represent rectifier side and in-
Fig. 10. Performance comparison of three controllers during a three-phase fault.
X. Tang, D.D.-C. Lu / Electrical Power and Energy Systems 54 (2014) 45–54
verter side respectively in following graphs. Moreover, the subscripts ‘dvc’, ‘fc’ and ‘pc’ of curve legends represent using the DVC, the PI-FFC and the proposed MDVC respectively. 4.1. Case 1: Motor start Initially, HVDC control is evaluated under a motor start as a common disturbance (refer to Fig. 7). In this case, the induction motor M1 starts at 3 s. As a result, the AC current suddenly changes from 0.65 p.u. to 1 p.u. in inverter station and a DC voltage dip occurs for the DC voltage control lags the active power balance in rectifier station. It can be seen that the curve shape of modulation index, which determines the voltage uc2 together with DC voltage, just follows the change of PCC2 voltage and barely responds to the change of load current at the beginning when the DVC is applied. So, the voltage at PCC2, based on (1) and (2) has the largest fluctuation. This may cause interruption of critical loads. The curve of modulation index of the proposed MDVC has the fastest response to load current change and has a shape against the change of the DC voltage. In comparison with the MDVC, the curve of modulation index of the PI-FFC responds slower during the change of load current and almost fails against the change of DC voltage. That means that the MDVC, based on (16) and (17), not only responds quickly to the change of load current but also overcomes the nonlinearity of the inverter. Compared with a cascaded control in [6], a smaller motor start has already caused a voltage dip of around 0.93 where rated apparent power of the motor is 597 kV A, It is necessary to point out that the maximum of uc2 is 0.929 p.u. for udc2 is 0.630 p.u. at t = 3.13 s. That is why the voltage fluctuation at PCC2 is still large when the MDVC is applied. The speed curves of the motor M2 show that the MDVC mitigates the speed drop and buffeting of M2 during transient period. 4.2. Case 2: Effect of voltage regulation margin The effect of modulation index at pre-disturbance on voltage quality at PCC2 is also evaluated by repeating the disturbance in case 1. The DC voltage at rectifier side is controlled at 11 kV (10 kV in Case 1). The DC voltage is 8.68 kV and the corresponding modulation-index is about 0.72 (0.83 in Case 1) at inverter side during pre-disturbance. This results in more margins for the voltage regulation at PCC2. Fig. 8 shows the voltage quality in the receiving AC system. Compared with Fig. 7, the voltage control ability is enhanced for all of the three control methods. That means that it is very important for voltage quality in the receiving AC system that inverter station has enough margin for voltage control. It is worth noting that the voltage fluctuation is almost eliminated during transient period when the MDVC is applied. This further verifies the validity of the MDVC to reject load disturbances. 4.3. Case 3: Loading shedding HVDC control is evaluated under a load shedding as another common disturbance (refer to Fig. 9). In this case, the induction motor M2 is shut down at 3 s. As a result, the AC current suddenly reduces from 0.76 p.u. to 0.19 p.u. in the inverter station and a DC voltage swell occurs. The curve shape of modulation index slowly responds to load current reduction and then the voltage at PCC2, based on (1) and (2) has the largest swell when the DVC is applied. This may cause interruption of critical loads too. The modulation index quickly responds to sudden load current reduction and therefore the voltage at PCC2 is regulated stably when the MDVC is applied. In comparison with the MDVC, the modulation index of the PI-FFC does not decrease small enough and consequently a relative large swell occurs in the voltage at PCC2. This suggests that the PI-FFC failed to cancel the sudden change of load current prop-
53
erly, as can be observed from (14) and (15) which indicate the influence of the inverter nonlinearities. 4.4. Case 4: Three-phase fault HVDC control is evaluated under a three-phase fault in the AC1 network which causes a balanced voltage dip with a retained voltage of 0.75 p.u at PCC1. and a duration of 0.1 s (refer to Fig. 10). In this case, the voltage dip happens at 3 s. As a result, a DC voltage dip occurs. The curve of modulation index of the proposed MDVC has the fastest response to DC voltage change and has a shape against the change of the DC voltage. That means the MDVC overcomes, based on (16) and (17), the nonlinearity of the inverter. In comparison with the MDVC, the curve of modulation index of both DVC and PI-FFC responses slowly to the change of DC voltage. In addition, it can been seen that the PCC2 voltage of 0.95 p.u. is higher than the PCC1 voltage of 0.75 p.u. This means that the VSC-HVDC has a capability of improving voltage quality superior to a pure AC transmission.
5. Conclusion This paper presents a modified direct voltage control using a feed-forward controller and a nonlinearity compensation to enhance voltage quality of a passive network where a VSC-HVDC transmission is connected. The proposed nonlinearity compensation of the inverter maximizes the performance of the feed-forward control in d–q rotating axis. It is found that the proposed control scheme can mitigate voltage fluctuation caused by sudden changes of load current. In comparison with the DVC and the PIFFC, the proposed control scheme has better dynamic performance to reject disturbances and therefore ensures the high quality voltage in the receiving AC network. Nevertheless, it is still necessary to improve voltage quality under disturbances by keeping enough voltage regulation margin in normal operation of the VSC-HVDC transmission. Acknowledgment The authors gratefully acknowledge the support of the National Natural Science Foundation of China (No. 51277013). References [1] O’Kelly D. Voltage control for an HVDC convertor. IEE Proc Gener Transm Distrib 1984;131(1):5–15. [2] Flourentzou N, Agelidis VG, Demetriades GD. VSC-based HVDC power transmission systems: an overview. IEEE Trans Power Electron 2009;24(3):592–602. [3] Zhang L, Harnefors L, Nee H-P. Interconnection of two very weak ac systems by VSC-HVDC links using power-synchronization control. IEEE Trans Power Syst 2011;26(1):344–55. [4] IEEE guide for planning DC links terminating at AC locations having low shortcircuit capacities, IEEE Std. 1204-1997; 1997. [5] IEEE guide for identifying and improving voltage quality, IEEE Std. 1250-2011; 2011. [6] Guo C, Zhao C. Supply of an entirely passive AC network through a doubleinfeed HVDC system. IEEE Trans Power Electron 2010;25(11):2835–41. [7] Han B-M, Baek S-T, Bae B-Y, Choi J-Y. Back-to-back HVDC system using a 36step voltage. IEE Proc Gener Transm Distrib 2006;153(6):677–83. [8] Li Y, Zhang ZW, Rehtanz C. A new voltage source converter-HVDC transmission system based on an inductive filtering method. IET Trans Gener Transm Distrib 2012;6(9):569–76. [9] Du Cuiqing, Bollern Math HJ, Sannino Ambra. A new control strategy of a VSCHVDC system for high-quality supply of industrial plants. IEEE Trans Power Del 2007;22(4):2386–94. [10] Du C, Agneholm E, Olsson G. Comparison of different frequency controllers for a VSC-HVDC supplied system. IEEE Trans Power Del 2008;23(4):2224–32. [11] Zhang L, Harnefors L, Nee H. Modeling and control of VSC-HVDC connected to island systems. IEEE Trans Power Syst 2011;26(2):783–93.
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Contents lists available at SciVerse ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Enhancement of voltage quality in a passive network supplied by a VSC-HVDC transmission under disturbances Xin Tang a,⇑, Dylan Dah-Chuan Lu b a b
Department of Electrical Engineering, The Changsha University of Science & Technology, Changsha 410076, China School of Electrical and Information Engineering, The University of Sydney, NSW 2006, Australia
a r t i c l e
i n f o
Article history: Received 22 February 2013 Received in revised form 18 June 2013 Accepted 28 June 2013
Keywords: AC voltage control Voltage quality Nonlinearity compensation VSC-HVDC
a b s t r a c t When a VSC-HVDC transmission is connected to a passive network, the receiving AC system is weak and is subject to power quality problems such as voltage sag and swell. Dynamic performance of voltage control would affect the voltage quality in the receiving AC system directly. The direct voltage control (DVC) method is simple but fails to quickly eliminate voltage fluctuation caused by load current change. One solution is to add a feed-forward controller to the DVC. The inverter nonlinearities, however, degrade the performance of the feed-forward controller. This paper presents a modified direct voltage control to enhance control dynamics in the receiving AC system by overcoming the effect of inverter nonlinearities. In the proposed control scheme, the influence of inverter nonlinearities on the performance of the feed-forward controller is first discussed. A compensation method for nonlinearities of the inverter is then designed in the d–q rotating axis. Moreover, to overcome parameter sensitivity of the feed-forward controller, a feed-back loop with a PI controller is implemented. Simulation results from PSCAD/EMTDC showed that the VSC-HVDC system using the proposed control scheme, as compared to that with the conventional control methods, has a better capability to mitigate voltage fluctuation during system disturbances. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction POWER supply from onshore utility grid to offshore drill platforms or islands has advantages of cost effectiveness and less emission of greenhouse gas. Due to the capacitive charging currents of AC cables, DC transmission offers a feasible solution for subsea transmission. There are two categories of high-voltage directcurrent (HVDC) schemes currently available – conventional HVDC [1] and voltage-source converter (VSC)-HVDC [2]. The conventional HVDC has several limitations and undesirable characteristics including being physically large and requiring the ac network with sufficient short-circuit ratio. The VSC-HVDC, which uses modern semiconductors with self-commuted ability, overcomes the disadvantages of conventional HVDC and is therefore more suitable for a weak ac network [3] or a passive network without any power sources. A passive network supplied by VSC-HVDC transmission is a relatively isolated power system for the reactive power supply is not from utility grid but mainly from the inverter station of VSC-HVDC transmission. The inverter station often possesses a relatively large phase reactor, the receiving AC system is therefore considerably ⇑ Corresponding author. E-mail addresses: [email protected] (X. Tang), [email protected] (D.D.-C. Lu). 0142-0615/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.06.030
weak and subject to power quality problems such as voltage sag and swell due to load changes [4,5]. Network voltage control becomes a challenging task as a result. However, existing literature mainly focuses on topologies [6–8] and control strategies for ride-through disturbances [9–11] and, to the best knowledge of the authors, rarely discusses voltage quality problem under disturbances. The root-mean-square voltage of AC bus at inverter station is usually expected to be constant in a passive network which is supplied by VSC-HVDC transmission. The inverter station then operates in constant AC voltage control mode. Since the short-circuit capacity of AC bus at the inverter station in a passive network is smaller than that in a grid, larger fluctuation of voltage at the AC bus in the passive network can occur under disturbances. An example of disturbances that causes voltage sag and swell is switching on and off of load. To improve voltage quality, voltage control of inverter station connecting to a passive network is required to have a faster response to disturbances than that connecting to a large AC system [12–16]. There are mainly two categories of constant voltage control methods, namely, direct voltage control (DVC) [6,17,18] and cascade vector control (CVC) [9,11]. The DVC method uses the deviation between the reference value and the measured value by means of a PI-controller to provide a suitable value for modulation index. The DVC method is simple but does not compensate load current disturbance. Consequently, it fails
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X. Tang, D.D.-C. Lu / Electrical Power and Energy Systems 54 (2014) 45–54
used to transform the abc-axis signals to a d–q rotating frame is expressed as
to eliminate quickly the voltage fluctuation caused by load current change. The CVC method with an outer voltage control loop and an inner current control loop has been proposed to control the inverter station which can independently control active and reactive powers. Normally, the control bandwidth of the outer voltage loop is designed to be five or ten times narrower than that of the inner current control loop. Hence, the cascaded vector controller has poorer dynamics response to voltage sag/swell. The aim of this paper is hence to improve voltage quality during disturbances through a modified direct voltage control in the receiving AC system (i.e. a passive network) which is supplied by a VSC-HVDC transmission. Firstly, a feed-forward controller is designed in rotating d–q frame. The influence of inverter nonlinearity on the control dynamic is further analyzed. Based on this analysis, a nonlinearity compensation method is proposed. In addition, a PI regulator is applied to overcome parameter sensitivity of the feedforward compensation. Simulation results using PSCAD/EMTDC are reported to confirm the designed control scheme under different operation conditions.
3 cos h cos h 23p cos h þ 23p 7 26 p ¼ 4 sin h sin h 23p sin h 23p 5 3 1=2 1=2 1=2 2
3. voltage control scheme 3.1. Feed-forward control The control goal is to regulate the voltage at PCC2 so that high quality power is fed to the loads. In other words, the d-axis voltage component us2D is expected to keep constant and the q-axis voltage component us2Q is expected to be zero when d-axis is fixed to the PCC2 voltage space vector. The control system will be able to not only regulate the output voltage according to the reference voltage but also reject properly disturbances from the load current. From (1) and (2), to the d–q voltage component us2D and us2Q, the disturbances from the load currents are (R + sL)is2D xLis2Q and (R + sL)is2Q + xLis2D respectively. When the inverter nonlinearities is not considered, the feed-forward compensation can be designed as (R + sL)is2D + xLis2Q and (R + sL)is2Q xLis2D to the respective voltage component us2D and us2Q. The feed-forward controller is shown in Fig. 2.
2. System description Fig. 1 shows the main circuit diagram of a VSC-HVDC transmission connected to a passive network in which the converter transformer and phase reactor between VSC and point of common-coupling (PCC) are represented as a series combination of an inductor L and a resistor R. The inverter station connects to a rectifier station, which is connected to a strong grid, through DC cables. The reactors are used for controlling the active and reactive power flow by regulating the current through them and for reducing the high frequency content of the AC line current caused by the switching of the VSC. Shunt AC filters are also implemented to reduce the switching ripple on AC voltage and current. The capacitor provides an energy buffer to keep the power balance during transients and for reducing the voltage ripple on the DC side. The rectifier station contains both DC voltage control and reactive power control. The inverter station regulates the voltage at PCC2. In Fig. 1, us1, uc1, udc1, us2, uc2 and udc2 denote PCC voltage, output voltage of VSC station and DC voltage on rectifier and inverter sides respectively. The dynamic voltage equations in the rotating dq frame can be written as follows:
L
dis2D ¼ Ris2D xLis2Q þ uc2D us2D dt
ð1Þ
L
dis2Q ¼ Ris2Q þ xLis2D þ uc2Q us2Q dt
ð2Þ
3.2. Influence analysis and compensation of inverter nonlinearities The abc-axis voltage references supply to the inverter station can be expressed as
uc2a ðtÞ ¼ U C cosðh þ dÞ
ð4Þ
2 uc2b ðtÞ ¼ U C cos h p þ d 3
ð5Þ
2 uc2c ðtÞ ¼ U C cos h þ p þ d 3
ð6Þ
where Uc is the magnitude of the voltage and d is the angular displacement of the voltage reference. The abc-axis voltage references can be transformed to the d–q rotating frame using (3) as
uc2D ¼
2 2 2 cos huc2a þ cos h p uc2b þ cos h þ p uc2c 3 3 3
¼ U C cos d uc2Q ¼
where uc2D, uc2Q and us2D, us2Q are the d–q components of the inverter output voltage and PCC2 voltage, respectively. is2D and iS2Q are the d–q components of currents in the phase reactor. The matrix
ð7Þ
2 2 2 sin huc2a þ sin h p uc2b þ sin h þ p uc2c 3 3 3
¼ U C sin d
ð8Þ M
idc
AC1
R + jω L
PCC1
uc1
u dc1
is 2 u dc 2
Rectifier AC filter
K1
2C dc
i s1
u s1
ð3Þ
us2
M1
M
M2
u c 2 R + jω L Inverter
Resistive Load
Dc cable
PCC2 Fig. 1. The main-circuit diagram of a VSC-HVDC transmission connected to a passive network.
AC filter
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X. Tang, D.D.-C. Lu / Electrical Power and Energy Systems 54 (2014) 45–54
u *s 2 D
+ +
1 R+sL
is 2 D
ωL
is 2Q
ωL
Feed-forward control
0
u s*2Q
+ +
I N V E R T E R
u c*2 D
R+sL
+ +
−
u *c2Q
−
− R+sL
uc 2 D
u c2Q +
+
frequency is usually set to around 1 kHz. The delay increases undesired damping and cross-coupling effects on the above feed-forward control when the switching frequency is down to around 1 kHz as sin u and cos u are approximately 0.31 and 0.95 in this situation respectively. Considering the influence of inverter nonlinearies, the transfer functions of us2D and us2Q versus is2Q are respectively
us 2 D ωL
is 2 D
ωL
is 2 Q
R+sL
−
Plant
us 2Q
Fig. 2. The block diagram of the feed-forward controller.
The delay introduced by the PWM inverter including the turnon and turn-off time of devices and digital signal process are approximately equal to a switching period [19,20]. So the abc-axis voltage outputs of the inverter can be expressed as
uc2a ðtÞ ¼ K w U C cosðh þ d uÞ
ð9Þ
2 uc2b ðtÞ ¼ K w U C cos h p þ d u 3
ð10Þ
2 uc2c ðtÞ ¼ K w U C cos h þ p þ d u 3
ð11Þ
where u = xT, x is the angular frequency, T is a switching period and Kw = udc2(t)/2UT, udc2(t) is the DC voltage on inverter side and UT is the peak value of carrier signal. The abc-axis voltage outputs of the inverter can be transformed to the d–q rotating frame using (3) as
uc2D
2 2 2 cos huc2a þ cos h p uc2b þ cos h þ p uc2c ¼ 3 3 3 ¼ K w cos uuc2D sin uuc2Q ð12Þ 2 2 2 sin huc2a þ sin h p uc2b þ sin h þ p uc2c 3 3 3 ¼ K w cos uuc2Q þ sin uuc2D
uc2Q ¼
ð13Þ
Fig. 3 shows the transfer function of the inverter in d–q rotating frame. Eqs. (12) and (13) show that the coefficient Kw and phase angle u are parameters causing the nonlinearities of the inverter. The gain of the inverter can be regarded as unity if UT is designed to be udc2/2 and the switching frequency fs is high enough (up to several kHz). However, to restrain the switching loss of the power semiconductor devices in the VSC-HVDC system, the switching
* usd 1
+ + R+sL
isd
ωL
isq
ωL
Feed-forward control
0 * u sq
U s2D ðsÞ ¼ sLK w sin u þ ðK w cos u 1ÞxL RK w sin u Is2Q ðsÞ
ð14Þ
U s2Q ðsÞ ¼ sLðK w cos u 1Þ þ RðK w cos u 1Þ þ xLK w sin u Is2Q ðsÞ
ð15Þ
where Us2D(s), Us2Q(s) and Is2Q(s) are the Laplace transforms of the respective us2D, us2Q and is2Q. From (14) and (15), we can see that in the ideal condition with Kw = 1 and u = 0, there will be no voltage fluctuation in the presence of load changes. However, there is always a time delay in the inverter and meanwhile Kw varies along with the change of DC voltage under disturbances. The performance of the feed-forward controller considering inverter nonlinearities is illustrated in Fig. 4. Fig. 4 shows that 30% load current change may cause a voltage dip of 0.67 p.u. when Kw = 0.9, fs = 1 kHz, L = 0.726 mH and R = 0.0076 X. This means that the inverter nonlinearities degrade the performances of the feed-forward controller and thus deteriorate voltage quality. In order to eliminate the influence of the inverter nonlinearities, the compensation in the d–q rotating frame is proposed and expressed as
uc2D ðtÞ ¼
1 u þ uc2Q K w sin u K w cos u c2D
ð16Þ
uc2Q ðtÞ ¼
1 u c2Q uc2D K w sin u K w cos u
ð17Þ
where u c2D and uc2Q are outputs of the feed-forward controller. The compensation method for the inverter nonlinearities is shown in Fig. 5. It is should be mentioned that ucd and ucq replace uc2D and uc2Q in the compensation method respectively for uc2Q is not available to the calculation of uc2D and vice versa.
3.3. Feed-back control In order to overcome the sensitivity of the feed-forward control to parameters, a feed-back control with a PI controller is designed for each d–q voltage component and shown in Fig. 6. The PI controller takes the form
GPI ðsÞ ¼ K P þ K I =s
where KP and KI are the proportional and integral gain respectively.
+ + * ucd
KW cos ϕ + KW sin ϕ KW sin ϕ
R+sL
+ +
ð18Þ
−
* ucq
KW cos ϕ
−
++ Inverter
−
R+sL
u cd
u cq +
−
u sd
−
ωL
isd
ωL
isq
R+sL +
Fig. 3. The transfer function of the inverter in d–q rotating frame.
u sq Plant
X. Tang, D.D.-C. Lu / Electrical Power and Energy Systems 54 (2014) 45–54
Voltage response
48
0 -0.1 -0.2 -0.3 -0.4 -0.5
Us2D Us2Q
-0.6 -0.7 0.099
0.0995
0.1
0.1005
0.101
0.1015
0.102
0.1025
Time Fig. 4. us2D and us2Q responds to 30% current is2Q change with Kw = 0.9 and fs = 1 kHz.
u c 2Q u
* s2 D
+ +
1 R+sL
is2 D
ωL
is 2Q
ωL
Feed-forward control
u
+
+
1 KW cos ϕ
u*c*2Q + +
* s 2Q
+
u*c*2 D
R+sL
0
KW sin ϕ
−
+
KW cos ϕ + KW sin ϕ
uc*2Q
1 KW cos ϕ
−
uc*2 D
KW sin ϕ KW cos ϕ
+
u c2 D −
u s2 D
+
u c2 Q
P L A N T u s 2Q
Inverter
KW sin ϕ Nonlinearity
u c2 D compensation Fig. 5. The block diagram of the feed-forward control with the nonlinearity compensation.
u
* s2D
1
uc 2Q
u s2D +
−
PI
+ +
R+sL
is 2 D
ωL
is 2 Q
ωL
Feed-forward control
0
u s*2Q
+
R+sL PI
−
KW sin ϕ
+
+
+
u *c*2 D
+ +
u s 2Q
Table 1 System parameters.
−
u *c2*Q +
−
1 KW cos ϕ
1 KW cos ϕ
u c*2 D
uc*2Q
uc 2 D
I N V E R T E uc 2Q R
us2D
P L A N T u s 2Q
KW sin ϕ
Us Udc L R f 2Cdc DC cable
Rated voltage of inverter and rectifier DC voltage Reactor inductance Reactor resistance System frequency DC capacitor Pi line Rdc, Ldc, Cdc
SRload VBAC VBDC SB
Resistive load AC based voltage DC based voltage Based power
4.16 kV 10 kV 0.000726 H 0.0076 X 50 Hz 5600 lF 1.39 X 15.9 mH 23.1 lF 0.526 MW 4.16 kV 10 kV 170 MV A
Nonlinearity u c 2 D compensation
Fig. 6. The block diagram of the proposed control scheme Table 1 system parameters.
4. Simulation results To evaluate the proposed control scheme, a model of a VSCHVDC supplying a passive network shown Fig. 1 is simulated in PSCAD/EMTDC. The rectifier station of the VSC-HVDC transmission under study is assumed to be connecting to a strong grid. Induction motors are considered as the dominant loads in a passive network. The simulation model consists of a resistive load, an induction motor M1 and an induction motor M2 which represents all other induction motors. All loads are connected to the PCC. The HVDC converter is based on two-level bridges with mid-point of the capacitor connected to ground. Sine-triangle modulation technique
Table 2 Induction motor data. Motor
M1
M2
Rs + jXs (p.u.) Xm (p.u.) Rr + jXr (p.u.) s (%) H (s) S (kV A) V (kV)
0.0163 + j0.0816 2.250 0.0287 + j0.0836 2.209 0.5 1260 4.16
0.0022 + j0.0759 2.620 0.0288 + j0.1037 2.147 0.33 10,260 4.16
is used for PWM generation. The parameters of the VSC-HVDC transmission and the induction motors are shown in Tables 1 and 2 [6].
X. Tang, D.D.-C. Lu / Electrical Power and Energy Systems 54 (2014) 45–54
In this simulation model, a cascaded vector control scheme with an outer voltage loop for constant DC voltage and reactive power control and an inner current loop for active and reactive current
49
control is implemented to control the rectifier station. The inverter station uses the proposed control scheme. The switching frequency is set to 1 kHz and parameters sin u and cos u are then set to 0.31
Fig. 7. Performance comparison of three controllers during M1 start.
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X. Tang, D.D.-C. Lu / Electrical Power and Energy Systems 54 (2014) 45–54
and 0.95 in the nonlinearity compensation respectively. The proportional and integral gains are 3 and 0.2 respectively.
The voltage quality of the passive network, which is supplied by the VSC-HVDC, is simulated. The simulation compares three meth-
Fig. 8. Effect of voltage regulation margin on voltage quality.
X. Tang, D.D.-C. Lu / Electrical Power and Energy Systems 54 (2014) 45–54
ods, namely, the proposed modified direct voltage control (MDVC), direct voltage control (DVC), PI control with feed-forward control (PI-FFC) and cascaded control for the inverter station. In compari-
51
son with the PI-FFC, the DVC does have not the feed-forward control part. In comparison with the MDVC, the PI-FFC does not have the nonlinearity compensation part. For fair comparison, the afore-
Fig. 9. Performance comparison of three controllers during load shedding.
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X. Tang, D.D.-C. Lu / Electrical Power and Energy Systems 54 (2014) 45–54
mentioned three methods used the same PI parameters. The performance comparison is evaluated under various operating condi-
tions in a wide neighborhood of the initial operating point. The subscripts ‘r’ and ‘i’ of curve legends represent rectifier side and in-
Fig. 10. Performance comparison of three controllers during a three-phase fault.
X. Tang, D.D.-C. Lu / Electrical Power and Energy Systems 54 (2014) 45–54
verter side respectively in following graphs. Moreover, the subscripts ‘dvc’, ‘fc’ and ‘pc’ of curve legends represent using the DVC, the PI-FFC and the proposed MDVC respectively. 4.1. Case 1: Motor start Initially, HVDC control is evaluated under a motor start as a common disturbance (refer to Fig. 7). In this case, the induction motor M1 starts at 3 s. As a result, the AC current suddenly changes from 0.65 p.u. to 1 p.u. in inverter station and a DC voltage dip occurs for the DC voltage control lags the active power balance in rectifier station. It can be seen that the curve shape of modulation index, which determines the voltage uc2 together with DC voltage, just follows the change of PCC2 voltage and barely responds to the change of load current at the beginning when the DVC is applied. So, the voltage at PCC2, based on (1) and (2) has the largest fluctuation. This may cause interruption of critical loads. The curve of modulation index of the proposed MDVC has the fastest response to load current change and has a shape against the change of the DC voltage. In comparison with the MDVC, the curve of modulation index of the PI-FFC responds slower during the change of load current and almost fails against the change of DC voltage. That means that the MDVC, based on (16) and (17), not only responds quickly to the change of load current but also overcomes the nonlinearity of the inverter. Compared with a cascaded control in [6], a smaller motor start has already caused a voltage dip of around 0.93 where rated apparent power of the motor is 597 kV A, It is necessary to point out that the maximum of uc2 is 0.929 p.u. for udc2 is 0.630 p.u. at t = 3.13 s. That is why the voltage fluctuation at PCC2 is still large when the MDVC is applied. The speed curves of the motor M2 show that the MDVC mitigates the speed drop and buffeting of M2 during transient period. 4.2. Case 2: Effect of voltage regulation margin The effect of modulation index at pre-disturbance on voltage quality at PCC2 is also evaluated by repeating the disturbance in case 1. The DC voltage at rectifier side is controlled at 11 kV (10 kV in Case 1). The DC voltage is 8.68 kV and the corresponding modulation-index is about 0.72 (0.83 in Case 1) at inverter side during pre-disturbance. This results in more margins for the voltage regulation at PCC2. Fig. 8 shows the voltage quality in the receiving AC system. Compared with Fig. 7, the voltage control ability is enhanced for all of the three control methods. That means that it is very important for voltage quality in the receiving AC system that inverter station has enough margin for voltage control. It is worth noting that the voltage fluctuation is almost eliminated during transient period when the MDVC is applied. This further verifies the validity of the MDVC to reject load disturbances. 4.3. Case 3: Loading shedding HVDC control is evaluated under a load shedding as another common disturbance (refer to Fig. 9). In this case, the induction motor M2 is shut down at 3 s. As a result, the AC current suddenly reduces from 0.76 p.u. to 0.19 p.u. in the inverter station and a DC voltage swell occurs. The curve shape of modulation index slowly responds to load current reduction and then the voltage at PCC2, based on (1) and (2) has the largest swell when the DVC is applied. This may cause interruption of critical loads too. The modulation index quickly responds to sudden load current reduction and therefore the voltage at PCC2 is regulated stably when the MDVC is applied. In comparison with the MDVC, the modulation index of the PI-FFC does not decrease small enough and consequently a relative large swell occurs in the voltage at PCC2. This suggests that the PI-FFC failed to cancel the sudden change of load current prop-
53
erly, as can be observed from (14) and (15) which indicate the influence of the inverter nonlinearities. 4.4. Case 4: Three-phase fault HVDC control is evaluated under a three-phase fault in the AC1 network which causes a balanced voltage dip with a retained voltage of 0.75 p.u at PCC1. and a duration of 0.1 s (refer to Fig. 10). In this case, the voltage dip happens at 3 s. As a result, a DC voltage dip occurs. The curve of modulation index of the proposed MDVC has the fastest response to DC voltage change and has a shape against the change of the DC voltage. That means the MDVC overcomes, based on (16) and (17), the nonlinearity of the inverter. In comparison with the MDVC, the curve of modulation index of both DVC and PI-FFC responses slowly to the change of DC voltage. In addition, it can been seen that the PCC2 voltage of 0.95 p.u. is higher than the PCC1 voltage of 0.75 p.u. This means that the VSC-HVDC has a capability of improving voltage quality superior to a pure AC transmission.
5. Conclusion This paper presents a modified direct voltage control using a feed-forward controller and a nonlinearity compensation to enhance voltage quality of a passive network where a VSC-HVDC transmission is connected. The proposed nonlinearity compensation of the inverter maximizes the performance of the feed-forward control in d–q rotating axis. It is found that the proposed control scheme can mitigate voltage fluctuation caused by sudden changes of load current. In comparison with the DVC and the PIFFC, the proposed control scheme has better dynamic performance to reject disturbances and therefore ensures the high quality voltage in the receiving AC network. Nevertheless, it is still necessary to improve voltage quality under disturbances by keeping enough voltage regulation margin in normal operation of the VSC-HVDC transmission. Acknowledgment The authors gratefully acknowledge the support of the National Natural Science Foundation of China (No. 51277013). References [1] O’Kelly D. Voltage control for an HVDC convertor. IEE Proc Gener Transm Distrib 1984;131(1):5–15. [2] Flourentzou N, Agelidis VG, Demetriades GD. VSC-based HVDC power transmission systems: an overview. IEEE Trans Power Electron 2009;24(3):592–602. [3] Zhang L, Harnefors L, Nee H-P. Interconnection of two very weak ac systems by VSC-HVDC links using power-synchronization control. IEEE Trans Power Syst 2011;26(1):344–55. [4] IEEE guide for planning DC links terminating at AC locations having low shortcircuit capacities, IEEE Std. 1204-1997; 1997. [5] IEEE guide for identifying and improving voltage quality, IEEE Std. 1250-2011; 2011. [6] Guo C, Zhao C. Supply of an entirely passive AC network through a doubleinfeed HVDC system. IEEE Trans Power Electron 2010;25(11):2835–41. [7] Han B-M, Baek S-T, Bae B-Y, Choi J-Y. Back-to-back HVDC system using a 36step voltage. IEE Proc Gener Transm Distrib 2006;153(6):677–83. [8] Li Y, Zhang ZW, Rehtanz C. A new voltage source converter-HVDC transmission system based on an inductive filtering method. IET Trans Gener Transm Distrib 2012;6(9):569–76. [9] Du Cuiqing, Bollern Math HJ, Sannino Ambra. A new control strategy of a VSCHVDC system for high-quality supply of industrial plants. IEEE Trans Power Del 2007;22(4):2386–94. [10] Du C, Agneholm E, Olsson G. Comparison of different frequency controllers for a VSC-HVDC supplied system. IEEE Trans Power Del 2008;23(4):2224–32. [11] Zhang L, Harnefors L, Nee H. Modeling and control of VSC-HVDC connected to island systems. IEEE Trans Power Syst 2011;26(2):783–93.
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