DC-Bus Voltage Control Stability Affected by AC-Bus ... - IEEE Xplore

IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL. 04, NO. 2, JUNE 2016

445

DC-Bus Voltage Control Stability Affected by AC-Bus Voltage Control in VSCs Connected to Weak AC Grids Yunhui Huang, Student Member, IEEE, Xiaoming Yuan, Senior Member, IEEE, Jiabing Hu, Senior Member, IEEE, Pian Zhou, Student Member, IEEE, and Dong Wang

Abstract— With the wide application of voltage source converters (VSCs) in power system, dc-bus voltage control instabilities increasingly occurred in practical conditions, especially in weak ac grid, which poses challenges on stability and security of power converters applications. This paper aims to give physical insights into the stability of dc-bus voltage control affected by ac-bus voltage control in VSC connected to weak grid. The concepts of damping and restoring components are developed for dc-bus voltage to describe the stability of dc-bus voltage control. The impact of ac-bus voltage control on dc-bus voltage control stability can be revealed by investigating the impact of ac-bus voltage control on damping and restoring components essentially. Furthermore, the detailed analysis for the impact of ac-bus voltage control on damping and restoring components is presented considering varied ac system strengths, operating points, and ac-bus voltage control parameters. The simulation results from 1.5-MW full-capacity wind power generation system are demonstrated which conform well to the analysis. Finally, the experimental results validate the analysis. Index Terms— AC-bus voltage control, dc-bus voltage control, small-signal stability, voltage source converter (VSC), weak grid.

I. I NTRODUCTION OWADAYS, grid-connected voltage source converters (VSCs) have been widely applied in modern power systems, such as wind/solar energy generations, high-voltage direct current (HVdc) transmissions, flexible ac transmission system devices, and motor drive systems [1]–[5]. In some situations, the VSCs-based electrical devices are subjected to operate in a weak ac grid. For instance, some wind farms, including offshore projects, are located far away from

N

Manuscript received March 31, 2015; revised June 16, 2015, August 18, 2015, and September 9, 2015; accepted September 15, 2015. Date of publication September 22, 2015; date of current version April 29, 2016. This work was supported in part by the National Basic Research Program of China (973 Program) under Grant 2012CB215100, in part by the Major Program through the National Natural Science Foundation of China under Grant 51190104, in part by the National Natural Science Foundation of China under Grant 51277196, and in part by the Program for New Century Excellent Talents in University through the Ministry of Education, China, under Grant NCET-12-0221. Recommended for publication by Associate Editor J. Choi. (Corresponding author: Jiabing Hu.) The authors are with the State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JESTPE.2015.2480859

load centers and have relatively weak transmission [6]. Loss of stability occurred in both ac current control and dc-bus voltage control of VSC integrated into weak ac grid [7]–[18]. For instance, the impact of constant power load (CPL) on VSC dynamics in VSC-CPL system, resonances between line inductance and dc-bus voltage in VSC-HVdc system, or outer control loops interactions in VSC all may lead to the instability of dc-bus voltage in VSCs. Weak grid poses significant challenges on the stability of dc-bus voltage control [10]–[18]. DC-bus voltage stability is maintained by balancing of power flows into and out of dc-link and realized majorly through the regulation of active power output as the dc-bus voltage deviates from its reference value. Weak ac grid not only imposes influence on active power output regulation ability of dc-bus voltage control but also causes control loops interactions that affect dc-bus voltage dynamics. As VSC is connected to weak ac system, the terminal voltage is sensitive to the active power output regulated by dc-bus voltage control. In turns, the terminal voltage variations make the active power deviate from the desired value and further influence the effectiveness of maintaining power flow balance in dc-link. In addition, terminal voltage variations will lead to responses of phase-locked loop (PLL) and ac-bus voltage control. PLL and ac-bus voltage control can impact active power output and further impact the stability of dc-bus voltage control as their bandwidths are close to that of dc-bus voltage control. The stability of dc-bus voltage control in VSC connected to weak grid has been investigated in some earlier papers. As declared in [12], weak ac system deteriorates dc-bus voltage control stability and limits power transfer ability in VSC-HVdc. Likewise, eigenvalue analysis in [13] and [14] shows that the damping ratio for dc-bus voltage control in variable-speed wind power generator becomes reduced with the decrease of ac system strength. Pinares et al. [15] conclude that the dc voltage stability of VSC-HVdc connected to weak grid gets damaged with increase of power flow through eigenvalue analysis and frequency domain approach, which conforms with the time-domain simulation results in [16]. In [17], it is revealed that the instabilities may be hard to prevent for very weak grids with a parallel resonance of fairly low frequency, which covers the bandwidth of dc-bus voltage control.

2168-6777 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

446


In addition, the impacts of control loops interactions, including PLL and ac-bus voltage control, on the stability of dc-bus voltage control have been investigated in a few papers. It is concluded that quick PLL response will deteriorate dc-bus voltage control stability as the power angle reaches about 50°–60° with very low short circuit ratio (SCR) in [18]. A similar conclusion is drawn in [19] that slowing the PLL response could improve VSC stability and increase power transfer capability in very weak grid. However, the VSC dynamic response turns slow with lower PLL bandwidth. In addition, some investigations show that the ac-bus voltage control has significant impact on the stability of dc-bus voltage control in VSC [20], [21]. It is declared in [20] that the rise of ac-bus voltage control proportional coefficient while the reduction of its integral coefficient will improve the stability of active power output which is related closely to the stability of dc-bus voltage control. Furthermore, Strachan and Jovcic [21] demonstrate that the increasing of ac-bus voltage control gains increases the damping ratio of modes in which mainly participated by dc-bus voltage control and ac-bus voltage control. Detailed analysis is not given. However, the dc-bus voltage stability analysis in earlier studies were primarily restricted to eigenvalue analysis or time-domain simulation while have not revealed physical explanation on the instability mechanism. Earlier studies did not realize the critical components or factors on which the acbus voltage control impacts to affect stability of dc-bus voltage control. In addition, the impacts of ac-bus voltage control on VSC stability were studied mostly with varying ac-bus voltage control parameters but without considering the variations of ac system strengths or operating points. The main contribution of this paper is to provide physical insights into the impact of ac-bus voltage control on the stability of dc-bus voltage control in VSC connected to weak grid. This paper is organized as follows. Section II briefly outlines the conventional VSC control system investigated in this paper and derives a small-signal model of grid-connected VSC. In Section III, the concepts of damping and restoring components are developed to evaluate the stability of dc-bus voltage control. In Section IV, the impact of ac-bus voltage control on damping and restoring components is investigated under various operating conditions. In Section V, the average-value model of full-scale wind turbine was established to validate the analysis. The experimental results are shown in Section VI. Finally, the conclusion is drawn in Section VII. II. VSC S MALL -S IGNAL M ODEL FOR DC-B US VOLTAGE S TABILITY A NALYSIS A VSC model is derived for dc-bus voltage stability analysis with considering the impacts of ac system strength, operating point, and control loops interactions, including ac-bus voltage control and PLL dynamics. In addition, the model is linearized for small-signal stability analysis. A. VSC System With the Conventional Control Scheme The conventional VSC control system investigated in this paper consists of two cascaded control loops [22], [23],

Fig. 1. Diagram of VSC main-circuit and control system with vector control.

as shown in Fig. 1. The outer control loops include dc-bus voltage control and ac-bus voltage control. DC-bus voltage control contributes to balancing the power flow through dc link and maintaining dc-bus voltage in VSC. Meanwhile, the ac-bus voltage control is employed to support the grid voltage and has been applied in VSC especially integrated to weak grid as reported in [12] and [24]–[26]. DC-bus voltage controller output is the reference of d-axis current, and the ac-bus voltage controller output is the reference of q-axis current. The inner current control loop is designed for tracking the outer loop output and current protection. Besides, the PLL is used to capture terminal voltage phase as a rotating reference frame employed by abc to dq transformation module. In Fig. 1, Uc , Ut , and Ug are the magnitudes of the voltage generated by the converter (the voltage behind the filter), terminal voltage, and infinite bus voltage, respectively. θc , θt , and θg are the phase of the voltage generated by the converter, terminal voltage, and infinite bus voltage, respectively. Udc and Ut represent the dc-bus voltage and terminal voltage, respectively. Ic represents the line current of VSC. X f and X g are the impedances of VSC filter and transmission line, respectively. θpll is the output of PLL. Pin and Pe are the active power input and output. B. Modeling of VSC for DC-Bus Voltage Stability Analysis In order to simplify the stability analysis of dc-bus voltage control, it is assumed that the following holds: 1) the current value can catch up with current reference value immediately in PLL reference frame before the dc-bus voltage control acts as the current control loop bandwidth is much higher than the dc-bus voltage control [18], [27]; 2) the active power input Pin is invariable; 3) the ac capacitor C f is simply not included in the analysis; 4) the system is lossless. Fig. 2 shows the PLL model block. PLL is employed to make sure that the d-axis is always aligned with terminal voltage vector to synchronize VSC with the grid. PLL model is described as ∗ − θpll u tq = Ut sin θpll (1) ki2 1 (2) θpll = u tq k p2 + s s

HUANG et al.: DC-BUS VOLTAGE CONTROL STABILITY AFFECTED BY AC-BUS VOLTAGE CONTROL

447

The equations related to dc-bus voltage control dynamics are described as dUdc dt ki1 ∗ = Udc − Udc k p1 + . s

Pm − Pe = Udc C Fig. 2.

∗ i cd

Block diagram of PLL model.

(14) (15)

Equations related to ac-bus voltage control dynamics are ∗ ki3 ∗ (16) i cq = Ut − Ut k p3 + s (17) Ut2 = u 2td + u 2tq . Linearizing (14)–(17), there are

Fig. 3. Phasor diagram for VSC control system dynamics. (a) VSC control system steady state. (b) VSC control system transient state.

where θpll represents the PLL output angle. Linearizing PLL model, there is ki2 1 . (3) θpll = u tq k p2 + s s

dUdc Pm − Pe = Udc0 C dt ki1 i cd = Udc k p1 + s ki3 ∗ i cq = Ut − Ut k p3 + s u tq0 u td0 u td + u tq . Ut = Ut 0 Ut 0

(18) (19) (20) (21)

From the main-circuit of VSC, the equations can be obtained as follows: Ut U g sin(θt − θg ) Xg Ut − Ug = j X g Ic . Pe =

(22)

Fig. 3 shows the phasor diagram for illustrating VSC control system dynamics. Assuming that x–y frame synchronizes with infinite bus voltage vector U g , and x-axis leads U g by the angle θt 0 constantly. The terminal voltage vector U t , d-axis, and x-axis are in the same phase with VSC operating in steady state, as shown in Fig. 3(a). Suppose a disturbance occurs, making the terminal voltage phase leading that in steady state, as shown in Fig. 3(b). Subsequently, the PLL responds to catch up with terminal voltage vector and d-axis leads x-axis by the angle θpllx. The corresponding transformation for terminal voltage U t and current I c from d–q frame to x–y frame is given as follows:

From (9)–(13), (18)–(21), and (24)–(26), it can be obtained that

u tx = u td cos θpllx − u tq sin θpllx

(4)

Pe = K 1 u tq + K 2 θpll + K 3 u td

(27)

u ty = u td sin θpllx + u tq cos θpllx

(5)

u tq = K 4 θpll + K 6 i cd

(28)

i cx = i cd cos θpllx − i cq sin θpllx

(6)

u td = K 5 θpll + K 7 i cq

(29)

i cy = i cd sin θpllx + i cq cos θpllx.

(7)

Ut = K 8 u td .

(30)

In addition, the relationship between θpllx and θpll is θpll = θpllx + θt 0 .

(8)

Linearizing (4)–(8), there are u tx = u td − u tq0 θpllx

(9)

u ty = u tq + u td0 θpllx

(10)

i cx = i cd − i cq0 θpllx

(11)

i cy = i cq + i cd0 θpllx

(12)

θ pll = θpllx.

(13)

(23)

Linearizing (22) and (23), there are u gx0u ty − u gy0 u tx Xg = −i cy X g = i cx X g .

Pe =

(24)

u tx u ty

(25) (26)

In (27)–(30), the parameters K 1 to K 8 imply particularly physical meanings. K 1 represents the impact of q-axis terminal voltage variation on active power output. K 2 , K 4 , and K 5 represent the impacts of PLL output variation on active power output, q-axis terminal voltage, and d-axis terminal voltage, respectively. K 6 and K 7 represent the impact of d-axis current variation on q-axis terminal voltage and the impact of q-axis current variation on d-axis terminal voltage. K 3 and K 8 represent the impacts of d-axis terminal voltage variation on active power output and terminal voltage, respectively. Mathematical expressions of parameters K 1 to K 8 are represented as follows, where the subscript 0 denotes the initial value of

448


Fig. 4. Small-signal model block of VSC for dc-bus voltage stability analysis. Fig. 6. Diagram for illustrating damping and restoring components of dc-bus voltage control.

A. Damping and Restoring Components for DC-Bus Voltage Control

Fig. 5.

Fig. 6(a) shows the schematic of synchronous machine rotor movement. The rotor speed varies because of imbalance between the mechanical torque Tm and the electromagnetic torque Te . The relationship between the torque and the rotor speed is

Simplified second-order model of dc-bus voltage control.

steady operating point: Ug0 cos(θt 0 − θg0 ) K1 = Xg

(31)

Ut 0 Ug0 cos(θt 0 − θg0 ) K2 = Xg

(32)

K3 = −

Ug0 sin(θt 0 − θg0 ) Xg

(33)

K 4 = Ug0 cos(θt 0 − θg0 ) − 2Ut 0

(34)

K 5 = Ug0 sin(θt 0 − θg0 )

(35)

K6 = X g

(36)

K 7 = −X g u td0 K8 = . Ut 0

(37) (38)

Based on (3), (18)–(21), and (27)–(30), the model block for VSC is shown in Fig. 4. III. DAMPING AND R ESTORING C OMPONENTS FOR DC-B US VOLTAGE E XEMPLIFIED W ITH A S IMPLIFIED M ODEL Neglecting the ac-bus voltage control and PLL dynamics in Fig. 4, the simplified second-order small-signal model of dc-bus voltage control is described in Fig. 5. Based on this model, the damping and restoring components are introduced. In addition, the dc-bus voltage stability is analyzed with investigating the damping and restoring components.

J

dω = Tm − Te dt

(39)

where J is defined as the inertia coefficient of synchronous machine. Corresponding second-order model of rotor movement is shown in Fig. 6(b). It shows that the electromagnetic torque consists of damping and synchronizing torques which act in electromechanical timescale. Damping torque acts to damp low-frequency oscillation (∼0.2–2 Hz) of rotor speed and synchronizing torque acts to restore rotor angle that follows an arbitrarily small displacement [28]. Compared with the rotor movement of synchronous machine, the dc-bus voltage control of VSC has similar characteristics. As shown in Fig. 6(c), the dc-bus voltage changes due to imbalance between active power input and output. The relationship is described as Pin − Pe = Udc0 C

dUdc . dt

(40)

The model block in Fig. 6(d) is derived from Fig. 5. It has similar form with the block in Fig. 6(b). Electromagnetic power is regulated to catch the value of active power input through the actions of dc-bus voltage PI controller. As the dc-bus voltage errors are imported into dc-bus voltage controller, the proportional coefficient kp1 generates damping force to damp the oscillations of dc-bus voltage, while the integral coefficient ki1 generates restoring force to eliminate the errors of dc-bus voltage. Consequently, the electromagnetic power Pe is divided into two components, viz., Pd and Pr . The former is termed damping component and latter restoring component.


Fig. 7.

Phasor diagram of damping and restoring components.

449

Fig. 8. Relationship between Bode plot and phasor diagram. (a) Bode plot of G0 (s). (b) Phasor diagram of Pe .

TABLE I S TABILITY D ESCRIPTIONS W ITH D IFFERENT Q UADRANTS

From Fig. 6(d), the following equations are obtained: Pin = H Udcs + K d Udc + K r

Udc s

(41)

where H = CUdc0 K d = K 1 K 6 k p1 K r = K 1 K 6 ki1

(42) (43) (44)

where K d represents the damping coefficient and K r represents the restoring coefficient. Parameters K d and K r in Fig. 6(d) are determined by ac system strength, VSC operating point, and dc-bus voltage controller parameters. B. Impact of Damping and Restoring Components on DC-Bus Voltage Stability Given an oscillation in dc-bus voltage, VSC active power output is developed into two parts, damping component in phase with the small variation of dc-bus voltage Udc and restoring component in phase with an integral term of Udc . Both impose particular impact on dc-bus voltage stability. Damping component produces an impact to damp the oscillation, contributing to smoothing dc-bus voltage. Meanwhile, the restoring component produces an impact to eliminate the errors of dc-bus voltage, contributing to restoring dc-bus voltage. Consequently, the dc-bus voltage stability can be damaged due to the lack of damping or restoring components. Fig. 7 shows the phasor diagram of damping and restoring components. VSC active power output Pe projects the damping component on Udc -axis, while projects the restoring component on Udc /s-axis. The quadrant in which Pe locates determines the stability of dc-bus voltage control, as shown in Table I.

Fig. 9. Typical responses of dc-bus voltage. (a) K d > 0, K r > 0. (b) K d < 0, K r > 0. (c) K d > 0, K r < 0. (d) K d < 0, K r < 0.

C. Computing Damping and Restoring Coefficients The transfer function G 0 (s) derived from Fig. 5 is defined as follows: K 1 K 6 k p1 s + K 1 K 6 ki1 Pe . (45) G 0 (s) = = Udc s Damping and restoring coefficients can be observed from the Bode diagram of G 0 (s). Fig. 8 shows G 0 (s)’s open-loop Bode diagram and corresponding phasor diagram of Pe with VSC operating in normal condition. The gain and phase of G 0 (s) at dc-bus voltage oscillation frequency correspond to the active power Pe ’s magnitude (Udc ’s magnitude is set as base value) and the angle θ0 by which Pe lags behind Udc , as shown in Fig. 8(b). Then, the damping and restoring components are projected on Udc -axis and Udc /s-axis, respectively, by Pe and can be calculated by the following equations: |Pd | = |Pe | cos θ0

(46)

|Pr | = |Pe | sin θ0 .

(47)

An average-value model of 1.5-MW full-capacity wind power generation system was built in MATLAB/Simulink. The grid-connected VSC parameters are shown in Table VI. Variations of K d and K r can be obtained with changing SCR and control parameters. Plots of time-domain simulations in Fig. 9 show the typical responses of dc-bus voltage with

450


Fig. 10. Diagram of small-signal model for analyzing ac-bus voltage control impact on dc-bus voltage control.

the variations of K d and K r . The values of K d and K r in Fig. 9(a)–(d) are computed as follows: K d = 0.68 pu and K r = 1.42 pu in SCR = 1.5, K d = −0.36 pu and K r = 1.09 pu in SCR = 1.23, K d = 0.89 pu and K r = −0.65 pu in SCR = 1.32 without ac-bus voltage control, and K d = −0.11 pu and K r = −1.56 pu in SCR = 1.22 without ac-bus voltage control. The results in Fig. 9 agree with the conclusions in Table I. IV. I MPACT OF AC-B US VOLTAGE C ONTROL ON THE S TABILITY OF DC- BUS VOLTAGE C ONTROL This section will reveal interactions among dc-bus voltage control, ac-bus voltage control, and PLL with VSC integrated to weak grid and particularly investigate the influence of ac-bus voltage control on the stability of dc-bus voltage control with contribution to damping and restoring components.

Fig. 11. Phasor diagram for illustrating the impact of ac-bus voltage control on dc-bus voltage control. (a) Phasor diagram. (b) Bode plot of G 1 (s). (c) Bode plot of G 2 (s). (d) Bode plot of G 0 (s). TABLE II VALUES OF A NGLES θ0 AND θ2 W ITH VARIED G RID S TRENGTH

A. Analysis of AC-Bus Voltage Control Impact on DC-Bus Voltage Control Stability Fig. 10 shows the model block for analyzing ac-bus voltage control impact on dc-bus voltage control stability, as derived from Fig. 4. It clearly shows the relationships among dc-bus voltage control, ac-bus voltage control, and PLL. The transfer functions G 1 (s) andG 2 (s) are defined as θpll(s) (48) i cd (s) P4 (s) (−K 2 K 7 k p3 + K 3 K 5 + K 2 )s − K 2 K 7 ki3 G 2 (s) = . = θpll(s) (1 − K 7 k p3 )s − K 7 ki3 (49) G 1 (s) =

Compared with Fig. 5, the model in Fig. 10 has other two branches affecting the stability of dc-bus voltage control, one due to the PLL branch denoted by G 1 (s) and the other due to the ac-bus voltage control branch denoted by G 2 (s) that is mainly investigated in this section. Consequently, P4 is generated by ac-bus voltage control branch and affects dc-bus voltage control stability through impacting total electromagnetic power Pe . Fig. 11 shows the impact of ac-bus voltage control on damping and restoring components of dc-bus voltage control. Fig. 11(a) shows the phasor diagram of dc-bus voltage control dynamics. Furthermore, Fig. 11(b) and (c) shows the openloop Bode diagrams of G 1 (s) and G 2 (s). Observe that G 1 (s) and G 2 (s) are both lagging regulators in dc-bus voltage control bandwidth (∼10 Hz). AC-bus voltage control behaves as lagging regulation for dc-bus voltage control and determines the angle θ2 by

which P4 lags behind P3 . From the lagging angle θ2 , it can analyze the additional damping and restoring components provided by ac-bus voltage control. As shown in Table II, in strong grid (SCR = 5), P4 is located in the first quadrant with a small angle θ2 . The damping component projected on Udc -axis by P4 is positive, so does the restoring component. While in a weak grid (SCR = 1.2), as θ2 becomes large enough to lead P4 located in the fourth quadrant, as shown in Fig. 11(a), the damping component provided by P4 is negative. It means that a small variation in dc-bus voltage will lead an opposite variation in the active power output contributed by ac-bus voltage control. In this situation, the ac-bus voltage control worsens the dc-bus voltage control stability. From (22), it is indicated that the frequency– phase characteristic of G 2 (s) is dependent on k p3 , ki3 , K 2 , K 3 , K 5 , and K 7 . Consequently, θ2 is closely related to ac-bus voltage controller parameters, VSC operating point, and ac system strength. As shown in Fig. 10, G 0 (s) represents the impacts of both ac-bus voltage control and PLL. The stability of dc-bus voltage control can be judged from the characteristic of G 0 (s). The angle θ0 by which Pe lags behind Udc can be obtained from G 0 (s)’s open-loop transfer function, as shown in Fig. 11(d). As shown in Table II, in strong grid (SCR = 5), Pe locates in the first quadrant with θ0 being smaller than 90°, contributing


Fig. 12. Impact of ac-bus voltage control on damping and restoring components with different ac system strengths. case 1: with ac-bus voltage control. case 2: without ac-bus voltage control. additional component provided by ac-bus voltage control. (a) Damping coefficients. (b) Restoring coefficients. (c) Oscillation frequency with ac-bus voltage control. (d) Oscillation frequency without ac-bus voltage control.

451

Fig. 13. Impact of ac-bus voltage control on damping and restoring case 1: with ac-bus voltage components with different operating points. control. case 2: without ac-bus voltage control. additional component provided by ac-bus voltage control. (a) Damping coefficients. (b) Restoring coefficients. (c) Oscillation frequency with ac-bus voltage control. (d) Oscillation frequency without ac-bus voltage control.

to positive damping and restoring components. However, as the grid becomes very weak (SCR = 1.2), the ac-bus voltage control increases the angle by which Pe lags behind P1 , which makes θ0 larger than 90°. Consequently, Pe locates in the fourth quadrant, resulting in unstable dc-bus voltage with a negative damping component. B. Impact of AC-Bus Voltage Control on Damping and Restoring Components Under Various Operating Conditions In order to gain more insights into the impact of ac-bus voltage control on the stability of dc-bus voltage control, the damping and restoring coefficients of dc-bus voltage control are investigated in two cases as follows. Case 1: VSC is controlled with a complete control system, as shown in Fig. 1. Case 2: VSC is controlled without ac-bus voltage control and q-axis current reference value is constant. Additional damping and restoring coefficients that the ac-bus voltage control provides can be calculated by comparing the results in the two cases above. The impacts of ac-bus voltage control on dc-bus voltage control stability are closely related to ac system strength, operating point, and ac-bus voltage control parameters. Consequently, the damping and restoring coefficients of dc-bus voltage control with two cases are calculated with one of the above factors varying and the others keeping invariable, as shown in Figs. 12–14. Setting that the damping and restoring coefficients of dc-bus voltage control secondorder model in the condition of SCR = 2 and Pe = 1 pu are basic values. The VSC control and main circuit parameters used are shown in Table VI.

Fig. 14. Impact of ac-bus voltage control on damping and restoring components with different ac-bus voltage control parameters. (a) Additional damping coefficients. (b) Additional restoring coefficients. (c) Oscillation frequency with SCR = 1.4. (d) Oscillation frequency with SCR = 1.3.

AC system strength is significantly related to grid impedance and ac-system inertia. The VSC is integrated to infinite bus through grid impedance without other generators. In this section, the ac system strength is changed by varying the value of grid impedance. Fig. 12 shows the impact of ac-bus voltage control on dc-bus voltage control’s damping

452


and restoring components under rated condition with varied ac system strengths. Fig. 12(a) shows that the dc-bus voltage control’s damping coefficients in case 1 are smaller than that in case 2 with SCR < 3. However, Fig. 12(b) shows the restoring coefficients in case 1 are larger than that in case 2 with SCR < 3. In case 1, VSC reaches stability limitation with SCR = 1.25. As SCR decreases from 1.25, the dc-bus voltage results in diverging oscillation because of negative damping component. In case 2, it reaches stability limitation with SCR = 1.3. As SCR decreases from 1.3, the dc-bus voltage gets aperiodic drift instability with negative restoring component. In addition, it shows that the ac-bus voltage control provides negative damping component and positive restoring component to dcbus voltage control in weak grid (SCR < 3). Besides, the additional damping component increases, while the additional restoring component reduces with the increase of ac system strength. In addition, K d and K r are frequency dependent. The values of K d and K r are changed with variation of oscillation frequencies. In addition, the oscillation frequency is related closely to SCR. Fig. 12(c) and (d) shows the variation of oscillation frequencies with varied SCR. VSC operating point is changed by varying the active power input of VSC Pin , and then active power output Pe is varied with the change of Pin . Several operating conditions are created to test the performance of dc-bus voltage control by varying active power input from 0.1 to 1.4 pu with keeping SCR equal to be 1.5. Fig. 13(a) shows that the damping coefficients in case 1 are smaller than that in case 2 with Pe > 0.5 pu. Nevertheless, the restoring coefficients in case 1 are higher than that in case 2 with Pe > 0.5 pu in Fig. 13(b). Furthermore, it shows that the additional negative damping and positive restoring components due to ac-bus voltage control increase with the rise of active power output. Fig. 13(c) and (d) shows the variation of oscillation frequencies with varied operating points. The operating points pose influence on oscillation frequencies and further impact the values of K d and K r . Fig. 14 shows the additional damping and restoring coefficients represented by K davc and K ravc with ac-bus voltage control gain k p3 changing from 0.2 to 8 and ki3 set to be 40k p3 in rated condition. Fig. 14(a) declares that the additional damping coefficients increase with the rise of ac-bus voltage control gain. K davc is larger with SCR = 1.4 than SCR = 1.3 as k p3 < 3, while is smaller with SCR = 1.4 than SCR = 1.3 as k p3 > 3. Fig. 14(b) shows that for each SCR, the additional restoring coefficient increases fast with a rise in k p3 , reaches maximum for some value of k p3 , and then starts reducing slowly. The maximum value for K ravc increases with a reduction of SCR. Another observation is that K ravc hardly changes as k p3 > 4. Therefore, it is better to increase ac-bus voltage control gain to get superior damping and restoring components in a weak grid. However, the gain of ac-bus voltage control cannot be designed too high to avoid coupling between ac-bus voltage control and current control dynamics. Fig. 14(c) and (d) shows the variation of oscillation frequencies with varied ac-bus voltage control parameters. AC-bus voltage control parameters produce influence on the oscillation frequencies and further impact the values of K d and K r .

Fig. 15. DC-bus voltage responses with varying ac system strengths. (a) SCR = 1.22. (b) SCR = 1.3. (c) SCR = 1.4. (d) SCR = 4.

V. S IMULATION R ESULTS To verify the analysis above, the time-domain simulations are conducted with the average model of 1.5-MW full-capacity wind power generation system described in Section III. Responses of dc-bus voltage are observed and analyzed with varied grid strengths, operating points, or ac-bus voltage control parameters. Figs. 15 and 16 show the dc-bus voltage and active power output responses with different ac system strengths. Under the condition that Pe = 1 pu and Vt = 1 pu, a small disturbance in grid occurs at 3 s. Fig. 15(a) shows that the dc-bus voltage gets aperiodic drift instability without ac-bus voltage control in the condition SCR = 1.22. In comparison, the system with ac-bus voltage control results in diverging the oscillation of dc-bus voltage. It is inferred that the restoring component of dc-bus voltage control increases, while the damping component decreases. Therefore, the ac-bus voltage control contributes to positive restoring


453

Fig. 17. DC-bus voltage responses with varying operating points. (a) Pe = 0.9 pu. (b) Pe = 1.2 pu.

Fig. 16. Active power output responses with varying ac system strengths. (a) SCR = 1.22. (b) SCR = 1.3. (c) SCR = 1.4. (d) SCR = 4.

component and negative damping component, which is in accordance with the conclusions from Fig. 12. Fig. 15(b) shows that the dc-bus voltage still keeps aperiodic drift oscillation without ac-bus voltage control as SCR increases to 1.3 while it becomes stable with ac-bus voltage control. Consequently, it infers that the additional negative damping component due to ac-bus voltage control decreases with the rise of SCR. Subsequently, Fig. 15(c) shows that the dc-bus voltage becomes stable without ac-bus voltage control as SCR increases to 1.4. Furthermore, the settling time is smaller and transient overshoot is higher without ac-bus voltage control than those with adding ac-bus voltage control, implying additional negative damping becomes smaller than that in SCR = 1.3. Fig. 15(d) shows that the dc-bus voltage response with adding ac-bus voltage control is close to that without ac-bus voltage control in SCR = 4. Thus, it is revealed that the ac-bus voltage control’s contribution to damping and restoring components is small in this situation, which also

Fig. 18. Active power output responses with varying operating points. (a) Pe = 0.9 pu. (b) Pe = 1.2 pu.

conforms to Fig. 12. Without ac-bus voltage control, it is obtained that K d = −0.11 pu and K r = −1.56 pu with SCR = 1.22, K d = 0.83 pu and K r = −0.71 pu with SCR = 1.3, K d = 0.89 pu and K r = 0.94 pu with SCR = 1.4, and K d = 1.11 pu and K r = 0.97 pu with SCR = 4. With ac-bus voltage control, it is obtained that K d = −0.48 pu and K r = 1.07 pu with SCR = 1.22, K d = 0.33 pu and K r = 1.21 pu with SCR = 1.3, K d = 0.56 pu and K r = 1.19 pu with SCR = 1.4, and K d = 1.1 pu and K r = 1.02 pu with SCR = 4. The computed results of K d and K r with varied grid strengths are well in accordance with the analysis from Fig. 15. Figs. 17 and 18 show the dc-bus voltage and active power output responses with varying operating points. Under the condition SCR = 1.5 and Vt = 1 pu, operating points

454


Fig. 19. DC-bus voltage responses with varying ac-bus voltage control gains.

Fig. 21.

Configuration of the test rig. TABLE III PARAMETERS OF GSC S YSTEM

Fig. 20. Active power output responses with varying ac-bus voltage control gains.

are changed by varying the active power input of VSC. In Fig. 17(a), observe that the settling time is smaller, while the transient overshoot is higher without ac-bus voltage control than those with adding ac-bus voltage control in the condition of Pe = 0.9 pu. This indicates that the ac-bus voltage control gives positive restoring component and negative damping component. As active power output increases to 1.2 pu in Fig. 17(b), it results in diverging the oscillation of dc-bus voltage with ac-bus voltage control added and aperiodic drift oscillation without ac-bus voltage control. Without ac-bus voltage, obtain that K d = 1.01 pu and K r = 0.95 pu with Pe = 0.9 pu, K d = 0.23 pu and K r = −1.26 pu with Pe = 1.2 pu. With ac-bus voltage, obtain that K d = 0.86 pu and K r = 1.11 pu with Pe = 0.9 pu, K d = −0.08 pu and K r = 1.17 pu with Pe = 1.2 pu. The computed results of K d and K r with varied operating points match the analysis from Fig. 17. Therefore, it is concluded that the negative damping and positive restoring components supplied by ac-bus voltage control get increased with higher active power output, which is in accordance with Fig. 13. Assume that the VSC operates in the condition of SCR = 1.3, Pe = 1 pu, and Vt = 1 pu with ac-bus voltage control added. DC-bus voltage and active power output responses with varying gains of ac-bus voltage control (and keeping ki3 set to 40k p3) are shown in Figs. 19 and 20. It is found that the dc-bus voltage turns to aperiodic drift oscillation as the ac-bus voltage control gain is small (k p3 = 0.5), revealing that the dc-bus voltage control’s restoring component is inadequate. However, the dc-bus voltage becomes stable with larger ac-bus voltage control gains (k p3 = 2 and k p3 = 4). Moreover, the settling time and transient overshoot of dc-bus voltage response are smaller in the condition k p3 = 4 than k p3 = 2. DC-bus voltage shows better damping and restoring characteristics with k p3 = 4. Corresponding values of K d and K r are computed as follows: K d = −0.52 pu

and K r = 0.99 pu with k p3 = 0.5, K d = 0.18 pu and K r = 1.26 pu with k p3 = 2, and K d = 0.56 pu and K r = 1.23 pu with k p3 = 4. The computed results agree with the analysis from Fig. 19. Thus, it is declared that the additional damping and restoring components supplied by ac-bus voltage control to dc-bus voltage control increase with the rise of ac-bus voltage control gains, which matches the conclusion from Fig. 14. VI. E XPERIMENTAL R ESULTS A test rig for emulating full-capacity wind turbine connected to grid was built, as shown in Fig. 21. The test rig consists of speed regulator, squirrel cage induction motor (SCIM), squirrel cage induction generator, machine-side converter, and grid-side converter (GSC). Both of the converters are controlled by dSPACE system equipped with DS1006, DS3001, DS2003, and DS5101 for data processing, speed sampling, AD sampling, and pulsewidth modulation generating, respectively. Parameters of GSC system are listed in Table III. Figs. 22 and 23 show the dc-bus voltage Udc , GSC current i c , and ac line voltage u tab in two cases with varied operating points. Figs. 24 and 25 compare the dc-bus voltage responses in two cases with varied operating points. Initial experimental situation is that the grid-side VSC works with L g = 5 mH in the operating points of Pe = 1.4 kW and 4.2 kW, respectively. Then, the active power input of grid-side VSC is suddenly increased (∼5% step change) by regulating the mechanical power output of SCIM. Fig. 24 shows that the dc-bus voltage overshoot is larger, while the setting time is shorter without ac-bus voltage control than that with ac-bus voltage control with Pe = 4.2 kW and


Fig. 22. Measured responses of dc-bus voltage, GSC current, and ac line voltage in two cases with L g = 5 mH and Pe = 4.2 kW. (a) Without ac-bus voltage control as L g = 5 mH and Pe = 4.2 kW. (b) With ac-bus voltage control as L g = 5 mH and Pe = 4.2 kW.

455

Fig. 23. Measured responses of dc-bus voltage, GSC current, and ac line voltage in two cases with Pe = 1.4 kW and L g = 5 mH. (a) Without ac-bus voltage control as Pe = 1.4 kW and L g = 5 mH. (b) With ac-bus voltage control as Pe = 1.4 kW and L g = 5 mH.

TABLE IV D AMPING AND R ESTORING C OMPONENTS W ITH VARIED O PERATING P OINTS

Fig. 24. Comparison of dc-bus voltage responses in two cases with L g = 5 mH and Pe = 4.2 kW.

L g = 5 mH, agreeing with the result in Fig. 15. Fig. 25 shows that the dc-bus voltage overshoot is larger, while the setting time is shorter without ac-bus voltage control than that with ac-bus voltage control in Pe = 1.4 kW and L g = 5 mH, which conforms the result in Fig. 17. The damping and restoring components with varied operating points in the experiment are shown in Table IV, which agrees with the experimental results. Fig. 26 shows the waveforms of dc-bus voltage Udc , GSC current i c , and ac line voltage u tab with varied ac-bus voltage control parameters in the condition of L g = 5 mH and Pe = 4.2 kW. DC-bus voltage responses with varied ac-bus voltage control parameters are collected in Fig. 27. DC-bus voltage responses are observed as the active power input of grid-side VSC suddenly increases from 4.2 to 4.41 kW. It shows that the overshoot of dc-bus voltage

Fig. 25. Comparison of dc-bus voltage responses in two cases with Pe = 1.4 kW and L g = 5 mH.

becomes lower and setting time becomes reduced with the rise of ac-bus voltage control gains. Therefore, it is revealed that the additional damping and restoring components supplied by ac-bus voltage control to dc-bus voltage control increase

456


TABLE V D AMPING AND R ESTORING C OMPONENTS W ITH VARIED AC-B US V OLTAGE C ONTROL PARAMETERS

Fig. 27. Comparison of dc-bus voltage responses with varied ac-bus voltage control parameters. TABLE VI G RID -C ONNECTED VSC PARAMETERS FOR S IMULATION

VII. C ONCLUSION

Fig. 26. Measured responses of dc-bus voltage, GSC current, and ac line voltage with varied ac-bus voltage control parameters. (a) Responses with k p3 = 0.1 and ki3 = 1. (b) Responses with k p3 = 0.4 and ki3 = 4. (c) Responses with k p3 = 1.6 and ki3 = 16.

with the rise of ac-bus voltage control gains. The damping and restoring components with varied ac-bus voltage control in the experiment is shown in Table V, which is in accordance with the experimental results.

The impact of ac-bus voltage control on the stability of dc-bus voltage control in VSC integrated to weak grid has been investigated. VSC model that neglects the fast current dynamics is derived for analyzing the stability of dc-bus voltage control. Based on the linearized model, damping and restoring components for dc-bus voltage are introduced to identify the stability of dc-bus voltage control. Furthermore, the phasor diagram for illustrating the dc-bus voltage control dynamics provides physical insight into the impact of ac-bus voltage control on damping and restoring components. Besides, the impact of ac-bus voltage control on the stability of dc-bus voltage control is analyzed with considering varied operating conditions, which include ac system strengths, operating points, and ac-bus voltage control parameters. Analysis results show that the following holds: 1) in weak grid, the ac-bus voltage control poses influence on dc-bus voltage control by performing as lagging regulation for VSC active power output compared with the regulation of dc-bus voltage controller; 2) due to ac-bus voltage control’s lagging regulation, the ac-bus voltage control provides dc-bus voltage control with additional negative damping and positive restoring


components both of which increase with the reduction of ac system strength or rise of active power output in a weak grid; 3) the increase of ac-bus voltage control gains can improve the dc-bus voltage control’s damping and restoring characteristics in a weak grid. R EFERENCES [1] Z. Chen, J. M. Guerrero, and F. Blaabjerg, “A review of the state of the art of power electronics for wind turbines,” IEEE Trans. Power Electron., vol. 24, no. 8, pp. 1859–1875, Aug. 2009. [2] R. E. Torres-Olguin, M. Molinas, and T. Undeland, “Offshore wind farm grid integration by VSC technology with LCC-based HVDC transmission,” IEEE Trans. Sustainable Energy, vol. 3, no. 4, pp. 899–907, Oct. 2012. [3] J. M. Carrasco et al., “Power-electronic systems for the grid integration of renewable energy sources: A survey,” IEEE Trans. Ind. Electron., vol. 53, no. 4, pp. 1002–1016, Jun. 2006. [4] N. Flourentzou, V. G. Agelidis, and G. D. Demetriades, “VSC-based HVDC power transmission systems: An overview,” IEEE Trans. Power Electron., vol. 24, no. 3, pp. 592–602, Mar. 2009. [5] B. Singh, R. Saha, A. Chandra, and K. Al-Haddad, “Static synchronous compensators (STATCOM): A review,” IET Power Electron., vol. 2, no. 4, pp. 297–324, Jul. 2009. [6] R. Piwko, N. Miller, J. Sanchez-Gasca, X. Yuan, R. Dai, and J. Lyons, “Integrating large wind farms into weak power grids with long transmission lines,” in Proc. IEEE/PES Transmiss. Distrib. Conf. Exhibit., Asia Pacific, Dalian, China, Aug. 2005, pp. 1–7. [7] M. Durrant, H. Werner, and K. Abbott, “Model of a VSC HVDC terminal attached to a weak AC system,” in Proc. IEEE CCA, vol. 1. Jun. 2003, pp. 178–182. [8] M. Liserre, R. Teodorescu, and F. Blaabjerg, “Stability of photovoltaic and wind turbine grid-connected inverters for a large set of grid impedance values,” IEEE Trans. Power Electron., vol. 21, no. 1, pp. 263–272, Jan. 2006. [9] J. Yao, H. Li, Y. Liao, and Z. Chen, “An improved control strategy of limiting the DC-link voltage fluctuation for a doubly fed induction wind generator,” IEEE Trans. Power Electron., vol. 23, no. 3, pp. 1205–1213, May 2008. [10] M. Cespedes and J. Sun, “Adaptive control of grid-connected inverters based on online grid impedance measurements,” IEEE Trans. Sustainable Energy, vol. 5, no. 2, pp. 516–523, Apr. 2014. [11] A. Egea-Alvarez, S. Fekriasl, F. Hassan, and O. Gomis-Bellmunt, “Advanced vector control for voltage source converters connected to weak grids,” IEEE Trans. Power Syst., vol. 30, no. 6, pp. 3072–3081, Nov. 2015. [12] L. Zhang, L. Harnefors, and H.-P. Nee, “Interconnection of two very weak AC systems by VSC-HVDC links using power-synchronization control,” IEEE Trans. Power Syst., vol. 26, no. 1, pp. 344–355, Feb. 2011. [13] Y. Huang, X. Yuan, J. Hu, and P. Zhou, “Modeling of VSC connected to weak grid for stability analysis of DC-link voltage control,” IEEE J. Emerg. Sel. Topics Power Electron., to be published. [14] J. Hu, Y. Huang, D. Wang, H. Yuan, and X. Yuan, “Modeling of grid-connected DFIG-based wind turbines for DC-link voltage stability analysis,” IEEE Trans. Sustainable Energy, vol. 6, no. 4, pp. 1325–1336, Oct. 2015. [15] G. Pinares, L. A. Tuan, L. Bertling-Tjernberg, and C. Breitholtz, “Analysis of the dc dynamics of VSC-HVDC systems using a frequency domain approach,” in Proc. IEEE PES Asia-Pacific Power Energy Eng. Conf. (APPEEC), Dec. 2013, pp. 1–6. [16] L. Xu, “Modeling, analysis and control of voltage-source converter in microgrids and HVDC,” Ph.D. dissertation, Dept. Elect. Eng., Univ. South Florida, Tampa, FL, USA, 2013. [17] L. Harnefors, M. Bongiorno, and S. Lundberg, “Input-admittance calculation and shaping for controlled voltage-source converters,” IEEE Trans. Ind. Electron., vol. 54, no. 6, pp. 3323–3334, Dec. 2007. [18] P. Zhou, X. Yuan, J. Hu, and Y. Huang, “Stability of DC-link voltage as affected by phase locked loop in VSC when attached to weak grid,” in Proc. IEEE PES General Meeting, Jul. 2014, pp. 1–5. [19] J. Z. Zhou, H. Ding, S. Fan, Y. Zhang, and A. M. Gole, “Impact of short-circuit ratio and phase-locked-loop parameters on the small-signal behavior of a VSC-HVDC converter,” IEEE Trans. Power Del., vol. 29, no. 5, pp. 2287–2296, Oct. 2014.

457

[20] G. O. Kalcon, G. P. Adam, O. Anaya-Lara, S. Lo, and K. Uhlen, “Smallsignal stability analysis of multi-terminal VSC-based DC transmission systems,” IEEE Trans. Power Syst., vol. 27, no. 4, pp. 1818–1830, Nov. 2012. [21] N. P. W. Strachan and D. Jovcic, “Stability of a variable-speed permanent magnet wind generator with weak AC grids,” IEEE Trans. Power Del., vol. 25, no. 4, pp. 2779–2788, Oct. 2010. [22] F. Blaabjerg, R. Teodorescu, M. Liserre, and A. V. Timbus, “Overview of control and grid synchronization for distributed power generation systems,” IEEE Trans. Ind. Electron., vol. 53, no. 5, pp. 1398–1409, Oct. 2006. [23] S. Li, T. A. Haskew, K. A. Williams, and R. P. Swatloski, “Control of DFIG wind turbine with direct-current vector control configuration,” IEEE Trans. Sustainable Energy, vol. 3, no. 1, pp. 1–11, Jan. 2012. [24] S. De Rijcke, H. Ergun, D. Van Hertem, and J. Driesen, “Grid impact of voltage control and reactive power support by wind turbines equipped with direct-drive synchronous machines,” IEEE Trans. Sustainable Energy, vol. 3, no. 4, pp. 890–898, Oct. 2012. [25] S. EI Itani, M. Dernbach, S. Williams, and M. Bishop, “Coordinated reactive power control to meet Quebéc’s interconnection requirements for wind power plants,” in Proc. 11th Int. Workshop Large-Scale Integr. Wind Power Power Syst., Lisbon, Portugal, Nov. 2012, pp. 1–7. [26] K. Clark, N. W. Miller, and J. J. Sanchez-Gasca, “Modeling of GE wind turbine-generators for grid studies,” General Electr. Int., Apr. 2010. [27] V. Blasko and V. Kaura, “A new mathematical model and control of a three-phase AC–DC voltage source converter,” IEEE Trans. Power Electron., vol. 12, no. 1, pp. 116–123, Jan. 1997. [28] G. Gurrala and I. Sen, “Synchronizing and damping torques analysis of nonlinear voltage regulators,” IEEE Trans. Power Syst., vol. 26, no. 3, pp. 1175–1185, Aug. 2011.

Yunhui Huang (S’12) was born in Wuhan, China, in 1986. He received the B.S. degree from the School of Electrical Engineering and Automation, Wuhan University of Technology, Wuhan, in 2009. He is currently pursuing the Ph.D. degree with the State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan. His current research interests include modeling and control of grid-integrated power converters, in particular on the stability analysis and control of grid-connected renewable generations in electromagnetic timescale.

Xiaoming Yuan (S’97–M’99–SM’01) received the B.Eng. degree from Shandong University, Jinan, China, in 1986, the M.Eng. degree from Zhejiang University, Hangzhou, China, in 1993, and the Ph.D. degree from the Federal University of Santa Catarina, Florianópolis, Brazil, in 1998, all in electrical engineering. He was with Qilu Petrochemical Corporation, Zibo, China, from 1986 to 1990, where he was involved in the commissioning and testing of relaying and automation devices in power systems, adjustable speed drives, and high-power uninterruptible power systems. From 1998 to 2001, he was a Project Engineer with the Swiss Federal Institute of Technology Zurich, Zurich, Switzerland, where he was involved in flexible ac transmission systems and power quality. From 2001 to 2008, he was with the GE Globel Research Center, Shanghai, China, as the Manager of the Low Power Electronics Laboratory. From 2008 to 2010, he was with the GE Global Research Center, Niskayuna, NY, USA, as an Electrical Chief Engineer. In 2010, he joined the Huazhong University of Science and Technology, Wuhan, China. His current research interests include stability and control of power system with multimachine multiconverters, control and grid-integration of renewable energy generations, and control of high-voltage dc transmission systems. Dr. Yuan was a recipient of the First Prize Paper Award from the Industrial Power Converter Committee of the IEEE Industry Applications Society in 1999. He is also a Distinguished Expert of the National Thousand Talents Program of China, and the Chief Scientist of the National Basic Research Program of China (973 Program).

458


Jiabing Hu (S’05–M’10–SM’12) received the B.Eng. and Ph.D. degrees from the College of Electrical Engineering, Zhejiang University, Hangzhou, China, in 2004 and 2009, respectively. He was supported by the Chinese Scholarship Council, and was a Visiting Scholar with the Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow, U.K., from 2007 to 2008. From 2010 to 2011, he was a Post-Doctoral Research Associate with the Sheffield Siemens Wind Power Research Center, Sheffield, U.K., and the Department of Electronic and Electrical Engineering, The University of Sheffield, Sheffield. Since 2011, he has been a Professor with the State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China. He has authored or co-authored over 70 peer-reviewed technical papers and one monograph entitled Control and Operation of Grid-Connected Doubly-Fed Induction Generators, and holds over 20 issued/pending patents. His current research interests include grid-integration of large-scale renewables, modular multilevel converter for high-voltage dc applications, and transient analysis and control of semiconducting power systems. Dr. Hu received the 2015 Delta Young Scholar Award from the Delta Environmental and Educational Foundation and the 2014 TOP TEN Excellent Young Staff Award from the Huazhong University of Science and Technology, and is currently supported by the National Natural Science of China for Excellent Young Scholars and the Program for New Century Excellent Talents in University from the Chinese Ministry of Education. He serves as an Associate Editor of IET Renewable Power Generation, and a Domestic Member of the Editorial Board of Frontiers of Information Technology and Electronic Engineering.

Pian Zhou (S’14) was born in Wuhan, China, in 1988. She received the B.S. degree from the School of Electrical Engineering and Engineering, Huazhong University of Science and Technology, Wuhan, in 2011, where she is currently pursuing the Ph.D. degree with the State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering. Her current research interests include dynamic modeling, stability analysis, and control of power system with multipower converters.

Dong Wang was born in Huanggang, Hubei, China, in 1988. He received the B.Eng. and M.Eng. degrees from the Huazhong University of Science and Technology, Wuhan, China, in 2012 and 2015, respectively. He is currently pursuing the Ph.D. degree with the Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong. His current research interests include modeling and control of wind turbines, in particular on small signal stability analysis and control of gridintegrated Doubly Fed Induction Generator-based wind turbines in electromagnetic timescale.