research article integral sliding mode control strategy of...

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013, Article ID 932389, 14 pageshttp://dx.doi.org/10.1155/2013/932389

Research ArticleIntegral Sliding Mode Control Strategy of D-STATCOM forUnbalanced Load Compensation under Various Disturbances

Mingchao Xia and Yanhui Mao

School of Electrical Engineering, Beijing Jiaotong University, No. 3 Shang Yuan Cun, Hai Dian District, Beijing 100044, China

Correspondence should be addressed to Mingchao Xia; [email protected]

Received 1 July 2013; Accepted 26 August 2013

Academic Editor: Rongni Yang

Copyright © 2013 M. Xia and Y. Mao. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Control strategies of D-STATCOM for unbalanced load compensation under internal and external disturbances were discussed.Linear control strategies do not have a satisfactory dynamic performance and become invalid under internal or externaldisturbances. To guarantee a good precision and robustness, a control strategy combining input-output feedback linearizationtechnique with integral sliding mode control (ISMC) method was applied to D-STATCOM for unbalanced load compensation.The strategy has features of simple structure and is easy to implement. A 10MVar/10 kV D-STATCOM simulation system was builtin PSCAD/EMTDC to verify the effectiveness and robustness of the control strategy proposed. Simulation results show that thecontrol strategy can compensate reactive power and eliminate unbalance simultaneously under various disturbances.

1. Introduction

With the fast development of modern society, requirementsof good power quality becomehigher andhigher.Unbalancedloads such as electric arc furnace and rolling mill will causeenormous impacts on power quality in the power distributiongrid by unbalanced current and by absorbing a large amountof reactive power, which endanger the normal operationof the power supply and electrical equipment. In order toimprove the power quality, compensating reactive power andunbalanced load current simultaneously was necessary. Dis-tribution Static Synchronous Compensator (D-STATCOM),which has features of fast dynamic response and compactstructure, can compensate reactive power and unbalancedcurrent [1]. Many control strategies have been proposed forD-STATCOM to compensate unbalanced load, while theypresented a poor performance under various disturbances.

Sliding mode control (SMC) has gained much attentionfor its robustness. Reference [2] presented a model referenceadaptive sliding mode control algorithm for the single-phaseshunt APF. The THD performance and power quality wereimproved by the control algorithm which was insensitive tothe nonlinear load and disturbance. Reference [3] presented

an adaptive variable structure control strategy for a classof uncertain switched delay systems with parameter uncer-tainties, unknown nonlinear perturbations, and externaldisturbance to adapt the unknown upper bounds of thenonlinear disturbances so that the objective of asymptoticstabilization with an H

∞-norm bound is achieved under

the hysteresis switching law. Reference [4] combined SMCwith adaptive tuning for the nonlinear system with uncer-tain parameters. The control system was robust againstparameter variation and external disturbances, the trackingcapacity was guaranteed, and the upper bound of the systemuncertainty was unnecessary. Reference [5] presented anadaptive fuzzy sliding mode controller (AFSMC) for linearsystems with mismatched time-varying uncertainties. Theavailable uncertainty bounds, which are necessary for thetraditional SMC, were not needed, the system was stableon the sliding surface and the chattering was reduced.Reference [6] presented a robust control scheme that consistsof sliding mode control, nonlinear disturbance observer,and radial basis function neural network for a class ofuncertain multi-input and multioutput (MIMO) nonlinearsystems with the unknown external disturbance, the systemuncertainty, and the backlash-like hysteresis. The scheme

2 Mathematical Problems in Engineering

L

...

...

Load

System busbar

iga

igc

igb

Vga

VgbVgc

ila

ilbilc

R R R

L L LVsa Vsb Vsc

udca1

udcaj

udcaN

ia ib ic

Figure 1: The main wiring diagram of D-STATCOM in power distribution grid.

had been successfully applied to near-space vehicles attitudedynamics. Reference [7] presented a proportional-integral-differential neural network-based sliding mode controller formodular multilevel high-voltage DC converter of offshorewind power, which could make the system globally stableand achieve a stronger robustness. Reference [8] presented aterminal SMC based on adaptive fuzzy-neural observer forthe nonaffine nonlinear uncertain system, where only themeasurable outputs were necessary. Reference [9] presenteda robust input–output sliding mode control method forthe buck converter that avoided state measurements, or theuse of observers. Reference [10] presented an ISMC-basedASMC algorithm for rigid spacecraft attitude maneuvers,which could reduce switching gain and chattering and get afaster convergence rate. Reference [11] combined the input–output linearization technique with the integral sliding modefor load pressure control of die-cushion cylinder drive inthe presence of unknown disturbances and parametricaluncertainties. Conducted tests showed a very good androbust performance of the closed loop control. Reference [12]combined rate reaching law with integral sliding manifoldto form a novel integral sliding mode controller which wassuitable for many nonlinear systems with approximate math-ematics model, especially with unmatched uncertainty orexternal disturbance, and had better performance in rapidity,stationarity, and robustness. Reference [13] presented a robustintegral sliding mode control method for a class of uncertainswitched nonlinear systems, by which the state of the systemremained on the integral sliding surface from the initial time.Reference [14] presented a new PD sliding mode observerto construct the accurate estimations for both system statesand sensor faults simultaneously for Lipschitz nonlinear andMarkovian jump systems with time delay subject to sensorfaults. Based on the state estimation, an observer-based fault-tolerant state-feedback controller is designed to stabilize theresulting closed-loop system.

As SMC has a good robustness against the disturbancesandhas been applied tomany applications, it can be applied toD-STATCOM for unbalanced load compensation so that theperformance of D-STATCOM under various disturbanceswill be improved. This paper proposes a control strategycombining integral sliding mode control with input-outputfeedback linearization for the compensation of unbalancedload. Two loops are designed: one is for the positive sequencecompensation where the positive sequence reactive poweris compensated and the other is for the negative sequencecompensation where the negative sequence current due toload unbalance is compensated. ISMC combined with input-output feedback linearization is used in the two loops. Theadvantages of the proposed control strategy are tripartite.First, the steady-state error in the presence of disturbancesis avoided by ISMC. Second, asymptotic state observers arenot need. Third, the two-loop control form makes it possibleto compensate positive sequence reactive power and negativesequence current separately to improve power quality. A10MVar/10 kV D-STATCOM simulation system was built inPSCAD/EMTDC. Simulation results proved that the con-trol strategy works well under unbalanced condition andcompensates reactive power and negative sequence currentsimultaneously in the presence of disturbances.

2. The Mathematical Model of D-STATCOMunder Unbalanced Load

As shown in Figure 1,𝑉𝑔and 𝑖𝑔represent the grid voltage and

current; 𝑉𝑠and 𝑖 represents the output voltage and current

of D-STATCOM; 𝑖𝑙represent the load current; 𝑢dc represents

the DC voltage of each capacitor where “𝑎”, “𝑏,” and “𝑐” insubscript represent the three phases of phase 𝑎, phase 𝑏, andphase 𝑐; L represents the connection inductance; R represents

Mathematical Problems in Engineering 3

the resistance and the inverter loss. The mathematical modelof D-STATCOM in the static three-phase coordinates is

𝐿𝑑𝑖𝑎(𝑡)

𝑑𝑡= 𝑉𝑔𝑎(𝑡) − 𝑉

𝑠𝑎(𝑡) − 𝑅𝑖

𝑎(𝑡) ,

𝐿𝑑𝑖𝑏(𝑡)

𝑑𝑡= 𝑉𝑔𝑏(𝑡) − 𝑉

𝑠𝑏(𝑡) − 𝑅𝑖

𝑏(𝑡) ,

𝐿𝑑𝑖𝑐(𝑡)

𝑑𝑡= 𝑉𝑔𝑐(𝑡) − 𝑉

𝑠𝑐(𝑡) − 𝑅𝑖

𝑐(𝑡) .

(1)

The dq transformation is usually used for three-phase anal-ysis, and the sequence component decomposition is usuallyused for unbalance analysis.When compensating unbalancedload, it would be better to compensate positive sequence reac-tive power and negative sequence current separately. Accord-ing to sequence component decomposition, D-STATCOMcan be equivalent to a positive sequence one and a negativeone, where both of them are independent. This is the basisof the control strategy proposed. The positive and negativesequence models are as (2) and (3):

𝐿𝑑

𝑑𝑡[𝑖𝑑𝑃

𝑖𝑞𝑃

] = [𝑉𝑑𝑃

𝑉𝑞𝑃

] + [−𝑅 𝜔

𝑃

𝐿 −𝑀𝑃 cos 𝛿𝑃

−𝜔𝑃

𝐿 −𝑅 −𝑀𝑃 sin 𝛿𝑃] ∗

[

[

𝑖𝑑𝑃

𝑖𝑞𝑃

𝑢dc

]

]

,

(2)

𝐿𝑑

𝑑𝑡[𝑖𝑑𝑁

𝑖𝑞𝑁

]

= [𝑉𝑑𝑁

𝑉𝑞𝑁

] + [−𝑅 𝜔

𝑁

𝐿 −𝑀𝑁 cos 𝛿𝑁

−𝜔𝑁

𝐿 −𝑅 −𝑀𝑁 sin 𝛿𝑁] ∗

[

[

𝑖𝑑𝑁

𝑖𝑞𝑁

𝑢dc

]

]

,

(3)

where 𝑖𝑑𝑃, 𝑖𝑞𝑃, 𝑖𝑑𝑁

, 𝑖𝑞𝑁

represent the 𝑑 and 𝑞 components ofthe output positive (𝑃) and negative (𝑁) sequence currentsof D-STATCOM; 𝑉

𝑑𝑃, 𝑉𝑞𝑃, 𝑉𝑑𝑁

, 𝑉𝑞𝑁

represent the 𝑑 and 𝑞components of the positive (𝑃) and negative (𝑁) sequencegrid voltage; 𝜔𝑃, 𝜔𝑁 represent the positive (𝑃) and negative(𝑁) sequence angular speed;𝑀𝑃,𝑀𝑁 represent the positive(𝑃) and negative (𝑁) sequence modulation ratio; 𝛿𝑃, 𝛿𝑁represent the positive (𝑃) and negative (𝑁) sequence phasedifference between the grid voltage and the output voltage ofD-STATCOM.

3. The Control Strategy for UnbalancedLoad Compensation

Unbalanced load compensation is a prominent problem forD-STATCOM both in theory and practice. Reference [15]compensated the positive sequence component of reactivepower and negative sequence current in a way that theduty ratio and the input phase currents satisfy a specialrelationship. Reference [16] treated STATCOM as threesingle-phase systems for unbalance compensation. Reference[17] employed the feed forward compensation scheme withsymmetrical componentsmethod to compensate unbalancedload. Reference [18] compensated unbalanced network faultand load by separate control of positive andnegative sequence

current with switching function modulation. Reference [19]combined linear PID feedback control with the admit-tance compensationmethod to compensate unbalanced load.Reference [20] presented a software sensor-based controlstrategy to compensate unbalanced load avoiding the use ofthe physical voltage sensors.

However, the common drawbacks of the above men-tioned control strategies are heavily reliant on the math-ematical model and sensitive to disturbances. Consideringthe drawbacks, it is worth applying SMC to D-STATCOMwhich is independent of the mathematical model and robustagainst disturbances. Some works have applied SMC to D-STATCOM to compensate reactive power [21–26]. But all ofthem cannot compensate unbalanced load.

This paper aims to apply a control strategy based onintegral sliding mode control to D-STATCOM to compen-sate unbalanced load under various disturbances. Since themathematical model of D-STATCOM under unbalancedcondition includes a positive sequence part and a negativesequence part, the separate control of positive and negativesequence currents can be achieved. Then, the integral slidingmode control combined with the input-output feedbacklinearization is used in the two parts to compensate positivesequence reactive power and negative sequence currentsimultaneously. The entire schematic diagram of the controlstrategy is as shown in Figure 2, where 𝑖

𝑑𝑃ref represents thecurrent used to stabilize DC voltage, 𝑖

𝑞𝑃 load represents thepositive sequence reactive load current, and 𝑖

𝑑𝑁 load and𝑖𝑞𝑁 load represent the negative sequence load current.

3.1. The Implementation of Input-Output Feedback Lineariza-tion. D-STATCOM is a multivariable, strong coupling, non-linear system which is complicated to design control strategy.The input-output feedback linearization is a straightforwardmethod to simplify such nonlinear system. The main idea ofthis method is to linearize and decouple the original systeminto a pseudo linear system through coordinate transforma-tion which is realized by the differential geometric theory.The control characteristics of the system remain unchangedsince the coordinate transformation is diffeomorphism. First,input-output feedback linearization method is applied to thepositive sequence mathematical model as in (2): the statevariables are 𝑋 = [𝑥

1, 𝑥2]𝑇

= [𝑖𝑑𝑝, 𝑖𝑞𝑝]𝑇, the control variables

are 𝑈 = [𝑢1, 𝑢2]𝑇

= [𝑀𝑃 cos 𝛿𝑃,𝑀𝑃 sin 𝛿𝑃]𝑇, and the

output variables are 𝑌 = [𝑦1, 𝑦2]𝑇

= [𝑖𝑑𝑝, 𝑖𝑞𝑝]𝑇. The positive

sequence mathematical model and the output equation canbe equivalent to (4) and (5), respectively,

[[[

[

⋅

𝑥1

⋅

𝑥2

]]]

]

=[[

[

−𝑅

𝐿𝑥1+ 𝜔𝑃

𝑥2+𝑉𝑑𝑃

𝐿

−𝜔𝑃

𝑥1−𝑅

𝐿𝑥2

]]

]

+ [

[

−𝑢dc𝐿

0

0 −𝑢dc𝐿

]

]

∗ [𝑢1

𝑢2

] ,

(4)

𝑦1= ℎ1(𝑥) = 𝑥

1,

𝑦2= ℎ2(𝑥) = 𝑥

2.

(5)


Positive sequence separation

Input/output feedback

linearization

Input/output feedback

linearization

Slidingmode

control

Slidingmode

control

Negative sequence separation

uabc

iabc

IdP

IqP

Udc ⨂

UdN

UqN

UdP

UqP

IdN

IqN

PI−

+

Iq

IdP load

P load

V1 P

V2 P

IdP ref

Id

IqN load

N load

V1 N

V2 N

MagN

PhaseN

MagP

PhaseP

Udc ref

ilabc

Figure 2: The entire schematic diagram of the control strategy.

Equation (6) can be deduced from (4) and (5):

[[[

[

⋅

𝑦1

⋅

𝑦2

]]]

]

= 𝐴 (𝑋) + 𝐸 (𝑋) [𝑢1

𝑢2

] , (6)

where

𝐴 (𝑋) =[[

[

−𝑅

𝐿𝑥1+ 𝜔𝑃

𝑥2+𝑉𝑑𝑃

𝐿

−𝜔𝑃

𝑥1−𝑅

𝐿𝑥2

]]

]

,

𝐸 (𝑋) = [

[

−𝑢dc𝐿

0

0 −𝑢dc𝐿

]

]

.

(7)

Two new input variables named V1 𝑃

and V2 𝑃

are introducedto linearize and decouple the positive sequencemathematicalmodel, where the relations of V

1 𝑃, V2 𝑃

, and 𝑢1, 𝑢2are as

follows:

[𝑢1

𝑢2

] = 𝐸(𝑋)−1

[−𝐴 (𝑋) + [V1 𝑃

V2 𝑃

]] . (8)

The final form of the model is as follows:

[[[

[

⋅

𝑦1

⋅

𝑦2

]]]

]

= [V1 𝑃

V2 𝑃

] . (9)

The DC voltage control of capacitors in series D-STATCOMis an internal dynamic system control issue. For the stability

of the internal dynamic system, the three-level DC voltagecontrol strategy as in [27] was adopted. Since the positive andnegative sequence mathematical models have the same form,the negative sequence model can be equivalent to (10) and(11):

[[[

[

⋅

𝑦3

⋅

𝑦4

]]]

]

= [V1 𝑁

V2 𝑁

] , (10)

[𝑢3

𝑢4

] = 𝐸(𝑋)−1

[−𝐵 (𝑋) + [V1 𝑁

V2 𝑁

]] , (11)

where [𝑥3, 𝑥4]𝑇

= [𝑖𝑑𝑁, 𝑖𝑞𝑁]𝑇, [𝑢

3, 𝑢4]𝑇

=

[𝑀𝑁 cos 𝛿𝑁,𝑀𝑁 sin 𝛿𝑁]𝑇, [𝑦

3, 𝑦4]𝑇

= [𝑖𝑑𝑁, 𝑖𝑞𝑁]𝑇.

𝐵 (𝑋) =[[

[

−𝑅

𝐿𝑥3+ 𝜔𝑁

𝑥4+𝑉𝑑𝑁

𝐿

−𝜔𝑁

𝑥3−𝑅

𝐿𝑥4

]]

]

. (12)

3.2. The Implementation of Integral Sliding Mode Control.Theoretically, the input-output feedback linearization is a rel-atively uncomplicated way to control D-STATCOM. Unfor-tunately, this control is also highly sensitive to disturbances,which in practice considerably restricts its performances.The sliding mode control has been widely applied becauseof its satisfactory operation characteristics such as fastness,robustness, and stability. A control strategy based on input-output linearization and SMC, which can considerably sim-plify the design progress and increase the overall systemrobustness, was proposed to guarantee the normal operation


of D-STATCOM and compensate positive sequence reactivepower and negative sequence current.

We define the tracking error named 𝑒 as follows:

𝑒1= 𝑖𝑑𝑃− 𝑖𝑑𝑃ref,

𝑒2= 𝑖𝑞𝑃− 𝑖𝑞𝑃 load,

𝑒3= 𝑖𝑑𝑁− 𝑖𝑑𝑁 load,

𝑒4= 𝑖𝑞𝑁− 𝑖𝑞𝑁 load.

(13)

Determining a sliding surface is the key of sliding modecontrol. While tracking the reference current, traditionalSMC such as in [21–23] cannot avoid steady state error in thepresence of disturbances. In this paper, an integral portionis added to the traditional SMC to solve this problem. Theswitch function can be described as follows:

𝑆1= 𝑘11× 𝑒1+ 𝑘12× ∫ 𝑒1,

𝑆2= 𝑘21× 𝑒2+ 𝑘22× ∫ 𝑒2,

𝑆3= 𝑘31× 𝑒3+ 𝑘32× ∫ 𝑒3,

𝑆4= 𝑘41× 𝑒4+ 𝑘42× ∫ 𝑒4.

(14)

In order to weaken the chattering and improve the conver-gence, exponential approach law is used in this paper asfollows:

𝑆1= −𝜀1sgn (𝑆

1) − 𝑘1𝑆1,


2) − 𝑘2𝑆2,


3) − 𝑘3𝑆3,


4) − 𝑘4𝑆4.

(15)

From (9), (10), and (15), we can obtain

V1 𝑃= −𝜀1sgn (𝑆

1) − 𝑘1𝑆1,

V2 𝑃= −𝜀2sgn (𝑆

2) − 𝑘2𝑆2,

V1 𝑁

= −𝜀3sgn (𝑆

3) − 𝑘3𝑆3,

V2 𝑁

= −𝜀4sgn (𝑆

4) − 𝑘4𝑆4.

(16)

Finally, from (8), (11), and (16), we get the control variables𝑢1, 𝑢2, 𝑢3, and 𝑢

4which are applied to generate PWM pulse

signals to control IGBTs in D-STATCOM.

4. Simulation

In order to verify the effectiveness of the control strategyproposed in this paper, a 10MVar/10 kV D-STATCOM sim-ulation system was built in PSCAD/EMTDC. The systemparameters are the rated line voltage at the point of commoncoupling: 𝑉

𝑔= 10 kV; the impedance of the power supply

and the line: 𝑍𝑠= 0.015 + 𝑗0.32 × 10

3

Ω. The parameters ofD-STATCOM are the joint inductance: 𝐿 = 3.18 × 10

−3H;the single capacitor in DC side: 𝐶 = 6.2mF; the cascadecount: 𝑁 = 12. The equivalent loss resistance between D-STATCOM and the point of common coupling is 𝑅 = 0.5Ω.The load of phase A is 𝑍

𝑎= 5 + 𝑗0.003Ω; the load of phase

B is 𝑍𝑏= 4.5 + 𝑗0.003Ω; the load of phase C is 𝑍

𝑐=

4 + 𝑗0.003Ω. The unbalanced degree of power grid current isΔ𝐼𝑠% = [(𝐼

𝑠max − 𝐼𝑠min)/𝐼𝑠 ave] × 100%, where 𝐼𝑠max represents

the maximum value of the three-phase current peak, 𝐼𝑠min

represents the minimum value of the three-phase currentpeak, and 𝐼

𝑠 ave represents the average value of the three-phasecurrent peak.

Figure 3 shows the reactive power compensation effectwhen there were no disturbances. The reactive power com-pensation effect of the ISMC is shown in Figure 3(a), wherethe reactive power in grid (Q grid) fell to 0.0Mvar from4.3Mvar at 0.4 s when the control strategy was put intooperation and fluctuated a little at 1.0 s and became stableat 1.2 s due to the DC voltages in the three phases thatwere forced to 1 kV. The reactive power generated by D-STATCOM (Q STATCOM) could track the reactive powerin load to guarantee the Q grid to be stable at 0.0Mvarand the voltage at the point of common coupling rose to10.0 kV from 9.7 kV. This proved that the positive sequencecontrol loop could make D-STATCOM generate reactivepower needed by load to improve the power factor andvoltage at the point of common coupling. The reactive powercompensation effect of the traditional SMC is shown inFigure 3(b), where the overshoot in the transient process islarger than ISMC. This proved that the integral portion canimprove the compensation performance.

Figure 4 shows the negative sequence current compensa-tion effect ofD-STATCOMunder no disturbances.The three-phase grid current before the control strategy was put intooperation is shown in Figure 4(a), where 𝐼

𝑎 grid = 1.641 kA,𝐼𝑏 grid = 1.778 kA, 𝐼

𝑐 grid = 1.820 kA, and Δ𝐼𝑠% = 10.25%.

The unbalance compensation effect of the ISMC is shownin Figure 4(b), where 𝐼

𝑎 grid = 1.738 kA, 𝐼𝑏 grid = 1.737 kA,

𝐼𝑐 grid = 1.737 kA, and Δ𝐼

𝑠% = 0.058%. The three-phase

grid current became stable and balanced due to the negativesequence control loop which made D-STATCOM generatenegative sequence current needed by load to avoid the unbal-ance thatappeared in grid. The unbalance compensationeffect of the traditional SMC is shown in Figure 4(c), where𝐼𝑎 grid = 1.735 kA, 𝐼𝑏 grid = 1.752 kA, 𝐼𝑐 grid = 1.722 kA, andΔ𝐼𝑠% = 1.73%. This proved that the integral portion can

improve the compensation performance.Figure 5 shows the reactive power compensation effect

of D-STATCOM under internal disturbances containingparameter and joint impedance variation.The reactive powercompensation effect of the ISMC is shown in Figure 5(a),where Q grid and Q DSTATCOMwere quickly stable after asmall fluctuation when parameter variation happened at 1.3sand joint impedance variation happened at 1.6 s, while V pcc,kept at 10.0 kV no matter what disturbance happened. Thisproved that the positive sequence control loopwhich contains


t (s)

t (s)

t (s)

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80−1.0

1.0

3.0

5.0

y

Q grid

−1.0

7.0

y(M

var)

(Mva

r)

Q DSTATCOM

0.0

10.0

y(K

V)

V pcc

(a)

−2.0

0.0

2.0

4.0

y(M

var)

Q grid

Q DSTATCOM

V pcc

t (s)0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

t (s)0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

t (s)0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

−1.0

9.0

y(M

var)

0.0

11.0

y(K

V)

(b)

Figure 3: The reactive power compensation effect of D-STATCOM under no disturbances.

t (s)0.190 0.200 0.210 0.220 0.230 0.240 0.250 0.260 0.270 0.280 0.290

−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0

y(K

A)

Ia gridIb gridIc grid

(a)

1.590 1.600 1.610 1.620 1.630 1.640 1.650 1.660 1.670 1.680 1.690−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0

y(K

A)


t (s)

(b)

1.590 1.6001.610 1.620 1.630 1.640 1.6501.660 1.6701.680 1.690−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0

y(K

A)


t (s)

(c)

Figure 4: The negative sequence current compensation effect of D-STATCOM under no disturbances.


V pcc

Q grid

Q DSTATCOM

−1.0

1.0

3.0

5.0

y(M

var)

−1.0

7.0

y(M

var)

0.0

10.0

y(K

V)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

t (s)

t (s)

t (s)

(a)

V pcc

Q grid

Q DSTATCOM

−2.0

0.0

2.0

4.0

y(M

var)

−1.0

9.0

y(M

var)

0.0

11.0

y(K

V)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

t (s)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

t (s)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

t (s)

(b)

Figure 5: The reactive power compensation effect of D-STATCOM under internal disturbances.

integral SMC can compensate reactive power needed by loadand has a good robustness against internal disturbances. Thereactive power compensation effect of the traditional SMC isshown in Figure 5(b), where the overshoot when the internaldisturbances happened is larger than the ISMC. This provedthat the integral portion can improve the robustness againstthe internal disturbances.

Figure 6 shows the negative sequence current compensa-tion effect of D-STATCOM under internal disturbances. Theunbalance compensation effect of the ISMC under parametervariation that happened at 1.3 s is shown in (a), wherethe three-phase grid current balanced again at 1.36 s withsmooth transient process and 𝐼

𝑎 grid = 1.740 kA, 𝐼𝑏 grid =

1.737 kA, 𝐼𝑐 grid = 1.738 kA, and Δ𝐼

𝑠% = 0.17%, while

the unbalance compensation effect of the traditional SMCis shown in Figure 6(b) where 𝐼



𝑠% = 3.23%. The

unbalance compensation effect of the ISMC under parameterand joint impedance variation that happened at 1.3 s and 1.6 s,respectively, is shown in Figure 6(c) where the three-phasegrid current balance again at 1.65 s with smooth transientprocess and 𝐼

𝑎 grid = 1.764 kA, 𝐼𝑏 grid = 1.766 kA, 𝐼

𝑐 grid =

1.765 kA, and Δ𝐼𝑠% = 0.11%, while the unbalance compen-

sation effect of the traditional SMC is shown in Figure 6(d)where 𝐼

𝑎 grid = 1.751 kA, 𝐼𝑏 grid = 1.790 kA, 𝐼

𝑐 grid =

1.763 kA, and Δ𝐼𝑠% = 1.64%. The current curves mentioned

above proved that the negative sequence control loop whichcontains integral SMC can compensate unbalance currentcaused by unbalanced load andhas a better robustness againstinternal disturbances than the traditional SMC.

Figure 7 shows the reactive power compensation effectof D-STATCOM when power supply was unbalance. Thereactive power compensation effect of the ISMC is shown inFigure 7(a), where Q grid and Q DSTATCOM were quicklystable after a small fluctuation when the degree of unbalancein power supply became 5% at 1.5 s and 10% at 1.7 s, andV pcc was kept at 10.0 kV all along, while the reactive powercompensation effect of the traditional SMC is shown inFigure 7(b), where the overshoot is larger than the ISMC.Thisproved that the positive sequence control loopwhich containsintegral SMC can compensate reactive power needed by loadand has a better robustness against power supply unbalancethan the traditional SMC.

Figure 8 shows the negative sequence current compensa-tion effect of D-STATCOM when power supply was unbal-ance. The unbalance compensation effect of the ISMC whenthe degree of unbalance became 5% at 1.5 s is shown inFigure 8(a), where the three-phase grid current balancedagain at 1.55s with smooth transient process and 𝐼

𝑎 grid =

1.733 kA, 𝐼𝑏 grid = 1.732 kA, 𝐼𝑐 grid = 1.732 kA, and Δ𝐼𝑠% =

0.058%, while the unbalance effect of the traditional SMCis shown in Figure 8(b), where 𝐼



𝑠% = 0.46%. The

unbalance compensation effect of the ISMC when the degreeof unbalance became 10% at 1.7 s is shown in Figure 8(c),where the three-phase grid current balanced again at 1.75swith smooth transient process and 𝐼


𝑐 grid = 1.739 kA, and Δ𝐼𝑠% = 0.17%,

while the unbalance compensation effect of the traditionalSMC is shown in Figure 8(d), where 𝐼

𝑎 grid = 1.743 kA,


t (s)

−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0

y(K

A)

1.290 1.300 1.310 1.320 1.330 1.340 1.350 1.360 1.370 1.380

(a)

t (s)

−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0

y(K

A)

1.290 1.300 1.310 1.320 1.330 1.340 1.350 1.360 1.370 1.380

(b)

−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0

y(K

A)

1.580 1.590 1.600 1.610 1.620 1.630 1.640 1.650 1.660 1.670 1.680


t (s)

(c)

−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0

y(K

A)

1.580 1.590 1.600 1.610 1.620 1.630 1.640 1.650 1.660 1.670 1.680


t (s)

(d)

Figure 6: The negative sequence current compensation effect of D-STATCOM under internal disturbances.

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20

0.0

4.0

8.0

12.0

t (s)

t (s)

t (s)

V pcc

Q grid

Q DSTATCOM

−1.0

1.0

3.0

5.0

y(M

var)

−1.0

7.0

y(M

var)

y(K

V)

(a)

−2.0

0.0

2.0

4.0

y(M

var)

Q grid

Q DSTATCOM

V pcc

−1.0

9.0

y(M

var)

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.200.0

4.0

8.0

12.0

t (s)

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20

t (s)

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20

t (s)

y(K

V)

(b)

Figure 7: The reactive power compensation effect of D-STATCOM when power supply was unbalanced.


1.480 1.490 1.500 1.510 1.520 1.530 1.5401.550 1.560 1.570 1.580−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0

y(K

A)

t (s)

(a)

1.480 1.490 1.500 1.510 1.520 1.530 1.5401.550 1.560 1.570 1.580−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0

y(K

A)

t (s)

(b)

1.680 1.690 1.700 1.710 1.720 1.730 1.740 1.750 1.760 1.770 1.780−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0

y(K

A)


t (s)

(c)

1.680 1.690 1.700 1.710 1.720 1.730 1.740 1.750 1.760 1.770 1.780−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0

y(K

A)


t (s)

(d)

Figure 8: The negative sequence current compensation effect of D-STATCOM when power supply was unbalanced.

V pcc

Q grid

Q DSTATCOM

−1.0

1.0

3.0

5.0

y(M

var)

−1.0

9.0

y(M

var)

0.0

10.0

y(K

V)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25

t (s)

t (s)

t (s)

(a)

−2.0

0.0

2.0

4.0

y(M

var)

−1.0

9.0

y(M

var)

V pcc

Q grid

Q DSTATCOM

0.0

11.0

y(K

V)

t (s)0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25

t (s)0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25

t (s)0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25

(b)

Figure 9: The reactive power compensation effect of D-STATCOM under load variation.


1.280 1.290 1.300 1.310 1.3201.330 1.340 1.350 1.360 1.370−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0y

(KA

)

t (s)

(a)

1.280 1.290 1.300 1.310 1.320 1.330 1.340 1.350 1.360 1.370−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0

y(K

A)

t (s)

(b)

1.590 1.600 1.610 1.620 1.630 1.640 1.650 1.660 1.670 1.680−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0

y(K

A)

t (s)

(c)

1.590 1.600 1.610 1.620 1.630 1.640 1.650 1.660 1.670 1.680−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0

y(K

A)

t (s)

(d)

1.890 1.900 1.910 1.920 1.9301.940 1.950 1.960 1.970 1.980 1.990−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0

y(K

A)

t (s)


(e)

1.890 1.900 1.910 1.920 1.9301.940 1.950 1.960 1.970 1.980 1.990

−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0

y(K

A)

t (s)


(f)

Figure 10: The negative sequence current compensation effect of D-STATCOM under load variation.

𝐼𝑏 grid = 1.727 kA, 𝐼

𝑐 grid = 1.740 kA, and Δ𝐼𝑠% = 0.92%.

The current curves above proved that the negative sequencecontrol loop which contains integral SMC can compensateunbalance current caused by unbalanced load and has abetter robustness against power supply unbalance than thetraditional SMC.

Figure 9 shows the reactive power compensation effectof D-STATCOM during load variation. The reactive powercompensation effect of the ISMC is shown in Figure 9(a),where Q grid and Q DSTATCOM were quickly stable aftera small fluctuation when load variation happened at 1.3 s,1.6 s and 1.9 s, and V pcc was kept at 10.0 kV all along, whilethe reactive compensation effect of the traditional SMC isshown in Figure 9(b), where the overshoot is larger thanthe ISMC. This proved that the positive sequence controlloop which contains integral SMC can compensate reactive

power needed by load and has a good robustness against loadvariation.

Figure 10 shows the negative sequence current com-pensation effect of D-STATCOM when load variation. Theunbalance compensation effect of the ISMC when load inphase 𝐵 became 4 + 𝑗0.003 and load in phases 𝐴 and 𝐶remained unchanged at 1.3 s is shown in Figure 10(a), wherethe three- phase grid current balanced again at 1.35 s withsmooth transient process and 𝐼



𝑠% = 0.11%, while

the unbalance compensation effect of the traditional SMCis shown in Figure 10(b), where 𝐼



𝑠% = 2.43%. The

unbalance compensation effect of the ISMC when load inphase 𝐴 and 𝐵 became 3 + 𝑗0.003 and 4 + 𝑗0.003 and load inphase𝐶 remained unchanged at 1.6 s is shown in Figure 10(c),


0.0

4.0

8.0

12.0

t (s)

V pcc

Q grid

Q DSTATCOM

−1.0

1.0

3.0

5.0

y(M

var)

−1.0

7.0

y(M

var)

y(K

V)

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

t (s)0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

t (s)0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

(a)

−2.0

0.0

2.0

4.0

y(M

var)

Q grid

Q DSTATCOM

V pcc

−1.0

9.0

y(M

var)

0.0

4.0

8.0

12.0

y(K

V)

t (s)0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

t (s)0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

t (s)0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

(b)

Figure 11: The reactive power compensation effect of D-STATCOM under internal and external disturbances.

where the three-phase grid current balanced again at1.66 s with smooth transient process and 𝐼

𝑎 grid=2.090 kA,𝐼𝑏 grid=2.091 kA, 𝐼𝑐 grid=2.092, and Δ𝐼𝑠% = 0.096%, whilethe unbalance compensation effect of the traditional SMCis shown in Figure 10(d), where 𝐼


2.084 kA, 𝐼𝑐 grid = 2.106, and Δ𝐼𝑠% = 1.05%. The unbalance

compensation effect of the ISMC when load in the three-phase restored to the original value at 1.9 s is shown inFigure 10(e), where the three-phase grid current balancedagain at 1.96 s with smooth transient process and 𝐼

𝑎 grid =

1.738 kA, 𝐼𝑏 grid = 1.737 kA, 𝐼𝑐 grid = 1.737 kA, and Δ𝐼𝑠% =

0.058%.The unbalance compensation effect of the traditionalSMC is shown in Figure 10(f) where 𝐼


𝑐 grid = 1.722 kA, and Δ𝐼𝑠% = 1.73%.

The current curves above proved that the negative sequencecontrol loop which contains integral SMC can compensateunbalance current caused by unbalanced load andhas a betterrobustness against load variation than the traditional SMC.

Figure 11 shows the reactive power compensation effectof D-STATCOM under internal disturbances containingparameter variation happened at 1.3 s, joint impedance vari-ation happened at 1.6 s, external disturbances containingpower supply unbalance happened at 2.0 s and 2.5 s, andload variation happened at 2.8 s and 3.2 s. The reactive powercompensation effect of the ISMC is shown in Figure 11(a)where Q grid and Q DSTATCOM were quickly stable aftera small fluctuation, and V pcc was kept at 10.0Mvar all alongunder internal and external disturbances, while the reactivepower compensation effect of the traditional SMC is shownin Figure 11(b), where the overshoot is larger than the ISMC.

This proved that the positive sequence control loop whichcontains integral SMC can compensate the reactive powerneeded by load and has a better robustness against internaland external disturbances than the traditional SMC.

Figure 12 shows the negative sequence current compensa-tion effect of D-STATCOM under internal and external dis-turbances. The DC voltage controlled by the ISMC is shownin Figure 12(a), where all DC voltages were stable at 1 kVunder internal and external disturbances. This is the basisof the normal operation. The unbalance compensation effectof the ISMC is shown in Figure 12(b), where the negativesequence current generated by D-STATCOM could track thenegative sequence current in load to make negative sequencecurrent in grid keep at 0.0 kA under internal and externaldisturbances, while the unbalance compensation effect of thetraditional SMC is shown in Figure 12(c), where the negativesequence current generated by D-STATCOM could not trackthe negative sequence current in load precisely. The finalwave form of three-phase current controlled by the ISMCis shown in Figure 12(d), where 𝐼



𝑠% = 0.057%, while

the final wave form of the three-phase current controlledby the traditional SMC is shown in Figure 12(e), where𝐼𝑎 grid = 1.787 kA, 𝐼

𝑏 grid = 1.739 kA, 𝐼𝑐 grid = 1.757 kA,

and Δ𝐼𝑠% = 2.73%. The current curves above proved that

the negative sequence control loop which contains the ISMCcan compensate unbalance current caused by unbalancedload and has a better robustness against internal and externaldisturbances than the traditional SMC.


Vdca ave

Vdcb ave

Vdcc ave

y(V

)

1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.00

1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.00

1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.00

1.2 k1.0 k0.8 k0.6 k

y(V

) 1.2 k1.0 k0.8 k0.6 k

y(V

) 1.2 k1.0 k0.8 k0.6 k

t (s)

t (s)

t (s)

(a)

1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.00

0.225

0.0

0.225

0.0

0.225

0.0

y(K

A)

y(K

A)

y(K

A)

The negative sequence current in load

The negative sequence current generated by D-STATCOM

The negative sequence current in grid

t (s)

1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.00

t (s)

1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.00

t (s)

(b)

1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.00

1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.00

1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.00

0.225

0.0

0.225

0.0

0.225

0.0

y(K

A)

y(K

A)

y(K

A)

The negative sequence current in load

The negative sequence current generated by D-STATCOM

The negative sequence current in grid

t (s)

t (s)

t (s)

(c)

−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0

y(K

A)

Ia gridIb grid

Ic grid

t (s)3.860 3.870 3.880 3.890 3.900 3.910 3.920 3.930 3.940 3.950 3.960

(d)

−3.0

−2.0

−1.0

0.0

1.0

2.0

3.0

y(K

A)

Ia gridIb grid

Ic grid

t (s)3.860 3.870 3.880 3.890 3.900 3.910 3.920 3.930 3.940 3.950 3.960

(e)

Figure 12: The negative sequence current compensation effect of D-STATCOM under internal and external disturbances.


5. Conclusions

Considering that D-STATCOM is a nonlinear and strongcoupling system and the impact caused by unbalanced loadon D-STATCOM and grid, a two-loop control strategy basedon the input-output feedback linearization and the integralsliding mode technique was applied to D-STATCOM forunbalanced load compensation. The positive and negativesequence separation technique were used to divide thecontrol strategy into positive sequence control loop for thepositive reactive power compensation and negative sequencecontrol loop for unbalance compensation. The combinationof input-output feedback linearization and integral slidingmode control was used in the two loops to strengthen thetracking capacity and robustness against the internal andexternal disturbances. The simulation results demonstratedthat the control strategy can simultaneously compensate thereactive power and negative sequence current caused byunbalanced load to improve the power quality and has agood robustness against internal and external disturbances.Moreover, the design of the integral sliding mode controlcompensator was straightforward.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgment

Theauthors gratefully acknowledge the support of the Funda-mental Research Funds for the Central Universities of Chinafor the financial support under Grant no. 2012JBM098.

References

[1] G. F. Reed, J. E. J. Greaf, T. M. Matsumoto et al., “Applicationof a 5MVA, 4.16 kV D-STATCOM system for voltage flickercompensation at Seattle iron & metals,” in Proceedings of thePower Engineering Society Summer Meeting, pp. 1605–1611,Seattle, Wash, USA, July 2000.

[2] F. Juntao, Z. Shenglei, and Z. Jian, “Adaptive sliding modecontrol of single-phase shunt active power filter,”MathematicalProblems in Engineering, vol. 2012, Article ID 809187, 22 pages,2012.

[3] J. Lian and J. Zhao, “Adaptive variable structure control foruncertain switched delay systems,” Circuits, Systems, and SignalProcessing, vol. 29, no. 6, pp. 1089–1102, 2010.

[4] Y.-J. Huang, T.-C. Kuo, and S.-H. Chang, “Adaptive sliding-mode control for nonlinear systemswith uncertain parameters,”IEEE Transactions on Systems, Man, and Cybernetics B, vol. 38,no. 2, pp. 534–539, 2008.

[5] C. W. Tao, M.-L. Chan, and T.-T. Lee, “Adaptive fuzzy slidingmode controller for linear systems with mismatched time-varying uncertainties,” IEEE Transactions on Systems, Man, andCybernetics B, vol. 33, no. 2, pp. 283–294, 2003.

[6] M. Chen, R. Mei, and B. Jiang, “Sliding mode control for a classof uncertainMIMOnonlinear systemswith application to near-space vehicles,”Mathematical Problems in Engineering, vol. 2013,Article ID 180589, 9 pages, 2013.

[7] S. Li, Z.Wang, andG.Wang, “Proportional-integral-differentialneural network based sliding-mode controller for modularmulti-level high-voltage DC converter of offshore wind power,”Electric Power Components and Systems, vol. 41, no. 4, pp. 427–446, 2013.

[8] D. Xu, B. Jiang, M. Qian, and J. Zhao, “Terminal sliding modecontrol using adaptive fuzzy-neural observer,” MathematicalProblems in Engineering, vol. 2013, Article ID 958958, 8 pages,2013.

[9] H. Sira-Ramırez, A. Luviano-Juarez, and J. Cortes-Romero,“Robust input-output sliding mode control of the buck con-verter,” Control Engineering Practice, vol. 21, no. 5, pp. 671–678,2013.

[10] Z. Chen, B. Cong, and X. Liu, “Switching gain reductionin adaptive sliding mode control for rigid spacecraft attitudemaneuvers,” Mathematical Problems in Engineering, vol. 2013,Article ID 602869, 9 pages, 2013.

[11] J. Komsta, N. van Oijen, and P. Antoszkiewicz, “Integral slidingmode compensator for load pressure control of die-cushioncylinder drive,” Control Engineering Practice, vol. 21, no. 5, pp.708–718, 2013.

[12] Q. Zong, Z. Zhao, L. Doll, and L. Sun, “Integral slidingmode control for a class of nonlinear mismatched uncertainsystems,” in Proceedings of the 2nd International Symposium onSystems and Control in Aerospace and Astronautics (ISSCAA’08), Shenzhen, China, December 2008.

[13] J. Lian, J. Zhao, and G. M. Dimirovski, “Integral sliding modecontrol for a class of uncertain switched nonlinear systems,”European Journal of Control, vol. 16, no. 1, pp. 16–22, 2010.

[14] M. Liu, P. Shi, L. Zhang, and X. Zhao, “Fault-tolerant controlfor nonlinear markovian jump systems via proportional andderivative sliding mode observer technique,” IEEE Transactionson Circuits and Systems I, vol. 58, no. 11, pp. 2755–2764, 2011.

[15] M. Slepchenkov and K. Smedley, “Flicker mitigation and loadbalancing in steel plants power systems by OCC-hexagramconverter based STATCOM,” inProceedings of the IEEE IndustryApplications Society Annual Meeting, Houston, Tex, USA, Octo-ber 2008.

[16] Q. Song andW. Liu, “Control of a cascade STATCOMwith starconfiguration under unbalanced conditions,” IEEE Transactionson Power Electronics, vol. 24, no. 1, pp. 45–58, 2009.

[17] W. Chang and K.-D. Yeh, “Design of D-STATCOM for fastload compensation of unbalanced distribution systems,” PowerElectronics and Drive Systems, vol. 2, pp. 801–806, 2001.

[18] B. Blazic and I. Papic, “Improved D-Statcom control for opera-tion with unbalanced currents and voltages,” IEEE Transactionson Power Delivery, vol. 21, no. 1, pp. 225–233, 2006.

[19] B. Yang, G. Zeng, and Y. Zhong, “Research on the controlsystem of cascaded multilevel STATCOM for unbalanced loadcompensation,” in Proceedings of the IEEE Power Engineeringand Automation Conference (PEAM ’11), pp. 88–91, Wuhan,China, September 2011.

[20] A. E. Leon, J. M. Mauricio, J. A. Solsona, and A. Gomez-Exposito, “Software sensor-based STATCOM control underunbalanced conditions,” IEEE Transactions on Power Delivery,vol. 24, no. 3, pp. 1623–1632, 2009.

[21] X. Sun and W. Wu, “A new sliding mode control of STATCOMand its effects on wind farm,” in Proceedings of the InternationalConference on Electronic and Mechanical Engineering and Infor-mation Technology (EMEIT ’11), pp. 2938–2941, Harbin, China,August 2011.


[22] C.-H. Shan, B. Wang, D. Chen, B.-F. Qian, and X.-H. Zhang,“Study of the reactive compensation of STATCOM based onthe sliding mode control theory,” Power System Protection andControl, vol. 38, no. 18, pp. 150–154, 2010.

[23] D.-Z. Jiang and Z.-H. Zhang, “Control scheme of three-phaseH-bridge cascaded STATCOM,” High Voltage Engineering, vol.37, no. 8, pp. 2024–2031, 2011.

[24] H.-C. Tsai and C.-C. Chu, “Nonlinear STATCOM controllerusing passivity-based sliding mode control,” in Proceedings ofthe IEEE Asia Pacific Conference on Circuits and Systems, pp.1996–1999, Singapore, December 2006.

[25] M. A. Eldery, E. F. El-Saadany, and M. M. A. Salama, “Slidingmode controller for pulse width modulation based DSTAT-COM,” in Proceedings of the Canadian Conference on Electricaland Computer Engineering (CCECE ’06), pp. 2216–2219, Ottawa,Canada, May 2006.

[26] F. Rong, A. Luo, C. Tu, and J. Ou, “Application of variablestructure space vector control in STATCOM,” Transactions ofChina Electrotechnical Society, vol. 22, no. 12, pp. 128–139, 2007.

[27] Y. Zhou, A Study on DC Capacitor Voltage Control Strategyof Cascade STATCOM, Beijing Jiao Tong University, Beijing,China, 2012.

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