Multi-objective Coordination Control of Distributed Power Flow ...

348 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL. 5, NO. 3, SEPTEMBER 2019

Multi-objective Coordination Control of DistributedPower Flow Controller

Aihong Tang, Yunlu Shao, Qiushi Xu, Xu Zheng, Hongsheng Zhao, and Dechao Xu

Abstract—In this paper, distributed power flow controller(DPFC) constraints are analyzed. The energy balance relationshipbetween fundamental wave and third harmonic in series andshunt-side converter is deduced. A proportional integral (PI)controller of the DPFC is constructed. The PI controller uses thevoltage amplitude and phase angle injected into the system in theseries side, along with the modulation ratio of the three-phaseconverter on the shunt side as the control variables. A multi-objective coordinated control equation is proposed, which factorsthe constraints of the energy balance between series and shuntside, device capacity limit, safe operation limit, fundamentalcomponent, as well as third harmonic component of the injectionvoltage at the series side. The equation minimizes the variancebetween the actual value of the control target and its given valueto ensure that the DC capacitor voltage, both in the series andshunt side, is stable at target value. Simulations are conductedto verify correctness and effectiveness of the proposed controlmethod.

Index Terms—Distributed power flow controller, energybalance, multi-objective coordinated control, PI controller.

I. INTRODUCTION

D ISTRIBUTED power flow controller (DPFC) functionsinclude power regulation, voltage regulation, power os-

cillation suppression, and power system stability enhance-ment [1]–[6]. DPFC also has the characteristics of unbalancecompensation and power quality control [7]. Since its introduc-tion in 2007, DPFC has been the subject of considerable study.In [8], a modular multilevel converter (MMC) technology isintroduced into the shunt-side, three-phase converter of theDPFC; its new topology and internal electromagnetic transientcharacteristics are then studied and analyzed. In [9], thecharacteristics of DPFC controller are studied, and the series

Manuscript received December 28, 2018; revised February 22, 2019;accepted May 7, 2019. Date of publication September 30, 2019; date ofversion May 7, 2019.

This work was supported in part by the State Grid Corporation of China(Grant No. 52150016000Y), and in part by the State Key Laboratory ofPower Grid Safety and Energy Conservation (China Electric Power ResearchInstitute) Open Fund, the Major Projects of Technical Innovation in Hubei(Grant No. 2018AAA050), and the Major Projects of Technical Innovation inHubei (Grant No. 2019AAA016).

A. H. Tang (corresponding author, e-mail: [email protected]), and Y. L.Shao are with the School of Automation, Wuhan University of Technology,Wuhan 430070, Hubei Province, China.

Q. S. Xu, X. Zheng, and H. S. Zhao are with the State Grid Hubei Economic& Technology Research Institute, Wuhan 430077, Hubei Province, China.

D. C. Xu is with the China Electric Power Research Institute, Beijing100085, China.

DOI: 10.17775/CSEEJPES.2018.01450

and shunt side controllers based on the third harmonic energybalance are designed. In [10], according to the characteristicsof MMC-DPFC, the equivalent mathematical model of MMC-DPFC is proposed and verified on the Advanced DigitalPower System Simulator (ADPSS). In [11], the interaction andinfluencing factors between series-side converters in DPFCand their structure and control principles are discussed indetail.

Flexible AC transmission systems (FACTS) based on powerelectronic switches are known for their strong interactionsand coupling that take place between devices, including theirnegative cancellation effect phenomenon. Thus, reference [12]based on Pareto co-evolutionary algorithm employs a mul-tiplicity cooperative strategy to carry out genetic operationsin order to obtain a Pareto optimal solution set. In [13],an improved version of a quantum genetic algorithm (QGA)is proposed based on multi-objective application expansion,niche initialization, and a new adaptive rotation angle. Thesetwo algorithms improve the negative cancellation among mul-tiple FACTS components. Reference [14] first presents thecontrol variable pairing method and coordinated operationstrategy. Then, using the Niederlinski index (NI) theory, whichis a method of multi-control variable pairing and is suitablefor large-scale and multiple variables, is proposed. The op-timal pairing combination of control variables with minimalinteraction among controllers is also obtained.

Negative cancellation also exists among all the controllersof a FACTS device, which impacts performance of the deviceand reduces its investment benefits [15]. To solve the problemof interactions that occur during coupling of multiple FACTSdevices and multiple control objectives of the same FACTS,researchers have studied coordinated optimal control, andhave achieved some results. In [16], it is observed that theinteraction effect increases with the shortening of electricaldistance when singular value decomposition (SVD) is used.Reference [17] studies the relative gain matrix and Pronytechnology on the Southern Power Grid. This work showsthe interaction among FACTS device, as well as that of theFACTS device and the HVDC transmission system. In [18],the coordinated control strategies of several STATCOM understeady-state modes are studied using a wide-area measurementsystem, which is then analyzed and verified in the IEEE39-bustest system.

DPFC consists of three-phase and single-phase converterson the shunt side, and hundreds of single-phase converterson the series side. The interaction between these convertersis complex and can become problematic. In power flow

2096-0042 © 2018 CSEE

TANG et al.: MULTI-OBJECTIVE COORDINATION CONTROL OF DISTRIBUTED POWER FLOW CONTROLLER 349

control, DPFC has the control objectives of bus voltage, lineactive power flow, and reactive power flow, while maintainingconstant DC capacitor voltage in the series and shunt con-verters, with the premise of realizing all control objectives.Coordination control among multiple objectives, thus, is animportant problem to be solved when DPFC, with its powerfulfunctions and low cost is applied in engineering.

This paper analyzes the functional relationship betweenthe control objectives and the control variables, and designscorresponding controllers based on the principle of DPFC. Themulti-objective coordinated optimization control equation ofDPFC with related constraints is studied and solved. Finally,the correctness and effectiveness of the equation are verifiedby simulations to lay a theoretical foundation for the industri-alization of DPFC.

The remainder of this paper is organized as follows. Sec-tion II introduces the principle of DPFC. Section III designsthe controller of DPFC based on PI. Section IV proposes aDPFC control strategy based on multi-objective coordinatedoptimization control. Section V proves the correctness andeffectiveness of the control method proposed in this paper bysimulations. Conclusions are drawn in Section VI.

II. PRINCIPLE OF DPFC

The topology diagram of DPFC is shown in Fig. 1. It con-sists of series-side single-phase converters, shunt-side three-phase converter VSC1, and single-phase converter VSC2.Fig. 1 shows that the DC capacitors of series and shuntconverters exchange energy through the transmission lineusing the third harmonic active power current to accomplishpower flow regulation.

Series side converter

AC

DC

AC

DC

AC

DC

DC DC

AC AC

Shunt side converter

VSC1 VSC2

BUS2Transmission line

BUS1T1T2

Vdc,shVdc,se

Fig. 1. DPFC topology diagram.

The VSC1 exchanges fundamental power with the system.The reactive power exchanged is used to control the busvoltage of the system, and the active power exchanged is usedto maintain the DC capacitor voltage on the shunt side asthe reference. The VSC2 is mainly used to inject the thirdharmonic active power needed by DC capacitors of series-side converters into transmission lines. On one hand, DPFCseries-side converters absorb the third harmonic active powertransmitted by shunt-side converter through the transmissionline from the system, which is used to maintain their DCcapacitor voltage as reference. On the other hand, based onpower flow regulation requirements, the fundamental voltage,with its adjustable amplitude and phase angle, is also injectedinto the system.

For further analysis, DPFC is replaced by the equivalentvoltage sources as shown in Fig. 2.

+ −

+ −

Vsh3Vsh1

Ish1 Ish3

Vs

Vse3

Vse1XTrI XTrIIXTsI XTsII XL

SL=PL+jQL

ILineVr

Fig. 2. The simplified model of DPFC.

In Fig. 2, Ish1 and Ish3 are fundamental and third harmoniccurrents, respectively, Iline is line current, XL is line reactance,XTsI and XTsII are the reactance of the ∆ − Y transformeron the primary and secondary sides, and XTrI and XTrII arethe reactance of the Y − ∆ transformer on the primary andsecondary sides. The power flow at the end of the transmissionline is SL = PL+jQL. Vs and Vr are the sending and receivingend line-to-ground phasor voltages, Vsh1 is the equivalentvoltage source of VSC1, Vsh3 is the equivalent voltage sourceof VSC2, and Vse1 and Vse3 are the fundamental and thirdharmonic equivalent voltage sources of series-side convertersrespectively.

When the DC capacitor voltage between VSC1 and VSC2is Vdc,sh, the DC capacitor voltage of series-side converter isVdc,se, the modulation ratio of converter VSC1 is msh1, itstrigger phase angle is θsh1, the modulation ratio of converterVSC2 is msh3, and the trigger phase angle is θsh3.

Vsh1 = (√

3/2)msh1Vdc,sh

Vsh3 = (√

3/2)msh3Vdc,sh(1)

According to the references of power flow regulation, PL,ref

and QL,ref , the reference of the Vse1, Vse1,ref , can be obtainedas follows:

Vse1,ref = Vr − Vs +

(jXL (PL,ref + jQL,ref)

∗)Vr

=n∑

i=1

Vse1,ref,i

(2)

For the ith converter on the series side, the relationshipbetween the fundamental voltage amplitude on the AC sideand the DC voltage is as follows:

Vse1,ref,i = (√

3/2)mse1,iVdc,se,ref,i (3)

where mse1,i is the modulation ratio of the ith converter andVdc,se,ref,i is the reference voltage of the DC capacitor of theith converter.

According to the theory that different frequencies of powerare independent of each other [2], [3], in order to keepVdc,se,ref,i constant, the series-side converter obtains the thirdharmonic active power current, Ish3,ref , from the shunt side.At this time, the voltage reflected on the AC side is Vse3,ref ,then for a single converter, the relationship between the thirdharmonic voltage amplitude of the AC side and the DC voltageis as follows:

Vse3,ref,i = (√

3/2)mse3,iVdc,se,ref,i. (4)


When active power loss of DPFC devices and transmissionlines are neglected, the power relationship between series andshunt converters is as follows:

Psh1 = −Psh3

Pse1 = −Pse3.(5)

That is to say, the fundamental active power absorbed bythe shunt converter from the system, Psh1, is equal to the thirdharmonic active power emitted, Psh3, while the third harmonicactive power absorbed by the series converter, Pse3, from thesystem is equal to the fundamental active power emitted, Pse1.And,

Pse3 = Psh3. (6)

III. CONTROLLER DESIGN FOR THE DPFC BASED ON PIBased on the DPFC principle, VSC1 is responsible for

controlling voltage Vs and maintaining constant Vdc,sh.For the series-side converter, the final control variables are

the modulation ratio of the converter, mse1, and the triggerphase angle, θse1, while the control objectives are active powerflow and reactive power flow of the controlled line, PL,ref andQL,ref . However, the control of Vdc,se is accomplished by thePse3 provided by VSC2.

In order to reduce the active power loss of the transmissionline and avoid the exchange of reactive power between seriesand shunt-side converters, this paper controls VSC2 to makeits active power satisfy the relationship of (6) and make itsreactive power Qsh3 = 0. When (5) and (6) are combined,PL3 = Pse3 = Psh3 and QL3 = Qse3 = Qsh3 = 0, i.e., thepower factor of the exchange power between series and shuntconverters is 1.

For a line with an initial power flow, SL(0) = PL(0)+jQL(0),when its power flow control reference is SL,ref = PL,ref +jQL,ref , the injected fundamental power at the DPFC seriesside is:

Pse1,ref + jQse1,ref =

[(SL,ref − SL(0))jXL

Vr

]∗SL,ref

Vr

=jXL

|Vr|2(SL,refSL(0) − |SL,ref |2).

(7)

Thus, the fundamental active power injected by the seriesside is:

Pse1,ref = Re

[jXL

|Vr|2(SL,refSL(0) − |SL,ref |2)

]

=XL

|Vr|2|SL,ref |

∣∣SL(0)

∣∣ sin(sin−1PL(0)

SL(0)

− sin−1PL,ref

SL,ref

).

(8)

Because the power injected into the system by the series-side converter is equal to the power generated by the fun-damental voltage injected into the system by the series-sideconverter and line current IL, the mathematical relationship isas follows:

Pse1,ref + jQse1,ref = Vse1,ref I∗L

= Vse1,refPL,ref + jQL,ref

Vr.

(9)

Thus, when Vr remains unchanged, the interaction betweenVse1, PL, and QL is as shown in Fig. 3.

0 11

00

0.4

0.3

0.2

0.1

0.5 0.5

PL (p.u.)QL (p.u.)

Vse

1 (

p.u

.)

Fig. 3. The relationship between Vse1, PL and QL.

This is to say that the amplitude and phase angle of Vse1directly affects the active power and reactive power flow ofthe transmission line.

Since the fundamental active power injected into the systemby the series-side converter comes entirely from the thirdharmonic power provided by the shunt-side, the mathematicalrelationship can be obtained from (5), (6), and (9),

Pse1,ref = Pse3,ref = Psh3,ref = Psh1,ref

= Re

[Vse3,ref

(Vsh3,ref − Vse3,ref

XTsII3

)∗](10)

Therefore, combining (1)–(4) and (10), the controller ofDPFC based on PI control can be obtained as follows:

θse1 =

(Kp1 +

Ki1

s

)(PL,ref − PL)

Vse1 =

(Kp2 +

Ki2

s

)(QL,ref −QL)

msh =

(Kp3 +

Ki3

s

)(Vs,ref − Vs)

Vdc,se =

(Kp4 +

Ki4

s

)(Ish3,ref − Ish3)

Vdc,sh =

(Kp5 +

Ki5

s

)(Ish1,d,ref − Ish1,d)

(11)

where Ish1,d is the d-axis component of the fundamentalcurrent in the shunt side after DQ decomposition, Ish1,d,refis its reference, msh is the control variable of the controlledbus voltage, and Kpk and Kik (k = 1, 2, 3, 4, 5) arethe proportional coefficient and integral coefficient of thecontroller, respectively.

IV. MULTI-OBJECTIVE COORDINATED CONTROL

The multi-objective optimization problem can be formulatedas follows: the vectors composed of design variables aredetermined in the feasible region to minimize the vectors


composed of a set of m conflicting objective functions, thatis,

Minimize/Maxmize [fm(X)], m = 1, 2, · · · ,msubject to gj(X) ≥ 0, j = 1, 2, · · · , jhk(X) = 0, k = 1, 2, · · · , k

(12)

In the equation, X is the variable to be designed or opti-mized, fm(X) is the mth objective function, and gj(X) andhk(X) are inequality and equality constraints, respectively.

The control objective of DPFC is to make the active andreactive power flow and bus voltage of DPFC access points asreferences, while maintaining the constant Vdc,sh and Vdc,se isthe prerequisite to achieve the goal. Thus, this paper choosesthe integral of the variance between the control variablesshown in (11) and the references set by the correspondingcontroller as the performance index, and thereby establishes amulti-objective function,

min

f1(Kpk,Kik) =

∫ t

0

|D (θse1)| dt

f1(Kpk,Kik) =

∫ t

0

|D (Vse1)|dt

f1(Kpk,Kik) =

∫ t

0

|D (Vs)|dt

f1(Kpk,Kik) =

∫ t

0

|D (Vdc,se)|dt

f1(Kpk,Kik) =

∫ t

0

|D (Vdc,sh)|dt

(13)

For DPFC, the variance of bus voltage, line active andreactive power with the reference should be minimized onthe basis of ensuring that Vdc,se and Vdc,sh are the constant asthe reference. Therefore, formula (13) can transform into theobjective function shown in (14).

J = min 1/2

(∫ t

0

|D (θse)|dt+

∫ t

0

|D (Vse1)|dt

+

∫ t

0

|D (Vs)|dt+

∫ t

0

|D (Vdc,se)|dt

+

∫ t

0

|D (Vdc,sh)|dt) (14)

The constraints include two parts. One is the energy balanceconstraints equation between DPFC and controlled system, andbetween DPFC series-parallel converters, which is shown inthe (15) by combining (5), (6), and (10).

PL = Pse + Psh + P1

Psh = Pse1 + Pdc,sh + Pdc,se

Psh3 = Pse1

(15)

The other part is the safety constraints of the controlledsystem and the limit constraints for the output of the device.

Vsmin ≤ Vs ≤ Vsmax

Vse1 ≤ Vse1,max

(16)

where Vsmin and Vsmax are the minimum and maximum safeoperation values allowed by bus voltage, respectively.

The maximum value of Vse1 is determined by the maximumvalue of Vdc,se and Vdc,se,max.

Vse1,max ≤ (√

3/2)mse1Vdc,se,max. (17)

For Vse3, the maximum allowable deviation for safe operationof the system, ξ, should be combined to give its limit value,that is, ∣∣∣Vse3,max

∣∣∣ ≤ ξ. (18)

Active and reactive power output from series and shunt sidesare constrained by device capacity.

Pse ≤ Psemax

Qse ≤ Qsemax

(19)

where Psemax + Qsemax = Sse is the capacity of the series-side device.

Combining (14)–(19), the multi-objective coordinated con-trol optimization equation of DPFC is constructed.

The essence of optimization is to find a set of solutionsthat can maximize the needs of the system control objectives.These solutions are Pareto optima [19], [20]. However, ingeneral, there is not necessarily a unique Pareto solution formulti-objective optimization problems, or even no optimalsolution. For the multi-objective optimization problem f(x),if and only if fn(x∗) ≤ fn(x) for any x in the search space,then f(x∗) is called the global optimal solution.

Aiming for the multi-objective coordinated control opti-mization problem that has the equality constraints of DPFCenergy balance as well as the inequality constraints of securityrestrictions, the genetic algorithm described in [21] is usedto solve the above stated problem, which, however, is notdiscussed here.

V. SIMULATIONS

A. Test Systems

Taking the single-machine, infinite-bus system with DPFCas an example, as shown in Fig. 4, a DPFC simulationmodel is constructed using a user-defined model in ADPSSsoftware [22], [23].

Y

Y Y

Y

Y

AC

AC

DC

AC

DC

DCAC

DC

Transmission line

T1

T2 XL2/3

L1

L2XL2/3

Tse

XL1

XL2/3

T3

T4

Tse

Series sideconverter

Shunt sideconverter

Tsh

Vs Vr

Fig. 4. Single-machine infinite-bus system with DPFC.

The parameters of the test system are shown in Tables Ito III, while the impedance of both lines, XL1 and XL2, is1.116 + j15.95 Ω. And the initial power flow at the end ofthe transmission line is SL(0) = PL(0) + jQL(0) = 0.74 kW−j0.12 kVar.


TABLE ITHE PARAMETERS OF VOLTAGES

Voltage Amplitude Phase Angle Internal ResistanceVs 0.38 kV 8.7 1 ΩVr 0.38 kV 0 —Vdc,sh 0.20 kV — —Vdc,se 0.10 kV — —

TABLE IITHE PARAMETERS OF TRANSFORMERS

Transformer Ratio ConnectionT1 1:1 ∆-YT2 1:1 ∆-YT3 1:1 Y-∆T4 1:1 Y-∆Tsh 380:100 Y-∆Tse 1:1 —

TABLE IIITHE PARAMETERS OF SIMULATION

Simulation step Sampling step Simulation time50 µs 100 µs 10 s

B. Controller Parameters

As mentioned above, this paper uses genetic algorithmto solve the DPFC multi-objective coordinated control op-timization equation composed of (14)–(19). The crossoverprobability is 0.8, mutation probability is 0.07, populationsize is 50, and the maximum optimization algebra is 50. Theparameters of DPFC’s PI controller range is from 0 to 1, whichcan be obtained as shown in Table IV.

TABLE IVTHE PARAMETERS OF DPFC’S PI CONTROLLER

Proportional Coefficient Integral CoefficientPL Kp1 0.82 Ki1 0.06QL Kp2 0.45 Ki2 0.03Vs Kp3 0.62 Ki3 0.05Vdc,se Kp4 0.65 Ki4 0.05Vdc,sh Kp5 0.56 Ki5 0.04

C. Simulation Analysis

At 0.5 s, DPFC’s shunt-side converter is switched into thesystem; at 1.2 s, its series-side converter is switched into thesystem.1) Power Flow Simulation Analysis

At 5 s, Vs,ref and QL,ref keep the initial values unchanged,and PL,ref changes from initial values to 1.5 kW. The corre-sponding waveforms of PL, QL, and Vs are shown in Fig. 5,where P ′L, Q′L, and V ′s represent the simulation waveforms ob-tained by optimizing the control parameters using the controlmethod proposed in this paper. PL, QL, and Vs represent thewaveform before the control parameters are optimized.

Figure 5 shows that P ′L and PL stabilize at 1.5 kW af-ter 0.6 s and 2.2 s, respectively, Q′L and QL stabilize at−0.12 kVar after 1.1 s and 2.9 s, respectively. There was nosignificant change in V ′s and Vs.

Similar to active power regulation, in order to observe thecontrastive simulation of reactive power regulation, at 5 s,Vs,ref and PL,ref keep the initial values unchanged, and QL,ref

0.0 1.0 2.0 3.0 4.0 5.00.00

0.40

0.80

1.20

1.60

PL /

kW

t /s

6.0 7.0 8.0 9.0 10.0

PL

P′L

0.0 1.0 2.0 3.0 4.0 5.0

t /s

6.0 7.0 8.0 9.0 10.0

QL

Q′L

QL /

kV

ar

0.10

0.00

−0.10

−0.20

−0.30

−0.40

340

380

400

420

360

0.0 1.0 2.0 3.0 4.0 5.0

t /s

6.0 7.0 8.0 9.0 10.0

Vs

V ′s

Vs

/V

(a)

(b)

(c)

Fig. 5. Contrastive simulation results of active power regulation.

changes from initial values to 0 kVar. The correspondingwaveforms of PL, QL, and Vs are shown in Fig. 6.

Figure 6 shows that Q′L and QL stabilize at 0 kVar after0.8 s and 2.2 s, respectively, P ′L and PL stabilize at 0.74 kWafter 0.8 s and 2.3 s, respectively, V ′s and Vs stabilize at 380V after 0.6 s and 2 s, respectively.

In conclusion, after optimization of control parameters, P ′L,Q′L, and V ′s can respond to references more quickly and withless fluctuation.

2) Fault Simulation Analysis

In order to compare the power flow regulation capability ofDPFC under two schemes in case of line faults, three-phasegrounding fault occurs on the end of line L2 at 5 s, and theduration is 0.1 s. While, Vs,ref , PL,ref , and QL,ref keep theinitial values unchanged. The corresponding waveforms of PL,QL, and Vs are shown in Fig. 7.

As displayed in the Fig. 7, the drops of P ′L and PL are1.04 kW when fault occurs, while the drops of Q′L and QL

are −3.2 kVar and −5.2 kVar, respectively; the drops of V ′sand Vs are 4 V. After fault clearing, P ′L and PL stabilizeat 0.74 kW after 0.2 s and 0.4 s, respectively; Q′L and QL

stabilize at −0.12 kVar after 0.3 s and 0.4 s, respectively; andV ′s and Vs stabilize at 380 V after 1.2 s and 2.2 s, respectively.

Thus it can be seen that the robustness of the controller afteroptimizing the control parameters is better than that beforeoptimizing the control parameters.


0.0 1.0 2.0 3.0 4.0 5.0

t /s

6.0 7.0 8.0 9.0 10.0

QL

Q′L

QL /

kV

ar

0.20

0.00

−0.20

−0.40

−0.60

0.0 1.0 2.0 3.0 4.0 5.0

t /s

6.0 7.0 8.0 9.0 10.0

PL

P′L

PL /

kW

1.00

0.80

0.60

0.40

0.20

340

360

380

400

420

Vs

V ′s

Vs

/V

0.0 1.0 2.0 3.0 4.0 5.0

t /s

6.0 7.0 8.0 9.0 10.0

(a)

(b)

(c)

Fig. 6. Contrastive simulation results of reactive power regulation.

PL

P′L

PL /

kW

4.0

3.0

2.0

1.0

0.0

−1.0

−2.04.50 5.00 5.50

t /s

6.00 6.50 7.00 7.50

QL

Q′L

QL /

kV

ar

3.02.01.00.0

−1.0−2.0−3.0−4.0−5.0−6.0−7.0

4.50 5.00 5.50

t /s

6.00 6.50 7.00 7.50

370372374376378380382384386388

Vs

V ′s

Vs

/V

4.50 5.00 5.50

t /s

6.00 6.50 7.00 7.50

(a)

(b)

(c)

Fig. 7. Contrastive simulation results of three-phase grounding fault.

VI. CONCLUSION

In this paper, the influence of DPFC control variables onpower flow is analyzed, and new DPFC controllers basedon PI are designed. A multi-objective coordinated optimalcontrol equation is constructed to coordinate bus voltage, linepower flow, and constant DC capacitor voltage, taking intoconsideration energy balance, overvoltage constraints, and ca-pacity constraints. The equation is then solved using a geneticalgorithm and verified by simulations based on ADPSS. Theresults show that the proposed multi-objective coordinatedoptimization control method improves the control performanceof the DPFC controller. The details are as follows:

1) After optimization of the control parameters using thecontrol method proposed in this paper, the power flow of thecontrolled line and the sending end voltage are able to respondto the control objectives more quickly, and with less fluctuationand taking approximately 66% less time to respond.

2) In fault conditionthe response of the controlled line val-idates the robustness of the controller with optimized controlparameters.

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Aihong Tang received the M.Sc. degree fromWuhan University of Hydraulic and Electrical En-gineering, China, in 1997, and the Ph.D. degreein Electrical Engineering from Huazhong Universityof Science and Technology, China, in 2007. Since2012, she has been a Professor with the AutomationSchool, Wuhan University of Technology. Her re-search interests include flexible AC/DC transmissionsystems, the control and operation of the powersystems, and the smart grid.

Yunlu Shao received the B.Sc. degree from WuhanUniversity of Science and Technology, China, in2016, and now she is pursuing the M.Sc. degreein Electrical Engineering at Wuhan University ofTechnology. Her research interests include flexibleAC/DC transmission systems, the control and oper-ation of the power systems, and the smart grid.

Qiushi Xu received the B.Sc., M.Sc. and Ph.D.degrees in Electrical Engineering from Wuhan Uni-versity, China, in 2008 and 2014, respectively. Since2014, he has been with the State Grid Hubei Eco-nomic & Technology Research Institute as an engi-neer. His research interests include flexible AC/DCtransmission systems, the control and operation ofthe power systems, and the smart grid.

Xu Zheng received the B.Sc. and M.Sc. degreesin Electrical Engineering from Huazhong Universityof Science and Technology, China, in 2002 and2005, respectively. Since 2012, he has been with theState Grid Hubei Economic & Technology ResearchInstitute as senior engineer. His research interestsinclude flexible AC/DC transmission systems, thecontrol and operation of the power systems, and thesmart grid.

Hongsheng Zhao received the B.Sc. and M.Sc.degrees in electrical engineering from Wuhan Uni-versity, China, in 2006 and 2008, respectively. Heis now a senior engineer at the State Grid HubeiEconomic & Technology Research Institute. His re-search interests include flexible AC/DC transmissionsystems, the control and operation of the powersystems, and the smart grid.

Dechao Xu received the M.Sc. degree from ChinaElectric Power Research Institute in 2000. He is aprofessor-level senior engineer. He is mainly en-gaged in the research and development of powersystem digital simulation technology.

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