Analysis of Transient Voltage Stability in a Low …downloads.hindawi.com/journals/jece/2018/3498491.pdfJournalofElectricalandComputerEngineering Bu 1 Flt Lw oltage distribution etwork

Research ArticleAnalysis of Transient Voltage Stability in a LowVoltage Distribution Network Using SST for the Integration ofDistributed Generations

Sheng Li Zhihao Zhou Qiqi Shan and Jiani An

School of Electric Power Engineering Nanjing Institute of Technology Nanjing 211167 China

Correspondence should be addressed to Sheng Li lisheng njit126com

Received 17 February 2018 Revised 19 April 2018 Accepted 22 April 2018 Published 3 June 2018

Academic Editor Chi-Seng Lam

Copyright copy 2018 Sheng Li et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Models of a low voltage distribution network using a typical tertiary-structure solid state transformer (SST) for the integrationof distributed generations (DGs) and a conventional low voltage distribution network integrated with DGs were established tostudy the transient voltage stability issue using the power system simulation software PSCAD Effects on the transient voltagestability of the load bus and DC bus in the SST system are analyzed when grid-side cable line faults (such as short circuit and linedisconnection) occur or the total output of DGs drops greatly The results show that comparing with the conventional systemthe SST has apparent advantages on enhancing the transient voltage stability of load bus while facing different disturbances eventhough SST has to regulate the voltage passively Short circuit faults at different location of the grid-side line have different effectson the transient voltage stability while the effect of disconnection fault is not related to fault location Moreover the DC bus voltageis easy to keep climbing continually when short circuit fault of the line occurs that is close to the SST input stage or disconnectionfault occurs at any location of the line If a battery energy storage station is installed the transient voltage stability of DC bus andload bus will be improved effectively because of the regulation function of battery storage

1 Introduction

With the technologies related to new energy generation beingmaturing day by day and the construction of the energyinternet being pushed forward constantly [1ndash3] penetrationsof distributed generations (DGs) in the distribution networkare increasing gradually [4 5] Before the electric powergrid and other energy networks connecting with each otherand forming an energy internet building a green smartgrid with the core of energy routers to accept large-scalerenewable energy sources widely is one way to constructthe energy internet [6] The intelligent dispatching andcontrolling center of the energy internet is the energy router[7] whose core is a high-frequency coupled device calledsolid state transformer (SST) based on the advanced powerelectronic technology [8]

The output of DG is random and the configuration of thedistribution network integrated with DGs is complex whichcan influence the stability of the distribution network [9 10]

Reference [11] pointed out that the voltage stability issue doesexist in distribution networks integrated with photovoltaiccell power and the voltage instability phenomenon can besolved effectively by photovoltaic inverter reactive powersupport [2 11] A typical simulation model that a distributedphotovoltaic power station is directly integrated into a lowvoltage distribution network was established in [12] andthe effects were analyzed on the transient voltage stabilityof load bus when the faults such as short circuit and linedisconnection occur or the output of distributed photovoltaicpower plant drops greatly In [13] the impacts of large-scalephotovoltaic generation on the steady state voltage stability ofdistribution system were studied and the conclusion that thephotovoltaic modules have to operate in the reactive powersupport mode to improve the system voltage stability wasobtained In [14] a DC microgrid containing photovoltaiccell wind turbine and fuel cell was proposed and connectedto the low voltage distribution network under variable loaddemands and the simulation results showed that the voltage

HindawiJournal of Electrical and Computer EngineeringVolume 2018 Article ID 3498491 9 pageshttpsdoiorg10115520183498491

2 Journal of Electrical and Computer Engineering

ACDC DCDC DCAC

Grid

SST

Load

DGs

Figure 1 A typical tertiary-structure solid state transformer

stability of DC bus can be maintained at different operatingmodes In [15] a method that can enhance the transientvoltage stability of a real distribution network with windpower was proposed bymeans of optimal rating and locationof the static synchronous compensator (STATCOM)

When using a SST for the integration of DGs and thedistribution network on the part of the grid the ability ofadopting the DGs will be enhanced and the situation of volt-age oscillation and instability will be avoided In this papera simulation model of a 038 kV low voltage distributionnetwork which uses a typical SST for the integration of DGswas established using the power system simulation softwarePSCADEMTDC and effects on the transient voltage stabilityof the system while facing various disturbances are studiedThe advantages of the transient voltage stability using a SSTfor the integration of DGs are analyzed and the differencesbetween whether there is a battery energy storage station arediscussed

2 Modeling and Control Strategy of SST

As shown in Figure 1 a typical tertiary-structure SST ischosen for discussion which consisted by a ACDC unit aDCDC unit and a DCAC unit The three units are inputstage isolation stage and output stage respectively To realizethe bidirectional power flow the full-controlled device IGBTis used for building the SST [16]

In this paper a voltage-source PMW rectifier is chosen asthe input stage of SST which can rectify the 038 kVAC of thelow voltage distribution network to 078 kV DC

The dual-loop decoupled control strategy is chosen forthe input stage [17] The voltage orientation control strategybased on 119889-119902 rotating coordinate system is selected for thevoltage loop and the direct current control is adopted forthe current loopThe grid-side power factor can be correctedaccording to the control goal The control equations of theSST input stage are

119894lowast1119889 = (119870P1 + 119870I1119904 ) (1198801015840dc minus 119880dc)119894lowast1119902 = 0119906lowast1119889 = 1199061119889 + 1205961198711198941119902 minus (119870P2 + 119870I2119904 ) (119894lowast1119889 minus 1198941119889)119906lowast1119902 = 1199061119902 minus 1205961198711198941119889 minus (119870P2 + 119870I2119904 ) (119894lowast1119902 minus 1198941119902)

(1)

where 119894lowast1119889 and 119894lowast1119902 are the grid-side current command valuesin 119889-119902 coordinate system and 1198941119889 and 1198941119902 are the actual values119906lowast1119889 and 119906lowast1119902 are the grid-side voltage command values in 119889-119902coordinate system and 1199061119889 and 1199061119902 are the actual values 1198801015840dc119880dc are the reference voltage and actual voltage of DC busrespectively 119870P1 119870I1 119870P2 and 119870I2 are the parameters of PIcontrollers L is the filter inductance of SST input stage

In isolation stage the 078 kV DC is converted to a high-frequency AC square wave and coupled to the secondaryside of a high-frequency isolated transformer which is usedto isolate the original side and subside Then the high-frequency AC will be rectified to 078 kV DC

In the output stage the 078 kV DC is inverted to 038 kVAC for power supplies The dual-loop decupled controlstrategy with the voltage and current feedforward is adoptedfor the control [18] The control equations of the SST outputstage are

119894lowast2119889 = 1198942119889 minus 1205961198621198911199062119902 + (119870P3 + 119870I3119904 ) (11990610158402119889 minus 1199062119889)119894lowast2119902 = 1198942119902 + 1205961198621198911199062119889 + (119870P3 + 119870I3119904 ) (11990610158402119902 minus 1199062119902)119906lowast2119889 = 1199062119889 minus 1205961198711198911198942119902 + (119870P4 + 119870I4119904 ) (119894lowast2119889 minus 1198942119889)119906lowast2119902 = 1199062119902 + 1205961198711198911198942119889 + (119870P4 + 119870I4119904 ) (119894lowast2119902 minus 1198942119902)

(2)

where 119894lowast2119889 and 119894lowast2119902 are the load current command values in119889-119902 coordinate system and 1198942119889 and 1198942119902 are the actual values119906lowast2119889 and 119906lowast2119902 are the load bus voltage command values in 119889-119902coordinate system 11990610158402119889 and 11990610158402119902 are the reference values and1199062119889 and1199062119902 are the actual values119870P3119870I3119870P4 and119870I4 are theparameters of PI controllers 119871119891 119862119891 are the filter inductanceand capacitance of SST output stage respectively

3 Model of Low Voltage Distribution NetworkIntegrated with DGs

A conventional system model of a low voltage distributionnetwork integrated with DGs (including distributed photo-voltaic andwind power) is established using the power systemsimulation software PSCAD as shown in Figure 2 1 and 2are the voltage of Bus 1 andBus 2 respectivelyThe impedanceof the cable is 119877 + 119895119883 and the value is 0096 + 1198950015Ω Thepower from the low voltage distribution network is noted as1198751+1198951198761 the power flow from the network to Bus 2 is noted as1198752 + 1198951198762 The outputs of photovoltaic power plant and windpower farm are 119875pv + 119895119876pv and 119875wind + 119895119876wind respectivelythe absorbed power of the three-phase induction motor andthe static load are 119875119872 + 119895119876119872 and 119875119904 + 119895119876119904 respectively

Some ancillary facilities such as reactive power com-pensation devices and inverters of photovoltaic or windpower systems can be left out because of the structure andflexible control characteristics of SST and the DGs can bedirectly connected to the DC busThe model of a low voltagedistribution network using a SST for the integration of DGsis shown in Figure 3

Journal of Electrical and Computer Engineering 3

M

Low voltage distribution

network Induction motor

Static load

Cable line

DGs

Bus 1 Bus 2U1

U2

P1 + jQ1 P2 + jQ2R + jX

Pwind + jQwind

Ppv + jQpv

PS + jQS

PM + jQM

Figure 2 Model of conventional low voltage distribution network integrated with DGs

SST

M

Low voltage distribution network

Photovoltaicpower plant

Wind farm

Battery energy The Battery

O2 H2storage station

Bus 1 Bus 2

ACDC DCDC DCAC

DC bus

P1 + jQ1 P2 + jQ2

R + jX

minus+

Figure 3 Model of low voltage distribution network integrated with DGs using SST

In Figures 2 and 3 the rated capacities of the photovoltaicpower station and the wind power plant both are 260 kWThe loads are composed of two parts of static load (includinga constant resistance load and a constant impedance load)and a three-phase induction motor The rated power of theconstant resistance 1198771199041 is 90 kW the rated power of theconstant impedance 1198771199042 + 1198951198831199042 is 60 kVA the rated capacityof the three-phase induction motor is 495 kVA

During the simulation analyses the environmental tem-perature is 29815 K the light intensity is 1000Wm2 thewindspeed is 11ms and these values will vary in a certain rageWhen the system operates normally the absorbed active andreactive power of the induction motor are about 46 kW and23 kvar respectively the absorbed active and reactive powerof the constant impedance load are about 48 kW and 35 kvarrespectively The grid-side unity power factor is realized dueto the control strategy of the SST input stage

4 Effects on Transient Voltage Stability ofGrid-Side Line Faults

The research results show that short circuit fault of grid-side cable line at different location has different effect onthe system transient voltage stability because of the controlfunction of the SST input stage while line disconnection faultis not associated with the fault location

The schematic diagram of fault position is shown inFigure 4 The grid-side cable line is divided into Line 1 andLine 2 equivalently by the signal collection device whichmonitors the distribution network Line 1 contains only asmall part of lines connecting the signal collection deviceand the SST input stage in practice and its fault possibility ismuch lower Line 2 contains the whole external distributionnetwork lines which are so complex that their fault possibilityis very high


Bus 1

FaultLow voltage

distribution networkSignal collection

deviceInput stage of

SST

Line 2 Line 1

Grid-side cable line

AV

Figure 4 Schematic diagram of line fault location

To save space and take the aesthetics into considerationmost urban low voltage distribution networks use cable linesInsulation aging or damage is the main cause of cable faults

41 Short Circuit Fault Occurs at Line 1 Line 1 may haveshort circuit faults though there are fewer lines in it Once thefault occurs each stage of the SST has to regulate the voltagepassively Therefore we focus on the influence on the systemtransient voltage stability when different short circuit faultsoccur at Line 1

Take the typical single-phase grounding short circuit faultas an example Now set the simulation time as 2 s After time119905 = 04 s the system enters stable operation When 119905 =06 s single-phase grounding short circuit fault occurs at themidpoint of Line 1 and the fault duration is 01 s The relayprotection acts and removes the fault line when 119905 = 065 sWe focus on the system transient voltage stability when thecut line is no longer reinput because 038 kV low voltage cableline has generally no reclosing device

After the line is cut off the grid loses power and theDGs enter the state of isolation island operation We do thisresearch on the condition that the outputs of DGs are richand can meet the need of local loads When the single-phasegrounding short circuit fault occurs the response curves ofload bus voltage and absorbed powers of induction motorin the conventional DGs grid-connected system (shown inFigure 2) the response curves of load bus (Bus 2) voltageabsorbed powers of induction motor and DC bus voltage areshown in Figure 5

In general if a 038 kV AC bus voltage in low voltagedistribution network is lower than 09 pu or higher than 11 puafter a large disturbance formore than the specified limit time(eg 1 s or above) it can be considered that the low voltageAC bus is transient voltage instability [12] In this paper thetransient voltage stability of low voltage DC bus obeys thesame rules too

As can be seen from Figures 5(a) and 5(b) for theconventional system after the single-phase grounding shortcircuit fault occurs and the relay protection acts the load busvoltage drops rapidly to 08 pu or less and the load bus isconsidered to be unstable thus causing the active and reactivepower absorbed by induction motor to have oscillations andfinally to be below rated values (rated active power is 1 puand rated reactive power is 05 pu) The limitation of theconventional system is that the inverter control function of

DGs is simple and the transient voltage stability of load buscannot be guaranteed while facing disturbances

In this paper the DGsrsquo inverters adopt outlet voltagecontrol strategy simulation results show that the transientvoltage stability of load bus cannot be maintained by theinverters without the support of power grid

If the inverters adopt constant power control strategythe outputs of DGs will remain constant under the normalenvironment after the disturbances After the relay protectionacts the load bus has the equation according to the powerbalance

119875pv + 119875wind = 119875119872 + 119875119878 = 119875119872 + ( 11198771199041 +119877s211987721199042 + 11988321199042)119880

22 (3)

It can be seen from Formula (3) in the case of rich outputsof DGs the load demand can be met so the load bus voltagerecovers quickly Accordingly the absorbed active power ofinduction motor begins to fall down after the oscillationFrom Formula (3) we can find that 1198802 will be lifted once119875119872 starts to decrease eventually causing the load bus voltageto climb continually And at this time the load bus is stillconsidered to be transient voltage instability It is necessaryto abandon the photovoltaic and wind power to protect themotor in time

The effectiveness of the control strategy of SST on thetransient voltage stability can be seen from Figures 5(a) and5(b) which reflects the SSTrsquos better ability of maintainingtransient voltage stability while facing disturbances Thoughthe fault is close to the SST input stage active control cannotbe taken by the SST to stabilize the grid-side surge currentand the current has to be regulated passively and the loadbus voltage can recover to the original rated value andmaintain the stability after experiencing rapid sagThereforethe absorbed powers of induction motor can recover to theoriginal rated values too

As shown in Figure 5(c) although the SST can maintainthe voltage stability of load bus by passive regulation if thereis no a battery energy storage station installed in the DC busthe DC bus voltage will keep climbing because the outputs ofDGs cannot be transmitted to the grid At this time we canconsider that the DC bus loses its transient voltage stability Itis harmful to the security and stability of the system and thephotovoltaic and wind power will have to be abandoned

The battery energy storage station plays an important rolein stabilizing the load bus voltage and DC bus voltage Asshown in Figure 5 in the DGs grid-connected system basedon SST the battery energy storage station can stabilize theload bus voltage and DC bus voltage greatly after the shotcircuit fault occurs and there is merely a slight oscillationAfter the relay protection acts theDCbus voltage is regulatedto the original rated value because of the function of energystorage station avoiding the voltage climbing phenome-non

Simulation results show there are similar conclusionswhen other short circuit faults occur at Line 1 for instancethe response curves of three-phase short circuit occurring atmidpoint of Line 1 are shown in Figure 6


SST system without battery storage

SST system with battery storage

Conventional system

0

02

04

06

08

1

12

14Vo

ltage

of B

us 2

(pu)

06 08 1 12 14 16 18 204Time (s)

(a) Load bus voltage

minus15

minus1

minus05

0

05

1

15

2

25

3

PM in SST system without battery storage

P－ in conventional system

Q－ in conventional systemQ－ in SST system without battery storage

06 08 1 12 14 16 18 204Time (s)

PM

andQ

M(p

u)(b) Absorbed power of induction motor



0

05

1

15

2

25

3

35

4

45

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(c) DC bus voltage

Figure 5 Response curves when single-phase grounding short circuit fault occurs at the midpoint of Line 1

42 Short Circuit Fault Occurs at Line 2 If short circuit faultoccurs at Line 2 the information can be picked up and thesurge current can be steadied by the active control of the SSTinput stage and it merely has little effect on the load busvoltage and DC bus voltage even if the most serious three-phase short circuit fault occurs as shown in Figure 7

43 Disconnection Fault Occurs at Any Location of Gird-Side Line When the line disconnection fault occurs at anylocation of the gird-side line (including Line 1 and Line 2)we can draw similar conclusions with the condition thatshort circuit faults occurs at Line 1 Taking the disconnectionoccurring at themidpoint of Line 1 for example the responsecurves are shown in Figure 8

5 Impact of Great Drop of DGsrsquo Total Outputon Transient Voltage Stability

The output of DG is affected by the weather greatly Thesudden changes in light intensity and wind speed will causesudden changes in the outputs of photovoltaic power plantand wind farm respectively which will affect the transientvoltage stability of the system

Considering the most adverse weather condition whenthe light intensity drops greatly and the wind turbine dropsout because wind speed is too large the sudden great dropof DGsrsquo total output can cause the load bus voltage to beinstability For the conventional system shown in Figure 2supposing that the total load power is 119875119871 + 119895119876119871 and the total


0



Conventional system

02

04

06

08

1

12

14

16Vo

ltage

of l

oad

bus (

pu)

06 08 1 12 14 16 18 204Time (s)




0

05

1

15

2

25

3

35

4

45

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage

Figure 6 Response curves when three-phase short circuit fault occurs at the midpoint of Line 1


Conventional system

0

02

04

06

08

1

12

14

Volta

ge o

f Bus

2 (p

u)

06 08 1 12 14 16 18 204Time (s)



0

01

02

03

04

05

06

07

08

09

1

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage


output of DGs is 119875Σ + 119895119876Σ the load bus voltage drops to 11988010158402when the DGsrsquo total output drops to 0 suddenly there will be[12]

1198802 minus 11988010158402 = 119875Σ119877 + 119876Σ1198831198802 + (119875119871119877 + 119876119871119883)( 111988010158402 minus11198802) (4)

Since both photovoltaic and wind power have maximumpower control119876Σ is almost 0 Suppose the voltage drop ratio

is 119886 that is11988010158402 = 1198861198802 Put119876Σ = 0 and11988010158402 = 1198861198802 into Formula(4) we can get the following

119875Σ = (1 minus 119886)11988022 minus (1119886 minus 1) (119875119871119877 + 119876119871119883)119877 (5)

In Formula (5) if 1198802 is the rated value (1 pu) then 119886 takes09 And we can get the upper limit approximate value of totaloutput active power of DGs that is just right for maintainingthe system transient voltage stability when the total output


Conventional system



0

02

04

06

08

1

12Vo

ltage

of B

us 2

(pu)

06 08 1 12 14 16 18 204Time (s)


04 06 08 1 12 14 16 18 2



Time (s)

0

05

1

15

2

25

3

35

4

45

Volta

ge o

f DC

bus (

kV)

(b) DC bus voltage

Figure 8 Response curves when disconnection fault occurs at the midpoint of Line 1

drops to 0When theDGsrsquo total output is equal or greater thanthe upper limited approximate value in the actual operationof the system and drops to 0 suddenly the load bus will loseits transient voltage stability in general

Using the parameters in the conventional system tocalculate according to Formula (5) it will figure out that theupper limit approximate value of DGsrsquo total output is 150 kWas 119886 takes 09 (because1198802 is very close to 1 pu) Now the totaloutput of DGs in the conventional system and the SST systemis set to be 150 kW respectively The simulation time is set tobe 2 s and the photovoltaic and wind power suddenly dropto 0 at 119905 = 06 s The response curves are shown in Figure 9

It can be known from Figures 9(a) and 9(b) that theload bus voltage in the conventional system is unstable afterthe great drop of DGsrsquo total output occurs and the voltagedrops to about 088 pu which is almost matching with thetheoretical value (09 pu) while in the SST system the loadbus and DC bus recover transient voltage stability quicklyWhen it comes to the SST system with a battery energystorage station the voltages of load bus and DC bus arealmost not affected by the disturbance As can be seen fromFigure 9(c) for the SST system without a battery energystorage station before the great drop of DGsrsquo total outputoccurs the reactive power transmitted from the grid is 0because of the control of the SST input stage while the activepower is minus02MW because of the plenty outputs of DGsAfter the total output of DGs drops to 0 the low voltagedistribution network supplies a certain amount of powers tohelp to maintain the bus voltage at this moment

6 Conclusions

The development of the technology of DGs has realized theeffective integration and efficient utilization of renewable

energies distributed around the world It has practical sig-nificance to study on the transient voltage stability of theDGs grid-connected system and it is meaningful for realizingthe change from a traditional fossil-fuel grid to a futuregreen smart grid In this paper we use PSCAD softwareto study the transient voltage stability of the low voltagedistributed network integrated with DGs based on SST underthe condition of cable line fault and sudden drop of DGsrsquo totaloutput and concluded as follows

(1) Using a SST for the integration of DGs and thedistribution network has advantages on the systemtransient voltage stability while facing different faultsThe influence of grid-side line short circuit faulton the transient voltage stability is related to faultlocation and the line disconnection fault is not thecase Even if SST has to regulate the voltage passivelywhen the fault occurs at the line close to the SST inputstage the regulation function of SST still canmaintainthe voltage transient stability of load bus This avoidsload bus in the conventional DGs gird-connectedsystem losing its transient voltage stability effectivelywhile facing such faults and improves utilization ofDGs and reliability of power supply

(2) Although the SST control makes the load bus havebetter transient voltage stability the DC bus voltageis easy to keep climbing continually when the shortcircuit occurs at the line side that is close to the SSTinput stage or the line disconnection occurs at anylocation of the line At this moment the DC bus canbe considered to be transient voltage instability andthis is a new transient voltage stability phenomenonin the DGs gird-connected system using SST It isharmful to the security and stability of the system


Conventional system


SST model without battery storage

0

02

04

06

08

1

12Vo

ltage

of B

us 2

(pu)

04 08 1 12 14 16 18 206Time (s)




0

01

02

03

04

05

06

07

08

09

1

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage

minus03

minus025

minus02

minus015

minus01

minus005

0

005

01

015

02

025

03

06 08 1 12 14 16 18 204Time (s)

P1

Q1

P1

(MW

) and

Q1

(MW

)

(c) Power supplies of distribution network without battery storage

Figure 9 Response curves when total output of DGs drops to 0

operation The DC bus voltage can be stabilized bythe DGs equipped with a certain amount of batteriesor a battery energy storage station installed in the DCbus when faults occur which can effectively avoid thetransient voltage instability of DC bus and guaranteethe system safety

(3) When the total output of DGs drops greatly underthe adverse weather condition the SST can ensurethe transient voltage stability thus avoiding the biggestvoltage drop of load bus in the conventional systemIf a battery energy storage station is installed theload bus voltage and DC bus voltage will be almostunaffected while facing the great drop of the DGsrsquo

total output It is of great significance to the stableoperation of low voltage distribution network that thebattery storage is installed

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper


Acknowledgments

Thiswork is supported by the Open Research Fund of JiangsuCollaborative Innovation Center for Smart DistributionNetwork (XTCX201613) the University Student Innovationamp Entrepreneurship Training Program of Jiangsu Province(201711276009Z) and the University Student Technologi-cal Innovation Project of Nanjing Institute of Technology(TZ20170009)

References

[1] S Li Z Wei Y Ma and J Cheng ldquoPrediction and controlof Hopf bifurcation in a large-scale PV grid-connected systembased on an optimised support vector machinerdquoThe Journal ofEngineering vol 2017 no 14 pp 2666ndash2671 2017

[2] A Eid and M Abdel-Akher ldquoVoltage control of unbalancedthree-phase networks using reactive power capability of dis-tributed single-phase PV generatorsrdquo International Transac-tions on Electrical Energy Systems vol 27 no 11 Article IDe2394 2017

[3] A Q Huang M L Crow G T Heydt J P Zheng and S JN I S Dale ldquoThe Future Renewable Electric Energy Deliveryand Management (FREEDM) System The Energy InternetrdquoProceedings of the IEEE 2010

[4] JM Sexauer and SMohagheghi ldquoVoltage quality assessment ina distribution system with distributed generation-a probabilis-tic load flow approachrdquo IEEE Transactions on Power Deliveryvol 28 no 3 pp 1652ndash1662 2013

[5] S Li Z Wei and Y Ma ldquoFuzzy Load-Shedding StrategyConsidering Photovoltaic Output Fluctuation Characteristicsand Static Voltage Stabilityrdquo Energies vol 11 no 4 p 779 2018

[6] J Cao and M Yang ldquoEnergy internet-towards smart grid 20rdquoin Proceedings of the 2013 Fourth International Conference onNetworking and Distributed Computing (ICNDC) pp 105ndash110Los Angeles CA USA December 2013

[7] W Sheng H Liu Z Zeng et al ldquoAn energy hub based onvirtual-machine controlrdquo in Proceedings of the CSEE vol 35 pp3541ndash3550 2015

[8] Qing Duan Chunyan Ma Wanxing Sheng and ChangkaiShi ldquoResearch on power quality control in distribution gridbased on energy routerrdquo in Proceedings of the 2014 InternationalConference on Power System Technology (POWERCON) pp2115ndash2121 Chengdu October 2014

[9] B Tamimi C Canizares and K Bhattacharya ldquoSystem stabilityimpact of large-scale and distributed solar photovoltaic gen-eration The case of Ontario Canadardquo IEEE Transactions onSustainable Energy vol 4 no 3 pp 680ndash688 2013

[10] R Majumder ldquoSome aspects of stability in microgridsrdquo IEEETransactions on Power Systems vol 28 no 3 pp 3243ndash32522013

[11] R Yan and T K Saha ldquoInvestigation of voltage stability forresidential customers due to high photovoltaic penetrationsrdquoIEEE Transactions on Power Systems vol 27 no 2 pp 651ndash6622012

[12] S Li C Jiang Z Zhao and Z Li ldquoStudy of transient voltagestability for distributed photovoltaic power plant integrationinto low voltage distribution networkrdquo Dianli Xitong Baohu yuKongzhiPower System Protection and Control vol 45 no 8 pp67ndash72 2017

[13] M M Aly M Abdel-Akher Z Ziadi and T Senjyu ldquoAssess-ment of reactive power contribution of photovoltaic energysystems on voltage profile and stability of distribution systemsrdquoInternational Journal of Electrical Power amp Energy Systems vol61 pp 665ndash672 2014

[14] A Eid ldquoUtility integration of PV-wind-fuel cell hybrid dis-tributed generation systems under variable load demandsrdquoInternational Journal of Electrical Power amp Energy Systems vol62 pp 689ndash699 2014

[15] Y K Gounder D Nanjundappan and V BoominathanldquoEnhancement of transient stability of distribution system withSCIG and DFIG based wind farms using STATCOMrdquo IETRenewable Power Generation vol 10 no 8 pp 1171ndash1180 2016

[16] A Huang and J Baliga ldquoFREEDM system role of powerelectronics and power semiconductors in developing an energyinternetrdquo in Proceedings of the 21st International Symposium onPower Semiconductor Devices ICrsquos (ISPSD pp 9ndash12 BarcelonaSpain 2009

[17] Y Ye M Kazerani and V Quintana ldquoA novel modeling andcontrol method for three-phase PWM convertersrdquo in Proceed-ings of the 2001 IEEE 32nd Annual Power Electronics SpecialistsConference pp 102ndash107 Vancouver BC Canada

[18] F Wang A Huang G Wang X She and R Burgos ldquoFeed-forward control of solid state transformerrdquo in Proceedings of the2012 IEEE Applied Power Electronics Conference and Exposition- APEC 2012 pp 1153ndash1158 Orlando FL USA Feburary 2012

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ACDC DCDC DCAC

Grid

SST

Load

DGs

Figure 1 A typical tertiary-structure solid state transformer

stability of DC bus can be maintained at different operatingmodes In [15] a method that can enhance the transientvoltage stability of a real distribution network with windpower was proposed bymeans of optimal rating and locationof the static synchronous compensator (STATCOM)

When using a SST for the integration of DGs and thedistribution network on the part of the grid the ability ofadopting the DGs will be enhanced and the situation of volt-age oscillation and instability will be avoided In this papera simulation model of a 038 kV low voltage distributionnetwork which uses a typical SST for the integration of DGswas established using the power system simulation softwarePSCADEMTDC and effects on the transient voltage stabilityof the system while facing various disturbances are studiedThe advantages of the transient voltage stability using a SSTfor the integration of DGs are analyzed and the differencesbetween whether there is a battery energy storage station arediscussed

2 Modeling and Control Strategy of SST

As shown in Figure 1 a typical tertiary-structure SST ischosen for discussion which consisted by a ACDC unit aDCDC unit and a DCAC unit The three units are inputstage isolation stage and output stage respectively To realizethe bidirectional power flow the full-controlled device IGBTis used for building the SST [16]

In this paper a voltage-source PMW rectifier is chosen asthe input stage of SST which can rectify the 038 kVAC of thelow voltage distribution network to 078 kV DC

The dual-loop decoupled control strategy is chosen forthe input stage [17] The voltage orientation control strategybased on 119889-119902 rotating coordinate system is selected for thevoltage loop and the direct current control is adopted forthe current loopThe grid-side power factor can be correctedaccording to the control goal The control equations of theSST input stage are

119894lowast1119889 = (119870P1 + 119870I1119904 ) (1198801015840dc minus 119880dc)119894lowast1119902 = 0119906lowast1119889 = 1199061119889 + 1205961198711198941119902 minus (119870P2 + 119870I2119904 ) (119894lowast1119889 minus 1198941119889)119906lowast1119902 = 1199061119902 minus 1205961198711198941119889 minus (119870P2 + 119870I2119904 ) (119894lowast1119902 minus 1198941119902)

(1)

where 119894lowast1119889 and 119894lowast1119902 are the grid-side current command valuesin 119889-119902 coordinate system and 1198941119889 and 1198941119902 are the actual values119906lowast1119889 and 119906lowast1119902 are the grid-side voltage command values in 119889-119902coordinate system and 1199061119889 and 1199061119902 are the actual values 1198801015840dc119880dc are the reference voltage and actual voltage of DC busrespectively 119870P1 119870I1 119870P2 and 119870I2 are the parameters of PIcontrollers L is the filter inductance of SST input stage

In isolation stage the 078 kV DC is converted to a high-frequency AC square wave and coupled to the secondaryside of a high-frequency isolated transformer which is usedto isolate the original side and subside Then the high-frequency AC will be rectified to 078 kV DC

In the output stage the 078 kV DC is inverted to 038 kVAC for power supplies The dual-loop decupled controlstrategy with the voltage and current feedforward is adoptedfor the control [18] The control equations of the SST outputstage are

119894lowast2119889 = 1198942119889 minus 1205961198621198911199062119902 + (119870P3 + 119870I3119904 ) (11990610158402119889 minus 1199062119889)119894lowast2119902 = 1198942119902 + 1205961198621198911199062119889 + (119870P3 + 119870I3119904 ) (11990610158402119902 minus 1199062119902)119906lowast2119889 = 1199062119889 minus 1205961198711198911198942119902 + (119870P4 + 119870I4119904 ) (119894lowast2119889 minus 1198942119889)119906lowast2119902 = 1199062119902 + 1205961198711198911198942119889 + (119870P4 + 119870I4119904 ) (119894lowast2119902 minus 1198942119902)

(2)

where 119894lowast2119889 and 119894lowast2119902 are the load current command values in119889-119902 coordinate system and 1198942119889 and 1198942119902 are the actual values119906lowast2119889 and 119906lowast2119902 are the load bus voltage command values in 119889-119902coordinate system 11990610158402119889 and 11990610158402119902 are the reference values and1199062119889 and1199062119902 are the actual values119870P3119870I3119870P4 and119870I4 are theparameters of PI controllers 119871119891 119862119891 are the filter inductanceand capacitance of SST output stage respectively

3 Model of Low Voltage Distribution NetworkIntegrated with DGs

A conventional system model of a low voltage distributionnetwork integrated with DGs (including distributed photo-voltaic andwind power) is established using the power systemsimulation software PSCAD as shown in Figure 2 1 and 2are the voltage of Bus 1 andBus 2 respectivelyThe impedanceof the cable is 119877 + 119895119883 and the value is 0096 + 1198950015Ω Thepower from the low voltage distribution network is noted as1198751+1198951198761 the power flow from the network to Bus 2 is noted as1198752 + 1198951198762 The outputs of photovoltaic power plant and windpower farm are 119875pv + 119895119876pv and 119875wind + 119895119876wind respectivelythe absorbed power of the three-phase induction motor andthe static load are 119875119872 + 119895119876119872 and 119875119904 + 119895119876119904 respectively

Some ancillary facilities such as reactive power com-pensation devices and inverters of photovoltaic or windpower systems can be left out because of the structure andflexible control characteristics of SST and the DGs can bedirectly connected to the DC busThe model of a low voltagedistribution network using a SST for the integration of DGsis shown in Figure 3


M



Static load

Cable line

DGs

Bus 1 Bus 2U1

U2

P1 + jQ1 P2 + jQ2R + jX

Pwind + jQwind

Ppv + jQpv

PS + jQS

PM + jQM


SST

M



Wind farm



Bus 1 Bus 2

ACDC DCDC DCAC

DC bus

P1 + jQ1 P2 + jQ2

R + jX

minus+








Bus 1

FaultLow voltage



SST

Line 2 Line 1


AV











119875pv + 119875wind = 119875119872 + 119875119878 = 119875119872 + ( 11198771199041 +119877s211987721199042 + 11988321199042)119880

22 (3)









Conventional system

0

02

04

06

08

1

12

14Vo

ltage

of B

us 2

(pu)

06 08 1 12 14 16 18 204Time (s)


minus15

minus1

minus05

0

05

1

15

2

25

3




06 08 1 12 14 16 18 204Time (s)

PM

andQ

M(p




0

05

1

15

2

25

3

35

4

45

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(c) DC bus voltage








0



Conventional system

02

04

06

08

1

12

14

16Vo

ltage

of l

oad

bus (

pu)

06 08 1 12 14 16 18 204Time (s)




0

05

1

15

2

25

3

35

4

45

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage



Conventional system

0

02

04

06

08

1

12

14

Volta

ge o

f Bus

2 (p

u)

06 08 1 12 14 16 18 204Time (s)



0

01

02

03

04

05

06

07

08

09

1

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage



1198802 minus 11988010158402 = 119875Σ119877 + 119876Σ1198831198802 + (119875119871119877 + 119876119871119883)( 111988010158402 minus11198802) (4)






Conventional system



0

02

04

06

08

1

12Vo

ltage

of B

us 2

(pu)

06 08 1 12 14 16 18 204Time (s)


04 06 08 1 12 14 16 18 2



Time (s)

0

05

1

15

2

25

3

35

4

45

Volta

ge o

f DC

bus (

kV)

(b) DC bus voltage





6 Conclusions






Conventional system



0

02

04

06

08

1

12Vo

ltage

of B

us 2

(pu)

04 08 1 12 14 16 18 206Time (s)




0

01

02

03

04

05

06

07

08

09

1

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage

minus03

minus025

minus02

minus015

minus01

minus005

0

005

01

015

02

025

03

06 08 1 12 14 16 18 204Time (s)

P1

Q1

P1

(MW

) and

Q1

(MW

)






Data Availability





Acknowledgments


References





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



M



Static load

Cable line

DGs

Bus 1 Bus 2U1

U2

P1 + jQ1 P2 + jQ2R + jX

Pwind + jQwind

Ppv + jQpv

PS + jQS

PM + jQM


SST

M



Wind farm



Bus 1 Bus 2

ACDC DCDC DCAC

DC bus

P1 + jQ1 P2 + jQ2

R + jX

minus+








Bus 1

FaultLow voltage



SST

Line 2 Line 1


AV











119875pv + 119875wind = 119875119872 + 119875119878 = 119875119872 + ( 11198771199041 +119877s211987721199042 + 11988321199042)119880

22 (3)









Conventional system

0

02

04

06

08

1

12

14Vo

ltage

of B

us 2

(pu)

06 08 1 12 14 16 18 204Time (s)


minus15

minus1

minus05

0

05

1

15

2

25

3




06 08 1 12 14 16 18 204Time (s)

PM

andQ

M(p




0

05

1

15

2

25

3

35

4

45

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(c) DC bus voltage








0



Conventional system

02

04

06

08

1

12

14

16Vo

ltage

of l

oad

bus (

pu)

06 08 1 12 14 16 18 204Time (s)




0

05

1

15

2

25

3

35

4

45

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage



Conventional system

0

02

04

06

08

1

12

14

Volta

ge o

f Bus

2 (p

u)

06 08 1 12 14 16 18 204Time (s)



0

01

02

03

04

05

06

07

08

09

1

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage



1198802 minus 11988010158402 = 119875Σ119877 + 119876Σ1198831198802 + (119875119871119877 + 119876119871119883)( 111988010158402 minus11198802) (4)






Conventional system



0

02

04

06

08

1

12Vo

ltage

of B

us 2

(pu)

06 08 1 12 14 16 18 204Time (s)


04 06 08 1 12 14 16 18 2



Time (s)

0

05

1

15

2

25

3

35

4

45

Volta

ge o

f DC

bus (

kV)

(b) DC bus voltage





6 Conclusions






Conventional system



0

02

04

06

08

1

12Vo

ltage

of B

us 2

(pu)

04 08 1 12 14 16 18 206Time (s)




0

01

02

03

04

05

06

07

08

09

1

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage

minus03

minus025

minus02

minus015

minus01

minus005

0

005

01

015

02

025

03

06 08 1 12 14 16 18 204Time (s)

P1

Q1

P1

(MW

) and

Q1

(MW

)






Data Availability





Acknowledgments


References





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Bus 1

FaultLow voltage



SST

Line 2 Line 1


AV











119875pv + 119875wind = 119875119872 + 119875119878 = 119875119872 + ( 11198771199041 +119877s211987721199042 + 11988321199042)119880

22 (3)









Conventional system

0

02

04

06

08

1

12

14Vo

ltage

of B

us 2

(pu)

06 08 1 12 14 16 18 204Time (s)


minus15

minus1

minus05

0

05

1

15

2

25

3




06 08 1 12 14 16 18 204Time (s)

PM

andQ

M(p




0

05

1

15

2

25

3

35

4

45

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(c) DC bus voltage








0



Conventional system

02

04

06

08

1

12

14

16Vo

ltage

of l

oad

bus (

pu)

06 08 1 12 14 16 18 204Time (s)




0

05

1

15

2

25

3

35

4

45

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage



Conventional system

0

02

04

06

08

1

12

14

Volta

ge o

f Bus

2 (p

u)

06 08 1 12 14 16 18 204Time (s)



0

01

02

03

04

05

06

07

08

09

1

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage



1198802 minus 11988010158402 = 119875Σ119877 + 119876Σ1198831198802 + (119875119871119877 + 119876119871119883)( 111988010158402 minus11198802) (4)






Conventional system



0

02

04

06

08

1

12Vo

ltage

of B

us 2

(pu)

06 08 1 12 14 16 18 204Time (s)


04 06 08 1 12 14 16 18 2



Time (s)

0

05

1

15

2

25

3

35

4

45

Volta

ge o

f DC

bus (

kV)

(b) DC bus voltage





6 Conclusions






Conventional system



0

02

04

06

08

1

12Vo

ltage

of B

us 2

(pu)

04 08 1 12 14 16 18 206Time (s)




0

01

02

03

04

05

06

07

08

09

1

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage

minus03

minus025

minus02

minus015

minus01

minus005

0

005

01

015

02

025

03

06 08 1 12 14 16 18 204Time (s)

P1

Q1

P1

(MW

) and

Q1

(MW

)






Data Availability





Acknowledgments


References





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Conventional system

0

02

04

06

08

1

12

14Vo

ltage

of B

us 2

(pu)

06 08 1 12 14 16 18 204Time (s)


minus15

minus1

minus05

0

05

1

15

2

25

3




06 08 1 12 14 16 18 204Time (s)

PM

andQ

M(p




0

05

1

15

2

25

3

35

4

45

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(c) DC bus voltage








0



Conventional system

02

04

06

08

1

12

14

16Vo

ltage

of l

oad

bus (

pu)

06 08 1 12 14 16 18 204Time (s)




0

05

1

15

2

25

3

35

4

45

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage



Conventional system

0

02

04

06

08

1

12

14

Volta

ge o

f Bus

2 (p

u)

06 08 1 12 14 16 18 204Time (s)



0

01

02

03

04

05

06

07

08

09

1

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage



1198802 minus 11988010158402 = 119875Σ119877 + 119876Σ1198831198802 + (119875119871119877 + 119876119871119883)( 111988010158402 minus11198802) (4)






Conventional system



0

02

04

06

08

1

12Vo

ltage

of B

us 2

(pu)

06 08 1 12 14 16 18 204Time (s)


04 06 08 1 12 14 16 18 2



Time (s)

0

05

1

15

2

25

3

35

4

45

Volta

ge o

f DC

bus (

kV)

(b) DC bus voltage





6 Conclusions






Conventional system



0

02

04

06

08

1

12Vo

ltage

of B

us 2

(pu)

04 08 1 12 14 16 18 206Time (s)




0

01

02

03

04

05

06

07

08

09

1

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage

minus03

minus025

minus02

minus015

minus01

minus005

0

005

01

015

02

025

03

06 08 1 12 14 16 18 204Time (s)

P1

Q1

P1

(MW

) and

Q1

(MW

)






Data Availability





Acknowledgments


References





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0



Conventional system

02

04

06

08

1

12

14

16Vo

ltage

of l

oad

bus (

pu)

06 08 1 12 14 16 18 204Time (s)




0

05

1

15

2

25

3

35

4

45

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage



Conventional system

0

02

04

06

08

1

12

14

Volta

ge o

f Bus

2 (p

u)

06 08 1 12 14 16 18 204Time (s)



0

01

02

03

04

05

06

07

08

09

1

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage



1198802 minus 11988010158402 = 119875Σ119877 + 119876Σ1198831198802 + (119875119871119877 + 119876119871119883)( 111988010158402 minus11198802) (4)






Conventional system



0

02

04

06

08

1

12Vo

ltage

of B

us 2

(pu)

06 08 1 12 14 16 18 204Time (s)


04 06 08 1 12 14 16 18 2



Time (s)

0

05

1

15

2

25

3

35

4

45

Volta

ge o

f DC

bus (

kV)

(b) DC bus voltage





6 Conclusions






Conventional system



0

02

04

06

08

1

12Vo

ltage

of B

us 2

(pu)

04 08 1 12 14 16 18 206Time (s)




0

01

02

03

04

05

06

07

08

09

1

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage

minus03

minus025

minus02

minus015

minus01

minus005

0

005

01

015

02

025

03

06 08 1 12 14 16 18 204Time (s)

P1

Q1

P1

(MW

) and

Q1

(MW

)






Data Availability





Acknowledgments


References





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Conventional system



0

02

04

06

08

1

12Vo

ltage

of B

us 2

(pu)

06 08 1 12 14 16 18 204Time (s)


04 06 08 1 12 14 16 18 2



Time (s)

0

05

1

15

2

25

3

35

4

45

Volta

ge o

f DC

bus (

kV)

(b) DC bus voltage





6 Conclusions






Conventional system



0

02

04

06

08

1

12Vo

ltage

of B

us 2

(pu)

04 08 1 12 14 16 18 206Time (s)




0

01

02

03

04

05

06

07

08

09

1

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage

minus03

minus025

minus02

minus015

minus01

minus005

0

005

01

015

02

025

03

06 08 1 12 14 16 18 204Time (s)

P1

Q1

P1

(MW

) and

Q1

(MW

)






Data Availability





Acknowledgments


References





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Conventional system



0

02

04

06

08

1

12Vo

ltage

of B

us 2

(pu)

04 08 1 12 14 16 18 206Time (s)




0

01

02

03

04

05

06

07

08

09

1

Volta

ge o

f DC

bus (

kV)

06 08 1 12 14 16 18 204Time (s)

(b) DC bus voltage

minus03

minus025

minus02

minus015

minus01

minus005

0

005

01

015

02

025

03

06 08 1 12 14 16 18 204Time (s)

P1

Q1

P1

(MW

) and

Q1

(MW

)






Data Availability





Acknowledgments


References





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Acknowledgments


References





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

Analysis of Transient Voltage Stability in a Low …downloads.hindawi.com/journals/jece/2018/3498491.pdfJournalofElectricalandComputerEngineering Bu 1 Flt Lw oltage distribution etwork