research article modeling and simulation of power

Research ArticleModeling and Simulation of Power Distribution System inMore Electric Aircraft

Zhangang Yang Junchao Qu Yingchuan Ma and Xudong Shi

Aeronautical Automation College Civil Aviation University of China Tianjin 300300 China

Correspondence should be addressed to Zhangang Yang yangcauc163com

Received 18 August 2015 Revised 20 November 2015 Accepted 10 December 2015

Academic Editor Yiyu Shi

Copyright copy 2015 Zhangang Yang et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

TheMore Electric Aircraft concept is a fast-developing trend in modern aircraft industry With this new concept the performanceof the aircraft can be further optimized and meanwhile the operating and maintenance cost will be decreased effectively In orderto optimize the power system integrity and have the ability to investigate the performance of the overall system in any possiblesituations one accurate simulation model of the aircraft power system will be very helpful and necessary This paper mainlyintroduces a method to build a simulation model for the power distribution system which is based on detailed component modelsThe power distribution systemmodel consists of power generation unit transformer rectifier unit DC-DC converter unit andDC-AC inverter unit In order to optimize the performance of the power distribution system and improve the quality of the distributedpower a feedback control network is designed based on the characteristics of the power distribution systemThe simulation resultindicates that this new simulationmodel is well designed and it works accurately Moreover steady state performance and transientstate performance of the model can fulfill the requirements of aircraft power distribution system in the realistic application

1 Introduction

The aircraft electrical power systems in next generationcommercial airlines are undergoing a significant develop-ment A prominent feature of the development is that manyfunctions that used to be operated by hydraulic pneumaticand mechanical power are being replaced by the electricpower [1 2] The aircraft power system includes powergeneration system power distribution system and loads Inthe future the ldquoMore Electricrdquo Aircraft power system willbe built based on the fact that most of the components areinterconnected with each other resulting in a significantlymore complex electrical distribution system with multipledistributed loads most of which are supplied and controlledby power electronic converters The power distribution sys-tem carries electricity from the power generation systemto the distributed loads and it plays a key role to ensurethe safety of the flight and the reliability of the airborneequipment

The More Electric Aircraft power distribution systemsare also likely to contain a large number of power electricconverters A typical power distribution system includes

DC-DC converter DC-AC inverter AC-DC rectifier anda variety of harmonic compensation devices In order tooptimize the power quality and transient behavior of thepower distribution system a well-designed simulationmodelof the aircraft power distribution system based on detailedcomponent models will be necessary Now a considerableresearch has been undertaken on the modeling of thepower distribution system The commonly used method istime domain simulation method with time domain sim-ulation using the detailed nonlinear time varying powersystem models which considers the switching behavior andtransients can provide accurate transient performance [3]However when analyzing the whole dynamic performanceof the overall system the time domain simulation methodwill be hard to implement because of the long computationtime and large memory consumption so how to improvethe simulation speed is the key issue of the time domainsimulation method In [4] a model order reduction methodwas proposed based on Krylov subspace theory for large-scale linear distribution grids the model scale of distributionsystems may be decreased effectively and the simulationefficiency is improved significantly In [5] an order reduction

Hindawi Publishing CorporationJournal of Electrical and Computer EngineeringVolume 2015 Article ID 847624 7 pageshttpdxdoiorg1011552015847624

2 Journal of Electrical and Computer Engineering

principle of multi-time scale system was proposed andapplied to ACDC power system and then the order of atypical ACDC power system was reduced In general thecomputation time and memory consumption are still therestrictions when the time domain simulation is applied Itis well known that the power electric converter model istime-varying because of the switching behavior From thesystem level point of view the switching behavior includesthe high frequency switching transients andharmonicswhichhave no significant influence on the dynamic performanceof the overall system The state-space averaging modelingmethod is the most commonly used method to eliminatethe switching actions to achieve time-invariant model [6] In[7 8] this method has been used to analyze 6 pulse dioderotating rectifiers and electromechanical actuators in aircraftpower system In [9] the state-space averaging model basedon DQ transformation has been used to build fault diagnosismodel of aircraft inverter In [10] an average-value modelingmethod has been used for 6 and 12 pulse diode rectifiers

However the converter that the state-space averagingmodeling method and the average-value modeling methodcan be used to is limited Conditions for the justification havebeen characterized by a ldquosmall ripplerdquo condition and a ldquolinearripplerdquo approximation With the small ripple approximationthe precision of the model is limited [11]

Given the focus of the paper as described above themodeling of the aircraft power system is mainly focused onthe part of the aircraft power system such as the AC-DCconverter and the DC-AC inverter In this paper a completemodel of power distribution system is built and a reasonablecontrol strategy for theMore Electric Aircraft is proposed thesteady and transient characteristics are analyzed and also thehigh simulation speed and good accuracy are obtained

2 Structure of Aircraft Distribution System

The schematic model of aircraft power distribution systemis shown in Figure 1 it consists of several componentsgenerator and transformer rectifier unit DC-DC converterunit and DC-AC inverter unit

21 Generator and Transformer Rectifier Unit Generator andtransformer rectifier unit consists of generator exciter trans-former and 12-pulse diode rectifier The rated frequency ofsynchronous generator is 400Hz A feedback proportional-integral control strategy is used to regulate the voltage of the270V-DC bus by appropriately modifying the field excitationcurrent of the synchronous generator

To implement the 30∘ phase shift required to obtain 12-pulse operation a YYD transformer is employedMoreovera low-pass filter is employed to improve the quality of theoutput current of the rectifier

22 DC-DC Converter Unit With different operation condi-tions the characteristics of DC loads are different in MoreElectric Aircraft Depending on the characteristics of loadsthe DC loads are classified as constant voltage (CV) constantcurrent (CC) and constant power (CP) loads

23 DC-AC Inverter Unit A voltage source inverter withtwo 6-pulse switching bridge inverters is connected to the270V-DC bus To maintain the phase voltage constant at115 Vrms a feedback proportional-integral controller is usedto regulate the duty cycle of the SPWM inverter Hencewith an appropriate filtering circuit the output voltage of theinverter is 115 V200Vrms and the frequency of the three-phase AC current is 400Hz

3 Control Strategy of AircraftDistribution System

31 Control Strategy of Generator and Transformer RectifierUnit Inside the power generation unit and transformerrectifier unit the input of synchronous generator is theangular velocity of the aircraft engine The constant voltagecontrol strategy which is used to maintain the voltage of the270V-DC bus by appropriately modifying the field excitationcurrent of the synchronous generator is applied to thetransformer rectifier unit Figure 2 shows the block diagramof the constant voltage control unit The constant voltagecontrol unit will collect the DC voltage signals output fromthe transformer rectifier unit to produce error signal Theerror signal is generated by comparing the DC voltage signalsto reference signals 119881ref In this paper 119881ref is set to 270VThe error signal will be operated by the proportional-integralcontrol unit then the operation signal will be produced ThePWM signal which is used to control the excitation voltagecan be generated by comparing the operation signal withtriangular wave

The following shows the transfer function of the controlunit

119881119891= (⟨119881DC⟩ minus 119881ref) (119870119901 +

1

119879119894

) minus Tri (1)

In this equation119870119901and119879119894are the adjustment parameters

of control unit Tri is the triangular signal The excitationsystem can control the output voltage of the synchronousgenerator by changing the proportional-integral parametersaccordingly

32 Control Strategy of DC-DC Converter Unit In thissection the circuit model is linearized and Figure 3 shows thechanged circuit model of the DC-DC converter

The following gives the transfer function of the PWMModulator which is shown in Figure 3

119866119898(119904) =

119889 (119904)

119881119888(119904)

=1

119881119898

(2)

In (2) 119889(119904) is the duty cycle of the PWM signal 119881119888(119904) is

the control variable of the converter119881119898is the sawtooth wave

amplitude of the PWM Modulator The transfer function ofthe feedback network is given in the following

119867(119904) =119861 (119904)

119881119900(119904) (3)

Journal of Electrical and Computer Engineering 3

Variable speedVgen

120596SG

Currentlimiter

PPF

Control signal

Zgminus1 IgrVgr

IfrY

Y

Δ

TRU

12-pulse diodeLPFrectifier

VP

minus

minus

+

minus

+

+ minus+

VN

VDCPI

RefTri

Sat

IΔminusr

IYminusrrDCIDCLDCVDC

Iload

IcCDC

270V-DC12-pulse voltagesource inverter

IiaminusY

IiaminusΔY

YΔ

Iinv IiaLf

LfLf

RfRfRf

VcaVcb

Vcc

CfCfCf

RfRfRf

Iin-CV

minus

+

minus

minus

+

+

VDC

r i L

Lcicrc

VCV

Vcc

iCV

icc

ifv

ifc

C

Cc

CV-TVL

CC-TVL

CP-TVL

IM

RL

Rt

Rt

Rt

Iin-cc

Iin-cp VDC

VDC

PI-SPWMControl unit 1



I1a

Cp

ifp

rp ip Lp

Vcp

icp

PF = 085

I998400gr

115Vrms 400Hz

Figure 1 Schematic diagram of aircraft distribution system

+

minus

Controlsignal

+

+ minus

TriError

signals+

1

Tis

VDC

Vref

Vf

Kp

Figure 2 Block diagram of the PWM closed-loop control unit

Compensationnetwork

PWMmodulation

Feedback signal

Transferfunction

ref (s)

B(s)

minus

+ E(s)Gc(s)

Vc(s) Gm(s)

H(s)

d(s)Gd(s)

o(s)

Figure 3 DC-DC converter model

In (3) 119861(119904) is the feedback signal 119881119900(119904) is the output

voltage of the converter The transfer function of Buckconverter is given in the following

119866V119889 (119904) =119881119900(119904)

119889 (119904)=

119881119892

119871CV119862V1199042 + 119871CV (119877119905 + 119903V) + 1

(4)

Assuming 119881119900(119904) is the output voltage of the Buck con-

verter 119889(119904) is the duty cycle of the modulator 119881119892is the

amplitude of the output voltage 119871CV and 119862V represent theinductance and capacitance of the circuit respectively 119903V isthe resistance of the wire

Substituting (2) (3) and (4) into (5) the gain function ofthe original circuit is given in the following

119866119900(119904) = 119866

119898(119904) 119866V119889 (119904)119867 (119904) (5)

In (5) 119881ref(119904) is the reference value of the DC-DCconverter 119881ref(119904) and the transfer function of the feedbacknetwork are different under different DC loads It means thatthe transfer function 119867(119904) is different to different networkBy analyzing the transfer function in the time domainand the frequency domain the appropriate compensationnetwork 119866

119900(119904) can be designed to optimize the performance

of switching circuit

33 Control Strategy of DC-AC Inverter Unit Figure 4 showsa typical structure of inverter unit with control system where119880119886 119880119887 and 119880

119888are output voltage of the three phase bridge

inverter 119894119871119886 119894119871119887 and 119894

119871119888are inductor current 119880

119900119886 119880119900119887 and

119880119900119888are output phase voltage and 119894

119886 119894119887 and 119894

119888are output load

currentThe output AC voltage of the three-phase SPWM inverter

can be converted to 119889-axis and 119902-axis components in two-phase rotating coordinate system and the components are ofDC value Considering these aspects (6) of the AC outputat three-phase inverter (converted to two-phase rotatingcoordinate system) can be obtained Consider the following

119871119889119894119871119889

119889119905= 119880119889minus 119880119900119889minus 120596119871119894

119871119902

119871

119889119871119902

119889119905= 119880119902minus 119880119900119902minus 120596119871119894

119871119889

119862119889119880119900119889

119889119905= 119894119871119889minus 119894119889minus 120596119862119880

119900119902

119862

119889119880119900119902

119889119905= 119894119871119902minus 119894119902minus 120596119862119880

119900119889

(6)


IM

RL

ia

ib

ic

L

L

L

C C C

RfRfRf

iLa

iLb

iLc

Y

Y

Δ

115V 400HzIia-Y

Iia-Δ

12-pulse voltage sourceinverter

Iinv Ua

Ub

Uc

SPWMmodulation

dq

dq dq

abc

abc abc

PIcontrol

Iabc

120579s 120579s

120579sId

Iq

Idlowast

Iqlowast

Uoabc

Ud Uqfs

Reference

PLL

signals

PIcontrol

minus

Figure 4 Structure of inverter module

Based on the equations in rotating coordinate systemthe constant voltage and constant frequency control structureof the inverter can be designed In ideal state the detectedoutput voltage can be converted to voltage in the two-phaserotating coordinate system which is given in (7) and (8)Consider the following

[

119880119889

119880119902

] = radic2

3119862 [119880119886119880119887119880119888]119879

[radic3

21198801198980]

119879

(7)

119862 =[[[

[

cos120596119905 cos(120596119905 minus 23120587) cos(120596119905 + 2

3120587)

minus sin120596119905 minus sin(120596119905 minus 23120587) minus sin(120596119905 + 2

3120587)

]]]

]

(8)

In (7) 119880119898

is the magnitude of the phase voltage and119862 is the coordinate transformation matrix The voltagecomponent on 119889-axis can be set to the per unit value of 1 andthe reference of 119902-axis component is set to 0 The error of 119889-axis and 119902-axis component can be separately adjusted by theproportional-integral control unit

4 Simulation of Aircraft Distribution System

The studies reported in this section are performed on theaircraft distribution system of Figure 1

41 Simulation of Generator and Transformer Rectifier UnitThe following parameters are used in the simulation ofsynchronous generator the output reference voltage is set to115200Vrms the rated reference operating frequency is setto 400Hz the engine speed changes from 0 to 12000 rpm

0 0002 0004 0006 0008 001minus350minus282

minus200

minus100

0

100

200

282350

Time (s)

(V)

Figure 5 Simulation of power generation module

Therefore the three-phase output voltage waveform of gen-erator can be shown in Figure 5

As shown in Figure 5 the amplitude of the AC voltageis 282V and the operating frequency is regulated to 400HzThe voltage ripplemeets theMILSTD-704F in [12]MILSTD-704F establishes the requirements and characteristics ofaircraft electric power provided at the input terminals ofelectric utilization equipment According to MILSTD-704Fthe normal operation characteristics of DC voltage shouldbe in accordance with Table 1 In the 28V DC system theDC steady state voltage in emergency operation should bebetween 22 and 29V In the 270V DC system the DC steadystate voltage in emergency operation should be between 250and 280V

The output voltage of transformer rectifier unit at 270V-DC bus terminals can be depicted in Figure 6(a) Figure 6(b)


0 005 01 015 02 025 03 0350

100

200270300

Time (s)

(V)

(a)

0 0005 001 0015 002 0025 003 0035 004

240

260

280

Time (s)

(V)

(b)

019 0195 02 0205 021 0215 022265

270

275

280

Time (s)

(V)

(c)

Figure 6 Simulation of transformer rectifier module

0 005 01 015 02 025 03 035

0

10

20

2835

Time (s)

(V)

(a)

0 005 01 015 02 025 03 0350

1

2

3

4

5

Time (s)

(A)

(b)

Figure 7 Simulation of buck-converter with constant voltage loads

Table 1 DC normal operation characteristics

Steady state characteristics 28V DC system 270V DC systemSteady state voltage 22 to 29V 250 to 280VRipple amplitude 15 V maximum 60V maximum

is the partial zoom of Figure 6(a) As shown in Figure 6(b) at1199050= 0015 s the output voltage increases to its normal value at

270V and the amplitude of theDC voltage is between 265 and275V at 119905

1= 002 s Figure 6(c) depicts the system response to

changes in power demand From 1199050= 002 s to 119905

1= 02 s half

of full-load power is activated while the transformer rectifierunit is connected to the aircraft power distribution system Ina shortly response time (02 s) the load power will reach thenominal value the transformer rectifier unitrsquos output voltageremains unchanged

42 Simulation of DC-DC Converter Unit As shown inFigure 1 various types of DC-DC converters interact withthe 270-DC bus while providing a regulated constant voltageconstant current and constant power to loads In this sectionloading profiles change over time and the dynamic behaviorof the converter may change according to loading conditions

Figure 7 gives the voltage and current curve of buckconverter with 28V-DC constant voltage loads

In 0ndash02 s the load power is set to half of the total load Ina shortly response time (005 s) the output voltage increasesto its normal value at 28V and the amplitude of the DCvoltage remains 28V from 119905

0= 005 s to 119905

1= 02 s as shown

in Figure 7(a) At 02 s the load of the CV-buck converterreaches the nominal power the DC bus voltage will return to28V after a short time vibration (02ndash022 s) and the outputcurrent will increase correspondingly as shown in Figures7(a) and 7(b)

Figure 8(a) gives the current curve of buck converter with30A constant current loads Figure 8(b) is the partial zoomof Figure 8(a) As shown in Figure 8(b) in a shortly responsetime (0015 s) the output current increases to its normal valueat 30A and the amplitude of the DC current remains 30A At02 s there is a sudden change of the CC buck converter loadFor the constant current control of the buck converter thecurrent will return to 30A after a short time vibration (02ndash0202 s) as shown in Figure 8(c)

Figure 9 gives the voltage current and power curve ofbuck converter with 5 kW constant power loads In a shortlyresponse time (0015 s) the output power increases to itsnormal value at 5 kW and the amplitude of the output powerremains 5 kW as shown in Figure 9(c)


0 005 01 015 02 025 03 0350

10

20

30

40

Time (s)

(A)

(a)

001 0012 0014 0016 0018 00229

295

30

305

31

Time (s)

(A)

(b)

019 0194 0198 0202 0206 021295

30

305

Time (s)

(A)

(c)

Figure 8 Simulation of buck-converter with constant current loads

(V)

0 005 01 015 02 025 03 0350

50100

15812

2236250

Time (s)

(a)

0 005 01 015 02 025 03 0350

10

22353162

405060

Time (s)

(A)

(b)

0 005 01 015 02 025 03 0350

357

10

Time (s)

(kW

)

(c)

Figure 9 Simulation of buck-converter with constant power loads

Initially the system is under a steady-state conditionwhile the obtained output voltage and inductor currentare calculated to be 2236V and 2235A respectively At02 s there is a sudden change of the CP buck converterload resistance For the constant power control of the buckconverter the output power will return to 5 kW after a shorttime vibration (02ndash0202 s) as shown in Figure 9(c) Thesystem responds to this variation by a step drop in voltagersquosaverage value to 15812 V also the averaged value of theinductor current reaches to 3162A at steady-state as shownin Figures 9(a) and 9(b)

43 Simulation of DC-AC Inverter Unit Figure 10 gives theoutput voltage curve of DC-AC inverter the amplitude of theAC voltage is 162V and RMS voltage is 115 V Furthermore

the operating frequency is regulated to 400Hz It can be seenthat the voltage ripple meets the standard of MIL-STD-704F

From the simulation results above it is demonstrated thatthe aircraft power distribution systemmodel of aircraft powersystem can be used to the steady and transient analysis ofdifferent aircraft types with high simulation speed and goodaccuracy

5 Conclusions

A simulation model of the power distribution system inMore Electric Aircraft was built in this paper The modelincludes power generation unit transformer rectifier unitDC-DC converter unit and DC-AC inverter unit Accordingto the different characteristics of each unit the structure of


0 001 002 003 004 005minus200minus162

minus100

minus50

050

100

162200

Time (s)

(V)

Figure 10 Simulation of inverter

the distribution system was analyzed and the feedbackcontrol network was designed The simulation results showthat the simulation model with control strategy can workaccurately andmeet the requirements of the standard ofMIL-STD-704F Hence the developed models can be used forstability assessment of the electric power systems of theMoreElectric Aircraft in the future

Conflict of Interests

The authors declared that they have no conflict of interests tothis work

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (Grants nos 51377161 and 51407185)the Innovation Experiment Technology Foundation of CivilAviation University of China (Grants no 17-14-03) and theTeaching Reform Project of Civil Aviation University ofChina (Grants no CAUC-ETRN-2014-27)

References

[1] J A Rosero J A Ortega E Aldabas and L Romeral ldquoMovingtowards a more electric aircraftrdquo IEEE Aerospace and ElectronicSystems Magazine vol 22 no 3 pp 3ndash9 2007

[2] X Roboam ldquoNew trends and challenges of electrical networksembedded in lsquomore electrical aircraftrsquordquo in Proceedings of theIEEE International Symposium on Industrial Electronics (ISIErsquo11) pp 26ndash31 IEEE Gdansk Poland June 2011

[3] J Y Huang L Y Chen and D C Sun Digital Simulation forPower System China Electric Power Press Beijing China 1998

[4] P Li H Yu C S Wang C Ding G Song and F Gao ldquoModelorder reduction of large scale distribution grid based on Krylovsubspace methodrdquo Power System Technology vol 37 no 8 pp2343ndash2348 2013

[5] F Ma W M Ma and L J Fu ldquoA model order reductionmethod for nonlinear multi-time scale systemsrdquo Proceedings ofthe CSEE vol 33 no 16 pp 162ndash170 2013

[6] R D Middlebrook and S Cuk ldquoA general unified approach tomodeling switching converter power stagesrdquo in Proceedings ofthe IEEE Power Electronics Specialists Conference (PESC rsquo76) pp18ndash34 June 1976

[7] T Wu S V Bozhko G M Asher and P W Wheeler ldquoFastreduced functional models of electromechanical actuators formore-electric aircraft power system studyrdquo in Proceedings ofthe SAE Power System Conference Washington DC USANovember 2008

[8] T Wu S V Bozhko G M Asher and D W P Thomas ldquoAfast dynamic phasor model of autotransformer rectifier unitfor more electric aircraftrdquo in Proceedings of the 35th AnnualConference of IEEE Industrial Electronics (IECON rsquo09) pp 2531ndash2536 IEEE Porto Portugal November 2009

[9] W Zhang X Shang Y Zhou X Liu and H Han ldquoAmaximumpower control method of three-phase voltage source rectifiersadapted to aircraft electric actuator loadrdquo Transactions of ChinaElectrotechnical Society vol 26 no 8 pp 91ndash98 2011

[10] S F Glover Modeling and stability analysis of power electronicsbased systems [PhD dissertation] Purdue University WestLafayette Ind USA 2003

[11] S R Sanders J M Noworolski X Z Liu and G C VergheseldquoGeneralized averaging method for power conversion circuitsrdquoIEEE Transactions on Power Electronics vol 6 no 2 pp 251ndash259 1991

[12] MIL-STD-704F Aircraft electric power characteristic USDepartment of Defense Std 2004 httpswwwwbdgorgccbFEDMILstd704fpdf

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principle of multi-time scale system was proposed andapplied to ACDC power system and then the order of atypical ACDC power system was reduced In general thecomputation time and memory consumption are still therestrictions when the time domain simulation is applied Itis well known that the power electric converter model istime-varying because of the switching behavior From thesystem level point of view the switching behavior includesthe high frequency switching transients andharmonicswhichhave no significant influence on the dynamic performanceof the overall system The state-space averaging modelingmethod is the most commonly used method to eliminatethe switching actions to achieve time-invariant model [6] In[7 8] this method has been used to analyze 6 pulse dioderotating rectifiers and electromechanical actuators in aircraftpower system In [9] the state-space averaging model basedon DQ transformation has been used to build fault diagnosismodel of aircraft inverter In [10] an average-value modelingmethod has been used for 6 and 12 pulse diode rectifiers

However the converter that the state-space averagingmodeling method and the average-value modeling methodcan be used to is limited Conditions for the justification havebeen characterized by a ldquosmall ripplerdquo condition and a ldquolinearripplerdquo approximation With the small ripple approximationthe precision of the model is limited [11]

Given the focus of the paper as described above themodeling of the aircraft power system is mainly focused onthe part of the aircraft power system such as the AC-DCconverter and the DC-AC inverter In this paper a completemodel of power distribution system is built and a reasonablecontrol strategy for theMore Electric Aircraft is proposed thesteady and transient characteristics are analyzed and also thehigh simulation speed and good accuracy are obtained

2 Structure of Aircraft Distribution System

The schematic model of aircraft power distribution systemis shown in Figure 1 it consists of several componentsgenerator and transformer rectifier unit DC-DC converterunit and DC-AC inverter unit

21 Generator and Transformer Rectifier Unit Generator andtransformer rectifier unit consists of generator exciter trans-former and 12-pulse diode rectifier The rated frequency ofsynchronous generator is 400Hz A feedback proportional-integral control strategy is used to regulate the voltage of the270V-DC bus by appropriately modifying the field excitationcurrent of the synchronous generator

To implement the 30∘ phase shift required to obtain 12-pulse operation a YYD transformer is employedMoreovera low-pass filter is employed to improve the quality of theoutput current of the rectifier

22 DC-DC Converter Unit With different operation condi-tions the characteristics of DC loads are different in MoreElectric Aircraft Depending on the characteristics of loadsthe DC loads are classified as constant voltage (CV) constantcurrent (CC) and constant power (CP) loads

23 DC-AC Inverter Unit A voltage source inverter withtwo 6-pulse switching bridge inverters is connected to the270V-DC bus To maintain the phase voltage constant at115 Vrms a feedback proportional-integral controller is usedto regulate the duty cycle of the SPWM inverter Hencewith an appropriate filtering circuit the output voltage of theinverter is 115 V200Vrms and the frequency of the three-phase AC current is 400Hz

3 Control Strategy of AircraftDistribution System

31 Control Strategy of Generator and Transformer RectifierUnit Inside the power generation unit and transformerrectifier unit the input of synchronous generator is theangular velocity of the aircraft engine The constant voltagecontrol strategy which is used to maintain the voltage of the270V-DC bus by appropriately modifying the field excitationcurrent of the synchronous generator is applied to thetransformer rectifier unit Figure 2 shows the block diagramof the constant voltage control unit The constant voltagecontrol unit will collect the DC voltage signals output fromthe transformer rectifier unit to produce error signal Theerror signal is generated by comparing the DC voltage signalsto reference signals 119881ref In this paper 119881ref is set to 270VThe error signal will be operated by the proportional-integralcontrol unit then the operation signal will be produced ThePWM signal which is used to control the excitation voltagecan be generated by comparing the operation signal withtriangular wave

The following shows the transfer function of the controlunit

119881119891= (⟨119881DC⟩ minus 119881ref) (119870119901 +

1

119879119894

) minus Tri (1)

In this equation119870119901and119879119894are the adjustment parameters

of control unit Tri is the triangular signal The excitationsystem can control the output voltage of the synchronousgenerator by changing the proportional-integral parametersaccordingly

32 Control Strategy of DC-DC Converter Unit In thissection the circuit model is linearized and Figure 3 shows thechanged circuit model of the DC-DC converter

The following gives the transfer function of the PWMModulator which is shown in Figure 3

119866119898(119904) =

119889 (119904)

119881119888(119904)

=1

119881119898

(2)

In (2) 119889(119904) is the duty cycle of the PWM signal 119881119888(119904) is

the control variable of the converter119881119898is the sawtooth wave

amplitude of the PWM Modulator The transfer function ofthe feedback network is given in the following

119867(119904) =119861 (119904)

119881119900(119904) (3)


Variable speedVgen

120596SG

Currentlimiter

PPF

Control signal

Zgminus1 IgrVgr

IfrY

Y

Δ

TRU


VP

minus

minus

+

minus

+

+ minus+

VN

VDCPI

RefTri

Sat

IΔminusr


Iload

IcCDC


IiaminusY

IiaminusΔY

YΔ

Iinv IiaLf

LfLf

RfRfRf

VcaVcb

Vcc

CfCfCf

RfRfRf

Iin-CV

minus

+

minus

minus

+

+

VDC

r i L

Lcicrc

VCV

Vcc

iCV

icc

ifv

ifc

C

Cc

CV-TVL

CC-TVL

CP-TVL

IM

RL

Rt

Rt

Rt

Iin-cc

Iin-cp VDC

VDC




I1a

Cp

ifp

rp ip Lp

Vcp

icp

PF = 085

I998400gr

115Vrms 400Hz


+

minus

Controlsignal

+

+ minus

TriError

signals+

1

Tis

VDC

Vref

Vf

Kp


Compensationnetwork

PWMmodulation

Feedback signal

Transferfunction

ref (s)

B(s)

minus

+ E(s)Gc(s)

Vc(s) Gm(s)

H(s)

d(s)Gd(s)

o(s)




119866V119889 (119904) =119881119900(119904)

119889 (119904)=

119881119892

119871CV119862V1199042 + 119871CV (119877119905 + 119903V) + 1

(4)





119866119900(119904) = 119866

119898(119904) 119866V119889 (119904)119867 (119904) (5)






inverter 119894119871119886 119894119871119887 and 119894


119900119886 119880119900119887 and


119886 119894119887 and 119894




119871119889119894119871119889

119889119905= 119880119889minus 119880119900119889minus 120596119871119894

119871119902

119871

119889119871119902

119889119905= 119880119902minus 119880119900119902minus 120596119871119894

119871119889

119862119889119880119900119889

119889119905= 119894119871119889minus 119894119889minus 120596119862119880

119900119902

119862

119889119880119900119902

119889119905= 119894119871119902minus 119894119902minus 120596119862119880

119900119889

(6)


IM

RL

ia

ib

ic

L

L

L

C C C

RfRfRf

iLa

iLb

iLc

Y

Y

Δ

115V 400HzIia-Y

Iia-Δ


Iinv Ua

Ub

Uc

SPWMmodulation

dq

dq dq

abc

abc abc

PIcontrol

Iabc

120579s 120579s

120579sId

Iq

Idlowast

Iqlowast

Uoabc

Ud Uqfs

Reference

PLL

signals

PIcontrol

minus



[

119880119889

119880119902

] = radic2

3119862 [119880119886119880119887119880119888]119879

[radic3

21198801198980]

119879

(7)

119862 =[[[

[

cos120596119905 cos(120596119905 minus 23120587) cos(120596119905 + 2

3120587)


3120587)

]]]

]

(8)

In (7) 119880119898





0 0002 0004 0006 0008 001minus350minus282

minus200

minus100

0

100

200

282350

Time (s)

(V)






0 005 01 015 02 025 03 0350

100

200270300

Time (s)

(V)

(a)

0 0005 001 0015 002 0025 003 0035 004

240

260

280

Time (s)

(V)

(b)

019 0195 02 0205 021 0215 022265

270

275

280

Time (s)

(V)

(c)


0 005 01 015 02 025 03 035

0

10

20

2835

Time (s)

(V)

(a)

0 005 01 015 02 025 03 0350

1

2

3

4

5

Time (s)

(A)

(b)








1= 02 s half





0= 005 s to 119905

1= 02 s as shown





0 005 01 015 02 025 03 0350

10

20

30

40

Time (s)

(A)

(a)

001 0012 0014 0016 0018 00229

295

30

305

31

Time (s)

(A)

(b)

019 0194 0198 0202 0206 021295

30

305

Time (s)

(A)

(c)


(V)

0 005 01 015 02 025 03 0350

50100

15812

2236250

Time (s)

(a)

0 005 01 015 02 025 03 0350

10

22353162

405060

Time (s)

(A)

(b)

0 005 01 015 02 025 03 0350

357

10

Time (s)

(kW

)

(c)






5 Conclusions



0 001 002 003 004 005minus200minus162

minus100

minus50

050

100

162200

Time (s)

(V)





Acknowledgments


References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Variable speedVgen

120596SG

Currentlimiter

PPF

Control signal

Zgminus1 IgrVgr

IfrY

Y

Δ

TRU


VP

minus

minus

+

minus

+

+ minus+

VN

VDCPI

RefTri

Sat

IΔminusr


Iload

IcCDC


IiaminusY

IiaminusΔY

YΔ

Iinv IiaLf

LfLf

RfRfRf

VcaVcb

Vcc

CfCfCf

RfRfRf

Iin-CV

minus

+

minus

minus

+

+

VDC

r i L

Lcicrc

VCV

Vcc

iCV

icc

ifv

ifc

C

Cc

CV-TVL

CC-TVL

CP-TVL

IM

RL

Rt

Rt

Rt

Iin-cc

Iin-cp VDC

VDC




I1a

Cp

ifp

rp ip Lp

Vcp

icp

PF = 085

I998400gr

115Vrms 400Hz


+

minus

Controlsignal

+

+ minus

TriError

signals+

1

Tis

VDC

Vref

Vf

Kp


Compensationnetwork

PWMmodulation

Feedback signal

Transferfunction

ref (s)

B(s)

minus

+ E(s)Gc(s)

Vc(s) Gm(s)

H(s)

d(s)Gd(s)

o(s)




119866V119889 (119904) =119881119900(119904)

119889 (119904)=

119881119892

119871CV119862V1199042 + 119871CV (119877119905 + 119903V) + 1

(4)





119866119900(119904) = 119866

119898(119904) 119866V119889 (119904)119867 (119904) (5)






inverter 119894119871119886 119894119871119887 and 119894


119900119886 119880119900119887 and


119886 119894119887 and 119894




119871119889119894119871119889

119889119905= 119880119889minus 119880119900119889minus 120596119871119894

119871119902

119871

119889119871119902

119889119905= 119880119902minus 119880119900119902minus 120596119871119894

119871119889

119862119889119880119900119889

119889119905= 119894119871119889minus 119894119889minus 120596119862119880

119900119902

119862

119889119880119900119902

119889119905= 119894119871119902minus 119894119902minus 120596119862119880

119900119889

(6)


IM

RL

ia

ib

ic

L

L

L

C C C

RfRfRf

iLa

iLb

iLc

Y

Y

Δ

115V 400HzIia-Y

Iia-Δ


Iinv Ua

Ub

Uc

SPWMmodulation

dq

dq dq

abc

abc abc

PIcontrol

Iabc

120579s 120579s

120579sId

Iq

Idlowast

Iqlowast

Uoabc

Ud Uqfs

Reference

PLL

signals

PIcontrol

minus



[

119880119889

119880119902

] = radic2

3119862 [119880119886119880119887119880119888]119879

[radic3

21198801198980]

119879

(7)

119862 =[[[

[

cos120596119905 cos(120596119905 minus 23120587) cos(120596119905 + 2

3120587)


3120587)

]]]

]

(8)

In (7) 119880119898





0 0002 0004 0006 0008 001minus350minus282

minus200

minus100

0

100

200

282350

Time (s)

(V)






0 005 01 015 02 025 03 0350

100

200270300

Time (s)

(V)

(a)

0 0005 001 0015 002 0025 003 0035 004

240

260

280

Time (s)

(V)

(b)

019 0195 02 0205 021 0215 022265

270

275

280

Time (s)

(V)

(c)


0 005 01 015 02 025 03 035

0

10

20

2835

Time (s)

(V)

(a)

0 005 01 015 02 025 03 0350

1

2

3

4

5

Time (s)

(A)

(b)








1= 02 s half





0= 005 s to 119905

1= 02 s as shown





0 005 01 015 02 025 03 0350

10

20

30

40

Time (s)

(A)

(a)

001 0012 0014 0016 0018 00229

295

30

305

31

Time (s)

(A)

(b)

019 0194 0198 0202 0206 021295

30

305

Time (s)

(A)

(c)


(V)

0 005 01 015 02 025 03 0350

50100

15812

2236250

Time (s)

(a)

0 005 01 015 02 025 03 0350

10

22353162

405060

Time (s)

(A)

(b)

0 005 01 015 02 025 03 0350

357

10

Time (s)

(kW

)

(c)






5 Conclusions



0 001 002 003 004 005minus200minus162

minus100

minus50

050

100

162200

Time (s)

(V)





Acknowledgments


References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










IM

RL

ia

ib

ic

L

L

L

C C C

RfRfRf

iLa

iLb

iLc

Y

Y

Δ

115V 400HzIia-Y

Iia-Δ


Iinv Ua

Ub

Uc

SPWMmodulation

dq

dq dq

abc

abc abc

PIcontrol

Iabc

120579s 120579s

120579sId

Iq

Idlowast

Iqlowast

Uoabc

Ud Uqfs

Reference

PLL

signals

PIcontrol

minus



[

119880119889

119880119902

] = radic2

3119862 [119880119886119880119887119880119888]119879

[radic3

21198801198980]

119879

(7)

119862 =[[[

[

cos120596119905 cos(120596119905 minus 23120587) cos(120596119905 + 2

3120587)


3120587)

]]]

]

(8)

In (7) 119880119898





0 0002 0004 0006 0008 001minus350minus282

minus200

minus100

0

100

200

282350

Time (s)

(V)






0 005 01 015 02 025 03 0350

100

200270300

Time (s)

(V)

(a)

0 0005 001 0015 002 0025 003 0035 004

240

260

280

Time (s)

(V)

(b)

019 0195 02 0205 021 0215 022265

270

275

280

Time (s)

(V)

(c)


0 005 01 015 02 025 03 035

0

10

20

2835

Time (s)

(V)

(a)

0 005 01 015 02 025 03 0350

1

2

3

4

5

Time (s)

(A)

(b)








1= 02 s half





0= 005 s to 119905

1= 02 s as shown





0 005 01 015 02 025 03 0350

10

20

30

40

Time (s)

(A)

(a)

001 0012 0014 0016 0018 00229

295

30

305

31

Time (s)

(A)

(b)

019 0194 0198 0202 0206 021295

30

305

Time (s)

(A)

(c)


(V)

0 005 01 015 02 025 03 0350

50100

15812

2236250

Time (s)

(a)

0 005 01 015 02 025 03 0350

10

22353162

405060

Time (s)

(A)

(b)

0 005 01 015 02 025 03 0350

357

10

Time (s)

(kW

)

(c)






5 Conclusions



0 001 002 003 004 005minus200minus162

minus100

minus50

050

100

162200

Time (s)

(V)





Acknowledgments


References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 005 01 015 02 025 03 0350

100

200270300

Time (s)

(V)

(a)

0 0005 001 0015 002 0025 003 0035 004

240

260

280

Time (s)

(V)

(b)

019 0195 02 0205 021 0215 022265

270

275

280

Time (s)

(V)

(c)


0 005 01 015 02 025 03 035

0

10

20

2835

Time (s)

(V)

(a)

0 005 01 015 02 025 03 0350

1

2

3

4

5

Time (s)

(A)

(b)








1= 02 s half





0= 005 s to 119905

1= 02 s as shown





0 005 01 015 02 025 03 0350

10

20

30

40

Time (s)

(A)

(a)

001 0012 0014 0016 0018 00229

295

30

305

31

Time (s)

(A)

(b)

019 0194 0198 0202 0206 021295

30

305

Time (s)

(A)

(c)


(V)

0 005 01 015 02 025 03 0350

50100

15812

2236250

Time (s)

(a)

0 005 01 015 02 025 03 0350

10

22353162

405060

Time (s)

(A)

(b)

0 005 01 015 02 025 03 0350

357

10

Time (s)

(kW

)

(c)






5 Conclusions



0 001 002 003 004 005minus200minus162

minus100

minus50

050

100

162200

Time (s)

(V)





Acknowledgments


References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 005 01 015 02 025 03 0350

10

20

30

40

Time (s)

(A)

(a)

001 0012 0014 0016 0018 00229

295

30

305

31

Time (s)

(A)

(b)

019 0194 0198 0202 0206 021295

30

305

Time (s)

(A)

(c)


(V)

0 005 01 015 02 025 03 0350

50100

15812

2236250

Time (s)

(a)

0 005 01 015 02 025 03 0350

10

22353162

405060

Time (s)

(A)

(b)

0 005 01 015 02 025 03 0350

357

10

Time (s)

(kW

)

(c)






5 Conclusions



0 001 002 003 004 005minus200minus162

minus100

minus50

050

100

162200

Time (s)

(V)





Acknowledgments


References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 001 002 003 004 005minus200minus162

minus100

minus50

050

100

162200

Time (s)

(V)





Acknowledgments


References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article modeling and simulation of power

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