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The 30th Annual Conference of the IEEE Industr ial Electronlcs Society, November 2 - 6,2004, Busan, Korea

Modeling of Multi-Converter More Electric Ship Power Systems usingthe Generalized State Space Averaging MethodMadan M. Jalla, Ali Emadi2,Geoffrey A. Williamson3,and Babak Fahimi4

*,adan M. Jalla, Ali Em adi, and Geoffrey A. Williamson, Electric Power and Power E lectronics Center,Electrical andComputer E ngineering Department, Illinois Institute of Technology, C hicago, IL 60616-3793,USA,Phone: +1/(3 12)567-8940, Fax: +1/(3 12)567-8976, e-mail: emadi@)iit.eduBabak Fahimi, E lectrical and Com puter Engineering Department, University of Missouri-Rolla, Rolla, MO 65409-0040,USA, Phone: +1/(573)341-4552, Fax: +1/(573)341-6771, e-mail: fahimi@umr.eduAbstruc+Based on the more electric ship (MES) oncept,conventional mechanical hydraulic, and pneumatic powertransfer systems are replaced by electrical systems in differentsea vehicles. Considering different levels of powerrequirements o f various electrical loads and for theachievement o f compact, light, safe, a n d efficient powersupplies, implementation o f multi-convertcr power electronicsbased power systems is the most feasible option in the

developmentof advanced navy vehicles. This paper presents amodu lar approach for the m odeling and simulation of m ulti-converter MES power systems based on the generalized statespace averaging method. MES power systems may consist o fmany individual converters connected togeth er to form largeand complex systems. In addition to simplifying the analysisprocedure, by using the proposed method, time step forsnaIysis of the system can be increased. Therefore, requiredcomp utation time and com puter memory for complex systemscan be reduced considerably. In this paper, after introducingthe proposed approach, r es u l t s of applying the method to arepresentative system are presented. E xperimentaI results arealso provided to verify the pro posed technique.I. l 0 D U C n O N

Navies utilize surface combatants an d aircraft carriers assea vehicles and submarines as undersea vehicles.Traditionally, segregated power system (SPS)configurations have been used in these types of vehicleswhere separate prime movers are used to supply power tothe propulsion system through geared drives, whichconsume almost 80-90% of th e total power [l], [2]. Theprime mo vets are also used to drive generators. Generatorssupply power to the electrical distribution systems thatcontain transformers, switchboards, and circuit breakers tosupply power to various electrical loads such as ship serviceand combatant loads. However, this type of power systemconfiguration has proved inefficient, as the high-speedpropulsion is not always the prime requirement of thesevehicles. Therefore, tactical diversion of this surplusmechanical power to electricity was needed for theprocurement of all distinct advantages of th e more electricship (MES) approach. In recent sea vehicles,implementation of integrated power system (IPS)configurations has brought revolution, where, as shown inFig. I , a common set of generators is used to supply powerto ship service and combatant loads as well as electricpropulsion systems [ I ] .This configuration has improvedfuel efficiency of these vehicles for different ranges ofspeed while ensuring quieter operation. IPS has also m ade

the modular equipment approach more realistic. As shownin Fig. 1, the power electronic interface contains modularhigh or medium power AC or DC converters with inbuiltcontrol assemblies that handle high generated electricalpower. These converters supply power to main AC or DCbus in sea vehicles via isolation transformers and generatorswitchboards (SBs). Power conversion and distributionsystem contains multiple interconnected power electronicconverters and inverters working in individual modules.

*%e c-U s*cm-F eig. 1. Integrated DC ower system.In these systems, due to interconnections betweendifferent converters, a large variety of dynamic interactionsis possible. If the system is defined as a large-signal model,as is required for the system level studies, linearized statespace models are invalid 131. Time domain simulation ofnon-linear time-varying system modules, which includes

the protection circuitry, system control dynamics, andlimitations, m ust be used for accuracy of t he overall systemperformance simulation. Transient simulations usingswitching models of power electronic converters requirevast computer resources and long simulation times [4], [5].Conventionally, averaging techniques are used formodeling of these systems. The averaged model runs muchfaster than the comparable switching model and does notrequire excessive computer resources [ 5 ] - [ 111 . However,rapid and large-signal dynamics cannot be followed by theaveraging methods. Therefore, we use a generalized methodin which we consider the average of the state variables aswell as the harmonics.

0-7803-8730-9/04/$20OOa2004 EE E508

mailto:emadi@)iit.edumailto:fahimi@umr.edumailto:fahimi@umr.edumailto:emadi@)iit.edu

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11. GENERALIZEDTATE SPACE AVERAGING METHODGeneralized state space averaging method [12], [I31 is

based on the fact that the waveform x ( t ) can beapproximated with arbitrary precision in the (t-r t] rangeby the Fourier series:

k - nwhere

In relation (I) , the value of n depends on the requireddegree of accuracy, and if n approaches infinity, theapproximation error approaches zero. If we only considerthe term K=O,we have the same state space averagingmethod [SI. If a state variable does not have an oscillatingform and is almost constant, we only use the term (K4).Also, if a state variable only has an oscillating form similarto a sine wave, we use the terms K=-1 , I . This method isnamed first harmonic approximation. In addition, if a statevariable has a DC coordinate, also has an oscillating form,we use the terms K =-I , O , l . However, more terms weconsider, more accuracy we have.Selection of T for modelling of each converter is veryimportant, which should be considered carefully. Forinstance, it is switching period in DC/DC converters andmain wave period of the output voltage in DCiAC inverters.Th e k ( t ) is complex Fourier coefficient. TheseFourier coeficients are functions of time since the intervalunder consideration slides as a function of time. Theanalysis computes the time-evolution of these Fouriercoefficients as the window of length T slides over the actualwaveform, Our approach is to determine an appropriatestate space model in which the coefficients (2) are the statevariables.In this paper, through the application of generalized statespace averaging method, we present a modular approach forthe modelling of multi-converter ME S power systems [3].The converters and subsystems of the system aremodularised and subsequently interconnected to form thecomplete system. Modularising the system into convertersand subsystems has several advantages: 1) converters andsubsystems models can be used in different systems, 2) itreduces the complexity of modelling large systems bymodelling a less complex subsystem, 3) the proposedmodels can be verified w ith manageab le test conditions.

; Otherloadsofthe Source Converter

Converter

Converter

ResistiveLoads

Each converter receives its voltage source from th epreceding converter along with other converters in thestage, and supplies outputs to the following load convertersno. 1, ..,N, in addition to resistive toad s represented all byresistance R [3].We suppose that the converter of Fig. 2 is a PW MD C D C buck, boost, or buck-boost converter op erating incontinuous conduction mode, with switching period T andduty cycle d. To apply the generalized state space averagingmethod, first a commutation function u ( t ) is defined as1,O

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By applying the time derivative property of the Fouriercoefficients n (4).

-Converter Module(CM1)ConverterModule (CMZ)ConverterModule (CM3)ConverterModule (CM4)ConvetterModule (CM5)ConverterModule(CM6)DCiDC Load ~ n v e r t e rcpL)DC/AC Load Inverter (MC)

inverter Module (IM)

One comes to

Buck ConverterBuck ConverterBuck ConvenerBuck ConverterBufk ConverterBuck ConverterBuck Converterwith HysteresisControl3-Phase nvmer3-Phaw Inverterwith RL b a d

Bairk

0 0 1

where i . is the input current of the load converter #j andR is the resistive load of the converter. Equations (9)-(I I )arc the generalized state space averaged modelof he buckconverter.

1nJ

u t . ANALYSIS OFTHE REPRESENTATIVE SYSTEMThe US. Navy strategy for power on surface ships isembodied in the Electric Ship concept based on the trend

toward more electric in commercial industry and utilities[ I ] , 121, [ l S ] , [IS]. The basic premise is, the use ofelechicpower as the primary medium or energy transfer aroundthe ship, with conversion to !he appropriate energy form atthe user equipment. Navies have been doing extensiveresearch for implementing DC zonal electrical distributionsystems in sea an d undersea vehicles. As shown in Fig. 4,in this type of distribution system, AC power is rectifiedfrom a high power AC bus to DC at the voltage levels of500-600V via three-phaseboost rectifiers to supply powerto main DC bus (either port bus or starboard bus). Then, thevoltage at the main bus is stepped down to 400-420 Vthrough DC/DC buck converters. The power conversionmodules (PCM) act as buffers between main DC bus andvarious zones separated by watertight bulkheads to supplysingle and three-phase inverters and other DC loads atsuitable vottages. The power distribution modules (PDM)consist of single and three-phase inverters, which supplyAC loads. A solid-state frequency changer is used to supplypower at 400Hz frequencies for gyros, radar, sonar, and

weaponry systems. These power conversion anddistribution modules can actively control the couplingsbehveen various parts of the system and, thus, manage toisolate and prevent propagation of fault. In this paper, wepresent a representative system, which is consistentwth thepractical multi-converter ME S power electronic systems.Then, we study the dynamics associated with the multi-converter environment in this system.

w

LY'. Y"Fig.4. A represeniativemulti-convekerMES ower electronic system.Fig. 4 shows the concept of a representative system.This system Is a hybrid system with main DC distributionsystem. AC loads are feeding from the main AC bus, whichisprovided by DC/AC inverters, Th e load convertersalongwith the loads are assumed ideal consrant power loads asshown in Fig. 4. Tables I & II show the bus voltages andthe type of power eIec!xonics converters for therepresentative system of Fig. 4, respectively.

TABLE IBUS VOLTAGEOF THE REPRESEUTATWESYSTEM

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of the load converter to reduce the ripples. It is assumedthat the starboard bus is out of service due to a fault an dremainder of the system is fed from the port power supply.All the loads are operating at the capacity listed in Table111.

+ - . - ; ~ - + ~ m ? + ~ ~m POAm

Fig. 5 . Interconnectingconstantpower and constant voltage loads toconverter module.TABLE 111LOAD PARAMETERS

Iv. MODELINGOF TH E mPRESENTATIYESYSTEMThe representative system of Fig. 4wa s analyzed by theproposed method. If the first- order approximation is used,the corresponding model matrix ha s twelve real state spacevariables for the converter module in Fig. 5 . The unified set of circuit state variable equations, incontinuous conduction mode of operation, is obtained byapplying (3) to the four sets of top~logicalcircuit statespace equations for the converter in Fig S.

Using the first-order approximation to obtain iLl, iL2,V C ~ndv,, we have twelve real state variables as belowo=xl, i,,>,=X,+jx,

Since i L l , iLz, Clan d v, are real,

The circuit state variables are calculated and given byiLl xl 2 x , C o s o t - 2 x 6 S i n o tvc , =xz+2x7Cosw - x8SinmiLz x 3+2 ~ ~ C o s w t - 2 x , , S i n o tv , =x4+~ X , ~ C U S O- xl,Sinw tAssuming low voltage rippIes compared to the averagevalue at the output DC bus, zero and first harmonics of thenonlinear term (1 /vo) an be written as

(15)

>=- 1vo x4

Using equations (31, (S), (12), (13), {14) an d (16), statespace equations of the converter can be written as

Du e to nonlinear behavior of constant power loads, themodel of the system is nonlinear. After linearizing theequations (17) around the o perating point, linearized m odelof the system can be expressed as

1 0 00

5 11

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The acquired outputs of this method along with theresults of the exact topological models of the system havebeen shown in Fi g 6 and Fi g 7. These are steady statewaveforms of voltages of bus #1,2 and 3 and inductorcurrent of converter modules 1 and 3.

I.I.* I l l l , 1 1 2 , , 1 1 1 , a . . I . I1.11 I 1 1 1 1 I * , " I 1 .111 , 1 1 1 . ..SI

TI." . 5 m c ,Fig. 6. Voltage simulationof the steady state operation by the exacttopoIogical models (solid line) and generalized state spaceaveragingmethod (dotted line).

1 . ,

I, . E l , . . * I , H I , 1 .111 1 .r.. ... , I L 1 1 . , 1 1 1 1 I I r l . , , E l . a 1 1 1

TI,". [ S . L IFig. 7 . Current simulation of the steady state operationby the exacttopological models (solid line) an d generalized state space averaging

method (dotted line).v. EXPEFU"TAL VEruPICATION

In th e experimental system of Fig. 8, there are twopower supplies (PSI an d PS2), one of which feeds the portbus and the other one feeds the starboard bus (only oneconnection is active at a time). There are three zones of DCdistribution. Each zone is fed by a converter module (CM)on the port bus (CMI , CM2, or CM3) and a converter

module on the starboard bus (CM4, CM4, or CM5)operating from one of th e two distribution busses. Diodesprevent a fault from one bus being fed by the opposite bus.The converter modules feature a droop characteristic so thatthey share power. The three loads consist of an invertermodule (IM) that, in turn, feeds an AC load bank (LB), amotor controller @IC), and a generic constant power load(CPL).Port Bus

StarboardBusFig. 8. Naval combat survivability DC distributiontest setup

Figs. 9 and 10depict the performance of the test systemfor hrro cases. Variables depicted include port bus voltage,zone 1 voltage (voltage at input to IM), zone 2 voltage(voltage at input to MC), and zone 3 voltage (voltage atinput to CPL). Initially, the parameters are those for Case I .

Fig.9.Measured syste m perfommce or Case 1.-U f

'& s i .a .I .I .I

H I e .IS .y br

w . - - t w - -..-5r c iFig 10 Measured system performance fo r Case 2

As can be s een, the waveforms are constant, aside fromthe switching induced ripple. Approximately, one-half ofthe way into the study, the parameters are changed to match

512

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Case 2. It should be observed that this change of parametersdoes not change the steady-state operating point.Comprehensive comparison between the simulation andexperimental results will be provided in the full version ofthe paper.

VI. CONCLUSIONSIn this paper, modelling and simulation of multi-converter MES power electronic systems have beenpresented. A modular modelling approach based on thegeneralized state space averaging technique has been usedto build large-signal models. In addition, the representativesystem was f 3 l y analysed by the proposed method.Simulation results were compared to the exact topological

state space model and to the well-known state spaceaveraging method. Furthermore, a detailed analysis waspresented regarding the influence of different parameters,such as switching frequency and duty cycle, on the m ovingaverage and harmonics obtained from the generalized statespace averaging method. Since this method can provide aunified time-invariant, large-signal state space model of theconverters, a software package like Matlab can be used forcontroller design and stability analysis. The modelsobtained in this paper can be used for stability assessmentand controller design for multi-converter MES powerelectronic systems.

ACKNOWLEDGEMENTWe would like to gratefully acknowledge the support ofthe Electrical and Computer Engineering Department of theUniversity of Missouri-Rolla in providing us the access tothe experime ntal test setup.

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