Stochastic Modeling of Integrated Power Systemcoupled to Hydrodynamics in the All-Electric Ship

P. Prempraneerach∗†, J. Kirtley¶, C. Chryssostomidis∗§, M.S. Triantafyllou∗, andG.E. Karniadakis∗‡

∗Department of Mechanical Engineering¶Department of Electrical Engineering and Computer Science

Massachusetts Institute of Technology, Cambridge, MA, USA 02138†Department of Mechanical Engineering

Rajamangala University of Technology Thunyaburi, Pathumthani, Thailand 12110‡Division of Applied Mathematics

Brown University, Providence, RI, USA 02912§Corresponding author

Abstract— In the paper, we model the integrated power sys-tem (IPS) of a typical destroyer ship coupled to hydrodynamics.This IPS is composed of a 21MW, 3-phase synchronous generatorsupplying electric power to 4160 V AC bus and to a 19 MW, 15-phase induction motor driven by an indirect rotor field orientedcontrol for the motor torque. Moreover, stochastic responses areexamined when there exists a variation in the induction motor’srotor resistance and a disturbance from the slowly-varying addedresistance, derived from a Pierson and Moskowitz sea spectrum.

Index Terms– Hydrodynamics, Marine vehicle power systems,Induction motor drives, Stochastic differential equations

I. INTRODUCTION

In the All-Electric Ship (AES) architecture, the powersharing between the propulsion units and the high-powerequipment, especially under heavy propulsion demands andcasualty conditions, has recently been identified as an impor-tant issue [2], [14], [17]. In the new AES configuration, thereis an increasing demand for electric power for ship systemautomation, electrical weaponry, electric propulsion, and shipservice distribution. About 70% to 90% of power from thegenerator units in the fully integrated power system (IPS) isconsumed in the propulsion systems [2]. Therefore, when alarge power demand is imposed on an electrical bus during amission or life critical situation, the power distribution mustbe optimally modified to yield the most efficient power usageand to maintain continuity of service [17].

This complex problem is compounded by the sea stateswhich are unpredictable, leading to stochastic time-varyingpropulsion loads. It is, therefore, challenging for the electricship designer to thoroughly investigate interactions betweenmachines, power electronics, and uncertain sea conditions.To date there have been no published papers that accountfor dynamic interactions of propeller and ship hydrodynamicswith a large-scale shipboard IPS. In this paper, we developmodels of the IPS and the propeller coupled to random wavedynamics and ship motion. In the following, we present some

details of the system that we model, the technical approach,and first results.

II. SYSTEM MODELING

To investigate the influence of the propeller loading onthe AC propulsion and power generation in the electric ship,modeling of both power systems and hydrodynamics of shipand propeller must be introduced. In our study, the IPS issimilar to the model described in [16] for a ship like theDDG51 destroyer. In summary, the main AC subsystem ofthis IPS consists of a 21 MW, 3-phase, 60Hz SynchronousMachine (SM) as a generator and a close-loop drive usingthe indirect rotor field oriented control of 19 MW, 15-phaseInduction Machine (IM) as a propulsor. The generator suppliesthe voltage to the 3-phase/4160V AC distribution bus, whichmust be filtered by a harmonic filter before connecting tothe induction motor drive. The detailed derivation of machineequations can be found in [12] and [16]. A power converterand the Indirect Field Oriented Control (IFOC) using thesine-triangle modulation technique for a current regulator areincorporated into the propulsion system to control the torqueof the induction machine. According to [6], IFOC employs aninner loop with a current feedback from IM and an outer loopwith IM’s shaft angular velocity feedback for computing themachine rotational angle in the IFOC. The IPS configurationconsidered in this study is shown in Figure 1, and two suchidentical systems are used in the ship we model.

A. Hydrodynamics

The propeller model, used in this study, is based on a fixed-pitch, non-ducted Wageningen B-screw series propeller [1].Several effects, such as fluctuation of in-line water inflow,ventilation, and in-and-out-of water effects [11], can cause areduction in the propeller thrust and torque from its nominaloperating condition. Both the in-line water inflow variationand the in-and-out-of water effects directly affect the propellerloading. To model the wave effects, first, we assume that

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Prime Mover(Ideal)

Exciter

Vs

3-phase, 4160 VAC Distribution Bus

IMSMPower Converter

With Torque Control

T*e

Is

rm

15-phase, 0-15 Hz19MW

3-phase, 60 Hz21 MW

Harmonic Filter

Fig. 1. A one-line diagram of the AC power generator and power distributionwith the closed-loop torque control of the induction machine. Two identicalsuch systems are installed in the ship we model.

TABLE I

SPECIFICATIONS OF THE DDG-51 ARLEIGH BURKE-CLASS.

Parameters full-scale DDG-51

Length [m] 153.90Draft [m] 9.45Beam [m] 20.12

Displacement [tons] 8,300Speed [knot] 31

Propeller Diameter [m] 5.20Propulsion Power [hp] 100,000

nonlinear and viscous effects are small compared to waveinertia for a ship motion in the sea. Moreover, we assume deepwater random waves, modelled through the one-parameterPierson and Moskowitz spectrum [5], derived on the basisof North Atlantic data and described by the significant waveheight, H1/3, and modal frequency, ωm.

To model ship hydrodynamics, we must consider the inter-action between the propeller and ship hull because the wakecreated by the hull modifies the propeller advance velocity(Va) with Va = (1−w)U , where U is the ship speed. The wakefraction (0 < w < 0.4) [8] indicates the velocity reductiondue to the wake. Moreover, the presence of the propeller atthe stern also increases the drag force on the vessel; thus,the propeller thrust must be decreased by a factor (1 − t),where t is the so-called ”thrust deduction” factor to accountfor the difference between the self-propelled and the towed-model resistance.

The specifications of the full-scale USS DDG-51 ArleighBurke-class [7], driven by the electrical propulsor, are givenin Table I. This full-scale ship is employed in the ship hydro-dynamics calculations for calm water and added resistances,and for propeller performance.

In this study, we consider only the surge motion of the elec-tric ship, driven by two propellers connected to two identicalIPS’s, in head sea. The ship’s motions in other directions i.e.,sway, heave, roll, pitch, and yaw are assumed to be small inthis study. Thus, the equation of ship motion with the inductionmotor directly driven the propeller can be described as:

(M + Ma)dU(t)

dt= 2(1 − t)Tp(n, U) − R(U) (1)

−RAR(U) − R2nd−AR(U, t),

Jsdωr(t)

dt= Te − Qp(n, U)ηbηr, (2)

where n denotes the revolution per minute of the propeller,n = ω ∗ 30/π, and M and Ma are the ship mass and addedmass in the surge direction, respectively. The rotational inertia,Js, includes the IM rotor and propeller inertia; also, Tp andQp are the propeller open-water thrust and torque, respec-tively, i.e., Tp = KT (J)ρn2D4 and Qp = KQ(J)ρn2D5,where J = Va

nD is the advance velocity. The KT and KQ

are thrust and torque coefficients of the propeller, while η b

and ηr denote the bearing and propulsive efficiency. Thedrag force, R, corresponds to the calm-water resistance; itcan be found from the non-dimensional drag coefficient,CD(Re, Fr), as R = CD

12ρSU2 where S is the wetted

surface area. The drag coefficient CD [5] is composed of africtional resistance coefficient (CF (Re)) and a residual resis-tance coefficient (CR(Fr)), where Re and Fr are Reynoldsand Froude numbers, respectively. The added resistance, RAR,is associated with the involuntary speed reduction due to thewaves. Assuming that the added resistance is the second-order nonlinear system, obeying the properties of quadraticsystems, the slowly-varying added resistance can be separatedinto two major components: mean or steady second-order force(RAR) (the first term) and slowly-varying second-order force(R2nd−AR) (the second term), given by:

RAR = RAR − R2nd−AR (3)

RAR =12

N∑k=1

(Ak)2H(ωk,−ωk) +

12

N∑k=1

N∑l=1

Re{AkAlH(ωk, ωl)ei[Δωt+Δφ]} (4)

where Δω and Δφ are ωk − ωl and φk − φl. Ak,l andφk,l are wave amplitudes and independent random phasesvarying between (0, 2π), respectively, corresponding to thewave frequency ωk,l. Note that Ak can be calculated fromthe one-side sea spectrum (S+(ω)) by discretizing S+(ω)into N equally intervals. Then, A2

k = 2∫ ωk

ωk+1S+(ω)dω for

k ∈ 1, ..., N . H(ωk, ωl) represents the second-order transferfunction of hydrodynamics force. The response amplitude ofthe steady force normalized by the wave amplitude squared isdenoted by R(ω); therefore, R(ω) is assumed to be equal to12H(ωk,−ωk). According to [10], the mean added resistanceis obtained from R(ω), and it is computed from the MIT5DCode [4]. For the slowly-varying added resistance, H(ωk, ωl)can be approximated as 2R( ωk+ωl

2 ). From Newman’s approx-imation [9], R2nd−AR is associated with the diagonal termsof H(ωk, ωl) if the difference of two frequency wave, ωk andωl, are very small, e.g., |ωk − ωl| < 0.2.

B. Control of Induction Motor

The Indirect Field Oriented Control (IFOC) of the 15-phase induction motor drive requires an input torque command

564

(T ∗e ) and a desired rotor flux command (λe∗

dr) and outputssemiconductor signals, driving the H-bridge type inverters. Allparameters of the 15-phase induction machine are given inTable II. Because of multiple phases in the induction motor,the power converter topology must be separated into threefive-phase parallel rectifier-dc link-inverter paths. As a result,each five phase of the induction machine can be independentlycontrolled using the paralleling control. The dc voltage froma six-pulse uncontrolled rectifier (vrj ) in each path or rail (j)must be filtered with a low-pass LC circuit before propagatingto five ith H-bridges inverters for each phase. In each rail,the smoothed dc voltage (vdcj ) can be expressed by vdc =[vdc1 , vdc2 , vdc3 ] where j = 1, 2, 3. The phase of the ith H-bridge is determined so that the AC voltage of ith H-bridge isdisplaced by (i − 1)24◦ from the first phase. The current andvoltage of i-th phase of the induction machine can be denotedas isi and vsi . The switching state (si), obtained from theIFOC, determines the on/off state of each switch, as shownbelow:

si =

⎧⎨⎩

1 D1i and D4i on0 (D1i and D2i on) or (D2i and D4i on)−1 D2i and D3i on

(5)

In this study, maintaining the induction machine’s torqueat a specified level is the main objective of IFOC. Accordingto [16], this control technique must be stable, the current beconstrained below a maximum semiconductor current limit,the switching frequency be kept constant at 2 kHz, and theIFOC act as a torque transducer. Thus, the structure of the fieldoriented control, shown in Figure 2, consists of 6 main parts:a paralleling control, a torque limiter, a dc link stabilizingcontrol, a current limiter, a field oriented supervisory control,and a current regulator. Five-phase inverter-rail voltages arecontrolled by the three independent control architectures inthe IFOC. Although there might exist a negative impedanceinstability in the dc link due to the tight control of switchcurrent, the IFOC fast response can help stabilize the powerconverter.

5w_e

4

3

2

1

T*_e3 That*_e3

T*_e2 That*_e2

T*_e1 That*_e1

In1

In3

In4

In5

Out1

Out2

Out3

T*_e

Le*_dr

T*_e1

Le*_dr1

T*_e2

Le*_dr2

T*_e3

Le*_dr3

That*_e3Le*_dr3

V_dc3Le*_dr

ie*_qs3

ie*_ds3

That*_e2

Le*_dr2V_dc2

Le*_dr

ie*_qs2

ie*_ds2

That*_e1Le*_dr1

V_dc1Le*_dr

ie*_qs1

ie*_ds1

ih*_qs

i*_ds

wrm

T_e

we

Ie*_qs3

Ie*_ds3

Ihe*_qs3

Ihe*_ds3

Ie*_qs2

Ie*_ds2

Ihe*_qs2

Ihe*_ds2

Ie*_qs1

Ie*_ds1

Ihe*_qs1

Ihe*_ds1

[0; 0; 0]

(0 0 0)

(0 0 0)

6V3

5V2

4V1

3w

2

1

TorqueLimiter

TorqueLimiter

TorqueLimiter Link

StabilizingControl

LinkStabilizing

Control

LinkStabilizing

Control

CurrentLimiter

CurrentLimiter

CurrentLimiter

ParallelingControl

*eT

*edr

1dcV

2dcV

3dcV

*1eT

*2eT

*3eT

*edr1

*edr 2

*edr3

*ˆ1eT

*ˆ2eT

*ˆ3eT

*ˆeqsi 1

*ˆeqsi 2

*ˆeqsi 3

*ˆedsi 1

*ˆedsi 2

*ˆedsi 3

*eqsi 1

*eqsi 2

*eqsi 3

*edsi 1

*edsi 2

*edsi 3

FieldOrientedControl

rm

CurrentRegulator

e

e

sd

si

Fig. 2. The link stabilized and indirect field oriented controller. For detailedexplanation see [16].

In the balancing motor operation, a paralleling controlequally divides T ∗

e and λe∗dr into T ∗

ei and λe∗dri commands for

each rail. Then, T ∗ei and λe∗

dri generates the desired qd-axisstator currents in the link stabilizing controller. When oneinverter malfunctions, both T ∗

e and λe∗dr must be divided for

two operating inverter rails. However, both a magnitude and arate of change of the T ∗

ei command must be limited at specifiedlevels by the torque limiter. Furthermore, the rate of changeof the output T ∗

ei command is governed by a constant gain,K .

Similar to the field oriented control concept of 3-phase in-duction motor [6], the torque can be maximized by controllingthe rotor flux linkage vector perpendicular to the rotor currentvector. With this assumption, the desired qd currents (ie∗

qsi, ie∗dsi)

can be computed from the T ∗ei and λe∗

dr commands. Further-more, this link stabilizing control helps to solve the negativeimpedance instability, mentioned in [13]. Combing the desiredqd output currents from the link stabilizing control withthe mechanical rotor speed (ωrm), the synchronous referenceframe speed (ωe) can be calculated as ωe = ωs+ωr, where the

slip speed (ωs) equals to r′r

L′rr

∑3i=1 ie∗

qsi∑3i=1 ie∗

dsi

. Then, integrating ωe

provides the synchronous reference frame position (θ e) usedin the ith-phase to qd0αβ-frame transformation.

Before passing the ie∗qsi, i

e∗dsi to the current regulator, the

current must be limited at a prescribed range. The currentlimiter shows that a tight constrain of ie∗

dsi requires to maintainthe desired rotor flux level, which governs a proper fluxorientation; ie∗

qsi is more flexible.The last component of the IFOC technique is the current

regulator, generating the duty cycle (d) for the sine-trianglemodulation technique. The current regulator structure, shownin Figure 3, requires the desired qd current from the IFOCand the current feedback from the induction machine as wellas ωe, θe, and vdci . Because of the highly coupled circuits of15-phase induction motor in the qd reference frame, three q-axis rail currents ie∗qsi = [ie∗qs1

, ie∗qs2, ie∗qs3

] must be transformedto ie∗qsxyz

= [ie∗qsx, ie∗qsy

, ie∗qsz] in a xyz reference frame, so as

three d-axis rail currents. Therefore, the current control canbe done in xyz axis independently. The detailed derivation ofthe decoupled voltage equations can be found in [16]. Thisdecoupled transformation (ie∗qsxyz

= Tie∗qsi) can be written as:

T =

√23

⎡⎢⎣

1 − 12 − 1

2

0 −√

32

√3

21√6

1√6

1√6

⎤⎥⎦ . (6)

This T transformation is not orthogonal. In the balanceoperation, both ie∗qsxy

and ie∗dsxyare fixed at zero and the z com-

ponent equals to the corresponding i component. Therefore,the X-component current control, similar to the proportionaland integral controller with a nonlinear feedforward, can bedesigned. The difference in the desired and measured currentmust pass through a low-pass filter to eliminate the switchingnoise. Likewise, the Y -component current control has thesame structure except that different gains can be employed.

565

e

e

T

T

X- AxisCurrentControl

Y- AxisCurrentControl

Y- AxisCurrentControl

ZeroSequence

CurrentControl

qs1e*î qsx

e*î

qsye*î

ds1e*î

ds2e*î

ds3e*î

qs2e*î

qs3e*î

dsxe*î

dsye*î

dsze*î

T

T

qs1e*i

qs3e*iqs2e*i

qsxe*i

qsze*iqsye*i

ds1e*i

ds3e*ids2e*i

dsxe*i

dsze*idsye*i

ZeroSequence

Current

K5se

si

qsze*î

Zero SequenceVoltage Commands

qsxe*v

dsxe*v

qsye*v

dsye*v

qsze*v

dsze*v

T -1

K5se-1

T -1

qs1e*v

qs2e*v

qs3e*v

ds1e*v

ds2e*v

ds3e*v

1,4,7,10,13*v

2,5,8,11,14*v

3,6,9,12,15*v

dc1v1

dc2v1

d

dc3v1

Fig. 3. The decouple current regulator.

Nevertheless, in the normal operation, the gains of X- andY -component are identical. According to [16], even thoughthe qd voltage equations of the Z-component depend onboth stator current and rotor flux linkage, the same controlstructure is still applicable but some parameters must bemodified corresponding to the coupling in the rotor circuit.The proportional and integral gains of the Z-component mustbe adjusted independently of the XY -components.

The zero sequence (0, α, β) must be controlled closely tozero. However, the zero sequence is uncoupled from the qdaxis, thus only a proportional gain is used as the controller,written below:

v0αβsi =K0

τ0s + 1i0αβsi (7)

Note that the low-pass filter in the zero sequence control helpsfiltering out the switching noise from the measured motorcurrent such that the instability does not occur in the IFOCtechnique.

Using the sine-triangle modulation technique, the switchingfunction (si) can be obtained as follows,

si ={

1 if di ≥ ti−1 if di < ti

(8)

Then, the rail voltage can be computed as a function of s i andisi, hence:.

vsi =

⎧⎪⎪⎨⎪⎪⎩

vdcj − 2vt if si = 1 and isi ≥ 0vdcj + 2vt if si = 1 and isi < 0−vdcj + 2vt if si = −1 and isi ≤ 0−vdcj − 2vt if si = −1 and isi > 0

(9)

TABLE II

PARAMETERS OF THE 19 MW, 15-PHASE INDUCTION MACHINE [16] IN SI

UNIT SYSTEM

rs = 122mΩ Lls = 6.79mH Lm = 145mH

r′r = 35.7mΩ L

′lr = 7.62mH P = 12

TABLE III

PARAMETERS OF THE INDIRECT FIELD ORIENTED CONTROLLER FOR

15-PHASE INDUCTION MACHINE [16]

Te,lim = 403kNm Te,slew = 4.03MNm/s K = 100Is,lim = 1000A vdcb = 5618V τ = 20ms

Kpqx = 17.07V/A Kiqx = 306.6V/As Kpqz = 61.65V/AKpqy = 17.07V/A Kiqy = 306.6V/As Kiqz = 504.9V/A

τx = 0.2ms τy = 0.2ms τz = 0.2msK0 = 4.175 τ0 = 4ms λ∗

dr = 44V s

where j ∈ 1, 2, 3 and i ∈ 1, ..., 5. Also, the dc current of eachith H-bridge is given by

idchi ={

isi if si = 1−isi if si = −1 (10)

To simplify the inverter model, the fast average voltage(vqdsj ) and current (idcj ) of the inverter model in the non-overmodulated case can be expressed as:

vqdsj = vdcj dqdj (11)

idcj =52(dqsiqs + ddsids + 2(d0si0s + dαsiαs + dβsiβs)) (12)

III. FIRST RESULTS

The time-varying random sea spectrum is modeled as astochastic process, but in addition, we may consider manycomponents of the IM and SM as uncertain parameters. Tosimulate this coupled stochastic system, we use the proba-bilistic collocation method [12], according to which samplesare obtained at specific points in the parameter space definedby the roots of the orthogonal polynomials employed inthe representation of all stochastic fields. Therefore, if thegoverning equations become more complex, the simplicity ofcollocation framework, which involves only repetition runs ofdeterministic solvers, can further reduce the computationalcost compared to the Monte Carlo method in low- andmoderate-dimensional problems.

To demonstrate results of this coupled stochastic system,we first simulated the surge motion of the scaled electric shipexcited by the Pierson and Moskowitz spectrum with H 1/3 =20 m. The interaction between the ship speed, propulsion load,and electric machines’ states are examined for sea states 6,very rough sea [1]. Two identical IPS, as shown in Figure 1,with the torque control using the IFOC, directly connected tothe propeller, drive the 1DOF ship motion in head and randomseas. In this simulation study, we assume that initially two

566

induction motors are down, while the ship moves forward at20 knots and two generators operate near their steady-stateconditions. Then, after 2 seconds the two propulsion drivesare turned back on. The motor torque command of each IMis kept constant at 720,609.4 N-m.

The mean added resistance, about 331,700 N at 20 knots,and the slowly-varying added resistance of this electric shipare computed using the Newman’s approximation and theadded resistance response amplitude operator [9]. Thus, thepropellers driven by IPS experience the slow-varying forcefrom the added resistance. Figure 4, 5, 6, and 7 show thestochastic results of the machines’ responses and ship velocitywith the effect of the slowly-varying added resistance whenthe rotor resistance of the 15-phase induction motor is auniform random variable with ±20 variation from its nominalvalue. Particularly, Figure 4 illustrates the slowly-varyingadded resistance and the stochastic response of ship forwardvelocity upto 110 seconds while the responses of generator,bus, and motor approach the steady-state within 30 seconds,as shown in Figure 5, 6, and 7. Depending on the fluctuationof IM’s rotor resistance, stochastic responses of IM’s ψqds1

and ψqdr, IM’s torque, SM’s ψrqs and ψr

kd vary within a widerange. Hence, this shows a very strong interaction betweeneach generator and motor during the motor start-up transient.However, there is a minor effect on the ship surge velocitywith IM’s rotor resistance variation. Initially, the ship speedgradually decreases due to increasing added resistance as wellas small torque and thrust after turning on the propulsion drivewith constant torque command. Notice that the ship speedfluctuates at similar rate as the slowly-varying added resistancewith a phase delay.

10 20 30 40 50 60 70 80 90 100 110−3

−2

−1

0

1

2x 10

4

Slo

wly−

vary

ing

Add

ed R

es. [

N]

10 20 30 40 50 60 70 80 90 100 11010.15

10.2

10.25

10.3

Ush

ip [m

/s]

time [sec]

Fig. 4. Slowly-varying second-order added resistance experienced bythe ship’s surge motion (Upper Plot) and ship’s forward velocity (LowerPlot). Blue: mean solution; Red and Green: mean +/- standard deviation,respectively.

IV. SUMMARY

We have investigated the influence of hydrodynamic forceon the IPS in the full scale electric ship, particularly in thesurge motion. The results show that the added resistance fromthe random sea spectrum has a small effect on the ship forward

0 5 10 15 20 25 30−200

−100

0

100

200

Ψqsr

[V]

0 5 10 15 20 25 30

103Ψ

dsr [V

]

0 5 10 15 20 25 30−150

−100

−50

0

50

Ψkqr

[V]

0 5 10 15 20 25 30

103Ψ

kdr [V

]

0 5 10 15 20 25 30

103

Ψfdr

[V]

time [sec]0 5 10 15 20 25 30

−1

−0.5

0

0.5

1x 10

6

Te [N

−m

]

time [sec]

Fig. 5. Effects of the slowly-varying second-order force on the SM statevariables. Blue: mean solution; Red and Green: mean +/- standard deviation,respectively.

0 5 10 15 20 25 30−50

0

50

Ψqs

1e

[V]

0 5 10 15 20 25 300

50

100

Ψds

1e

[V]

0 5 10 15 20 25 30−50

0

50

Ψqre

[V]

0 5 10 15 20 25 300

50

100

Ψdre

[V]

0 5 10 15 20 25 30−2

−1

0

1

2x 10

10

Te [N

−m

]

time [sec]0 5 10 15 20 25 30

0.1

0.15

0.2

0.25

0.3

ωrm

[rad

/s]

time [sec]

Fig. 6. Effects of the slowly-varying second-order force on the IM statevariables. Blue: mean solution; Red and Green: mean +/- standard deviation,respectively.

5 10 15 20 25 305800

5850

5900

5950

6000

6050

6100

Vfil

ter [V

]

5 10 15 20 25 30

−60

−40

−20

0

20

40

60

I filte

r [A]

5 10 15 20 25 305800

5850

5900

5950

6000

6050

6100

Vre

c1 [V

]

time [sec]5 10 15 20 25 30

−60

−40

−20

0

20

40

60

I rec1

[A]

time [sec]

Fig. 7. Effects of the slowly-varying second-order force on the AC bus andharmonic filter state variables. Blue: mean solution; Red and Green: mean +/-standard deviation, respectively.

567

speed as well as the IM’s variables. In the presence of IM’srotor resistance fluctuation along with a deterministic slowly-varying added resistance as a disturbance, the indirect fieldoriented control of the 15-phase induction motor can stillmaintain the motor torque very well. Nevertheless, there arestrong dynamic interactions between SM and IM during theIM start-up transient. Having obtained here the first coupledresults, future simulations will address more realistic scenariosincluding multiple uncertainty effects due to IPS.

ACKNOWLEDGMENT

This work is supported by the Office of Naval Research(N00014-02-1-0623 ESRD Consortium, Also N00014-07-1-0846) and Sea Grant (NA060AR4170019 NOAA/DOC).

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[4] Loukakis T.A., Chryssostomidis C., Seakeeping Standard Series forCruiser-Stern Ships, Transactions SNAME 83, 1975, pp. 67-127.

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[6] Krause P.C., Wasynczuk O., and Sudhoff S.D., Analysis of ElectricMachinery and Drive Systems, Second Edition, IEEE Press and Wiley-Interscience, NY, 2002.

[7] Military Analysis Network, Federation of American Scientists, DDG-51 Arleigh Burke-class, ”http://www.fas.org/man/dod-101/sys/ship/ddg-51.htm”.

[8] Newman J.N., Marine Hydrodynamics, Ninth Edition, The MIT Press,MA, 1999.

[9] Newman J.N., Second-order, Slowly-Varying Forces on Vessels in Irreg-ular Waves, Paper 19, International Symposium on Dynamics of MarineVehicles and Structures in Waves, London, April 1999.

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