Stochastic modeling of integrated power system coupled ... - CiteSeerX

SPEEDAM 2008 International Symposium on Power Electronics, Electrical Drives, Automation and Motion

Stochastic Modeling of Integrated Power System coupled to Hydrodynamics in the All-Electric Ship P. Prempraneerach ∗† , J. Kirtley¶ , C. Chryssostomidis∗§ , M.S. Triantafyllou∗ , and G.E. Karniadakis∗‡ ∗ Department

of Mechanical Engineering 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 ¶ Department

Abstract— In the paper, we model the integrated power system (IPS) of a typical destroyer ship coupled to hydrodynamics. This IPS is composed of a 21MW, 3-phase synchronous generator supplying electric power to 4160 V AC bus and to a 19 MW, 15phase induction motor driven by an indirect rotor field oriented control for the motor torque. Moreover, stochastic responses are examined when there exists a variation in the induction motor’s rotor resistance and a disturbance from the slowly-varying added resistance, derived from a Pierson and Moskowitz sea spectrum. Index Terms– Hydrodynamics, Marine vehicle power systems, Induction motor drives, Stochastic differential equations

I. I NTRODUCTION In the All-Electric Ship (AES) architecture, the power sharing between the propulsion units and the high-power equipment, especially under heavy propulsion demands and casualty conditions, has recently been identified as an important issue [2], [14], [17]. In the new AES configuration, there is an increasing demand for electric power for ship system automation, electrical weaponry, electric propulsion, and ship service distribution. About 70% to 90% of power from the generator units in the fully integrated power system (IPS) is consumed in the propulsion systems [2]. Therefore, when a large power demand is imposed on an electrical bus during a mission or life critical situation, the power distribution must be optimally modified to yield the most efficient power usage and to maintain continuity of service [17]. This complex problem is compounded by the sea states which are unpredictable, leading to stochastic time-varying propulsion loads. It is, therefore, challenging for the electric ship designer to thoroughly investigate interactions between machines, power electronics, and uncertain sea conditions. To date there have been no published papers that account for dynamic interactions of propeller and ship hydrodynamics with a large-scale shipboard IPS. In this paper, we develop models of the IPS and the propeller coupled to random wave dynamics and ship motion. In the following, we present some

978-1-4244-1663-9/08/$25.00 ©2008 IEEE

details of the system that we model, the technical approach, and first results. II. S YSTEM M ODELING To investigate the influence of the propeller loading on the AC propulsion and power generation in the electric ship, modeling of both power systems and hydrodynamics of ship and propeller must be introduced. In our study, the IPS is similar to the model described in [16] for a ship like the DDG51 destroyer. In summary, the main AC subsystem of this IPS consists of a 21 MW, 3-phase, 60Hz Synchronous Machine (SM) as a generator and a close-loop drive using the indirect rotor field oriented control of 19 MW, 15-phase Induction Machine (IM) as a propulsor. The generator supplies the voltage to the 3-phase/4160V AC distribution bus, which must be filtered by a harmonic filter before connecting to the induction motor drive. The detailed derivation of machine equations can be found in [12] and [16]. A power converter and the Indirect Field Oriented Control (IFOC) using the sine-triangle modulation technique for a current regulator are incorporated into the propulsion system to control the torque of the induction machine. According to [6], IFOC employs an inner loop with a current feedback from IM and an outer loop with IM’s shaft angular velocity feedback for computing the machine rotational angle in the IFOC. The IPS configuration considered in this study is shown in Figure 1, and two such identical systems are used in the ship we model. A. Hydrodynamics The propeller model, used in this study, is based on a fixedpitch, 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 a reduction in the propeller thrust and torque from its nominal operating condition. Both the in-line water inflow variation and the in-and-out-of water effects directly affect the propeller loading. To model the wave effects, first, we assume that

563

¯ AR (U ) − R2nd−AR (U, t), −R

T*e Ȧrm

Exciter

Prime Mover (Ideal)

Power Converter With Torque Control

SM

IM 15-phase, 0-15 Hz 19MW

3-phase, 60 Hz 21 MW Harmonic Filter

3-phase, 4160 V AC Distribution Bus

Fig. 1. A one-line diagram of the AC power generator and power distribution with the closed-loop torque control of the induction machine. Two identical such systems are installed in the ship we model. TABLE I S PECIFICATIONS OF THE DDG-51 A RLEIGH B URKE - CLASS . Parameters Length [m] Draft [m] Beam [m] Displacement [tons] Speed [knot] Propeller Diameter [m] Propulsion Power [hp]

full-scale DDG-51 153.90 9.45 20.12 8,300 31 5.20 100,000

nonlinear and viscous effects are small compared to wave inertia for a ship motion in the sea. Moreover, we assume deep water random waves, modelled through the one-parameter Pierson and Moskowitz spectrum [5], derived on the basis of North Atlantic data and described by the significant wave height, H 1/3 , and modal frequency, ω m . To model ship hydrodynamics, we must consider the interaction between the propeller and ship hull because the wake created by the hull modifies the propeller advance velocity (Va ) with Va = (1−w)U , where U is the ship speed. The wake fraction (0 < w < 0.4) [8] indicates the velocity reduction due to the wake. Moreover, the presence of the propeller at the 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 account for the difference between the self-propelled and the towedmodel resistance. The specifications of the full-scale USS DDG-51 Arleigh Burke-class [7], driven by the electrical propulsor, are given in Table I. This full-scale ship is employed in the ship hydrodynamics calculations for calm water and added resistances, and for propeller performance. In this study, we consider only the surge motion of the electric ship, driven by two propellers connected to two identical IPS’s, in head sea. The ship’s motions in other directions i.e., sway, heave, roll, pitch, and yaw are assumed to be small in this study. Thus, the equation of ship motion with the induction motor directly driven the propeller can be described as: (M + Ma )

dU (t) dt

=

2(1 − t)Tp (n, U ) − R(U )

dωr (t) = Te − Qp (n, U )ηb ηr , (2) dt where n denotes the revolution per minute of the propeller, n = ω ∗ 30/π, and M and M a are the ship mass and added mass in the surge direction, respectively. The rotational inertia, Js , includes the IM rotor and propeller inertia; also, T p and Qp are the propeller open-water thrust and torque, respectively, i.e., Tp = KT (J)ρn2 D4 and Qp = KQ (J)ρn2 D5 , Va where J = nD is the advance velocity. The K T and KQ are thrust and torque coefficients of the propeller, while η b and ηr denote the bearing and propulsive efficiency. The drag force, R, corresponds to the calm-water resistance; it can be found from the non-dimensional drag coefficient, CD (Re, F r), as R = CD 21 ρSU 2 where S is the wetted surface area. The drag coefficient C D [5] is composed of a frictional resistance coefficient (C F (Re)) and a residual resistance coefficient (CR (F r)), where Re and F r are Reynolds and Froude numbers, respectively. The added resistance, R AR , is associated with the involuntary speed reduction due to the waves. Assuming that the added resistance is the secondorder nonlinear system, obeying the properties of quadratic systems, the slowly-varying added resistance can be separated into two major components: mean or steady second-order force ¯ AR ) (the first term) and slowly-varying second-order force (R (R2nd−AR ) (the second term), given by: Js

Is

Vs

(1)

RAR

=

RAR

=

¯ AR − R2nd−AR R N 1 (Ak )2 H(ωk , −ωk ) + 2 1 2

k=1 N  N 

(3)

Re{Ak Al H(ωk , ωl )ei[Δωt+Δφ] } (4)

k=1 l=1

where Δω and Δφ are ω k − ωl and φk − φl . Ak,l and φk,l are wave amplitudes and independent random phases varying between (0, 2π), respectively, corresponding to the wave frequency ω k,l . Note that Ak can be calculated from the one-side sea spectrum (S + (ω)) by discretizing S + (ω) ωk into N equally intervals. Then, A 2k = 2 ωk+1 S + (ω)dω for k ∈ 1, ..., N . H(ωk , ωl ) represents the second-order transfer function of hydrodynamics force. The response amplitude of the steady force normalized by the wave amplitude squared is denoted by R(ω); therefore, R(ω) is assumed to be equal to 1 2 H(ωk , −ωk ). According to [10], the mean added resistance is obtained from R(ω), and it is computed from the MIT5D Code [4]. For the slowly-varying added resistance, H(ω k , ωl ) l can be approximated as 2R( ωk +ω ). From Newman’s approx2 imation [9], R 2nd−AR is associated with the diagonal terms of H(ωk , ωl ) if the difference of two frequency wave, ω k and ωl , are very small, e.g., |ω k − ωl | < 0.2. B. Control of Induction Motor The Indirect Field Oriented Control (IFOC) of the 15phase induction motor drive requires an input torque command

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(Te∗ ) and a desired rotor flux command (λ e∗ dr ) and outputs semiconductor signals, driving the H-bridge type inverters. All parameters of the 15-phase induction machine are given in Table II. Because of multiple phases in the induction motor, the power converter topology must be separated into three five-phase parallel rectifier-dc link-inverter paths. As a result, each five phase of the induction machine can be independently controlled using the paralleling control. The dc voltage from a six-pulse uncontrolled rectifier (v rj ) in each path or rail (j) must be filtered with a low-pass LC circuit before propagating to five ith H-bridges inverters for each phase. In each rail, the smoothed dc voltage (v dcj ) can be expressed by v dc = [vdc1 , vdc2 , vdc3 ] where j = 1, 2, 3. The phase of the ith Hbridge is determined so that the AC voltage of ith H-bridge is displaced by (i − 1)24 ◦ from the first phase. The current and voltage of i-th phase of the induction machine can be denoted as isi and vsi . The switching state (s i ), obtained from the IFOC, determines the on/off state of each switch, as shown below: ⎧ D1i and D4i on ⎨ 1 0 (D1i and D2i on) or (D 2i and D4i on) si = ⎩ −1 D2i and D3i on

In the balancing motor operation, a paralleling control ∗ e∗ equally divides T e∗ and λe∗ dr into Tei and λdri commands for ∗ e∗ each rail. Then, T ei and λdri generates the desired qd-axis stator currents in the link stabilizing controller. When one inverter malfunctions, both T e∗ and λe∗ dr must be divided for two operating inverter rails. However, both a magnitude and a ∗ command must be limited at specified rate of change of the T ei levels by the torque limiter. Furthermore, the rate of change ∗ of the output Tˆei command is governed by a constant gain, K. Similar to the field oriented control concept of 3-phase induction motor [6], the torque can be maximized by controlling the rotor flux linkage vector perpendicular to the rotor current e∗ vector. With this assumption, the desired qd currents (i e∗ qsi , idsi ) ∗ can be computed from the Tˆei and λe∗ dr commands. Furthermore, this link stabilizing control helps to solve the negative impedance instability, mentioned in [13]. Combing the desired qd output currents from the link stabilizing control with the mechanical rotor speed (ω rm ), the synchronous reference frame speed (ω e ) can be calculated as ω e = ωs +ωr , where the   r

(5)

In this study, maintaining the induction machine’s torque at a specified level is the main objective of IFOC. According to [16], this control technique must be stable, the current be constrained below a maximum semiconductor current limit, the switching frequency be kept constant at 2 kHz, and the IFOC act as a torque transducer. Thus, the structure of the field oriented control, shown in Figure 2, consists of 6 main parts: a paralleling control, a torque limiter, a dc link stabilizing control, a current limiter, a field oriented supervisory control, and a current regulator. Five-phase inverter-rail voltages are controlled by the three independent control architectures in the IFOC. Although there might exist a negative impedance instability in the dc link due to the tight control of switch current, the IFOC fast response can help stabilize the power converter. Te*1 Torque That*_e1 Limiter

T*_e1

Tˆe*1

T*_e1

That*_e1

Link ie*_qs1 Stabilizing Controlie*_ds1

Le*_dr1

e* dr1

V_dc1

O

* 1 e

T

T*_e

Le*_dr1

T*_e2

Te*2 Torque That*_e2 Limiter

T*_e2

Paralleling Control Le*_dr2

e* 2 dr

O

Le*_dr

T*_e3

That*_e2

Link ie*_qs2 Stabilizing ie*_ds2 Le*_drControl

O Te*3

Torque That*_e3 Limiter

T*_e3

e* dr 3

idse*1 e* qs 2

idse* 2

That*_e3

iqse* 3

Tˆe*3 Link ie*_qs3 Stabilizing ie*_ds3 Le*_drControl Le*_dr3 V_dc3

Ie*_qs1

Ihe*_qs1

Current Limiter Ihe*_ds1

ds1

Ie*_ds1

(0 0 0)

idse* 3

Ie*_qs2

In1

iˆqse*2 iˆ e*

i

V_dc2

Le*_dr2

e* dr 2

O Le*_dr3

Tˆe*2

iˆqse*1 iˆ e*

iqse*1

Le*_dr

Ihe*_qs2

Current Limiter Ie*_ds2 Ihe*_ds2

Out1

In3

(0 0 0)

Ie*_qs3

iˆqse*3 iˆ e*

Ihe*_qs3

Current Limiter Ie*_ds3 Ihe*_ds3



1

ds

ds 2

Out2

T=

2

In4

Current In5 Regulator

Out3

3

4 V1 ih*_qs

5 V2 6 V3

Z rm

3 w

Field Oriented Control

Ti*_ds e wrm Ze

⎡

1 2⎢ ⎣ 0 3 √1

6

ds 3

[0; 0; 0]

T_e

4

we

5 w_e

3

ˆie∗

qsi . Then, integrating ω e slip speed (ωs ) equals to Lr  3i=1 ˆie∗ rr i=1 dsi provides the synchronous reference frame position (θ e ) used in the ith-phase to qd0αβ-frame transformation. e∗ Before passing the i e∗ qsi , idsi to the current regulator, the current must be limited at a prescribed range. The current limiter shows that a tight constrain of i e∗ dsi requires to maintain the desired rotor flux level, which governs a proper flux orientation; i e∗ qsi is more flexible. The last component of the IFOC technique is the current regulator, generating the duty cycle (d) for the sine-triangle modulation technique. The current regulator structure, shown in Figure 3, requires the desired qd current from the IFOC and the current feedback from the induction machine as well as ωe , θe , and vdci . Because of the highly coupled circuits of 15-phase induction motor in the qd reference frame, three qˆe∗ ˆe∗ ˆe∗ axis rail currents ˆie∗ qsi = [iqs1 , iqs2 , iqs3 ] must be transformed e∗ e∗ ˆe∗ ˆe∗ ˆ ˆ to iqsxyz = [iqsx , iqsy , iqsz ] in a xyz reference frame, so as three d-axis rail currents. Therefore, the current control can be done in xyz axis independently. The detailed derivation of the decoupled voltage equations can be found in [16]. This ˆe∗ decoupled transformation (ˆie∗ qsxyz = Tiqsi ) can be written as:

is

Vdc1 Vdc 2 Vdc 3

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

−√12 − 23 √1 6

1 − √2 3 2 √1 6

⎤ ⎥ ⎦.

(6)

This T transformation is not orthogonal. In the balance ˆe∗ operation, both ˆie∗ qsxy and idsxy are fixed at zero and the z component equals to the corresponding i component. Therefore, the X-component current control, similar to the proportional and integral controller with a nonlinear feedforward, can be designed. The difference in the desired and measured current must pass through a low-pass filter to eliminate the switching noise. Likewise, the Y -component current control has the same structure except that different gains can be employed.

565

TABLE II

vqsxe* îqsxe*

îqs1e* e* qs2

î

T

îqs3e*

îqsye* îqsze*

T

iqs1e* iqs2e* iqs3e*

is

e K5s

ids1e* ids2e*

T

Y- Axis Current Control

iqsxe* iqsye*

* v1,4,7,10,13

vqs1e* T -1

vqsze*

rs = 122mΩ  rr = 35.7mΩ

vqs3e* * v2,5,8,11,14

1

vdc2

vds1e* T -1

UNIT SYSTEM

v

e-1

v

1

vdc1

e* qs2

K5s

e* dsy

îdsye* îdsze*

îds3e*

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

vdsxe* vqsye*

Y- Axis Current Control

îdsxe*

îds1e* îds2e*

X- Axis Current Control

d

vds2e* vds3e*

vdsze*

T

Zero Sequence Current

Lm = 145mH P = 12

TABLE III * v3,6,9,12,15

PARAMETERS OF THE INDIRECT FIELD ORIENTED CONTROLLER FOR 15- PHASE INDUCTION MACHINE [16]

1

vdc3

iqsze*

Te,lim = 403kN m Is,lim = 1000A Kpqx = 17.07V /A Kpqy = 17.07V /A τx = 0.2ms K0 = 4.175

idsxe*

ids3e*

Lls = 6.79mH  Llr = 7.62mH

idsye* idsze* Zero Sequence Current Control

Zero Sequence Voltage Commands

ѯe ѭe

Fig. 3.

Nevertheless, in the normal operation, the gains of X- and Y -component are identical. According to [16], even though the qd voltage equations of the Z-component depend on both stator current and rotor flux linkage, the same control structure is still applicable but some parameters must be modified corresponding to the coupling in the rotor circuit. The proportional and integral gains of the Z-component must be adjusted independently of the XY -components. The zero sequence (0, α, β) must be controlled closely to zero. However, the zero sequence is uncoupled from the qd axis, thus only a proportional gain is used as the controller, written below: K0 i0αβsi τ0 s + 1

K = 100 τ = 20ms Kpqz = 61.65V /A Kiqz = 504.9V /A τz = 0.2ms λ∗dr = 44V s

where j ∈ 1, 2, 3 and i ∈ 1, ..., 5. Also, the dc current of each ith H-bridge is given by  if si = 1 isi idchi = (10) −isi if si = −1

The decouple current regulator.

v0αβsi =

Te,slew = 4.03M N m/s vdcb = 5618V Kiqx = 306.6V /As Kiqy = 306.6V /As τy = 0.2ms τ0 = 4ms

(7)

Note that the low-pass filter in the zero sequence control helps filtering out the switching noise from the measured motor current such that the instability does not occur in the IFOC technique. Using the sine-triangle modulation technique, the switching function (s i ) can be obtained as follows,  1 if di ≥ ti (8) si = −1 if di < ti Then, the rail voltage can be computed as a function of s i and isi , hence:. ⎧ vdcj − 2vt if si = 1 and isi ≥ 0 ⎪ ⎪ ⎨ vdcj + 2vt if si = 1 and isi < 0 (9) vsi = −v + 2v if si = −1 and isi ≤ 0 ⎪ dc t j ⎪ ⎩ −vdcj − 2vt if si = −1 and isi > 0

To simplify the inverter model, the fast average voltage (¯ vqdsj ) and current (i dcj ) of the inverter model in the nonovermodulated case can be expressed as:

idcj

v¯qdsj = vdcj dqdj (11) 5 = (dqs iqs + dds ids + 2(d0s i0s + dαs iαs + dβs iβs )) (12) 2 III. F IRST R ESULTS

The time-varying random sea spectrum is modeled as a stochastic process, but in addition, we may consider many components of the IM and SM as uncertain parameters. To simulate this coupled stochastic system, we use the probabilistic collocation method [12], according to which samples are obtained at specific points in the parameter space defined by the roots of the orthogonal polynomials employed in the representation of all stochastic fields. Therefore, if the governing equations become more complex, the simplicity of collocation framework, which involves only repetition runs of deterministic solvers, can further reduce the computational cost compared to the Monte Carlo method in low- and moderate-dimensional problems. To demonstrate results of this coupled stochastic system, we first simulated the surge motion of the scaled electric ship excited 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 to the propeller, drive the 1DOF ship motion in head and random seas. In this simulation study, we assume that initially two

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induction motors are down, while the ship moves forward at 20 knots and two generators operate near their steady-state conditions. Then, after 2 seconds the two propulsion drives are turned back on. The motor torque command of each IM is 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 ship are computed using the Newman’s approximation and the added resistance response amplitude operator [9]. Thus, the propellers driven by IPS experience the slow-varying force from the added resistance. Figure 4, 5, 6, and 7 show the stochastic results of the machines’ responses and ship velocity with the effect of the slowly-varying added resistance when the rotor resistance of the 15-phase induction motor is a uniform random variable with ±20 variation from its nominal value. Particularly, Figure 4 illustrates the slowly-varying added resistance and the stochastic response of ship forward velocity 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 fluctuation of IM’s rotor resistance, stochastic responses of IM’s ψ qds1 r r and ψqdr , IM’s torque, SM’s ψ qs and ψkd vary within a wide range. Hence, this shows a very strong interaction between each generator and motor during the motor start-up transient. However, there is a minor effect on the ship surge velocity with IM’s rotor resistance variation. Initially, the ship speed gradually decreases due to increasing added resistance as well as small torque and thrust after turning on the propulsion drive with constant torque command. Notice that the ship speed fluctuates at similar rate as the slowly-varying added resistance with a phase delay.

200

Ψr [V]

Ψr [V]

100 ds

qs

0

3

10

−100 −200 0

5

10

15

20

25

30

5

10

15

20

25

30

0

5

10

15

20

25

30

5

10

15

20

25

30

5

10

15

20

25

30

50

Ψr [V]

Ψr [V]

0 kd

kq

−50 −100 −150 0

3

10

0 6

x 10

0.5 0

e

Ψrfd [V]

T [N−m]

1

3

10

0

5

10

15

time [sec]

20

25

−0.5 −1 0

30

time [sec]

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

100

[V] ds1

50

Ψe

Ψe

qs1

[V]

50

0

−50 0

5

10

15

20

25

0 0

30

5

10

15

20

25

30

5

10

15

20

25

30

5

10

15

20

25

30

100

dr

Ψe [V]

qr

Ψe [V]

50

0

−50 0

5

10

15

20

25

50

0 0

30

10

x 10

0.3

[rad/s]

1

0.25 0.2

rm

0

ω

e

T [N−m]

2

−1 −2 0

5

10

15

time [sec]

20

25

0.15 0.1 0

30

time [sec]

Slowly−varying Added Res. [N]

4

2

x 10

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

1 0 −1 −2 −3

10

20

30

40

50

60

70

80

90

100

110

10.3 6100 6050

40

5950

filter

filter

10.2

[A]

[V]

6000

I

V

Uship [m/s]

60 10.25

5900 30

40

50

60

time [sec]

70

80

90

100

5850

110

−60 5800

5

10

15

20

25

30

5

10

5

10

15

20

25

30

15

20

25

30

6100

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

60 6050

40

5950

V

rec1

[V]

6000

[A]

20

rec1

10

0

−40

I

10.15

20

−20

5900

20 0 −20 −40

5850

−60 5800

IV. S UMMARY We have investigated the influence of hydrodynamic force on the IPS in the full scale electric ship, particularly in the surge motion. The results show that the added resistance from the random sea spectrum has a small effect on the ship forward

5

10

15

time [sec]

20

25

30

time [sec]

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

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speed as well as the IM’s variables. In the presence of IM’s rotor resistance fluctuation along with a deterministic slowlyvarying added resistance as a disturbance, the indirect field oriented control of the 15-phase induction motor can still maintain the motor torque very well. Nevertheless, there are strong dynamic interactions between SM and IM during the IM start-up transient. Having obtained here the first coupled results, future simulations will address more realistic scenarios including multiple uncertainty effects due to IPS. ACKNOWLEDGMENT This work is supported by the Office of Naval Research (N00014-02-1-0623 ESRD Consortium, Also N00014-07-10846) and Sea Grant (NA060AR4170019 NOAA/DOC). R EFERENCES [1] Carlton J.S., Marine Propellers and Propulsion, first edition, ButterworthHeinemann Ltd, 1994. [2] Clayton D.H., Sudhoff S.D., Grater G.F., Electric Ship Drive and Power System, Conf. Rec. 2000 24th Int. Power Modulation Symp., 2000, pp. 85-88. [3] Dalzell J.F., Kim C.H., An Analysis of the Quadratic Frequency Response for Added Resistance, Journal of Ship Research, Vol. 23, No. 3, 1979, pp. 198-208. [4] Loukakis T.A., Chryssostomidis C., Seakeeping Standard Series for Cruiser-Stern Ships, Transactions SNAME 83, 1975, pp. 67-127. [5] Lewis E.V. (Editor), Principles of Naval Architecture, Second Revision, The Society of Naval Architects and Marine Engineers, NJ, 1989. [6] Krause P.C., Wasynczuk O., and Sudhoff S.D., Analysis of Electric Machinery and Drive Systems, Second Edition, IEEE Press and WileyInterscience, NY, 2002. [7] Military Analysis Network, Federation of American Scientists, DDG51 Arleigh Burke-class, ”http://www.fas.org/man/dod-101/sys/ship/ddg51.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 Irregular Waves, Paper 19, International Symposium on Dynamics of Marine Vehicles and Structures in Waves, London, April 1999. [10] Salvesen N., Second-order Steady-State Forces and Moments on Surface Ships in Oblique Regular Waves, Paper 22, International Symposium on Dynamics of Marine Vehicles and Structures in Waves, London, April 1999. [11] Smogeli Ø.V., Control of Marine Propellers From Normal to Extreme Conditions, Ph.D. thesis, Norwegian University of Science and Technology, 2006. [12] Prempraneerach P., Uncertainty Analysis in a Shipboard Integrated Power System using Multi-Element Polynomial Chaos, Ph.D. thesis, Massachusetts Institute of Technology, 2007. [13] Sudhoff S.D., Corzine K.A., Glover S., Hegner H.N. Robey, Jr., DC Link Stabilized Field Oriented Control of Electric Propulsion Systems, IEEE Trans. on Energy Conversion, Vol. 13, No. 1, March 1998. [14] Sudhoff S.D., Kuhn B.T., Zivi E., Delisle D.E., and Clayton D., Impact of Pulsed Power Loads on Naval Power and Propulsion Systems, Electric Ship Research and Development Consortium (ESRDC), Recent Papers, nerc.aticorp.org/esrdc recent papers.html. [15] Sudhoff S.D., Pekarek S., Kuhn B., Glover S., Sauer J., Delisle D., Naval Combat Survivability Testbeds for Investigation of Issues in Shipboard Power Electronics Based Power and Propulsion Systems, Power Engineering Society Summer Meeting, IEEE, Vol. 1, July 2002, pp. 347 - 350. [16] Sudhoff S.D., Wasynczuk O., Krause P.C., Dynamic Simulation of HighPower Machinery, Final Report to Naval Surface Warfare Center, Carderock Division, Annapolis Detachment, Contract N61533-95-C-0107, July 1996. [17] Zivi E., McCoy T.J., Control of a Shipboard Integrated Power System, Proceedings of the 33th Annual Conference on Information Sciences and Systems, March 1999.

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