Documentation for Notional Baseline System Models
Version 0.1
DRAFT
November 2010
ii
TABLE OF CONTENTS
1.0
Introduction ......................................................................................................................... 1
2.0
System Models .................................................................................................................... 3
2.1
MVDC System ................................................................................................................ 3
2.1.1
Main Generators...................................................................................................... 3
2.1.2
Auxiliary Generators ............................................................................................... 5
2.1.3
Propulsion Systems ................................................................................................. 6
2.1.4
Ship Service Loads ................................................................................................. 7
2.1.5
Pulse Load ............................................................................................................. 16
2.1.6
Energy Storage ...................................................................................................... 17
2.2
MVAC System .............................................................................................................. 20
2.2.1
Gearbox for Auxiliary Generators in the MVAC System .................................... 20
2.2.2
MVAC System Generators ................................................................................... 20
2.2.3
AC/DC Rectifiers .................................................................................................. 21
2.3
HFAC System ............................................................................................................... 21
2.3.1
Prime Movers ........................................................................................................ 22
2.3.2
Generators ............................................................................................................. 23
3.0
Component and Subsystem Models .................................................................................. 24
3.1
Components of Generator Sets ..................................................................................... 24
3.1.1
3.1.1.1
Notional Single-Shaft Gas Turbine ................................................................... 24
3.1.1.2
Notional Twin-Shaft Gas Turbine .................................................................... 27
3.1.2
3.1.2.1
3.1.3
3.1.3.1
3.1.4
3.2
Prime Movers ........................................................................................................ 24
Electric Machines.................................................................................................. 30
Notional Round Rotor Synchronous Machine .................................................. 30
Exciters and Voltage Regulators ........................................................................... 32
Simplified IEEE Type AC8B Exciter ............................................................... 32
Generator Load Sharing Controls ......................................................................... 33
Components of Propulsion Systems ............................................................................. 35
3.2.1
3.2.1.1
3.2.2
3.2.2.1
3.2.3
Propulsion Motors................................................................................................. 35
Notional Permanent Magnet Machine .............................................................. 35
Motor Drives ......................................................................................................... 36
Two-Level IGBT Bridge................................................................................... 36
Motor Drive Controls ............................................................................................ 37
iii
3.2.3.1 Hysteresis Current Control for Two-Level Drive for Permanent Magnet
Synchronous Machine ....................................................................................................... 37
3.2.4
3.2.4.1
3.2.5
3.2.5.1
3.3
Notional Supercapacitor Energy Storage System ................................................. 45
3.4.1.2
DC/DC converter control .................................................................................. 47
Specialized Loads ......................................................................................................... 47
3.5.2
Radar Systems ....................................................................................................... 47
Notional Radar Load ......................................................................................... 47
Notional Free Electron Laser Pulse Power Load .................................................. 47
Power Conversion Modules .......................................................................................... 49
3.6.1
3.6.1.1
3.6.2
3.6.2.1
AC/DC Rectifiers .................................................................................................. 49
Notional Diode Rectifier ................................................................................... 49
DC/DC Converters ................................................................................................ 50
Isolated DC/DC Converter ................................................................................ 50
Ancillary Components .................................................................................................. 54
3.7.1
3.7.1.1
3.7.2
Transformers ......................................................................................................... 54
Three-phase, Two Winding Transformer ......................................................... 54
Circuit Breakers .................................................................................................... 55
3.7.2.1
Three-phase Circuit Breaker ............................................................................. 55
3.7.2.2
Notional Unidirectional DC Switch .................................................................. 56
3.7.3
3.7.3.1
4.0
Notional Ship Service Loads ................................................................................ 43
PWM inverter and controls ............................................................................... 46
3.5.1.1
3.7
Notional Destroyer Hydrodynamic Characteristics .......................................... 42
3.4.1.1
3.5.1
3.6
Ship Hydrodynamic Characteristics ..................................................................... 42
Bulk Energy Storage Systems ....................................................................................... 45
3.4.1
3.5
Notional Fixed-Pitch Propeller ......................................................................... 39
Ship Service Loads ....................................................................................................... 43
3.3.1
3.4
Propellers .............................................................................................................. 39
Overvoltage Mitigation ......................................................................................... 57
Shunt Braking Resistor ..................................................................................... 57
References ......................................................................................................................... 58
5.0
Appendix A: List of possible case studies to assess the performance of the baseline
power system architectures ............................................................................................................. 1
5.1
Case studies requiring a dynamic model for transient analyses ..................................... 1
iv
5.1.1
Typical ship maneuvering and operation scenario: ................................................ 1
5.1.2
Load pick-up ........................................................................................................... 1
5.1.3
Load rejection ......................................................................................................... 2
5.1.4
Loss of a generator .................................................................................................. 2
5.1.5
Fault in a high-power rectifier ................................................................................ 2
5.1.6
Faults in propulsion motor windings ...................................................................... 2
5.1.7
Series faults in DC loads ......................................................................................... 2
5.1.8
Power restoration to vital load requiring load shedding ......................................... 3
5.1.9
Power restoration to vital load requiring use of energy storage ............................. 3
5.1.10
Harmonic analysis ................................................................................................... 3
5.1.11
Steady State Operation (extended study of scenario 1) .......................................... 3
5.2
Case studies requiring model for top-level system analyses ......................................... 3
5.2.1
1. Power balance analysis during early stage ship design ...................................... 4
5.2.2
Fuel consumption analysis ...................................................................................... 4
5.2.3
Power system mass, volume, and cost ................................................................... 4
5.2.4
Prime power optimization ....................................................................................... 4
5.2.5
Reliability/Survivability Assessment ...................................................................... 4
v
LIST OF FIGURES
Figure 1: General Topology for Baseline System Models............................................................. 1
Figure 2: General Topology for Baseline MVDC System............................................................. 3
Figure 3: Main Generator Sets for Baseline MVDC System ......................................................... 4
Figure 4: Propulsion System Module and Hydrodynamics Module for Baseline MVDC System 7
Figure 5: Five load types represent the detailed zonal load demand (Zone 1) .............................. 8
Figure 6: Zonal load DC 1 (constant resistance) ........................................................................... 9
Figure 7: Zonal load DC 2 (constant power using current injection model) ................................. 9
Figure 8: Zonal load AC 1 (constant impedance) ........................................................................ 10
Figure 9: Zonal load AC 2 (uncontrolled induction motor and RL-impedance) ......................... 10
Figure 10: Zonal load AC 3 (single-phase constant impedances) ............................................... 11
Figure 11: PWM-Inverter Voltage Regulator .............................................................................. 11
Figure 12: Simplified zonal load (masked zone and DC bus interconnection) ........................... 15
Figure 13: Simplified zonal load (shown here is Zone 2) ............................................................ 15
Figure 14: Pulse load model ........................................................................................................ 16
Figure 15: MVDC energy storage circuit and controls ................................................................ 19
Figure 16: General Topology for Baseline MVAC System......................................................... 20
Figure 17: General Topology for Baseline HFAC System .......................................................... 22
Figure 18: Single-shaft Gas Turbine ............................................................................................ 24
Figure 19: General Model for Single-shaft Gas Turbine ............................................................. 25
Figure 20: Notional Single-shaft Gas Turbine Model ................................................................. 25
Figure 21: Acceleration Control for Notional Single-shaft Gas Turbine Model ......................... 25
Figure 22: Simple-cycle Twin-shaft Gas Turbine ....................................................................... 27
Figure 23: Notional Twin-shaft Gas Turbine Model ................................................................... 28
Figure 24: Gas Generator (Engine) Model for Notional Twin-shaft Gas Turbine Model ........... 28
Figure 25: Engine Shaft Dynamics for Gas Generator (Engine) Model for Notional Twin-shaft
Gas Turbine Model ....................................................................................................................... 28
Figure 26: Acceleration Control for Notional Twin-shaft Gas Turbine Model ........................... 29
Figure 27: Interface for Notional Round Rotor Synchronous Machine ...................................... 31
Figure 28: Default Saturation Curve for Notional Round Rotor Synchronous Machine ............ 32
Figure 29: Simplified Implementation of the IEEE type AC8B exciter model. .......................... 33
Figure 30: Configuration of Droop Control for Turbine/Governor ............................................. 34
Figure 31: Configuration of Droop Control for Voltage Regulator/Exciter ................................ 34
vi
Figure 32: Load Divider Control ................................................................................................. 35
Figure 33: Interface for Notional Permanent Magnet Machine ................................................... 36
Figure 34: Two-Level IGBT Bridge ............................................................................................ 37
Figure 35: Hysteresis Current Control for Two-Level Drive for Permanent Magnet Synchronous
Machine......................................................................................................................................... 38
Figure 36: Interface for Notional Fixed-Pitch Propeller Model .................................................. 39
Figure 37: Thrust Coefficient Curves for Notional Fixed-Pitch Propeller Model ....................... 40
Figure 38: Torque Coefficient Curves for Notional Fixed-Pitch Propeller Model ...................... 41
Figure 39: Taylor Wake Fraction Curve for Notional Fixed-Pitch Propeller Model .................. 41
Figure 40: Notional Destroyer Hydrodynamic Characteristics ................................................... 42
Figure 41: Hydrodynamic Resistance for Notional Destroyer Model ......................................... 43
Figure 42: 4.16KV/60Hz ac source with an energy storage system (ESS) and a test load ......... 45
Figure 43: Notional Supercapacitor Energy Storage System Inverter/converter control ............ 46
Figure 44: Notional Supercapacitor Energy Storage System DC/DC (buck-boost) converter
control ........................................................................................................................................... 47
Figure 45: Sub-loads of Notional Free Electron Laser System ................................................... 48
Figure 46: Circuit Model of Notional Diode Rectifier ................................................................ 49
Figure 47: Isolated DC-DC Converter Block .............................................................................. 51
Figure 48: Isolated DC-DC Converter Circuit ............................................................................. 52
Figure 49: Interface for Three-phase, Two-winding Transformer Model ................................... 54
Figure 50: Single-phase Element of Three-phase Circuit Breaker Model ................................... 55
Figure 51: Interface for Three-phase Circuit Breaker Model ...................................................... 56
Figure 52: Interface for Notional Unidirectional DC Switch Model ........................................... 56
Figure 53: Shunt Breaking Resistor ............................................................................................. 57
vii
LIST OF TABLES
Table 1. Salient Features of Baseline System Architectures ......................................................... 2
Table 2. Parameters for Main Generator Modules of Baseline MVDC System ............................ 4
Table 3. Parameters for Prime Mover Model of Main Generator Module of Baseline MVDC
System ............................................................................................................................................. 4
Table 4. Parameters for Exciter Model of Main Generator Module of Baseline MVDC System . 5
Table 5. Parameters for Auxiliary Generator Modules of Baseline MVDC System ..................... 5
Table 6. Parameters for Prime Mover Model of Auxiliary Generator Module of Baseline MVDC
System ............................................................................................................................................. 5
Table 7. Parameters for Synchronous Machine Model of Auxiliary Generator Module of
Baseline MVDC System ................................................................................................................. 5
Table 8. Parameters for Exciter Model of Auxiliary Generator Module of Baseline MVDC
System ............................................................................................................................................. 6
Table 9. Parameters for Rectifier of Auxiliary Generator Module of Baseline MVDC System ... 6
Table 10. Parameters for Propulsion Modules of Baseline MVDC System .................................. 7
Table 11. Parameters for Permanent Magnet Machine for Propulsion Module of Baseline
MVDC System ................................................................................................................................ 7
Table 12. Parameters for Motor Drive Controls for Propulsion Module of Baseline MVDC
System ............................................................................................................................................. 7
Table 13. Parameters for Braking Resistor for Propulsion Module of Baseline MVDC System .. 7
Table 14. Parameters for detailed MVDC zonal loads: DC1—constant resistance .................... 12
Table 15. Parameters for detailed MVDC zonal loads: DC2—constant power .......................... 12
Table 16. Parameters for detailed MVDC zonal loads: AC1—constant impedance ................... 12
Table 17. Parameters for detailed MVDC zonal loads: AC2—uncontrolled induction motor and
constant impedance ....................................................................................................................... 13
Table 18. Parameters for detailed MVDC zonal loads: AC3—single-phase loads ..................... 14
Table 19. Parameters for simplified zonal load representation (Zones 2, 3, 4, and 5) ................ 16
Table 20. Parameters for pulse load ............................................................................................. 17
Table 21. MVDC Supercapacitor Parameters .............................................................................. 17
Table 22. Parameters for MVDC Energy Storage’s Isolated DC-DC converter ......................... 17
Table 23. Controller Parameters for MVDC Energy Storage’s Isolated DC-DC converter ........ 18
Table 24. Parameters for Generator Models of MVAC System .................................................. 20
Table 25. Parameters for Uncontrolled Diode Rectifier Models of MVAC System ................... 21
Table 26. Parameters for Gas Turbine Models of HFAC System ............................................... 22
Table 27. Parameters for Generator Models of HFAC System ................................................... 23
viii
Table 28. Parameters for Notional Single-Shaft Gas Turbine Model .......................................... 26
Table 29. Parameters for Notional Twin-Shaft Gas Turbine Model ........................................... 30
Table 30. Parameters for Notional Round Rotor Synchronous Machine .................................... 31
Table 31. Parameters for Simplified IEEE Type AC8B Exciter ................................................. 33
Table 32. Parameters for Generator Load Sharing Controls........................................................ 35
Table 33. Parameters for Notional Permanent Magnet Machine ................................................. 36
Table 34. Parameters for Two-Level IGBT Bridge Model.......................................................... 37
Table 35. Parameters for Hysteresis Current Control for Two-Level Drive for Permanent
Magnet Synchronous Machine ..................................................................................................... 38
Table 36. Parameters for Notional Fixed-Pitch Propeller Model ................................................ 40
Table 37. Additional Parameters Associated with Notional Fixed-Pitch Propeller Model ......... 42
Table 38. Parameters for Notional Destroyer Hydrodynamic Characteristics Model ................. 42
Table 39. Ship Service Load Data ............................................................................................... 43
Table 40. General Parameters for Notional Supercapacitor Energy Storage System .................. 45
Table 41. Parameters for Notional Supercapacitor Energy Storage System Inverter .................. 46
Table 42. Parameters for Notional Supercapacitor Energy Storage System Buck/boost converter
....................................................................................................................................................... 47
Table 43. Notional Free Electron Laser Data .............................................................................. 48
Table 44. Parameters for Notional Diode Rectifier Model .......................................................... 49
Table 45. Parameters for Isolated DC-DC converter ................................................................... 53
Table 46. Controller Parameters for Isolated DC-DC converter ................................................. 53
Table 47. Parameters for Three-phase, Two Winding Transformer ............................................ 55
Table 48. Parameters for Three-phase Circuit Breaker ............................................................... 56
Table 49. Parameters for Notional Unidirectional DC Switch Model ......................................... 56
Table 50. Parameters for Shunt Braking Resistor ........................................................................ 57
ix
GLOSSARY
ATG – Auxiliary Turbine-Generator Set
ESRDC – Electric Ship Research and Development Consortium
HFAC – High Frequency Alternating Current
MTG – Main Turbine-Generator Set
MVAC – Medium Voltage Alternating Current (60 Hz)
MVDC – Medium Voltage Direct Current
PGM – Power Generation Module
UPS – Uninterruptible Power Supply
x
1.0 INTRODUCTION
This document describes baseline system models developed by the Electric Ship Research and
Development Consortium (ESRDC) for the study of three power system architectures. These
are: the medium-voltage dc architecture (MVDC), the conventional 60 Hz medium-voltage
architecture (MVAC), and the high-frequency medium-voltage architecture (HFAC), all of
which are primarily based upon the information originally provided to the consortium in [1].
The fundamental topology used by each of the baseline models is illustrated by Figure 1. In this
topology, four turbo-generators are connected to a ring-bus which supplies two propulsion power
trains, four ship service zonal loads, a radar load, and a pulse load. A bulk energy storage system
is also connected to the distribution bus for Uninterruptable Power Supply (UPS) and/or ridethrough power capabilities. The salient features and components of the three baseline
architectures are summarized in Table 1. The details for the system models are given in
Section 2.0. To the extent reasonable, attempts have been made to construct the three baseline
models from consistent component models. The details of the component models, from which
the system models have been constructed, are given in Section 3.0.
Auxilary
PGM 1
Main PGM 1
Energy
Storage
VSD
Stern
Cross-hull
Disconnect
Special
Load
Zonal
Ship’s
Service
Loads
Starboard
Power
Distribution Bus
Zonal
Ship’s
Service
Loads
VSD
Auxilary
PGM 2
Port PM
Zonal
Ship’s
Service
Loads
Port
Power
Distribution Bus
Zonal
Ship’s
Service
Loads
Starboard
PM
Main PGM 2
PGM = Power Generation Module
VSD = Variable Speed Drive
PM = Propulsion Motor
Figure 1: General Topology for Baseline System Models
1
High
Power
Pulsed
Load
Table 1. Salient Features of Baseline System Architectures
Feature
Generation
power
Distribution
Voltage
Prime movers
Generators
Turbogenerator
coupling
Generator
Rectifiers
Common to All Architectures
 80 MW
MVDC
MVAC
HFAC
 Ring bus
DC
5 kV
60 Hz
4.16 kV
240 Hz
4.16 kV
3600 rpm
3600 rpm
Indirect (1
gear box)
3600 rpm
14400 rpm
Direct (no
gear boxes)
NA
NA
 Gas turbines
 2×36 MW, 3600 rpm twin-shaft
(MTG)
 2×4 MW, 14400 rpm single-shaft
(ATG)
 Synchronous
wound-field
cylindrical rotor
3600 rpm
 2×47 MVA (MTG)
14400 rpm
 2×5 MVA (ATG)
Direct (no
gear boxes)
6-pulse
Diode
bridges
 Fixed pitch propeller
 Permanent magnet synchronous
propulsion motors (36.5 MW,
120 rpm)
 Current-controlled PWM variable
speed drive (hysteresis control)
 Variable duty cycle breaking
resistor
for
dissipation
of
regenerative power.
Hydrodynamics  Mass and hydrodynamic resistance
of notional destroyer-class ship
Service loads
 4 distribution zones (22 total loads)
Special load
 Radar load
Pulse
power  Notional free electron laser
load
Switch gear
 3-phase AC breakers
 Semiconductor switches for DC
busses
Propulsion
power trains
2
2.0 SYSTEM MODELS
2.1 MVDC System
The general topology of the MVDC system is illustrated by Figure 2. The models used for each
of the modules of the system are described in the following sections.
Main AC
Generator 1
Energy Storage
GT
DC/DC
Converter
Generator
Rectifier
Auxilary AC
Generator 1
Generator
Rectifier
MTG1
ATG1
Capacitor
Bank
GT
AC Circuit
Breaker
AC Circuit
Breaker
Port
Propulsion
Motor
Propulsion Motor
Drive
DC Sectionalizer
5000 VDC
Port Bus
DC/DC
Converter
Stern
Cross-hull
Disconnect
Radar
Zone 4
Load
Center
Zone 3
Load
Center
Zone 2
Load
Center
Bow
Cross-hull
Disconnect
Zone 1
Load
Center
Zone 5
Deck house
5000 VDC
Starboard Bus
AC Circuit
Breaker
GT
ATG2
Auxilary AC
Generator 2
Pulsed
Load
AC Circuit
Breaker
GT
Generator
Rectifier
Propulsion Motor Drive
Starboard Propulsion
Motor
MTG2
Main AC
Generator 2
Generator
Rectifier
DC/DC
Converter
Pulse
Charging
Circuit
Figure 2: General Topology for Baseline MVDC System
2.1.1 Main Generators
The main generator modules make use of the notional twin-shaft gas turbine model
(Section 3.1.1.2) for the prime mover, the notional round rotor synchronous machine model
(Section 3.1.2.1) for the synchronous machine, the IEEE Type AC8B exciter model
(Section 3.1.3.1) for the exciter, and the notional diode rectifier (Section 3.6.1.1) for the rectifier,
as illustrated by Figure 3. The inputs to the generator module are the requested speed, ωr, the
requested DC voltage at the terminals of the rectifier, Vdc-r, and the requested power to be
supplied from the unit, Pr. The two exposed electrical nodes, p and n, are the positive and
negative rail connection points, respectively. The prime mover model provides an input power,
Pshaft, to the synchronous machine model, which, in turn, provides the shaft speed, ωshaft, as
feedback. (Note that the per unit power from the prime mover must be scaled before being input
to the synchronous machine if the prime mover rated power is not the same as the base apparent
power for the synchronous machine.) The synchronous machine model also accepts a field
winding excitation voltage, Ef, from the exciter model and exposes three electrical nodes (A, B,
and C), which are connected to the rectifier model. At these nodes, the power supplied by the
generator, P, is measured. From the positive and negative rail electrical nodes, the rail-to-rail
DC voltage, Vdc, is measured. The measured voltage is supplied to the exciter model, and the
3
measured power is used, in conjunction with the power reference, to provide an adjustment to the
reference voltage to the exciter, based on the power droop characteristic. The parameter values
employed for the model are given in Table 2. Note that the default speed governor model for the
twin-shaft gas turbine was replaced by a PI controller, given by (1), with anti-windup controls
enabled. Deviations from the default parameter values for the prime mover and exciter models
are given in Table 3 and Table 4.
kdroop
+
Σ
Pr
Vdc-r
+
+
Σ
Vdc
Exciter
P
Ef
ωr
Prime
Mover
Pshaft
kscale
A
Synchronous B
Machine
C
Rectifier
p
n
ωshaft
Figure 3: Main Generator Sets for Baseline MVDC System
H SG ( s )  k p  SG  k i  SG
1
s
(1)
Table 2. Parameters for Main Generator Modules of Baseline MVDC System
Parameter
kdroop
kscale
Description
Value
Power droop factor.
0.05
Prime mover scaling factor (prime mover rated 0.7660
power (36 MW) divided by synchronous
machine base apparent power (47 MVA).)
Source
Table 3. Parameters for Prime Mover Model of Main Generator Module of Baseline MVDC System
Parameter
kp-SG
ki-SG
Description
Speed governor proportional gain.
Speed governor integral gain.
4
Value
25
8
Source
Table 4. Parameters for Exciter Model of Main Generator Module of Baseline MVDC System
Parameter
kDR
kIR
kPR
Description
PID controller derivative gain.
PID controller integral gain.
PID controller proportional gain.
Value
0
6.0
6.0
Source
2.1.2 Auxiliary Generators
The main generator modules make use of the notional single-shaft gas turbine model
(Section 3.1.1.1) for the prime mover, the notional round rotor synchronous machine model
(Section 3.1.2.1) for the synchronous machine, the IEEE Type AC8B exciter model
(Section 3.1.3.1) for the exciter, and the notional diode rectifier (Section 3.6.1.1) for the rectifier,
as illustrated by Figure 3. The connection of models within this subsystem is described in
Section 2.1.1. The parameter values employed for the model are given in Table 5. Note that the
default speed governor model for the sing-shaft gas turbine was replaced by a PI controller,
given by (1), with anti-windup controls enabled. Deviations from the default parameter values
for the prime mover, synchronous machine, exciter, and rectifier models are given in Table 6,
Table 7, Table 8, and Table 9, respectively.
H SG ( s )  k p  SG  k i  SG
1
s
(2)
Table 5. Parameters for Auxiliary Generator Modules of Baseline MVDC System
Parameter
kdroop
kscale
Description
Value
Power droop factor.
0.05
Prime mover scaling factor (prime mover rated 0.8
power (4 MW) divided by synchronous
machine base apparent power (5 MVA).)
Source
Table 6. Parameters for Prime Mover Model of Auxiliary Generator Module of Baseline MVDC System
Parameter
kp-SG
ki-SG
Description
Speed governor proportional gain.
Speed governor integral gain.
Value
25
8
Source
Table 7. Parameters for Synchronous Machine Model of Auxiliary Generator Module of Baseline
MVDC System
Parameter
Sr
Rs
Description
Rated apparent power (MVA).
Stator resistance (pu).
Value
5
5.0e-3
5
Source
Ll
Lmd
Lmq
Rfd
Llfd
H
p
Stator leakage reactance
D-axis unsaturated magnetizing inductance
Q-axis unsaturated magnetizing inductance
Field resistance
Field leakage inductance
Inertia constant (MW*s/MVA)
Pole pairs
0.1
1.0
1.0
1.0e-3
0.05
10
1
Table 8. Parameters for Exciter Model of Auxiliary Generator Module of Baseline MVDC System
Parameter
kDR
kIR
kPR
Description
PID controller derivative gain.
PID controller integral gain.
PID controller proportional gain.
Value
0
6.0
6.0
Source
Table 9. Parameters for Rectifier of Auxiliary Generator Module of Baseline MVDC System
Parameter
Cd
Ls
Description
DC side filter capacitance (F).
AC side series inductance (H).
Value
0.111e-3
1.1e-3
Source
2.1.3 Propulsion Systems
The propulsion system modules are modeled as shown in Figure 4. The notional fixed-pitch
propeller model and notional destroyer hydrodynamic characteristics models are described in
Section 3.2.4.1 and Section 3.2.5.1, respectively. The notional permanent magnet synchronous
machine, described in Section 3.2.1.1, is used to model the permanent magnet machine. The
motor drive is modeled as a two-level IGBT bridge, as described in Section 3.2.2.1, and the
hysteresis current control described in Section 3.2.3.1 is employed for the motor drive controls.
The shunt breaking resistor model, described in Section 3.7.3.1, is employed for the braking
resistor model in order to dissipate power regenerated from the drive during braking of the
propellers. The modules each expose two electrical nodes, p and n, which are connected to the
positive and negative rails, respectively, of the medium voltage distribution bus, as illustrated in
Figure 2. The modules also take a requested propeller speed, ωr. Each of the modules provides
propeller thrust, Fship1 and Fship2, to the hydrodynamics model, which, in turn, provides the ship
speed, vship. The propeller model takes the shaft speed, ωshaft, as an input from the machine
model, and provides the counter torque on the shaft, Tprop, as an output which is fed back to the
machine model. The motor drive controls make use of the requested propeller speed, ωr, the
actual propeller speed, ωshaft, the rotor angle, θ (obtained from integration of the shaft speed), and
the phase currents of the propulsion motor, Ia, Ib, and Ic. The gating pulses for the motor drive,
g1 through g6, are supplied from the controls to the motor drive. The parameters for the modules
are given in Table 10, and the deviations from the default values for the parameters of the
propulsion motors, motor drive controls, and braking resistor models are given in Table 11,
Table 12, and Table 13, respectively. The values for the moments of inertia for the permanent
magnet machines reflect the inclusion of the moments of inertia of the propellers, propeller
shafts, and entrained water, given by Table 37. Here, an inertia constant of H=0.5 MW∙s/MVA
6
was assumed for each of the synchronous machines, and this moment of inertia was added to the
values indicated in Table 37.
Starboard Propulsion Module
p
Rf
Lf
Drive
Cf
n
Tprop
Motor
Drive
BR1
A
B
C
Braking
Resistor
Permanent
Magnet
Machine
ωshaft
Notional
Fixed-Pitch
Propeller Model
Fship1
Ia … Ic
Fship2
Notional Destroyer
Hydrodynamic
Characteristics
Vship
(From Port Propeller)
g1 … g6
Motor
Drive
Controls
ωr
1
s
θ
Figure 4: Propulsion System Module and Hydrodynamics Module for Baseline MVDC System
Table 10. Parameters for Propulsion Modules of Baseline MVDC System
Parameter
Cf
Lf
Rf
Description
Filter capacitance (F).
Filter inductance (H).
Filter resistance (Ω).
Value
15.0e-3
10.0e-6
0.001
Source
Table 11. Parameters for Permanent Magnet Machine for Propulsion Module of Baseline MVDC System
Parameter
J
J
Description
Moment of inertia (kg∙m2) (Starboard)
Moment of inertia (kg∙m2) (Port)
Value
4.3687e5
4.5881e5
Source
Table 12. Parameters for Motor Drive Controls for Propulsion Module of Baseline MVDC System
Parameter
Iq-r-max
Iq-r-min
Description
PI controller upper limit (A).
PI controller lower limit (A).
Value
8.9550e3
0
Source
Table 13. Parameters for Braking Resistor for Propulsion Module of Baseline MVDC System
Parameter
Vmax
Description
Maximum voltage set point (V).
Value
6500
Source
2.1.4 Ship Service Loads
The implementation of the zonal loads follows the power ratings for cruise and battle mode (see
Section 3.3.1) and connects each load type using or-ing diodes to the medium voltage DC bus.
7
Due to the computational complexity, only Zone 1 has been implemented in detail, see Figure 5.
The implementation of the individual load types are: DC 1—constant resistance (Figure 6), DC
2—constant power using current injection (Figure 7), AC 1—constant impedance (Figure 8), AC
2—uncontrolled induction motor (10% of load level) and constant impedance (90% of load
level) (Figure 9), and single-phase loads allowing for unbalanced demands (Figure 10). The load
level can be switched between cruise (Mode = 2) and battle mode (Mode = 1).
1
V+
V+
Mode
Type 3
AC load
1 phase
208 V (L-L)
V-
Type 2
AC load
IM/RL
V-
V-
V-
3
V-
Mode
V+
Type 1
AC load
3 phase
208 V (L-L)
Constant
power
DC 2
Constant
impedance
DC 1
Vstb+
Mode
V+
Mode
1
V+
Vport+
Mode
Mode
2
V-
Figure 5: Five load types represent the detailed zonal load demand (Zone 1)
8
1
ZoneData.CruiseMode
== 0
Constant1
Compare
To Zero1
1
RDC 1
Battle
Data Type Conversion
g
1
m
2
C ruise
Battle
int32
Mode
1
Compare
To Zero
g
Constant
2
== 0
m
ZoneData.BattleMode
V+
+ v
-
out_LoadCenter_Vdc_RDC1_Z1
V
2ws 1
RDC 1
C ruise
i
+ -
out_LoadCenter_Idc_RDC1_Z1
I
2ws 2
2
V-
Figure 6: Zonal load DC 1 (constant resistance)
ZoneData.PDC2(ZoneData.BattleMode)
ZoneData.RDC2fp.num{1}(z)
Product1
Constant3
Product2
Compare
To Zero
CCS
DC 2
Rp
ZoneData.CruiseMode
== 0
Constant1
Compare
To Zero1
int32
Data Type Conversion
-
== 0
Constant
Saturation
s
ZoneData.BattleMode
V+
+
1
1
ZoneData.RDC2fi.den{1}(z)
Product
TF current
TF power
ZoneData.PDC2(ZoneData.CruiseMode)
Mode
ZoneData.RDC2fi.num{1}(z)
ZoneData.RDC2fp.den{1}(z)
Constant2
i
+ -
+ v
-
out_LoadCenter_Vdc_RDC2_Z1
V
2ws 1
out_LoadCenter_Idc_RDC2_Z1
2ws 2
I
2
V-
Figure 7: Zonal load DC 2 (constant power using current injection model)
9
V+
out_LoadCenter_Vabc_AC1_Z1
out_LoadCenter_Iabc_AC1_Z1
RLdc
ZoneData.PT150ms.num{1}(z)
Cf
A
B
C
PT1 filter
g
out_LoadCenter_p_AC1_Z1
C
SwBC
SwAB
SwBB
1
g
1
g
1
g
g
SwC C
SwC B
2
SwAC
-K-
m
Gain2
Vabc (pu)
2
Vabc_inv
m
Uref
m
Pulses
2
1
V-
m
Voltage Regulator
2
m
g
out_LoadCenter_Idc_AC1_Z1
I
1
Three-Phase
V-I Measurement
1
Universal
Bridge
+ i
-
B
Rf Lf
Dot Product
g
C
Vabc
Iabc
a
b
c
2
B
-
A
A
B
C
m
A
B
C
1
A
2
+
Cdc
out_LoadCenter_pAvg_AC1_Z1
ZoneData.PT150ms.den{1}(z)
2
1
z
Discrete
PWM Generator
m
Vd_ref (pu)
Vref (pu)
B
C
B
C
B
C
B
C
C
B
A
RsB
A
A
ZoneData.BattleMode
A
Pp
RsC
A
B
C
A
C
B
1
A
out_LoadCenter_m_AC1_Z1
== 0
Compare
To Zero
ZoneData.CruiseMode
1
== 0
int32
Mode
Three-Phase
Parallel RLC Load
C ruise
Compare
To Zero1
Three-Phase
Parallel RLC Load
Battle
Data Type Conversion
Figure 8: Zonal load AC 1 (constant impedance)
out_LoadCenter_Vabc_AC2_Z1
out_LoadCenter_Iabc_AC2_Z1
PT1 filter
m
Vd_ref (pu)
1
RL
C ruise
B
C
<Rotor speed (wm)>
<Rotor speed (wm)>
int32
-K-
<Electromagnetic
Gain1
torque Te (N*m)>
Mode
out_LoadCenter_rpm_AC2_Z1
out_LoadCenter_Tem_AC2_Z1
1
(2*pi*1800/60)^3
ZoneData.PAC2(ZoneData.CruiseMode)
,2
Product
*
Multiport
Switch
ZoneData.BattleMode
== 0
Compare
To Zero
ZoneData.CruiseMode
== 0
Compare
To Zero1
Figure 9: Zonal load AC 2 (uncontrolled induction motor and RL-impedance)
10
g
1
2
C
m
out_LoadCenter_m_AC2_Z1
ZoneData.PAC2(ZoneData.BattleMode)
m
SwC C 1
Induction Motor
1
1
g
1
g
SwBC 1
2
1
g
SwAC 1
2
A
Vref (pu)
Discrete
PWM Generator
SwC C
-K-
Vabc (pu)
z
SwBC
m
Vabc_inv
B
V-
Uref
A
T=kw ^2
Tn=P/(2*pi*w s)
k=Tn/w s^2
rpm=1800
SwAC
Gain2
Tm
Pulses
m
Voltage Regulator
1
2
C
out_LoadCenter_Idc_AC2_Z1
I
2
C
Three-Phase
V-I Measurement
m
B
C
R-Lf
1
C
g
C
Universal
Bridge
out_LoadCenter_p_AC2_Z1
Dot Product
2
B
Vabc
Iabc
a
b
c
m
B
B
A
B
A
A
A
g
-
A
m
Cdc
i
+ -
ZoneData.PT150ms.den{1}(z)
g
+
out_LoadCenter_pAvg_AC2_Z1
1
Relay breaking R
C
2
Vbus
Rbrk
ZoneData.PT150ms.num{1}(z)
Cf
2
+
- v
RLdc
A
B
brk
m
V+
1
g
1
RL
Battle
V+
out_LoadCenter_Vabc_AC3_Z1
out_LoadCenter_Iabc_AC3_Z1
RLdc
ZoneData.PT150ms.num{1}(z)
Cf
B
C
A
out_LoadCenter_p_AC3_Z1
B
C
C
R-Lf
SwAB
1
g
1
g
1
g
SwC C
SwBB
1
SwBC
g
SwAC
-K-
2
Gain2
m
Vabc (pu)
SwC B
2
Vabc_inv
m
Uref
2
Pulses
m
1
V-
m
Voltage Regulator
2
m
g
out_LoadCenter_Idc_AC3_Z1
I
1
Three-Phase
V-I Measurement
g
Universal
Bridge
Dot Product
2
C
Vabc
Iabc
a
b
c
m
B
C
A
A
B
1
A
B
2
A
-
+ -i
PT1 filter
g
+
Cdc
out_LoadCenter_pAvg_AC3_Z1
ZoneData.PT150ms.den{1}(z)
2
1
z
Discrete
PWM Generator
m
Vd_ref (pu)
A
B
C
C
RsB
C
B
A
ZoneData.BattleMode
B
Pp
RsC
A
B
A
B
C
A
1
C
Vref (pu)
out_LoadCenter_m_AC3_Z1
== 0
Compare
To Zero
ZoneData.CruiseMode
1
== 0
Compare
To Zero1
int32
Mode
PQ Load ab
C ruise
Data Type Conversion
PQ Load bc
C ruise
PQ Load ab
Battle
PQ Load ca
C ruise
PQ Load bc
Battle
PQ Load ca
Battle
Figure 10: Zonal load AC 3 (single-phase constant impedances)
Demux
hypot
modulation index
2
m
1
abc
dq0
Vabc (pu)
PI
sin_cos
abc_to_dq0
Transformation
Selector
Vd Vq
Vd Vq inv erter
Discrete
PI Controller
2
dq0
abc
sin_cos
1
Vabc_inv
dq0_to_abc
Transformation
Vd_ref (pu)
0
0
Freq
V0
Vq_ref (pu)
Sin_Cos
wt
Discrete
Virtual PLL
Figure 11: PWM-Inverter Voltage Regulator
The corresponding parameters of the implementation are given in Table 14 through Table 18.
The dq0-abc transformations used in the PWM-inverter controls are taken from the
SimPowerSystems library. Figure 11 depicts the dq-based control scheme using the nominal
11
fixed frequency as reference, the phase voltages are per-unitized using the peak-value of the
nominal phase-voltage.
Table 14. Parameters for detailed MVDC zonal loads: DC1—constant resistance
Parameter
PDC1
RDC1
Description
taken from zonal data
equivalent resistance (ohm)
Default Value
Source
(5000V)2/PDC1
Table 15. Parameters for detailed MVDC zonal loads: DC2—constant power
Parameter
PDC2
RDC2
VUL
VLL
RDC2p
Tp
Ti
Description
taken from zonal data
equivalent resistance (ohm)
upper voltage limit for current injection (V)
lower voltage limit for current injection (V)
parallel resistance (ohm)
power demand time constant (s)
current injection time constant(s)
Default Value
Source
(5000V)2/PDC2
10000
4000
5000
1/(2π)
1/(2π1000)
Table 16. Parameters for detailed MVDC zonal loads: AC1—constant impedance
Parameter
VAC1
fAC1
PAC1
QAC1
kp
kI
PI limits
fc
Rf
Lf
QCf
PCf
RdcL
Ldc
Cdc
Pp
RsC
RsB
Ron
Rs
[Vf Vfd]
[Tf Tt]
Description
AC line-to-line voltage (V)
frequency (Hz)
from zonal load data
computed using PF = 0.8 (kVAR)
proportional gain of voltage regulator
integral gain of voltage regulator
PI control upper and lower limits
PWM carrier frequency (Hz)
filter resistance (ohm)
filter inductance (H)
parallel filter capacitive demand (VAR)
parallel filter active demand (W)
resistor in parallel to DC inductor (ohm)
DC filter inductance (H)
DC filter capacitance (F)
permanent resistive load (W)
series resistance (ohm)
series resistance (ohm)
on-resistance of switches (breakers, bridge)
(ohm)
snubber resistance of switches (breakers,
bridge) (ohm)
Forward voltages (V)
Fall time and tail time of bridge switches (s)
12
Default Value
450
60
[682.5 300]
0.02
25
[1 -1]
1260
1e-4
200e-6
30e3
100
5000
100e-6
2.5e-3
5000
1e-3
1e-3
1e-4
5000
[0.6 0.6]
[Ts 2Ts}
Source
Table 17. Parameters for detailed MVDC zonal loads: AC2—uncontrolled induction motor
and constant impedance
Parameter
VAC2
fAC2
PAC2
PAC2RL
QAC2RL
kp
kI
PI limits
fc
Rf
Lf
QCf
PCf
RdcL
Ldc
Cdc
Rbrk
VUL
VLL
Ron
Rs
[Vf Vfd]
[Tf Tt]
Pn
Vn
fn
Rs
Lls
Rr’
Llr’
Lm
J
F
p
Description
AC line-to-line voltage (V)
frequency (Hz)
induction motor load (from zonal load data,
10%) (W)
constant impedance load (from zonal load data,
90%) (kW)
computed using PF = 0.8 (kVAR)
proportional gain of voltage regulator
integral gain of voltage regulator
PI control upper and lower limits
PWM carrier frequency (Hz)
filter resistance (ohm)
filter inductance (H)
parallel filter capacitive demand (VAR)
parallel filter active demand (W)
resistor in parallel to DC inductor (ohm)
DC filter inductance (H)
DC filter capacitance (F)
breaking resistance (ohm)
upper voltage limit (V)
lower voltage limit (V)
on-resistance of switches (breakers, bridge)
(ohm)
snubber resistance of switches (breakers,
bridge) (ohm)
Forward voltages (V)
Fall time and tail time of bridge switches (s)
Induction motor
Nominal power (VA), nominal PF = 0.8
Nominal voltage (V)
Nominal frequency (Hz)
Stator resistance (ohm)
Stator leakage inductance (H)
Rotor resistance (ohm)
Rotor leakage inductance (H)
Mutual inductance (H)
Inertia (kg m2)
Friction (N m s)
Pole pairs
13
Default Value
450
60
[643.5 576]
[482.6 432]
0.04
50
[1 -1]
1260
1e-5
200e-6
100e3
10
5000
50e-6
5e-3
1
850
810
1e-4
5000
[0.6 0.6]
[Ts 2Ts}
PAC2 / 0.8
VAC2
fAC2
0.029
6e-4
0.022
6e-4
34.6e-3
8
0.048
2
Source
Table 18. Parameters for detailed MVDC zonal loads: AC3—single-phase loads
Parameter
VAC3
fAC3
PAC3
QAC3
PAB
QAB
PBC
QBC
PCA
QCA
kp
kI
PI limits
fc
Rf
Lf
QCf
PCf
RdcL
Ldc
Cdc
Rp
Description
Default Value
AC line-to-line voltage (V)
208
frequency (Hz)
60
from zonal load data, divided by 3 as base
power level
computed using PF = 0.8 (kVAR)
[682.5 300]
phase A-B (kW), 110% of base power
[146.7 130]
phase A-B (kVAR), PF=0.85
[82.6 80.6]
phase A-B (kW), 90% of base power
[120 117]
phase A-B (kVAR) , PF=0.85
[74.4 72.5]
phase A-B (kW), 105% of base power
[140 136.5]
phase A-B (kVAR) , PF=0.85
[86.8 84.6]
proportional gain of voltage regulator
0.02
integral gain of voltage regulator
25
PI control upper and lower limits
[1 -1]
PWM carrier frequency (Hz)
1260
filter resistance (ohm)
1e-4
filter inductance (H)
200e-6
parallel filter capacitive demand (VAR)
40e3
parallel filter active demand (W)
100
resistor in parallel to DC inductor (ohm)
5000
DC filter inductance (H)
100e-6
DC filter capacitance (F)
2.5e-3
breaking resistance (ohm)
5000
Source
The remaining zones 2 through 5 have been implemented using a constant power load, modeled
through current injection. The masked zone is shown in Figure 12, the details are shown in
Figure 13. The implementation allows the nominal power demand to be augmented by a
harmonic component, see Table 19 for parameter values chosen.
14
1
Vport+
1
V+
Mode
Mode
V-
Constant
power
DC load
2
V3
Vstb+
Figure 12: Simplified zonal load (masked zone and DC bus interconnection)
Sine Wave
Sine Wave1
-CZoneData.Fi.num{1}(z)
P battle
Product1
-C-
Product
P cruise
ZoneData.Fi.den{1}(z)
TF current
Product2
Battle
Compare
To Zero
Rp
ZoneData.CruiseMode
== 0
Cruise
Compare
To Zero1
CCS
DC 2
-
== 0
Saturation
s
ZoneData.BattleMode
V+
+
1
+
- v
> ZoneData.Vmin
V
Compare To Constant
out_LoadCenter_Vdc_Z2
2ws 1
1
Mode
int32
Data Type Conversion
+ -i
out_LoadCenter_Idc_Z2
2ws 2
I
2
V-
Figure 13: Simplified zonal load (shown here is Zone 2)
15
Table 19. Parameters for simplified zonal load representation (Zones 2, 3, 4, and 5)
Parameter
P
Pr
fr
Ti
Rp
eta
Description
Power demand (taken from zonal load data)
power ripple, 10% of power demand (W)
ripple frequency (Hz)
current injection time constant (s)
parallel resistance (ohm)
interface efficiency (%)
Vmin
minimum voltage level (V)
Default Value
Source
1000
1/(2π700)
5000
97 (battle),
94 (cruise)
4000
2.1.5 Pulse Load
The pulse load is based on a simplified version of that described in Section 3.5.2 and is
implemented using as constant power load. See Figure 14 for the model and Table 20 for
parameter values. The pulse is a sequence of power demands that can be triggered through the
positive edge of the “trigger input.” The look-up table (see the model in Figure 14) uses the
vectors tpulse and Ppulse to generate the pulse pattern.
out_PulseLoad_Pd
2ws 3
K Ts
PulseLoad.Fi.num{1}(z)
Lookup
Table
PulseLoad.Fi.den{1}(z)
Gain
efficiency
1
Product
TF current
V+
Saturation
Rp
-
T
10 s
Discrete-Time
Discrete
Integrator
Monostable
s
Trigger
-K-
z-1
CCS
+
- v
> PulseLoad.Vmin
V
Compare To Constant
+
1
out_PulseLoad_Vdc
+ -i
out_PulseLoad_Idc
I
2
V-
Figure 14: Pulse load model
16
Table 20. Parameters for pulse load
Parameter
tpulse
Description
pulse timing (s)
Ppulse
pulse power (kW)
fr
Ti
Rp
eta
Vmin
ripple frequency (Hz)
current injection time constant (s)
parallel resistance (ohm)
interface efficiency (%)
minimum voltage level (V)
Default Value
Source
[0 1 1.01 3.5 3.51 7 7.01
9.25 9.26 10]
[0 0 400 400 1300 1300
25000 25000 0 0]
1000
1/(2π700)
5000
97
4000
2.1.6 Energy Storage
The energy storage model is based on the supercapacitor (see Section XX) with an isolated DCDC converter interface to the MVDC bus. The circuit model and controls are shown in Figure 15,
the data are given in Table 21, Table 22, and Table 23.
Table 21. MVDC Supercapacitor Parameters
Parameter
RSC
LSC
CSC
VSC0
Description
Series resistance (ohm)
Series inductance (H)
Capacitance (F)
Initial capacitor voltage (V)
Default Value
100e-6
200e-6
300
850
Source
Table 22. Parameters for MVDC Energy Storage’s Isolated DC-DC converter
Parameter
RHV1
RHVC
CHVC
LHV
VH
VL
f
S
R1
L1
R2
L2
Rm
Lm
Description
High-voltage side circuit
Resistance towards ground (ohm)
Series resistance (ohm)
Capacitor (mF)
Inductance (uH)
Transformer
high-side voltage (V)
low-side voltage (V)
frequency (Hz)
Nominal power (MVA)
Primary side winding resistance (pu)
Primary side leakage reactance (pu)
Secondary side winding resistance (pu)
Secondary side leakage reactance (pu)
Magnetization resistance (pu)
Magnetization reactance (pu)
Low-voltage side circuit
17
Default Value
500
0.001
2.7
300
5000
850
700
4
0
0
0
0
5000
5000
Source
RCC
CCC
LCP
RLV1
RLVC
CLVC
RLV
RON
RS
CS
f
Clamping capacitor series resistance (ohm)
Clamping capacitor (mF)
Inductance low-voltage side (H)
Resistance towards ground (ohm)
Series resistance of capacitor (ohm)
Low-voltage capacitor (F)
Resistance low-voltage side (ohm)
Switch parameters
resistance (ohm)
snubber resistance (ohm)
snubber capacitance (F)
switching frequency (Hz)
1e-4
4.86
12e-3
500
1e-4
7e-3
10e-6
10e-6
1e5
1e-6
700
Table 23. Controller Parameters for MVDC Energy Storage’s Isolated DC-DC converter
Parameter
Tfbu
kP
kI
kD
N
max
min
Escale
VSCREF
VSCDB
ISCmaxC
Tfbu
kP
kI
kD
N
max
min
Escale
VHVREF
VSCMIN
ISCmaxD
Description
Buck mode PI-controller with anti-windup
filter time constant (s)
proportional gain
integral gain
derivative gain
derivative filter factor
maximum control signal
minimum control signal
Scaling factor on error signal
Reference voltage for charging (V)
Deadband on capacitor voltage (V)
Maximum charging current (A)
Boost mode PI-controller with anti-windup
filter time constant (s)
proportional gain
integral gain
derivative gain
derivative filter factor
maximum control signal
minimum control signal
Scaling factor on error signal
HV reference voltage (V)
Minimum voltage (stop discharging) (V)
Maximum discharging current (A)
18
Default Value
10e-3
0.13
1.4
0
100
0.48
0.02
1e-2
850
200
6000
10e-3
0.042
0.5625
0
100
0.48
0
1e-3
5010
500
6000
Source
Figure 15: MVDC energy storage circuit and controls
19
1
[VHV]
v +
-
Multimeter
7
[ILV]
[VLV]
[IHV]
[VHV]
[VCc]
[ICc]
[Iw2]
[Iw1]
[VLVC]
[IHVC]
[VHVC]
2
|u|
|u|
out_es_ICc
out_es_VCc
[ICc]
[VCc]
buck.filter.den{1}(z)
buck.filter.num{1}(z)
buck.filter.den{1}(z)
buck.filter.num{1}(z)
buck.filter.den{1}(z)
buck.filter.den{1}(z)
buck.filter.num{1}(z)
out_es_PLV
1
out_es_VHVC
[VHVC]
out_es_PHV
out_es_Iw2
out_es_Iw1
[Iw1]
[Iw2]
out_es_boostCtrl
[BoostCtrl]
out_es_VLV
[VLV]
out_es_buckCtrl
out_es_ILV
[ILV]
[BuckCtrl]
out_es_VLVC
out_es_IHV
[VLVC]
[IHV]
out_es_VHV
out_es_IHVC
S7
1
[FP78]
2
[FP34]
[FP12]
max
1
S2
S4
max
0
>
,2
Multiport
Switch
*
1
0
current filter
boost.filter.den{1}(z)
boost.filter.num{1}(z)
es.Ctrl.VSCmin
[VLV]
[VHV]
-K-
Mode
2
3
1
[VLV]
[ILV]
==
100
Cc
Sc1
==
Relay
current filter1
AND
0
>
-K-
PID(z)
[FPScBuck]
[FP78]
[FP56]
Constant5
0.5
RLV
2
out_es_FPScBuck
out_es_FP78
>
>
[BoostCtrl]
>
>
[BuckCtrl]
BrkLVstat
out_es_FP56
Triangle 2
Triangle 1
Buck PID
PID(z)
scaleEi Boost
Switch1
PID
>
-K-
C LV
scaleEv
RLV2
RLV1
LC P
Switch
Sc2
[FPScBoost]
out_es_eff
AND
buck.filter.den{1}(z)
buck.filter.num{1}(z)
es.Ctrl.ISCmaxC
S3
S1
[FPScBuck]
boost.filter.num{1}(z)
-Kboost.filter.den{1}(z)
es.Ctrl.ISCmaxD
droop1
droop
filter4
[ILV]
es.Ctrl.VHVref
Linear Transformer
LHV
[VHV]
S6
S5
[IHVC]
C HV
S8
[FP56]
buck.filter.num{1}(z)
RHV12
RHV11
BrkHV
1
BrkHVstat
VHV
VnHV
2
VpHV
[IHV]
m
g
m
E
C
g
m
g
1
g
m
C
E
m
g
E
C
g
m
C
E
g
m
C
E
g
m
C
E
m
g
E
C
g
m
C
E
g
m
C
E
E
C
[FPScBoost]
[FP34]
[FP12]
AND
AND
NOT
VLV
+ v
-
2
m
BrkLV
NOT
1
g
XOR
AND
AND
AND
AND
[VLV]
[FP78]
[FP56]
[FPScBuck]
[FPScBoost]
out_es_FPScBoost
out_es_FP34
out_es_FP12
[FP34]
[FP12]
AND
Super
C apacitor
[ILV]
2.2 MVAC System
The general topology of the MVAC ship power system is shown in Figure 16. The main
distribution bus has 4.16 KV voltage and 60 Hz frequency. Each component in the system model
has been tested individually in Matlab/Simulink platform, and they all work properly.
Auxiliary AC
Generator 1
Main AC
Generator 1
DC/DC
Converter
PWM
Inverter/converter
AC Circuit
Breaker

=
=
GT
MTG1
Energy Storage System
AC/DC
Converter
AC
Disconnect
=
GT

=
Capacitor
bank
Stern Cross-hull
Disconnect
ATG1
GB
AC Circuit
Breaker
AC Disconnect
Drive Inverter
=

Port
PM
MVAC (4.16 KV, 60 Hz)
Port Bus
Radar
Zone 4
Zone 3
Zone 2
Load center
Load center
Load center
Zone 1
Load center
Bow
Cross- hull
Disconnect
Zone 5
Deck house
MVAC (4.16 KV, 60 Hz)
Starboard Bus

=
AC/DC Converter
AC Circuit
Breaker
ATG2
GB
Auxilary AC
Generator 2
GT
Starboard
PM
=

Drive Inverter
GT
Pulsed load
MTG2
Main AC
Generator 2
Figure 16: General Topology for Baseline MVAC System
2.2.1 Gearbox for Auxiliary Generators in the MVAC System
In case of the auxiliary generators of the MVAC system, in order to reduce the speed from
14,400 rpm to 3600 rpm, gear box (in terms of gearbox friction) is added between the turbine
and generator. In order to demonstrate the gear box in Matlab/Simulink model, a gain is added in
"wm" to change the pu value into actual value; also in turbine block, "wm" is changed back to
the pu value.
2.2.2 MVAC System Generators
The main parameters of the synchronous generators selected for the MVAC ship power system
are presented in Table 24.
Table 24. Parameters for Generator Models of MVAC System
Generators 1
and 2 (main)
20
Generator 3 and
4 (auxiliary)
Main specifications
Power (MVA)
Speed (rpm)
Number of poles
Frequency (Hz)
Voltage (kV)
Power factor
Parameters in (p.u); where
p.u.=actual value/base value;
Base impedance=base (KV)2/base MVA
Stator winding resistance
Stator winding leakage inductance
Stator d-axis mutual inductance
Stator q-axis mutual inductance
Field-winding resistance
Field-winding leakage inductance
d-axis damper resistance
d-axis damper leakage inductance
q-axis damper1 resistance
q-axis damper1 leakage inductance
q-axis damper2 resistance
q-axis damper2 leakage inductance
Inertia Constant
Friction factor (N.m.s)
Rs
Ll
Lmd
Lmq
Rf
Llf
Rkd
Llkd
Rkq1
Llkq1
Rkq2
Llkq2
H
F
47
3600
2
60
4.16
0.8
5
3600
2
60
4.16
0.8
0.002
0.135
1.35
1.35
0.001
0.081
0.045
0.0225
0.01
0.0405
0.01
0.0405
4s
0.04
0.005
0.09
0.9
0.9
0.001
0.045
0.04
0.018
0.04
0.018
0.04
0.018
5s
0.04
2.2.3 AC/DC Rectifiers
MVAC system uses uncontrolled diode rectifiers in four zonal loads (Zone1-Zone4). Table 25
shows the parameters for the uncontrolled diode rectifiers in the zonal loads.
Table 25. Parameters for Uncontrolled Diode Rectifier Models of MVAC System
Parameters
Snubber capacitance, Cs
Snubber resistance, Rs
On-state resistance, Rd
Forward voltage, Vf
Values
1e-7 F
10000 Ohm
0.001 Ohm
0.8 V
2.3 HFAC System
The general topology of the HFAC power system is shown in Figure 17.
21
Figure 17: General Topology for Baseline HFAC System
2.3.1 Prime Movers
The prime movers consists of two large twin-shaft gas turbines rated at 36MW with a nominal
shaft speed of 3600rpm, and two smaller single-shaft gas turbines rated at 4MW with a nominal
speed of 14400rpm. The total number of generating units used in this study and their ratings, are
not necessarily optimal. They were chosen as a baseline system which will, eventually, be
compared to other configurations with different number of units and power ratings. The main
turbine parameters are shown in Table 26.
Table 26. Parameters for Gas Turbine Models of HFAC System
Main turbine specifications
Type
Turbine cycle
Power (MW)
Speed (rpm)
Engine speed (rpm)
Main turbine control parameters
Speed governor gain
Speed governor time constant
Maximum power limit
Minimum power limit
Valve positioning gain
Gas turbines 1 and 2 (main)
Gas turbines 3 and 4 (aux)
Twin-shaft
Simple-cycle
36
3600
~5000 (assumed)
Single-shaft
Simple-cycle
4
14400
N/A
25(4% droop)
0.01
1.5
-0.1
1
25
0.05
1.5
-0.1
1
22
Valve positioning time constant
Fuel system gain
Fuel system time constant
Combustor time constant
Compressor time constant
No load fuel (p.u)
Engine speed control parameters
Governor gain
Governor time constant
Governor lag
0.05
1
0.4
0.01
0.2
0.20
0.05
1
0.4
0.01
0.2
0.20
30
1
1
N/A
N/A
N/A
2.3.2 Generators
The electric generators are similar to those used in all three architectures in terms of type and
topology but they differ in some of their parameters. The main parameters of the synchronous
generators selected for the high-frequency power system are presented in Table 27. The
mathematical models are described in Section 3.0.
Table 27. Parameters for Generator Models of HFAC System
Generators 1 and 2 (main)
Generator 3 and 4 (aux)
47
3600
8
240
4.16
0.8
96%
5.25
14400
2
240
4.16
0.8
95.5%
0.002
0.15
1.5
1.5
0.001
0.09
0.01
0.045
0.01
0.045
0.01
0.045
0.005
0.1
1
1
0.001
0.05
- 0.02
0.04
0.02
0.04
0.02
0.04
Main specifications
Power (MVA)
Speed (rpm)
Number of poles
Frequency (Hz)
Voltage (kV)
Power factor
Efficiency
Parameters in (p.u)
Stator winding resistance
Stator winding leakage inductance
Stator d-axis mutual inductance
Stator q-axis mutual inductance
Field-winding resistance
Field-winding leakage inductance
d-axis damper resistance
d-axis damper leakage inductance
q-axis damper1 resistance
q-axis damper1 leakage inductance
q-axis damper2 resistance
q-axis damper2 leakage inductance
Rs
Ll
Lmd
Lmq
Rf
Llf
Rkd
Llkd
Rkq1
Llkq1
Rkq2
Llkq2
23
3.0 COMPONENT AND SUBSYSTEM MODELS
3.1
Components of Generator Sets
3.1.1 Prime Movers
3.1.1.1 Notional Single-Shaft Gas Turbine
A schematic representation of a simple-cycle, single-shaft gas turbine is illustrated by Figure 18.
In this type of setup the generator and turbine share the same shaft.
Air
Fuel Input
Exhaust
Figure 18: Single-shaft Gas Turbine
The gas turbine model described herein a transfer function-based model that consider the effects
of various components on the working fluid as it enters the compressor and exits through an
exhaust after transferring some of its energy to the turbine shaft that drives the generator. A
tested model using this approach, originally proposed by GE [6], is shown in Figure 19. In
general, the model includes a speed control loop, an acceleration control loop, and a temperature
control loop. This model is often used by the utility industry for power system stability studies of
power plants that use gas turbines [7]. Further simplifications of the model are often made when
they are justified by testing conditions. For example, the temperature loop can be omitted if the
temperature in the turbine can't reach critical limits that activate the control system. In addition,
the acceleration control loop is usually only needed during the start-up stage of the turbine, and
during normal operation this loop can be omitted as well. For the model employed as the
baseline notional single-shaft gas turbine, illustrated by Figure 20 and Figure 21 (acceleration
control), the temperature control has been omitted, but the acceleration control loop has been
retained. The parameters and default values for the model are given in Table 28, and the
corresponding equations and transfer functions are given in (3) through (8). Note that the
governor model can operate in either droop or isochronous mode, given the appropriate choice of
parameter values.
24
Figure 19: General Model for Single-shaft Gas Turbine
Speed
Governor
ωr
+
Σ
-
kflma
HSG(s)
π
min
kflmb
Compressor
+ +
Σ
HFS(s)
HC(s)
HCP(s)
WF
f1
Valve
Fuel Combustor
Positioner System
Limit 1
Fα
HVP(s)
π
Acceleration
Control
ωshaft
Figure 20: Notional Single-shaft Gas Turbine Model
kα-limit
ωshaft
+
s
-
Σ
ki-α
1
s
Fα
Figure 21: Acceleration Control for Notional Single-shaft Gas Turbine Model
25
Pshaft
W ( sX  1)
Z
H SG ( s ) 
Y
1 s
Z
(3)
a
H VP ( s)  c
b
1 s
c
(4)
H FS ( s ) 
1
(5)
1   FS s
H C ( s )  e  sTc
H CP ( s ) 
f1 (WF ,  shaft ) 
1
k flmb
W
F
(6)
1
(7)
1   CP s

 k flma   0.51   shaft 
(8)
Table 28. Parameters for Notional Single-Shaft Gas Turbine Model
Parameter
a
b
c
kflma
kflmb
kα-limit
ki-α
Llower-Limit1
Lupper-Limit1
Tc
W
X
Y
Z
τFS
τCP
Description
Valve positioner constant.
Valve positioner constant.
Valve positioner constant.
No-load fuel parameter.
No-load fuel parameter (1- kflma).
Acceleration limit (pu/s).
Acceleration control integral gain.
Lower limit for limit block “Limit 1” (fuel
limit).
Upper limit for limit block “Limit 1” (fuel
limit).
Combustor delay time (s).
Speed governor constant.
Speed governor constant.
Speed governor constant.
Speed governor constant.
Fuel system time constant (s).
Compressor discharge volume time constant (s).
26
Default Value
1
0.05
1
0.2
0.8
0.01
100
-0.1
1.5
0.01
25
0
0.05
1
0.4
0.2
Source
3.1.1.2 Notional Twin-Shaft Gas Turbine
In a twin-shaft system, the compressor is connected to a high-pressure turbine, on a separate
shaft from the generator that extracts power from the low-pressure turbine (see Figure 22). The
mathematical model representing a twin-shaft gas turbine is similar to that of a single-shaft
turbine (described in Section 3.1.1.1), but with an additional speed control loop for the generator
shaft. The model employed for the baseline notional twin-shaft gas turbine is illustrated by the
Figure. This model is very similar to that described in [8], which was tested in a power plant
installation. The notional twin-shaft gas turbine model is illustrated by Figure 23, Figure 24
(Gas Generator), Figure 25 (Engine Shaft Dynamics), and Figure 26 (acceleration control). The
parameters and default values for the model are given in Table 29, and the corresponding
equations and transfer functions are given in (9) through (17). Note that the governor model can
operate in either droop or isochronous mode, given the appropriate choice of parameter values.
As reported in [7], the use of turbine parameters obtained through field testing results in models
that are more representative of turbine dynamics than typical models that use assumed
parameters, which often require a tedious trial and error process until the simulation data
matches the experimental results. In the model for the twin-shaft turbine, the parameters for the
engine speed calculation are based on test data for a 46.5 MW gas turbine, as reported in [8].
This turbine rating is somewhat higher than the 36 MW turbine considered in this study.
Nevertheless, at this stage of this modeling effort, it is assumed that the data is representative. In
addition, the functions that define the turbine's torques are usually given by the manufacturer, as
a function of the fuel flow parameter and output shaft speed, in a format that includes the no-load
value of the fuel parameter. In the present twin-shaft model the torque functions were written in
the format just described, and using test parameters reported in [8] whenever applicable. During
this modeling period and in the near future, additional turbine test data will be sought, as those
reported in [7] and [8], in order to enhance the understanding of how to use published turbine
test data in developing accurate gas turbine models for power system dynamic studies.
Ultimately, a high-fidelity gas turbine model can be obtained when a gas turbine installation
becomes available and steady state tests can be performed to determine the needed parameters.
Air
Fuel Input
Exhaust
Figure 22: Simple-cycle Twin-shaft Gas Turbine
27
Speed
Governor
ωr
+
Σ
-
kflma
HSG(s)
π
Fα
Compressor
+ +
Σ
kflmb
HFS(s)
HC(s)
HCP(s)
WF
f1
Valve
Fuel Combustor
Positioner System
Limit 1
min
HVP(s)
π
Pshaft
Acceleration
Control
ωshaft
FE
Gas Generator
(Engine)
Figure 23: Notional Twin-shaft Gas Turbine Model
Engine
Speed
Governor
Engine Speed
Request
ωg-r
f3
WF
f2
Engine
Torque
Tg
HES(s)
+
FE
Σ
HESG(s)
-
ωg
Engine Shaft
Dynamics
Figure 24: Gas Generator (Engine) Model for Notional Twin-shaft Gas Turbine Model
Tg
+ Σ-
1
1
s
 Ig
ωg
x2
Figure 25: Engine Shaft Dynamics for Gas Generator (Engine) Model for Notional Twin-shaft Gas
Turbine Model
28
kα-limit
ωshaft
+
s
-
Σ
ki-α
Fα
1
s
Figure 26: Acceleration Control for Notional Twin-shaft Gas Turbine Model
W ( sX  1)
Z
H SG ( s ) 
Y
1 s
Z
(9)
a
H VP ( s)  c
b
1 s
c
(10)
H FS ( s ) 
1
(11)
1   FS s
H C ( s )  e  sTc
H CP ( s ) 
f1 (WF ,  shaft ) 
1
k flmb
f 2 (WF ,  g ) 
W
1
k flmb
(12)
1
(13)
1   CP s

 k flma   0.51   shaft 
F
W
F

 k flma   31   g 
(14)
(15)
f 3 (WF )  k EFR1WF  k EFR2
(16)
WE ( sX E  1)
ZE
H ESG ( s) 
Y
1 s E
ZE
(17)
29
Table 29. Parameters for Notional Twin-Shaft Gas Turbine Model
Parameter
a
b
c
kflma
kflmb
kEFR1
kEFR2
kα-limit
ki-α
Llower-Limit1
Lupper-Limit1
Tc
W
WE
X
XE
Y
YE
Z
ZE
τIg
τFS
τCP
Description
Valve positioner constant.
Valve positioner constant.
Valve positioner constant.
No-load fuel parameter.
No-load fuel parameter (1- kflma).
Engine speed request function slope.
Engine speed request function intercept.
Acceleration limit (pu/s).
Acceleration control integral gain.
Lower limit for limit block “Limit 1” (fuel
limit).
Upper limit for limit block “Limit 1” (fuel
limit).
Combustor delay time (s).
Speed governor constant.
Engine speed governor constant.
Speed governor constant.
Engine speed governor constant.
Speed governor constant.
Engine speed governor constant.
Speed governor constant.
Engine speed governor constant.
Time constant for engine shaft dynamics (s).
Fuel system time constant (s).
Compressor discharge volume time constant
(s).
Default Value
1
0.05
1
0.2
0.8
0.25
0.75
0.01
100
-0.1
Source
1.5
0.01
25
30
0
1
0.01
1
1
0
8
0.4
0.2
3.1.2 Electric Machines
3.1.2.1 Notional Round Rotor Synchronous Machine
The model employed for the notional round rotor synchronous machine for the baseline system
makes use of the synchronous machine model in Simulink SimPowerSystems [12]. The
interface to the model is illustrated by Figure 27. As shown, the model takes an input shaft
power, Pshaft, from a prime mover model and a field winding excitation voltage, Ef, from an
excitation system. The model provides the speed of rotation, ωshaft, as an output, and exposes
three electrical nodes, A, B, and C. For future reference it is important to note that models of
synchronous machines in the software packages Matlab\Simulink and PSCAD are slightly
different. Mainly, the field and d-axis damper-windings mutual inductance, also referred to as the
differential leakage inductance, is neglected in the Simulink synchronous machine models while
it is included in PSCAD. However, it can be set to zero if needed for model consistency between
the two software packages. The default parameters of the model are given in Table 30.
30
Ef
Pshaft
Synchronous
Machine
A
B
C
ωshaft
Figure 27: Interface for Notional Round Rotor Synchronous Machine
Table 30. Parameters for Notional Round Rotor Synchronous Machine
Parameter
Sr
Vr
fr
Rs
Ll
Lmd
Lmq
Rfd
Llfd
Rkd
Llkd
Rkq1
Llkq1
Rkq2
Llkq2
H
F
p
Vsat(Ifd)
Description
Rated apparent power (MVA).
Rated voltage (line-line, RMS) (kV).
Rated frequency (Hz).
Stator resistance (pu).
Stator leakage reactance
D-axis unsaturated magnetizing inductance
Q-axis unsaturated magnetizing inductance
Field resistance
Field leakage inductance
D-axis damper resistance
D-axis damper leakage inductance
Q-axis damper resistance
Q-axis damper leakage inductance
Q-axis damper resistance (2nd damper winding)
Q-axis damper leakage inductance (2nd damper
winding)
Inertia constant (MW*s/MVA)
Friction factor (pu).
Pole pairs
Saturation curve.
31
Default Value
47
4.16
240
2.0e-3
0.15
1.5
1.5
1.0e-3
0.09
0.01
0.045
0.01
0.045
0.01
0.045
6
0
4
See Figure 28
Source
Generator Power
2 Terminal Voltage (pu)
Terminal Voltage (pu)
1.8
1.6
1.4
1.2
1
0.8
0
2
4
6
Field Current (pu)
8
10
Figure 28: Default Saturation Curve for Notional Round Rotor Synchronous Machine
3.1.3 Exciters and Voltage Regulators
3.1.3.1 Simplified IEEE Type AC8B Exciter
The model employed is a simplified version of the IEEE type AC8B model, which is described
in [10]. The actual model employed is illustrated by Figure 29, in conjunction with (18). The
model takes a requested voltage, Vr, and feedback of the actual voltage, Vm, as inputs, and
provides the field winding excitation voltage, Ef, as an output. The parameters and default
values of the model are described in Table 31.
32
VEMAX
VRMAX
Vr
+
Vm
Σ
-
k
sk DR
k PR  IR 
s 1  sTDR
PID
Controller
kA
1  TA s
+
-
Ef
1
Te s
Σ
VEMIN
VRMIN
Voltage
Regulator
Σ
+
kE
+
π
SE
fEF
Figure 29: Simplified Implementation of the IEEE type AC8B exciter model.
f EF ( E f )  k EF1e
k EF 2 E f
(18)
Table 31. Parameters for Simplified IEEE Type AC8B Exciter
Parameter
kA
kDR
kIR
kE
kEF1
kEF2
kPR
TA
Te
TDR
VEMAX
VEMIN
VRMAX
VRMIN
Description
Voltage regulator gain.
PID controller derivative gain.
PID controller integral gain.
Default Value
1
0.001
0.08
1
1.0119
0.0875
200
0.0001
1
controller 0.001
Saturation function coefficient.
Saturation function coefficient.
PID controller proportional gain.
Voltage regulator time constant (s).
Integration time constant (s).
Filter time constant for PID
derivative branch (s).
Field winding excitation voltage upper limit.
Field winding excitation voltage lower limit.
Voltage regulator upper limit.
Voltage regulator lower limit.
Source
∞
0
5
0
3.1.4 Generator Load Sharing Controls
The approach for implementing real and reactive power sharing among paralleled generators
makes use of droop controls for both the turbine/governor and voltage regulator/exciter of each
unit, as illustrated by Figure 30 and Figure 31 (where all quantities are considered to be in per
33
unit values). Figure 30 illustrates the configuration for the turbine/governor, for which a
requested speed (ωs) and requested power (Ps) are provided. The droop control loop allows
generators with potentially different speed references (or biases on the speed feedback
measurements) to be stably operated in parallel. When connected in parallel with a generator
operating in isochronous mode, the power supplied by the unit in droop control mode is
controlled through the power reference. The machine in isochronous mode maintains the system
frequency to its 1reference frequency, supplying any additional load on the system. Similarly,
when two machines are paralleled on the same bus (with little impedance between them),
reactive power droop control can be employed, as illustrated by Figure 31. However, if all of the
0.9
paralleled generators
employ droop control, the system frequency and voltage can vary from the
respective set point values according to loading conditions and the droop characteristics. For
example, if the 0.8
typical droop gain of 5% is employed, this implies that the deviation in system
frequency from the nominal value may vary up to 5%, depending on the loading conditions.
Droop
0.7
Ps
+
Σ
kD
0.6
P
1
0.5
ωs
+
+
Σ
System
Turbine/Governor
ω
0.9
0.4
0.8
0.3
Figure
30: Configuration of Droop Control for Turbine/Governor
Droop
0.7
0.2
+
Σ
kD
Qs
0.6
0.1
Q
Vs
0.5
0
+
+
Σ
System
VR/Exciter
-
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7 V
0.8
0.9
1
0.4
Figure0.3
31: Configuration of Droop Control for Voltage Regulator/Exciter
In the approach employed, all generators are operated with droop control for both real and
reactive power, 0.2
and a master load sharing control is employed. This slower outer control loop is
used to adjust the real and reactive power set points for each unit in order to properly distribute
the real and reactive
power load among units and maintain nominal frequency and voltage. A
0.1
load divider control, such as that illustrated by Figure 32 (illustrated for the real power set point
control for generator 1), is employed for each quantity (real and reactive power) for each
0
0.1 of the
0.2load 0.3
0.5
machine, where the0 output
divider0.4component
(P0.6s1-c) is0.7
given 0.8
by (19).0.9 In this1 context,
each Pi quantity represents the real power supplied by generator i, and each Pbi quantity
represents the rated power of generator i. Each Si1 quantity is a binary quantity ({0,1})
indicating whether generator i should share power with generator 1 (a value of 1) or not (a value
34
1
of 0). The0.9output of the load divider component is then filtered in order to avoid potential
interference with the faster inner loops of the control structure, and then provided as the power
reference for generator 1. In this way, the real and reactive power set points for each machine
are obtained0.8such that paralleled generators equally share the real and reactive power load on a
per unit basis.
0.7
Pb1 Pb2
Pb3 Pb4
P1
0.6
P2
Ps1-c
Load Divider
Control
0.5
1
1  s
P3
Ps1
P4
0.4
S11
0.3
S21
S31 S41
Figure 32: Load Divider Control
4
Ps1c 
0.2
PP S
i bi
i 1
4 0.1
P S
i 1
bi
0
0
i1
(19)
i1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
The settings of the binary status signals must be determined through an algorithm appropriate for
the topology. This could be done in an automated fashion by considering the status of breakers
in the system, or these might be configured manually for a given scenario through a script or
some other method. The default parameter values for the load sharing controls are given in
Table 32.
Table 32. Parameters for Generator Load Sharing Controls
Parameter
τ
3.2
Description
Filter time constant (s).
Default Value
1.0
Source
Components of Propulsion Systems
3.2.1 Propulsion Motors
3.2.1.1 Notional Permanent Magnet Machine
The model employed for the notional permanent magnet machine for the baseline system makes
use of the permanent magnet machine model in Simulink SimPowerSystems [13]. The interface
to the model is illustrated by Figure 33. As shown, the model takes an input shaft torque, Tshaft,
from a torque load model, and provides the speed of rotation, ωshaft, as an output. The model
35
exposes three electrical nodes, A, B, and C. The parameters and default values for the model are
given in the Table.
Tshaft
Permanent
Magnet
Machine
A
B
C
ωshaft
Figure 33: Interface for Notional Permanent Magnet Machine
Table 33. Parameters for Notional Permanent Magnet Machine
Parameter
Rs
Ld
Lq
λ
J
F
p
Description
Stator resistance (Ω).
D-axis stator inductance (H).
Q-axis stator inductance (H).
Flux linkage established by magnets (V∙s).
Moment of inertia (kg∙m2)
Friction (N∙m∙s)
Pole pairs.
Default Value
0.005
0.8e-3
0.8e-3
16.58
1.6e3
0.0005
12
Source
The Simulink permanent-magnet machine model does not include damper windings, while the
PSCAD model does. However, for permanent-magnet machines that include metallic shields, for
example, corresponding models with damper windings can easily be built using native library
components in any software package.
3.2.2 Motor Drives
3.2.2.1 Two-Level IGBT Bridge
The basic topology for the model is illustrated by Figure 34. The model exposes five electrical
nodes, A, B, C, p, and n, and receives six gating signals, g1 through g6. The model makes use of
the Simulink Universal Bridge model [14], using three bridge arms and using “IGBT/Diode” for
the power electronic device. Although not explicitly shown in Figure 34, snubber circuits are
employed on the IGBTs. The parameters and default values are described in the Table.
36
g1
g3
g5
p
A
B
C
n
g2
g6
g4
Figure 34: Two-Level IGBT Bridge
Table 34. Parameters for Two-Level IGBT Bridge Model
Parameter
Cs
Ron
Rs
Tf
Tt
Vf
Vfd
Description
Snubber capacitance (F).
IGBT on-state resistance (Ω).
Snubber resistance (Ω).
Fall time for the IGBT (s).
Tail time for the IGBT (s).
IGBT forward voltage drop (V).
Diode forward voltage drop (V).
Default Value
1.0e-6
1.0e-3
1000
1.0e-6
2.0e-6
0.8
0.8
Source
3.2.3 Motor Drive Controls
3.2.3.1 Hysteresis Current Control for Two-Level Drive for Permanent Magnet Synchronous
Machine
The general control approach is illustrated by Figure 35. The controller takes a reference speed,
ωr as an input, along with feedback signals for the actual shaft speed, ωshaft, the rotor angle, θ,
and the instantaneous phase currents for the machine, Ia, Ib, and Ic. The controller provides the
binary gating signals, g1 through g6, for a two-level, three-phase bridge motor drive using
force-commutated devices. The convention for the DQ to ABC transformation is given by (20).
The blocks labeled “fhys” implement a hysteresis-based comparison function. For example,
consider the block receiving input from the reference phase-A current, Ia-r, and the actual
phase-A current, Ia. If gating signal g1 is on (a value of 1), the signal will remain on until Ia
becomes larger than an upper threshold, given by Ia-r+ΔI, at which point g1 will be turned off (a
value of 0). Signal g1 will then remain in the off-state until Ia drops below a lower threshold,
given by Ia-r-ΔI, at which point g1 will again be turned on. Throughout the process, gating signal
37
g2 is maintained as the complement of gating signal g1. The parameters for the model are given
in Table 35.
Ic
Iq-r-max
ωr
+
ωshaft
Σ
-
kP 
Ia
Ia-r
Id-r
fhys
g1
g2
Ib-r
Iq-r
kI
s
DQ→ABC
fhys
Ic-r
Iq-r-min
PI
Controller
Ib
fhys
p
g3
g4
g5
g6
θ
Figure 35: Hysteresis Current Control for Two-Level Drive for Permanent Magnet Synchronous
Machine
sin(  )
cos( )
1  I d r 
 I a r  
 I   0.5( sin(  )  3 cos( )) 0.5( cos( )  3 sin(  )) 1  I 
 br  
  q r 
 I c r  0.5( sin(  )  3 cos( )) 0.5( cos( )  3 sin(  )) 1  0 
(20)
Table 35. Parameters for Hysteresis Current Control for Two-Level Drive for Permanent Magnet
Synchronous Machine
Parameter
Id-r
Iq-r-max
Iq-r-min
ki
kp
p
ΔI
Description
Requested d-axis current (A).
PI controller upper limit (A).
PI controller lower limit (A).
PI controller integral gain.
PI controller proportional gain.
The number of pole pairs of the machine.
Hysteresis comparator dead-band width
parameter.
38
Default Value
0
∞
-∞
10
7500
12
0
Source
3.2.4 Propellers
3.2.4.1 Notional Fixed-Pitch Propeller
The propeller modeled is generally based on the description provided in [1]. The model provides
the counter torque exerted on the shaft (Tprop) and the thrust exerted on the ship (Fship) as a
function of the propeller angular frequency (ωprop) and the ship speed (Vship), as illustrated by
Figure 36. The particular mathematical model employed is that described in [3], given by (21)(25). The default parameters for the model are given by Table 36. As noted, most of the
information for the model was taken from [1]. However, while [1] provides information about
propeller thrust and torque coefficients (black curves of Figure 37 and Figure 38), the
information does not cover the entire range of the advance ratio, ν. In order to develop complete
characteristics, information provided by [4] (dotted curves of Figure 37 and Figure 38) was used
to supplement the information from [1]. As use of the complete curves from [4] would result in
powering data inconsistent with that provided in [1], a curve-fitting routine was used to smoothly
merge the data provided in [4] with the data provided in [1], resulting in the solid curves (red and
black) of Figure 37 and Figure 38.
ωprop
Vship
Tprop
Notional
Fixed-Pitch
Propeller Model
Fship
Figure 36: Interface for Notional Fixed-Pitch Propeller Model
 D3  2
(Va  (nD) 2 )
T prop  CQ ( )  
 r 
(21)
Fship  C ( ) D 2 (Va  (nD) 2 )(1  t )
(22)
2
n

 prop
2
(23)
nD
2
Va  (nD) 2
(24)
Va  Vship ( 1  wT )
(25)
39
Table 36. Parameters for Notional Fixed-Pitch Propeller Model
Parameter
ρ
D
ηr
CQ(ν)
Cτ(ν)
1-wT
1-t
Description
Density of salt water.
Propeller diameter.
Relative rotative efficiency.
Open water propeller torque coefficient
Open water propeller thrust coefficient
Taylor wake fraction.
Thrust deduction factor.
Default Value
1027 kg/m3
7.01 m
1.0
See Figure 37
See Figure 38
See Figure 39
0.96, Vship  0

0.97, Vship  0
Source
[1]
[1], [4]
[1], [4]
[1]
[1]
Figure 37: Thrust Coefficient Curves for Notional Fixed-Pitch Propeller Model
40
Figure 38: Torque Coefficient Curves for Notional Fixed-Pitch Propeller Model
Taylor Wake Factor
1.025
Taylor Wake Factor
1.02
1.015
1.01
1.005
1
-10
-5
0
5
10
15
20
Ship Speed (knots)
25
30
35
Figure 39: Taylor Wake Fraction Curve for Notional Fixed-Pitch Propeller Model
As this model takes the propeller angular velocity as an input and provides a torque as an output,
it is assumed that the moment of inertia of the propeller, entrained water, and propeller shaft are
modeled as part of the component to which the propeller model is coupled (e.g. gear box model,
propulsion motor model, etc.). So that this can be properly modeled in the accompanying
component, the total moment of inertia of the propeller, shaft, and entrained water is given in
Table 36 for a two-propeller notional destroyer, for which the model parameters are intended.
41
Table 37. Additional Parameters Associated with Notional Fixed-Pitch Propeller Model
Parameter
J1
J2
Description
Default Value
Moment of inertia of the starboard propeller 2.0573e5 kg∙m2
(not used in the model).
Moment of inertia of the port propeller (not 2.2767e5 kg∙m2
used in the model).
Source
[1]
[1]
3.2.5 Ship Hydrodynamic Characteristics
3.2.5.1 Notional Destroyer Hydrodynamic Characteristics
The ship hydrodynamic characteristics are based on those given in [1]. The general model,
illustrated by Figure 40, takes the thrust of two propellers, Fship1 and Fship2, as inputs, and
provides the ship speed, Vship, as an output. The model simply accounts for the mass of the ship,
mship, and the ship hydrodynamic resistance, Fdrag, as a function of the ship speed. The
parameters for the model are described in Table 38. Information for the ship hydrodynamic
resistance was provided by [1] for values of the ship velocity at 10 knots and above. For ship
speeds at less than 10 knots, the values of the hydrodynamic resistance were estimated through
extrapolation and curve fitting of the data, using the same values for astern ship speeds up to
10 knots.
Fship1
Fship2
+
-
Σ
+
1
Vship
mships
Fdrag (Vship )
Figure 40: Notional Destroyer Hydrodynamic Characteristics
Table 38. Parameters for Notional Destroyer Hydrodynamic Characteristics Model
Parameter
mship
Fdrag(Vship)
Description
Mass of the ship.
Hydrodynamic resistance.
Default Value
14.29e6 kg
See Figure 41
42
Source
[5]
[1]
See text
Hydrodynamic Resistance
6
3.5
x 10
Force (N)
3
Force (N)
2.5
2
1.5
1
0.5
0
-10
-5
0
5
10
15
20
Ship Speed (knots)
25
30
35
Figure 41: Hydrodynamic Resistance for Notional Destroyer Model
3.3
Ship Service Loads
3.3.1 Notional Ship Service Loads
There are 22 loads distributed within 4 zones. Load definition and initial implementation in the
baseline models are shown in Table 39. In the initial set-up, simple constant impedance loads are
used for simplicity but they can be replaced later with other loads such as uncontrolled induction
machines and other power electronics controlled equipment.
Table 39. Ship Service Load Data
ID
1
Typ
e
ID2
Z1
DC
Z2
DC
Z3
AC
Z4
AC
Z5
AC
Z6
AC
Z1L
1
Z1L
2
Z1L
3
Z1L
4
Z1L
5
Z1L
6
Battle
mode
(kW)
Cruise
mode
(kW)
Original
lumped
category
Syntek ESRDC Initial baseline
load implementation
150
70
DC loads 1
615
0
DC loads 2
Constant impedance load
(resistive load)
Same as Z1
715
640
Type 1 AC loads
Same as Z1
400
390
120/208 VAC loads
910
275
0
7
Non-vital type 1 AC
loads
Non-vital single-phase
AC loads
450 Vac 3-phase (resistive
load)
450 Vac 3-phase constant
impedance load (RL)
120/208 AC load (constant
impedance load (RL))
1460 1330
2790
735
647
1382
43
Z7
DC
Z8
DC
Z9
AC
Z1
0
Z1
1
Z1
2
AC
Z1
3
Z1
4
Z1
5
Z1
6
Z1
7
AC
AC
DC
AC
AC
AC
AC
Z2L
1
Z2L
2
Z2L
3
Z2L
4
Z2L
5
Z2L
6
Z3L
1
Z3L
2
Z3L
3
Z3L
4
Z3L
5
1
0
Non-vital DC loads
Lumped DC load (resistive)
75
20
DC loads
Same as Z2
1400
930
Type 1 AC loads
Same as Z3
750
300
120/208 VAC loads
Same as Z4
975
400
Same as Z5
40
35
Non-vital type 1 AC
loads
Non-vital 120/208 AC
loads
1726 1515
3241
40
700
20
DC loads
Same as Z1
1200
1200
Type 1 AC loads
Same as Z2
1900
550
120/208 VAC loads
Same as Z3
750
375
Same as Z4
0
4
Non-vital, type 1 AC
loads
Non-vital, 120/208 AC
loads
60
1750 399
2149
0
DC loads
Same as Z2
480
200
Type 1 AC loads
Same as Z3
1750
415
120/208 VAC loads
Same as Z4
675
220
Same as Z5
0
4
Non-vital, 120/208 AC
loads
Non-vital, 120/208 AC
loads
735
224
HP Radar
DC const. impedance load
790
Z1
8
Z1
9
Z2
0
Z2
1
Z2
2
Z2
3
DC
AC
AC
AC
AC
DC
Z4L
1
Z4L
2
Z4L
3
Z4L
4
Z4L
5
Z5L
1
3100
3890
223
0
2965
3750
Same as Z6
985
1685
Same as Z5
Same as Z6
615
839
2850
4701
817 3409 264
5
6
Total Load Power
12872 (kW)
6055 (kW)
Loads initially connected to upper
bus
Loads initially connected to lower
bus
44
3.4
Bulk Energy Storage Systems
3.4.1 Notional Supercapacitor Energy Storage System
In power systems, energy storage devices are usually used to minimize fluctuations of line power,
frequency and grid voltage, and also to support voltage sag. In case of the ship power system that
we are currently addressing, the main purpose of using the capacitor energy storage system is to
provide a maximum of 4MW of power to the 4.16 KV distribution bus/grid in case of a loss of
one of the 4 MW auxiliary generators. Figure 42 shows that a 4.16 KV/60 Hz ac source, an
energy storage system (ESS), and a test load are connected to a grid point through breakers
eBrk1, eBrk2, and eBrk3, respectively. The energy storage system consists of a Wye-Wye
4.16KV/0.45KV transformer, a 6-pulse pulse width modulation (PWM) inverter/converter using
insulated-gate-bipolar-transistors (IGBT), a DC-DC (buck-boost) converter using IGBT, and a
supercapacitor (SC). The PWM inverter/converter and the DC-DC converter are linked by a dc
link capacitor C1. eVc, eid, eV0, and ei0 indicate the voltage across the supercapacitor, output
current of the supercapacitor, voltage across the dc link, and inverter current, respectively. The
value of test load should be less than or equal to 4 MW. The ESS inverter gate signal
(gDischgInvP) and the DC-DC converter gate signals (gchgP for charge and gDischgP for
discharge) are determined according to control logics as described in following two subsections.
The specifications of the ESS are described in Table 40.
gchgP
+
v
-
eid
eR eL
+
i
-
E
gDischgP
eV0
g
C
Charge
(Buck mode)
eL1
+
i
-
ei0
gDischgInvP
g C
SC
(Capbank)
+
C1
Discharge
(Boost mode)
E
+
v
-
-
g
A
a
A
A
a
a
A
A
B
b
B
B
b
b
B
B
C
c
C
C
c
c
C
ESS
eBrk2
inverter 0.45/4.16KV
eVc
A
A
a
B
B
b
C
C
c
Test load
eBrk1
C
4.16KV/60
Hz source
eBrk3
Figure 42: 4.16KV/60Hz ac source with an energy storage system (ESS) and a test load
Table 40. General Parameters for Notional Supercapacitor Energy Storage System
Parameter
Description
Supercapacitor (SC) Power
Supercapacitor (SC) energy
Capacitance of Supercapacitor (SC)
Supercapacitor (SC) initial voltage
45
Default Value
4.0 MW
100 MJ
(approximately)
850.5 F
500 V
Source
eL
eR
C1
eL1
Inductance
Resistance
Dc link capacitance
Inductance
Transformer Nominal power
Transformer Nominal frequency
Transformer Winding 1 voltage, V1 Ph-Ph
(Vrms)
Transformer Winding 1 resistance, R1 (pu)
Transformer Winding 1inductance, L1 (pu)
Transformer Winding 2 voltage, V2 Ph-Ph
(Vrms)
Transformer Winding 2 resistance, R2 (pu)
Transformer Winding 2 inductance, L2 (pu)
Transformer Magnetization resistance, Rm (pu)
Transformer Magnetization inductance, Lm
(pu)
2×10-4 H
0.0001 ohm
0.2 F
5×10-8 H
5 MVA
60 Hz
4.16KV
0.002
0.045
0.45KV
0.002
0.045
500
500
3.4.1.1 PWM inverter and controls
PWM based inverter/converter is the main interface between the grid and the supercapacitor
energy storage unit as shown in Figure 43. The control block for the inverter/converter is
described in Figure 49. Table 47 describes the parameters for the inverter and controls.
ESS Inverter/ Converter
Pulses
Transformer
4.16/0.45kV
Y
Y
ED
DC link
>0
C
gDischgInvP
Timer Discharge1
0
a)
3-phase ESS Inverter/ Converter
b)
Discharge
Switch2
Discharge Inverter
Figure 43: Notional Supercapacitor Energy Storage System Inverter/converter control
Table 41. Parameters for Notional Supercapacitor Energy Storage System Inverter
Parameter
ecarrierF
eModIndex
Rs
Cs
Description
Carrier frequency
Modulation index
Snubber resistance
Snubber capacitance
Default Value
2400 Hz
0.84
1×105 Ohm
1×10-9 F
46
Source
3.4.1.2 DC/DC converter control
Figure H.4 shows the control strategy for the DC-DC (buck-boost) converter. Table H.4 shows
the buck-boost converter data.
Boost Converter
Buck Converter
0
-eIcharge
eVc
Relay
eid
Relay1
eVc
>0
>0
Timer
Discharge
0
a)
gDischgP
Timer
Charge
Discharge
Switch1
DISCHARGE CONTROL
0
>=
gchgP
gchgP
Charging
Switch
Stop Charging
when V=Capbank
voltage
b) CHARGE CONTROL
Figure 44: Notional Supercapacitor Energy Storage System DC/DC (buck-boost) converter control
Table 42. Parameters for Notional Supercapacitor Energy Storage System Buck/boost converter
Parameter
eIcharge
eboostV
eboostF
3.5
Description
Charging current
Boost voltage
Boost frequency
Default Value
6000 A
825 V
1,000 Hz
Source
Specialized Loads
3.5.1 Radar Systems
3.5.1.1 Notional Radar Load
The radar load is presently modeled as a constant impedance load requiring 300 Vdc and up to
3.75 MW of continuous DC power. The 300 Vdc is obtained through power conditioning
modules that are specific to each architecture.
3.5.2 Notional Free Electron Laser Pulse Power Load
The free electron laser system (FEL) is a pulse power system that is expected to be installed on
future Navy ships. This system is highly inefficient. It requires about 25 MW to produce a 3 MW
laser beam. The FEL has eleven sub-loads and requires AC and DC power at various voltage
levels as shown in Figure 45 and Table 43. In addition some of the sub-loads are powered
continuously while others are energized at different times during operation. This is indicated by
the transition times in Table 43.
47
Figure 45: Sub-loads of Notional Free Electron Laser System
Table 43. Notional Free Electron Laser Data
FEL load definitions
Z6L1
Filament(1)
10KW
Z6L2
RF
16MW
Z6L3
Beam dump
7.7MW
Z6L4
Cooling
300kW
Z6L5
Cryogenics
1MW
Z6L6
Beam control
20KW
Z6L7
Vacuum
5kW
Z6L8
Beam optics
1KW
Z6L9
Computers
5KW
Z6L1
0
Z6L1
1
Housekeeping
5KW
Wiggler(2)
~0(2)
A
C
D
C
A
C
A
C
A
C
A
C
A
C
A
C
A
C
A
C
D
C
4.16kV\240H
z
45 KV
Pier
side
10
Modes of operation (required power in KW)
Under
Operational Hot
Engagemen
way
readiness
standby
t
10
10
10
10
-
-
80
16000
16000
4.16KV\60Hz
-
-
38.5
7700
7700
4.16kV\60Hz
300
300
300
300
300
450V\60Hz
100
1000
1000
1000
1000
450V\60Hz
-
-
-
-
20
450V\60Hz
5
5
5
5
5
1
1
1
112.5V\60Hz
112.5V\60Hz
5
5
5
5
5
112.5V\60Hz
5
5
5
5
5
600 V
-
-
-
-
-
48
Total power during each mode of operation (kW)
Transition times
425
days
1325
hours
1444.5
minutes
25026
seconds
25046
~ 1 second
Some of the assumptions for the model are described below:
(1): It is assumed that the filament is a simple resistive load that can be heated by any supply. In
the HFAC system, for example, the 4.16 kV\240 Hz power available at the main distribution bus
is used.
(2): The wiggler load shows 600 Vdc with 300kW (EM) but ~0 permanent power. In the model,
it is assumed to be a load that requires 600 Vdc with basically 0 real power (modeled as a very
large resistor). This is the device where the accelerated electrons exchange energy with the wave.
3.6
Power Conversion Modules
3.6.1 AC/DC Rectifiers
3.6.1.1 Notional Diode Rectifier
A notional six-pulse diode rectifier with AC side line reactance and DC filter capacitor is
illustrated by the circuit model of Figure 46. The parameters of the model, along with the default
values used for MTG rectifiers for the MVDC system, are given in Table 44. For convenience,
the equations associated with the rectifier model are given by (26).
Figure 46: Circuit Model of Notional Diode Rectifier
Table 44. Parameters for Notional Diode Rectifier Model
Parameter
Cd
Csnub
Description
DC side filter capacitance (F).
Diode snubber capacitance (F).
Default Value
1e-3
1e-5
49
Source
Ls
Ld
Rd
Rs
Rsnub
AC side series inductance (H).
Diode on-state inductance (H).
Diode on-state resistance (Ω).
AC side series resistance (Ω).
Diode snubber resistance (Ω).
1.24e-4
0
1e-5
7.5e-3
100
R  RD 2
R
R
di
v
di D1  v ac Rs  RD1
di
di


i D1  s
iD 2  s iD 4  s iD5  D 2  D 4  D5  d
dt
Ls
Ls
Ls
Ls
Ls
dt
dt
dt
Ls
R  RD3
R
R
di
di
di
v
di D 2  vcb Rs  RD 2


iD 2  s
iD3  s iD5  s iD6  D3  D5  D6  d
dt
Ls
Ls
Ls
Ls
Ls
dt
dt
dt
Ls
di D 3  vba Rs  RD 3
R  RD 4
R
R
di
v
di
di


iD3  s
i D 4  s i D 6  s i D1  D 4  D 6  D1  d
dt
Ls
Ls
Ls
Ls
Ls
dt
dt
dt
Ls
R  RD 5
R
R
di
v
di D 4  v ac Rs  RD 4
di
di


iD 4  s
i D 5  s i D1  s i D 2  D 5  D1  D 2  d
dt
Ls
Ls
Ls
Ls
Ls
dt
dt
dt
Ls
(26)
di D 5  vcb Rs  RD 5
R  RD 6
R
R
di
di
v
di


iD5  s
iD6  s iD 2  s iD3  D6  D 2  D3  d
dt
Ls
Ls
Ls
Ls
Ls
dt
dt
dt
Ls
di D 6  vba Rs  RD 6
R  RD1
R
R
di
v
di
di


iD6  s
i D1  s i D 3  s i D 4  D1  D 3  D 4  d
dt
Ls
Ls
Ls
Ls
Ls
dt
dt
dt
Ls
dv d (i D1  i D 3  i D 5 )
vd


dt
Cd
Cd * RL
3.6.2 DC/DC Converters
3.6.2.1 Isolated DC/DC Converter
This model provides an interface between two DC voltages levels using a high-frequency
transformer. The transformer serves two purposes namely isolation and bridging the high voltage
difference. Further details on circuit and switching can be found in [18]. The converter uses two
full bridges to achieve the high-power levels required. The switching scheme implemented
makes use of a clamping capacitor for improved efficiency. The masked Simulink converter
model with its connections to the high-voltage bus, low-voltage bus, and controlling signals is
shown in Figure 47.
50
IsoDCDC
BrkLVstat
4
VH+
1
2
mea
V+
DC
805V
Buck Vref
Boost Iref
2
V-
enable
enable
3
m
Brk
Energy
Storage
1
VpLV
Mode
Buck = 1
Boost = 0
1
Constant3
BrkHVstat
Breaker HV&LV
g
1
VH-
VpHV
VnLV
VnHV
Iref boost
Vref buck
Figure 47: Isolated DC-DC Converter Block
Control signals include the high- and low-voltage breaker status information, the mode of
operation, i.e., buck or boost, enabling of power electronics switching, and reference command
for voltage (buck mode, low voltage side) and current (boost mode). The arrangement shown
here includes an example of connecting an energy source on the low voltage side for boost mode
operation.
The Isolated Dc-DC converter circuit diagram is shown in Figure 48. The main components are
the two full-bridges, transformer, and clamping capacitor. The default parameters for the circuit
and controls are given in Table 45 and Table 46.
51
Figure 48: Isolated DC-DC Converter Circuit
52
1
+
v -
[VHV]
[ILV]
[VLV]
[IHV]
[VHV]
|u|
|u|
[VCc]
[ICc]
[Iw2]
[Iw1]
[VLVC]
[IHVC]
[VHVC]
C HV
buck.filter.den{1}(z)
buck.filter.num{1}(z)
buck.filter.den{1}(z)
buck.filter.num{1}(z)
buck.filter.den{1}(z)
buck.filter.den{1}(z)
buck.filter.num{1}(z)
S6
S8
[FP56]
buck.filter.num{1}(z)
RHV12
Multimeter
7
2
RHV11
BrkHV
1
BrkHVstat
VHV
VnHV
2
VpHV
[IHV]
1
2
out_IsoDCDC_VCc_Z1P
[VCc]
1
out_IsoDCDC_PLV_Z1P
max
max
out_IsoDCDC_ICc_Z1P
[ICc]
1
out_IsoDCDC_VHVC_Z1P
[VHVC]
out_IsoDCDC_PHV_Z1P
out_IsoDCDC_Iw2_Z1P
out_IsoDCDC_Iw1_Z1P
[Iw1]
[Iw2]
out_IsoDCDC_boostCtrl_Z1P
[BoostCtrl]
out_IsoDCDC_VLV_Z1P
out_IsoDCDC_buckCtrl_Z1P
out_IsoDCDC_ILV_Z1P
[ILV]
[VLV]
S2
S4
[BuckCtrl]
out_IsoDCDC_VLVC_Z1P
[VLVC]
out_IsoDCDC_IHV_Z1P
out_IsoDCDC_IHVC_Z1P
[IHVC]
[IHV]
out_IsoDCDC_VHV_Z1P
Linear Transformer
LHV
[FP34]
[FP12]
[VHV]
S7
S5
[FP78]
-1
>
boost.filter.num{1}(z)
[IHV]
boost.filter.den{1}(z)
100
current filter
I droop
-K-
Cc
Sat
Sc1
1
out_IsoDCDC_eff_Z1P
AND
0
>
-K-
PID(z)
Triangle 2
Triangle 1
Buck PID
PID(z)
[FPScBuck]
[FP78]
[FP56]
Constant5
0.5
RLV
>=
>=
[BoostCtrl]
>=
>=
out_IsoDCDC_FPScBuck_Z1P
out_IsoDCDC_FP78_Z1P
[FPScBoost]
[FP34]
[FP12]
AND
AND
NOT
VLV
+ v
-
2
m
BrkLV
NOT
1
[BuckCtrl]
g
2
BrkLVstat
out_IsoDCDC_FP56_Z1P
scaleEi Boost
Switch1
PID
>
-K-
C LV
scaleEv
RLV2
RLV1
LC P
Switch
Sc2
[FPScBoost]
AND
voltage filter
buck.filter.den{1}(z)
buck.filter.num{1}(z)
boolean
Boost Iref
5
[VLV]
Buck Vref
4
filter4
buck.filter.den{1}(z)
buck.filter.num{1}(z)
enable
Mode
6
3
[ILV]
S3
S1
[FPScBuck]
m
g
m
E
C
g
m
g
1
g
m
C
E
m
g
E
C
g
m
C
E
g
m
C
E
g
m
C
E
m
g
E
C
g
m
C
E
g
m
C
E
E
C
AND
AND
AND
AND
[FPScBuck]
[FPScBoost]
[FP78]
out_IsoDCDC_FPScBoost_Z1P
out_IsoDCDC_FP34_Z1P
out_IsoDCDC_FP12_Z1P
[FP34]
[FP12]
XOR
AND
4
VnLV
[FP56]
[ILV]
[VLV]
VpLV
3
Table 45. Parameters for Isolated DC-DC converter
Parameter
RHV1
RHVC
CHVC
LHV
VH
VL
f
S
R1
L1
R2
L2
Rm
Lm
RCC
CCC
LCP
RLV1
RLVC
CLVC
RLV
RON
RS
CS
f
Description
High-voltage side circuit
Resistance towards ground (ohm)
Series resistance (ohm)
Capacitor (mF)
Inductance (uH)
Transformer
high-side voltage (V)
low-side voltage (V)
frequency (Hz)
Nominal power (MVA)
Primary side winding resistance (pu)
Primary side leakage reactance (pu)
Secondary side winding resistance (pu)
Secondary side leakage reactance (pu)
Magnetization resistance (pu)
Magnetization reactance (pu)
Low-voltage side circuit
Clamping capacitor series resistance (ohm)
Clamping capacitor (mF)
Inductance low-voltage side (H)
Resistance towards ground (ohm)
Series resistance of capacitor (ohm)
Low-voltage capacitor (F)
Resistance low-voltage side (ohm)
Switch parameters
resistance (ohm)
snubber resistance (ohm)
snubber capacitance (F)
switching frequency (Hz)
Default Value
Source
500
0.001
2.7
300
5000
850
700
4
0
0
0
0
5000
5000
1e-4
4.86
12e-3
500
1e-4
7e-3
10e-6
10e-6
1e5
1e-6
700
Table 46. Controller Parameters for Isolated DC-DC converter
Parameter
Tfbu
kP
kI
kD
N
max
min
Escale
Description
Buck mode PI-controller with anti-windup
filter time constant (s)
proportional gain
integral gain
derivative gain
derivative filter factor
maximum control signal
minimum control signal
Scaling factor on error signal
Boost mode PI-controller with anti-windup
53
Default Value
25e-3
0.0325
0.35
0.0025
50
0.02
0.048
1e-2
Source
Tfbu
kP
kI
kD
N
max
min
Escale
3.7
filter time constant (s)
proportional gain
integral gain
derivative gain
derivative filter factor
maximum control signal
minimum control signal
Scaling factor on error signal
10e-3
0.252
1.125
0
100
0.48
0
1e-3
Ancillary Components
3.7.1 Transformers
3.7.1.1 Three-phase, Two Winding Transformer
This model makes use of the Simulink SimPowerSystems three-phase, two-winding transformer
model, as described in [16]. As illustrated by Figure 49, the model exposes thee electrical nodes
(A1, B1, and C1) for the side 1 windings, and three electrical nodes (A2, B2, and C2) for the side 2
windings. If a side is configured in a Y configuration, an electrical node for the neutral point (N1
or N2) may also be exposed. Figure 49 illustrates a view in which each of the electrical nodes is
explicitly exposed, as well as single-line view. The parameters for the model are described in
Table 47.
A1
B1
C1
3P-2W
1
2
XFMR
N1
T1
1
A2
B2
C2
N2
T2 Single Line
2
N1 N2
Figure 49: Interface for Three-phase, Two-winding Transformer Model
54
Table 47. Parameters for Three-phase, Two Winding Transformer
Parameter
C1
C2
C1-Y
C2-Y
Sb
fb
V1
R1
X1
V2
R2
X2
Rm
Xm
Φ(i)
Description
Configuration of side 1 windings ({Y, Delta})
Configuration of side 2 windings ({Y, Delta})
Configuration of side 1 Y (if applicable)
({exposed neutral, unexposed neutral, NA})
Configuration of side 2 Y (if applicable)
({exposed neutral, unexposed neutral, NA})
Rated apparent power (MVA).
Rated frequency (Hz).
Winding 1 rated RMS line-line voltage (kV).
Winding 1 resistance (pu).
Winding 1 leakage reactance (pu).
Primary side rated RMS line-line voltage (kV).
Primary side winding resistance (pu).
Primary side leakage reactance (pu).
Magnetization resistance (pu).
Magnetization reactance (pu).
Saturation characteristic.
Default Value
Delta
Delta
NA
Source
NA
5
60
4.16
0.001
0.01
4.16
0.001
0.01
500
500
NA (saturation
disabled)
3.7.2 Circuit Breakers
3.7.2.1 Three-phase Circuit Breaker
The 3-phase breaker model consists of three single-phase breakers, one for each phase. The
breaker is modeled as a small conducting resistance when closed and infinite resistance when
open, with a series R-C snubber, as illustrated by Figure 50. In addition, the breaker is modeled
to reflect actual high-power breakers. When ordered to close, it first senses the voltage and
closes only when the voltage reaches zero value (zero crossing). Similarly, when ordered to open,
it first senses the current and opens only when the current is zero. The model employed is the
Simulink SimPowerSystems Three-Phase Breaker model, as described in [17]. As illustrated by
Figure 51, the model exposes six electrical nodes (A1, B1, C1, A2, B2, and C2), and accepts a
binary input, s1, to control the state of the breaker. The parameters for the model are given in the
Table.
.
Figure 50: Single-phase Element of Three-phase Circuit Breaker Model
55
s1
A1
B1
C1
3P
Breaker
A2
B2
C2
s1
T2 Single Line
T1
.
Figure 51: Interface for Three-phase Circuit Breaker Model
Table 48. Parameters for Three-phase Circuit Breaker
Parameter
Cbs
Rbs
Ron
Description
Snubber capacitance (F).
Snubber resistance (Ω).
Breaker on-state resistance (Ω).
Default Value
∞
1000
0.001
Source
3.7.2.2 Notional Unidirectional DC Switch
A basic unidirectional DC switch controlling input power to DC loads is modeled by a semiconductor switch. This is an assumption used until more elaborate DC switch models are
developed. The Simulink SimPowerSystems IGBT component, described in [15], is employed
for this model. As illustrated by Figure 52, the model exposes two electrical nodes, N1 and N2,
and accepts a binary input, s1, to control the state of the switch. With this model, DC current can
only flow from node N1 to node N2. The parameters for the model are described in Table 49.
s1
N1
N2
.
Figure 52: Interface for Notional Unidirectional DC Switch Model
Table 49. Parameters for Notional Unidirectional DC Switch Model
Parameter
Csnub
Description
Snubber capacitance (F).
Default Value
10e-6
56
Source
Lon
Ron
Rsnub
Tf
Tt
Vf
On-state inductance of the semiconductor
switch (H).
On-state resistance of the semiconductor switch
(Ω).
Snubber resistance (Ω).
Current 10% fall time of semiconductor switch
(s).
Current 10% tail time of semiconductor switch
(s).
Forward voltage drop of semiconductor switch
(V).
0
0.001
50
1.0e-6
2.0e-6
0.8
3.7.3 Overvoltage Mitigation
3.7.3.1 Shunt Braking Resistor
This voltage regulator is a simple shunt regulator with a force-commutated semiconductor switch
(e.g. IGBT or GTO) in series with a shunt resistor, as in Figure 53. The model takes a maximum
voltage set point, Vmax, as a parameter, and exposes two electrical nodes, p and n. The IGBT
switching is controlled by comparing the measured voltage across the terminals, Vm, with Vmax
through an on-off comparator, such that when the measured voltage is above the reference
voltage, the bus is closed into the resistor through the switch. The parameters for the model are
given in Table 50. The Simulink SimPowerSystems “IGBT” model [15] is used to model the
semiconductor switch.
p
Vmax
+
Σ
Comparator
Rshunt
+
Vm
-
n
Figure 53: Shunt Breaking Resistor
Table 50. Parameters for Shunt Braking Resistor
Parameter
Csnub
Description
Snubber capacitance (F).
Default Value
∞
57
Source
Lon
Rshunt
Ron
Rsnub
Tf
Tt
Vf
Vmax
On-state inductance of the semiconductor
switch (H).
Resistance of shunt resistor (Ω).
On-state resistance of the semiconductor switch
(Ω).
Snubber resistance (Ω).
Current 10% fall time of semiconductor switch
(s).
Current 10% tail time of semiconductor switch
(s).
Forward voltage drop of semiconductor switch
(V).
Maximum voltage set point (V).
0
2.0
0.001
1.0e5
1.0e-6
2.0e-6
0.8
5616
4.0 REFERENCES
[1]
Syntek, “DD(X) Notional Baseline Modeling and Simulation Development Report,”
Internal Report, August 2003.
[2]
Syntek, “CAPS DD IPS Electrical Distribution One-Line Diagram.,” Internal Report,
August 2003.
[3]
E. J. Lecourt, Jr., “Using Simulation To Determine the Maneuvering Performance of
the WAGB-20,” Naval Engineer’s Journal, January 1998, pp. 171-188.
[4]
Robert F. Roddy, David E. Hess, and Will Faler, “Neural Network Predictions of the
4-Quadrant Wageningen Propeller Series, NSWCCD-50-TR-2006/004, Naval Surface
Warfare Center, Carderock Division, West Bethesda, MD, April 2006.
[5]
Collins, M., “DD(X) Transformational Technologies for the Navy’s Surface
Combatant”, in Proc. of FIATECH, Wilmington, DE, April 6-7, 2004.
[6]
W.I. Rowen, “Simplified mathematical representations of heavy-duty gas turbines”,
Journal of Engineering for Power, Vol. 105, 1983.
[7]
L.N. Hannet and A. H. Khan, “Combustion turbine dynamic model validation from
tests”, IEEE Transactions on Power systems, vol. 8, pp. 152-8.
[8]
L.N. Hannet, G. Jee, and B. Fardanesh, “A governor/turbine model for a twin-shaft
combustion turbine”, IEEE Transactions on Power systems, Vol. 10, no.1, pp. 133140.
[9]
IEEE Standards 1110-2002.
[10]
L.M. Hajagos and M.J. Basler, “Changes to IEEE 421.5 recommended practice for
excitation system models for power system stability studies”, IEEE/PES 2005 Meeting,
San Francisco, CA.
58
[11]
A.E. Fitzgerald, Charles Kingsley, Jr., and Stephen D. Umans, Electric Machinery,
Fifth Ed. McGraw/Hill.
[12]
Mathworks, “Synchronous Machine,” MATLAB R2010b Documentation, November,
2010,
http://www.mathworks.com/help/toolbox/physmod/powersys/ref/synchronousmachine
.html
[13]
Mathworks, “Permanent Magnet Synchronous Machine,” MATLAB R2010b
Documentation,
November,
2010,
http://www.mathworks.com/help/toolbox/physmod/powersys/ref/permanentmagnetsyn
chronousmachine.html
[14]
Mathworks, “Universal Bridge,” MATLAB R2010b Documentation, November, 2010,
http://www.mathworks.com/help/toolbox/physmod/powersys/ref/universalbridge.html
[15]
Mathworks, “IGBT,” MATLAB R2010b Documentation, November, 2010,
http://www.mathworks.com/help/toolbox/physmod/powersys/ref/igbt.html
[16]
Mathworks, “Three-Phase Transformer (Two Windings),” MATLAB R2010b
Documentation,
November,
2010,
http://www.mathworks.com/help/toolbox/physmod/powersys/ref/threephasetransform
ertwowindings.html
[17]
Mathworks, “Three-Phase Breaker,” MATLAB R2010b Documentation, November,
2010,
http://www.mathworks.com/help/toolbox/physmod/powersys/ref/threephasebreaker.ht
ml
[18]
Kunrong Wang, Fred C. Lee, and Jason Lai, “Operation Principles of Bi-Directional
Full-bridge DC/DC Converter with Unified Soft-Switching Scheme and Soft-Starting
Capacity,” in Proceedings of the Fifteenth Annual IEEE Applied Power Electronics
Conference and Exposition (APEC), pp. 111–118, vol.1, New Orleans, LA , USA, Feb.
6–10, 2000.
59
5.0 APPENDIX A: LIST OF POSSIBLE CASE STUDIES TO ASSESS THE
PERFORMANCE OF THE BASELINE POWER SYSTEM ARCHITECTURES
The proposed case studies are organized in two sets of scenarios. The first set deals with cases
that require short time scales, μs to ms, and necessitate a detailed dynamic model. This is the
model that is under development in Matlab\Simulink and PSCAD and will be used to address
case studies listed under Section 5.1. The second set of scenarios addresses system-level cases
that are characterized by long time scales, seconds and higher, and requires a system-level model
that is less detailed so that fast iterations can be achieved during the early design stages of
electric ship power systems. This model will be developed once the dynamic models have been
completed and will be used to address case studies listed under Section 5.2.
5.1
Case studies requiring a dynamic model for transient analyses
5.1.1 Typical ship maneuvering and operation scenario:
This could be one of the maneuvering scenarios proposed by Syntek in their original modeling
document (2003). A modified scenario would be to simulate ship acceleration to a prescribed
speed and provide power to all ship service loads, radar load, and a high-power pulsed load.
Loads are switched on and off intermittently while keeping total load power within the installed
power.
a.
Verify that frequencies, voltages, currents, and output powers of generating units are
as expected
b.
Verify that output voltages and currents of power conversion units (converters,
transformers) are as expected
c.
Verify that all loads get their prescribed powers
d.
Observe effects on bus voltage, especially, when a pulse load is initiated
e.
Observe gas turbines’ response
f.
Monitor bus voltage distortions when loads are turned on and off using existing
software tools to calculate the bus voltage THD level (total harmonic distortion)
g.
Perform other analyses to ascertain that the model is giving results within a range that
is reasonable
These initial observations and qualitative analyses are excellent verification exercises that show
that the software is solving model equations correctly.
5.1.2 Load pick-up
Sudden connection of large loads to ship grid, such as a large uncontrolled motor, a high power
pulse load directly connected to the grid, a sudden ship acceleration, etc…
a.
Prime movers initially loaded ~ 50%
b.
10%, 20%, or any xx% power is added by connecting a large load
1
c.
Study dynamics/transients (including, but not limited to)
•
Deviations from nominal of generator frequencies (generally check frequency
deviations against requirements in MIL standard 1399) (maximum deviation, duration of
time that fluctuations exceed a specified limit, etc.)
•
Deviation from nominal of voltage of main distribution bus
•
Deviation from nominal of voltages/frequencies at ship service loads
One scenario might include operation in a split plant configuration in order to assess how the
disturbance on one bus may propagate through the load zones to the other part of the system.
5.1.3 Load rejection
Sudden loss of large load (load breaker(s) trip) (Also consider the effect in split plant operation)
a.
Prime movers operating close to capacity
b.
Open breakers to selected loads
c.
Study transients…(see response variables identified in 2)
5.1.4 Loss of a generator
Sudden loss of a generator:
a.
Case 1: remaining generation capacity larger than connected loads
b.
Case 2: remaining generation capacity less than connected loads (load shedding
required).
c.
Study transients…(see response variables identified in 2)
5.1.5 Fault in a high-power rectifier
Fault in a high-power rectifier (propulsion rectifier for MVAC and HFAC or main rectifier for
MVDC system)
a. Specific fault TBD
b. Study transients…
5.1.6 Faults in propulsion motor windings
Balanced (3-phase) ground faults and unbalanced faults (single-phase and phase-phase faults).
a.
Study transient…
5.1.7 Series faults in DC loads
Effect of arc formation across a DC load (requires arc models etc…).
a.
Simulate fault condition where arc across faulted load maintains a possibly large
current in the circuits that can cause heating, fire, and other damages…
b.
This scenario requires special development…
2
5.1.8 Power restoration to vital load requiring load shedding
One of two buses connected to a vital load and initially supplying power to it is damaged. The
second bus is already supplying power at full capacity to other loads. Non-vital loads are shed to
free enough power for the vital load.
a.
Look at transients during power switching events
b.
Estimate time needed to restore power
5.1.9 Power restoration to vital load requiring use of energy storage
Total power loss to a vital load requires the use of energy storage to act as a UPS unit until
regular power is restored.
a.
Look at transients during power transfer
b.
Estimate time needed to restore power
c.
Estimate needed energy storage capacity
5.1.10 Harmonic analysis
Calculate harmonic distortion on main distribution bus, as various loads are turned-on, especially
high-power loads requiring rectification, and evaluate filtering needs.
5.1.11 Steady State Operation (extended study of scenario 1)
Assess the behavior of the model over a range of steady state operating conditions.
Parameters to be varied: Propeller speed (i.e. propulsion power), Ship service loading
Response Variables to be observed:
 Generator frequency, terminal voltage, real and reactive power
 Efficiency of all major components (including, but not limited to):
a.
propulsion motors (shaft power/terminal electrical power)
b.
propulsion drives (electrical power delivered to propulsion motor/electrical
power drawn at point of coupling to the main distribution bus)
c.
generators (terminal electrical power/shaft power)
d.
architecture-specific power conversion modules
e.
transformers
 Voltage ripple on DC busses
 Harmonic distortion on AC busses
5.2
Case studies requiring model for top-level system analyses
3
5.2.1 1.
Power balance analysis during early stage ship design
Is installed power adequate to supply all loads, under expected operational conditions? The loads
include special loads such as intermittent pulse loads and energy storage during charging cycle.
Total peak power is usually higher than installed power but loads do not need power
simultaneously. For example, in situation where the ship needs to take evasive actions while
defending itself using special loads, how fast can it sail? If the calculated speed is 15 knots for
example, how much additional power is needed to increase that speed to 25 knots? Alternatively,
what other loads can be shed, if any, in order for the ship to sail at 25 knots? Similar scenarios
can be set-up and analyzed to ascertain that installed power is adequate to accomplish ship
missions under expected operational conditions. A probabilistic approach could also be
employed to assess, for example, the expected maximum speed (in the context of the
distributions of the loads), or the maximum attainable speed for which a given level of
confidence exists.
5.2.2 Fuel consumption analysis
For a given power system, calculate fuel consumption for a prescribed ship mission profile (e.g.
typical DDG 51 ship mission profile is available in the open literature and can be used as a
benchmark or a similar profile can be developed). Again, probabilistic techniques could be
applied to account for uncertainty in conditions or significant uncertainty in model parameters.
5.2.3 Power system mass, volume, and cost
Calculate total mass and volume, and estimate cost, of a given power system, using typical data
for current commercial equipments.
5.2.4 Prime power optimization
Under given operational load demand what generating units should be used so that fuel
consumption is minimal?
a.
Use initial ratings of 4 prime movers: calculate minimum fuel consumption.
b.
Change ratings of prime movers and determine minimum fuel consumption.
c.
Repeat case b) as necessary.
d.
Compare results and determine the most efficient rating combination of the four
prime movers.
e.
Similar analyses can be done for weight, volume, cost, etc…
5.2.5 Reliability/Survivability Assessment
For a given system topology, set of component ratings, and load request profile, the proportion of
the load demand that could be met by the system in the event of failure of one or more of system
components could be assessed. For given probability distributions for the failure/loss of
components and/or the probability of load profiles, the reliability/survivability of the system
could be assessed through quantitative indices. In this way, the reliability and survivability of
systems could be compared, facilitating the design process.
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