Shipboard Power Management Using Constrained
Nonlinear Model Predictive Control
Philip Stone and
Daniel F. Opila
GE Power Conversion
Pittsburgh, PA USA
Hyeongjun Park and
Jing Sun
University of Michigan
Ann Arbor, MI, USA
Abstract— Both new and existing naval vessels of all sizes face
ever-increasing power supply requirements to support advanced
mission loads including high power sensors, weapons, and
launchers. Adding additional conventional generators to support
these loads is infeasible given size and weight constraints and
given the pulsed nature of those new loads. Instead, an
optimization-based Power Management Controller (PMC) is used
to dynamically control power system sources and loads in real
time in order to serve system needs with a minimal amount of
power supply equipment. In this paper, a Model Predictive
Control (MPC) approach is used to dynamically coordinate
sources and loads based on future demand. A cost function is used
to prioritize various ship goals and objectives, and constraints are
added to reflect hardware limitations. A Constrained Nonlinear
MPC algorithm is then used to minimize the cost over a finite
future horizon and generate control commands in real-time. The
PMC is demonstrated to successfully control and improve system
performance on a hardware test bed for ship power system
research.
I.
INTRODUCTION
The power generation capacity of a shipboard power system
is inherently restricted by the weight and footprint limitations of
a ship hull. Modern advanced defense systems such as the air
and missile defense radar (AMDR) [1], electromagnetic rail
guns [2], electromagnetic launch systems [3], and solid-state
and free electron lasers [4] represent high power electrical loads
that are beginning to place a high demand on the limited
capacity [5]. As the respective technologies mature, these
weapons are becoming increasingly critical to countering
hostile surface, air, and missile targets and maintaining state-ofthe-art offensive capability should it be necessary. Many of
these weapons are typically pulsed with a demand on the order
of seconds [4]. However, the sum of the total power capacity of
each of these weapons plus the ship service loads could quickly
exceed the power generation capacity of the ship and thus limit
the number of weapons that can be installed unless the available
generation capacity is intelligently allocated.
To enable the effective employment of multiple high power
weapons within the ship power system, a power management
controller (PMC) is essential. A shipboard PMC dynamically
coordinates the ship power sources (main generators, auxiliary
generators, UPS devices, energy storage modules, etc.) and
loads to most effectively provide power to the weapons only
when they need it. The PMC thus enables multiple high power
weapons, a reduction of system mass/volume through reduction
Steve Pekarek and
Ray DeCarlo
Purdue University
West Lafayette, IN, USA
Eric Westervelt, James Brooks,
and Gayathri Seenumani
GE Global Research Center
Schenectady, NY, USA
of power generation requirements, and reduced troop levels due
to automated decision-making.
The proposed PMC approach employs model predictive
control (MPC) [6] that resides at a supervisory level to provide
power to loads as they need them while optimizing ship
performance. MPC considers a known model of the plant (the
ship and its loads/weapons) and looks ahead over a prediction
horizon to determine the optimal control references to provide
to the local controllers of the power system elements. In this
way the PMC can prepare the power system for a short-term
high power weapon by taking preemptive action such as
ramping up generators, ramping non-vital loads, charging
energy storage devices, and reconfiguring the system so as to
optimize system performance and deliver the requested power
at the required time of the high power pulse (weapon firing).
This concept of a PMC is not limited to future ship
arrangements with multiple high power weapons. Among other
capabilities, existing sophisticated ship power managers can
reconfigure breakers and add or shed sources and loads based
upon pre-defined load priorities and following a set of rules [7].
The proposed PMC can do these things as well as other tasks
such as tracking optimal efficiency points for multiple gas
turbine generators to decrease fuel consumption and thus cost.
The predictive PMC considers the defined goals and priorities
of the ship to ramp up/down generation sources and
enforce/relax load demands as necessary on-the-fly. The model
predictive approach enables the PMC to look ahead as far as the
established prediction horizon and begin compensating for
pulse loads before they actually occur and then gracefully
recover. Instead of installing a surplus of energy storage
modules on a ship, the PMC can coordinate a reduced number
of modules along with existing generation capacities to
accommodate the ship load demands.
The proposed PMC is demonstrated on the medium voltage
DC test bed for ship power system research at Purdue
University and this test bed is described in Section II. The MPC
approach as it pertains to a shipboard PMC is discussed in
further detail in Section III. The proposed PMC is tested by
establishing a baseline behavior and then attempting to improve
that behavior by adjusting the relative priorities of the ship
goals with two successive test cases. The test cases for
demonstrating the effectiveness of the PMC on the test bed are
outlined in Section IV. The testing results are presented and
analyzed in Section V. Conclusions regarding the level of
success in employing the MPC approach to shipboard power
management are discussed in Section VI.
II.
TEST BED FOR SHIP POWER SYSTEM RESEARCH
In order to validate research relative to ship power systems
a medium voltage (MV) DC test bed has been constructed at
Purdue University [8]. A one-line diagram of the portion of
this test bed used for testing the proposed PMC is shown in
Figure 1. The system consists of two sources totaling 70 kW of
capacity and three loads connected in parallel to a 750 V DC
bus.
Generation system 1 (GS-1) consists of a four quadrant
dynamometer serving as the prime mover (PM-1) that regulates
a 59 kW wound rotor synchronous generator (SG-1) to 1800
rpm. AC-DC conversion is performed by a passive diode
rectifier (R-1) and the field voltage of the generator is
controlled by a voltage regulator (VR-1) to control the output
voltage. GS-1 is intended to represent the prime ship power
source such as a main gas turbine generator (GTG) set.
Generation system 2 (GS-2) consists of a four quadrant
dynamometer that regulates the speed of an 11 kW permanent
magnet synchronous generator (SG-2) to 3600 rpm. AC-DC
conversion is performed by an IGBT-based active rectifier (R2) and the output voltage of the generator may be controlled
through the active rectifier by a voltage regulator (VR-2).
Alternatively, the PMC may provide a power command to the
GS-2 which is then translated to a torque/current command at
the local level. GS-2 is intended to represent a smaller, faster
ship power generation source such as a diesel generator.
The primary load on the system is the ship propulsion
system (SPS) which consists of a propulsion drive (PD) and a
37 kW induction machine (IM). A dynamometer typically
regulates the IM speed to the rated 1800 rpm, but for PMC
Figure 2. Square wave pulse power load (SWPPL) profile.
testing the speed will be regulated to 900 rpm limiting the
effective maximum propulsion power to 18.5 kW. The PD
consists of an IGBT-based inverter with speed and torque
control modes; the latter is employed for PMC testing.
The pulse power load (PPL) emulates a pulse-power
weapon with an energy storage buffer between the load and
DC bus. A buck converter charges a capacitor from the bus
until a threshold voltage is reached at which time the capacitor
disconnects from the bus and discharges into a resistive load.
Thus the pulse profile as seen by the bus is a ramp that
increases from 0 to 8 kW in ~10 seconds. To place an even
greater burden on the system, the square wave pulse power
load (SWPPL) may be utilized. The SWPPL consists of a high
power buck converter (PS-1) that steps the voltage down to
500 V across a purely resistive load. The SWPPL can sink up
to 8 kW for 1 second on, 1 second off intervals for up to 7
cycles before needing time to recover thermally. The profile as
seen by the bus can be seen in Figure 2. The PMC testing will
only consider the more severe SWPPL as a disturbance to the
system.
The PMC is implemented in MATLAB Simulink and is
converted to real-time-compatible code via Simulink Coder to
reside on a B&R 810 industrialized PC. This PC interfaces
with the test bed components via a common network switch.
The PMC functions in real time using the MATLAB xPC
kernel and communicates using the user datagram protocol
(UDP). The GS-2 and SPS receive power commands from the
PMC via the switch and convert those power commands first to
torque commands and then to inverter current commands
which they attempt to track using hysteresis control. Each
component provides the necessary measurements (e.g., rotor
speed, electrical power, mechanical power, DC voltage) back
to the PMC via the same switch.
Figure 1. Purdue MVDC test bed one-line diagram.
The GS-1 is treated as a slack generator by the PMC. Only
the droop gain (DGS1) of the voltage controller is exposed as a
control input to the PMC. The GS-1 provides the power
necessary to balance the power on the bus such that the sum of
the power sourced by the GS-1 and the GS-2 is equal to the
sum of the power sunk by the SPS and the SWPPL. The PMC
thus has three controls: the GS-1 droop gain command DGS1,
the GS-2 power command PGS2*, and the SPS power command
PSPS*.
III.
MODEL PREDICTIVE CONTROL APPROACH
The PMC optimizes the ship performance to achieve a set of
pre-specified objectives while respecting performance and
operability constraints. To do so, a multi-objective cost function
denoted by J is minimized subject to system dynamic and safety
constraints over a given period of time. In this work, the PMC
is formulated as a discrete-time optimal control problem
described by the following:
P(x0 ) :
min
x: [0, N ]→ R n ,
u: [0, N ]→ R m
J ( x(⋅), u (⋅))
N −1
where J ( x(⋅), u (⋅)) = Φ( x( N )) + ∑ L( x(k ), u ( k ))
k =0
s.t. x( k + 1) = f ( x(k ), u ( k )), f : R n + m → R n ,
x(0) = x0 ,
x0 ∈ R n ,
C ( x(k ), u (k )) ≤ 0,
C : R n + m → Rl , k = 0, ", N − 1
(1)
where, x ( k ), u ( k ) are the power system states and control
inputs, respectively, and N is the length of the prediction
horizon over which the cost function (J) is minimized and the
point wise state and input constraints need to be satisfied. The
equality constraint is the dynamic state evolution that describes
the power system f ( x (k ), u ( k )) , while the inequality
constraint represents the bounds on the states and the control
inputs.
A model predictive control approach is adopted in order to
solve the PMC problem. The approach employs a receding
horizon based MPC, where the above optimization problem is
solved repeatedly at every time step k and the input elements of
the optimal control sequence corresponding to the first time
index are applied as the control inputs to the plant. The MPC
considers a model of the power system and can leverage apriori information about known load disturbances such as pulse
loads in order to optimize ship performance.
Computing the solutions to (1) in deterministic real-time is
difficult, so two methods were considered to solve the PMC
problem in this program, namely, Interior Point Optimizer
(IpOpt) (see [9] and references there-in) and Integrated
Perturbation Analysis – Sequential Quadratic Programming
(IPA-SQP) [10].
The IpOpt is an interior-point based general purpose
nonlinear programming solver which is applicable to large
scale systems. More specifically, the algorithm is
computationally efficient for problems where the gradient and
hessians associated with the optimization problem have sparse
structure which is the case for the optimal control problem
associated with the PMC. In addition, the IpOpt enables using
implicit discretization for the equality dynamic constraint
which alleviates any numerical issues associated with the
discretization.
The IPA-SQP is an algorithm developed at the University of
Michigan that specifically addresses the computational
efficiency of optimization arising in the MPC formulation. It
exploits the complementary features of perturbation analysis
and sequential quadratic programming, and provides the
optimal solution in the predictor-corrector form. In both
methods, the optimal control sequence computed at any given
instant can be used as a feasible initial guess for the
optimization solved at the successive time instant, thereby
improving the computational efficiency.
A third algorithm employing deterministic dynamic
programming (DDP) was also developed under the Compact
Power Conversion Technologies program that funded this work.
This approach differs from the MPC approach by precomputing most of the optimal solution offline. Due to this
feature the DDP algorithm is relatively fast and deterministic,
but less flexible than an MPC algorithm. Due to space
limitations, this work will only show results from the IpOpt
algorithm to sufficiently prove the efficacy of model predictive
control as a ship power management tool. Further details on this
control algorithm and test results are available [11].
IV.
POWER MANAGEMENT CONTROLLER TEST PLAN
Ship performance is optimized by minimizing a cost
function which defines the performance goals of the ship and
assigns relative priority to each goal. The cost function
employed by the proposed PMC for the Purdue DC test bed is
L( x(k ), u (k )) = p1 (Vbusk − Vbus* )2 + p2 PTotalk 2 + p3 ( PGS 2k − PGS 2* )2 + ...
p4 ( PSPSk − PSPS * ) 2 + p5 (ωSPSk − ωSPS * )2 + p6 ( DGS1k − DGS1k −1 )2 + ...
(2)
p7 ( PGS1k − PGS1k−1 ) 2 + p8 ( PGS 2k − PGS 2k−1 ) 2 + p9 ( PSPSk − PSPSk −1 )2 .
Each parameter of this cost function represents an interest of the
power system. The weighting factor, p, for each parameter
assigns a relative priority to the parameter. The description of
each parameter is shown in Table 1. The main bus voltage is Vbus, the powers PTotal, PGS1, PGS2, and PSPS are the total, GS1,
GS2, and SPS powers respectively. An asterisk on each
represents a target or desired power. The droop gain for GS1 is
DGS1, and the SPS shaft speed is ωSPS .
Table 1. PMC test plan.
Quantity
Bus voltage deviation
Power tracking error
Fuel efficiency
Ship velocity deviation
GS-1 droop gain ramp rate
GS-1 prime mover ramp rate
GS-2 prime mover ramp rate
SPS prime mover ramp rate
Purdue Test Bed Equivalent
DC bus voltage deviation
Pulsed load power deviation
GS-2 tracking to efficiency point
SPS induction machine power
SPS induction machine speed
Ramp rate of GS-1 droop gain
Ramp rate of GS-1 electrical power
Ramp rate of GS-2 electrical power
Ramp rate of SPS electrical power
The error between the bus voltage measurement and the
target value of 750 V is critical to the proper operation of power
system elements. The total power tracking error has some
overlap with the bus voltage deviation term and adds another
layer of stability by ensuring that the power at the bus is
balanced between generation and load. It is assumed that an
efficiency curve for the GS-2 is known and that PGS2* is the
most efficient point on the curve.
The equivalent of ship velocity deviation is accounted for
with the target deviation of the SPS power and rotor speed. The
ramp rate of the GS-1output power is included to provide a
means of limiting the burden on this unit. The GS-1 represents a
main turbine generator in this test bed, and therefore it is of
interest to limit the power ramp rate so as to limit the wear of
the machine and increase its expected lifetime. Finally, ramp
rate terms for each of the PMC control inputs are included to
prevent large, sudden changes in demand.
Based upon the parameters included in the cost function,
metrics are developed to quantify the performance of the PMC.
The metrics used for the PMC testing on the Purdue test bed
were chosen to be the maximum and average deviations of the
GS-2 output power, the SPS output power, and the bus voltage
from their respective targets. Other metrics are the maximum
ramp rate of the GS-1 power and the total time during which the
ramp rate exceeds a threshold value. The ramp rate is a basic
slope calculation that considers the present value and the value
0.1 seconds ahead. The threshold is an arbitrary value that
would be chosen by the user based upon the specific generator
tolerance levels.
The test plan to demonstrate the effectiveness of the PMC
consists of three test cases which are outlined in Table 1. Before
testing the PMC, baseline measurements are observed during a
Test A
Test B
p1
p1
Test C
p1
p2
p2
p2
p3
p3
p3
p4
p4
p4α ↑
p5
p5
p5
p6
p6
p6
p7
p7α ↑
p7α
p8
p8
p8
p9
p9
p9
full SWPPL pulsing cycle (7 pulses as shown in Figure 2)
without a PMC and constant power targets being fed to GS-2
and SPS in open loop. After closing the control loop between
the PMC and the test bed, the weighting factors are tuned so
that the test bed behavior is similar to the behavior without a
PMC, thus establishing a baseline PMC behavior as the first
PMC test case, Test A. Two follow up test cases seek to
improve upon this behavior. The second test case (Test B)
consists of increasing the penalty on the GS-1 power ramp rate,
which is the equivalent of extending the lifetime of the
generator. The third test case (Test C) maintains the new GS-1
power ramp rate penalty and increases the SPS tracking penalty
to decrease the deviation from the target. This is the equivalent
of asking the ship to maintain a velocity closer to a set point.
A trade-off exists between the selection of the PMC
sampling time, the prediction horizon over which the PMC can
look ahead to assess the optimal control inputs, and the
hardware capabilities. Considering these trade-offs and the
fastest/slowest dynamics of the system, the test cases consider a
model-predictive PMC with a sampling time of 60 ms and a
prediction horizon of 6 steps (equivalent to 0.36 s).
V.
RESULTS AND ANALYSIS
The test plan was carried out on a low-order simulation
model of the test bed described in Sec. II to assess the expected
PMC behavior and reduce risk before testing in the lab. The
results for simulation and lab testing are shown and conclusions
are drawn based upon comparison of both waveforms and
metrics. The chosen set points for the test cases are for GS-2 to
generate 3 kW and SPS to sink 10 kW.
Time that GS-1 Ramp Rate Exceeds
Threshold (60 kW/s)
GS-1 Maximum Ramp Rate
1
seconds
kW/s
150
100
50
0
A
B
0.5
0
C
SPS Maximum Power Deviation
B
C
SPS Average Power Deviation
30
40
20
%
60
%
A
20
0
10
A
B
0
C
A
GS-2 Maximum Power Deviation
C
15
100
10
%
150
%
B
GS-2 Average Power Deviation
50
0
5
A
B
0
C
A
3
C
0.8
0.6
%
%
2
1
0
B
Vbus Average Deviation
Vbus Maximum Deviation
0.4
0.2
A
B
Test
C
0
A
B
Test
C
Figure 4. PMC simulation metrics.
system was disturbed with the 14 second pulse cycle shown in
Figure 2, but because the results for each pulse were identical
only the results due to the first pulse in the cycle are shown in
Figure 3. The 8 kW pulse disturbs the system just after 6
seconds of simulation time and the first pulse lasts for one
second.
Figure 3. PMC simulation results: a) GS-1 electrical power, b) SPS
electrical power, and c) GS-2 electrical power.
A. Simulation Results
With the PMC in a closed control loop with the model of the
test bed, the SWPPL profile was introduced to the system as a
known disturbance. The disturbance is “known” to the PMC in
the sense that the profile of the disturbance (magnitude and
pulse width) is stored offline and the PMC is given a warning
signal that the profile is going to be introduced to the system
within a preset amount of time (5 seconds in this set of test
cases). The amount of warning time could be as low as the
prediction horizon without impacting the PMC performance.
The simulated electrical power waveforms for GS-1, SPS,
and GS-2 are shown in Figure 3 and the chosen metrics for
quantifying the system performance are shown in Figure 4. The
Observing the GS-1 electrical power in Figure 3(a) it is
demonstrated that under Test A the GS-1 is absorbing most of
the pulse disturbance power resulting in a very high ramp rate
(73.0 kW/s). This abusive ramp rate would limit the expected
lifetime of a ship GTG, so under Test B the penalty on the GS-1
ramp rate is increased in the PMC cost function. The results
under Test B (shown in red) demonstrate that increasing the
GS-1 ramp rate penalty results in a decreased GS-1 ramp rate.
The ramp rate is reduced by 45% down to 40.4 kW/s as
reflected in Figure 4 and the ramp rate does not exceed the
specified threshold of 60 kW/s at all.
The PMC accomplishes this by looking ahead over the
prediction horizon to control the SPS and GS-2 to sink and
source power before and after the pulse as necessary to keep the
power on the main bus balanced without placing too much
stress on the GS-1. The PMC is effectively ramping up the GS1 power before the pulse occurs. This is reflected in the plot of
the SPS power in Figure 3(b). Under Test A the SPS tracks its
reference value of 10 kW (shown in yellow) with minimal
deviation. Under Test B the deviation increases to compensate
for the reduced GS-1 ramp rate. Before the pulse the SPS sinks
more power to allow the GS-1 to generate more power and still
keep the power on the bus balanced. After the pulse the SPS
sinks less power because the GS-1 power has only increased to
about half of the pulse power demand. The deviation decreases
until the GS-1 is sufficiently ramped up to accommodate the
pulse amplitude.
GS-1 Maximum Ramp Rate
1.5
seconds
kW/s
150
100
50
0
40
A
B
B
C
15
10
%
%
A
SPS Average Power Deviation
SPS Maximum Power Deviation
30
20
5
10
0
1
0.5
0
C
Time that GS-1 Ramp Rate Exceeds
Threshold (60 kW/s)
A
B
0
C
A
B
C
GS-2 Average Power Deviation
GS-2 Maximum Power Deviation
100
40
%
%
30
50
20
10
0
A
B
0
C
Bus Voltage Maximum Deviation
1
B
C
%
1.5
2
%
3
A
Bus Voltage Average Deviation
1
0
0.5
A
B
Test
C
0
A
B
Test
C
Figure 6. PMC test bed metrics.
ramps up in anticipation of the pulse. After the pulse the GS-2
unit provides excess power to accommodate the pulse on the
bus while the GS-1 unit gets fully ramped up without exceeding
an overly stressful ramp rate. Under Test C emphasis is placed
on the SPS tracking and this forces the GS-2 to have to deviate
even further from its reference during the pulse. This effect is
shown in the third row of Figure 4 as both the maximum and
average deviations increase with each test.
The last row of Figure 4 shows the metrics for the measured
bus voltage. These metrics are important from a stability
standpoint. The maximum and average bus voltage deviations
do not exceed 1% under any test indicating highly stable
conditions. The simulations indicate that the PMC algorithm is
working as designed and that bus stability is maintained.
Figure 5. PMC test bed results: a) GS-1 electrical power, b) SPS
mechanical power, and c) GS-2 mechanical power.
The SPS deviation from its reference is analogous to ship
speed velocity deviating from a set point. The SPS deviation
under Test B is considered to be too extreme, so Test C (shown
in green) increases the penalty on SPS tracking and the SPS
power more closely tracks the set point of 10 kW. This is
reflected in the SPS deviation metrics in the second row of
Figure 4. It should also be noted that the GS-1 ramp rate also
maintains a significant level of reduction. It was forced to
increase slightly, but the value of 44.5 kW/s is still 39.0% less
than it was under Test A and the ramp rate did not exceed the
threshold at all.
Observing the GS-2 electrical power in Figure 3(c), the
trend from Test A to Test B is similar to the SPS. The source
tracks its 3 kW reference well in steady state, but before the
pulse the source reduces its generated power as the GS-1 unit
B. Purdue Test Bed Results
The system measurements from the Purdue test bed under
the control of the PMC for the three test cases are shown in
Figure 5. Mechanical power is measured for SPS and GS-2 due
to excessive noise on the electrical measurements. The
corresponding metrics are shown in Figure 6. As is expected
from simulation, the GS-1 absorbs most of the pulse power
under Test A and the ramp rate is excessive. Under Test B, the
GS-1 ramp rate metrics indicate a reduction in both the
maximum ramp rate and the time during which the ramp rate
exceeds the 60 kW/s threshold during the pulse cycle.
The GS-1 power begins to ramp up in anticipation of the
pulse, but there is a sudden transient event lasting ~0.2 s.
Analysis of the measured SWPPL data shows that this event
occurs because there is a timing mismatch between the expected
pulse event and the actual pulse event. The reason for this
discrepancy is that the SWPPL in the lab is controlled by a local
computer employing a non-real-time operating system. Because
the timing of the pulse is not enforced in real time, there is
inherently a delay between when the pulse should arrive (5
seconds after requesting the pulse) and when it actually arrives;
this delay is uncontrolled and inconsistent. This is a test bed
hardware issue that is not an issue on a ship system which
typically employs a real time operating system. Thus, the
measured data is an indication of how well the PMC works
despite the hardware limitation.
the reduced primary power ramp rate. The tests demonstrate
that the predictive PMC can improve the performance of a ship
power system with pulse loads by coordinating sources and
loads to optimally minimize a cost function encompassing ship
goals and their priorities.
The PMC is successful in reducing the GS-1 ramp rate and
this is reflected in the metrics, but the PMC performance has
the potential to be even further improved as indicated by the
measured waveforms outside of the pulse mismatch duration
and the simulated data (approximated with dotted lines in
Figure 5). From the GS-1 power measurements it can be
observed that the GS-1 power begins ramping up over the
prediction horizon before the pulse occurs and begins ramping
down before the pulse ends. The metrics are reduced from Test
A to Test B, but they are also reduced from Test B to Test C.
This is because the pulse mismatch was less for Test C than for
Test B. Observing the waveforms and the simulated data, it is
fair to extrapolate that the GS-1 ramp rate under Test B would
have been slightly less than that of Test C if the mismatches
were the same.
This material is based upon work supported by the Office of
Naval Research under Contract No. N00014-09-D-0726. Any
opinions, findings and conclusions or recommendations
expressed in this material are those of the authors
and do not necessarily reflect the views of the Office of Naval
Research.
The SPS measurements in Figure 5(b) are similar to the
simulations. Under Test B the deviation from the reference
increases to accommodate the reduced GS-1 ramp rate, but
when the penalty for this deviation is increased in the cost
function for Test C, the PMC forces the SPS power to more
closely track its reference once again. This trend is reflected in
the second row of metrics in Figure 6. The GS-2 power in
Figure 5(c) is allowed to increasingly deviate as emphasis is
placed on other system goals. The average GS-2 deviation
decreases from Test B to Test C, but this is again due to the
greater timing mismatch. The bus voltage deviation shown in
the last row of Figure 6 is slightly larger than it was in
simulation, but all excursions are less than 2.5% indicating
acceptable stability under all tests cases.
VI.
CONCLUSION
As advanced high power weaponry and mission loads
become more readily available, ships are facing and will
continue to face the challenge of providing sufficient electrical
power to all loads. A Power Management Controller can
dynamically allocate generation sources and loads to provide
power for constant and pulse loads with reduced generation
capacity requirements.
Such a PMC employing model predictive control was
demonstrated on a representative scaled ship electrical system.
The measured data and analysis show that the PMC is
successfully able to establish a stable baseline performance
under pulse load conditions, reduce an undesirably high ramp
rate on the primary generation source, and then reduce the ship
propulsion power deviation from a reference while maintaining
ACKNOWLEDGMENT
REFERENCES
[1]
Air and Missile Defense Radar (AMDR), ONR Fact Sheet [Online].
Available:http://www.navy.mil/navydata/fact_display.asp?cid=2100&tid
=306&ct=2
[2] R. Ellis, “Electromagnetic Railgun,” ONR Fact Sheet [Online].
Available:http://www.onr.navy.mil/~/media/Files/Fact%20Sheets/35/Ele
ctromagnetic-Railgun-July-2012.ashx
[3] Converteam (now GE Power Conversion), EMKIT: Electromagnetic
Kinetic Integrated Technology Datasheet [Online]. Available:
http://www.converteam.com/majic/dl/4/doc/Restricted/Naval/EMKIT_da
tasheet_GB.7001.gb.06.09.03.pdf
[4] R. O’Rourke. (2013, Jan. 22), “Navy Shipboard Lasers for Surface, Air,
and Missile Defense: Background and Issues for Congress,”
Congressional Research Service Report for Congress [Online].
Available: www.fas.org/sgp/crs/weapons/R41526.pdf
[5] R. O’Rourke. (2013, Feb. 14), “Navy DDG-51 and DDG-1000 Destroyer
Programs: Background and Issues for Congress,” Congressional
Research Service Report for Congress [Online]. Available:
http://www.fas.org/sgp/crs/weapons/RL32109.pdf
[6] J. B. Rawlings and D. Q. Mayne, Model Predictive Control: Theory and
Design, Nob Hill Publishing, 2009.
[7] J. D. Stevens, H. J. Hegner, and J. Yan, “The Value of an Integrated
Power System Land Based Test Site to the U.S. Navy,” Proceedings of
the Electric Machines Technology Symposium (EMTS), 2012 [Online].
Available:https://www.navalengineers.org/ProceedingsDocs/EMTS2012/
Papers/44_Stevens_EMTS2012Paper.pdf
[8] M. Bash et al., "A Medium Voltage DC Testbed for Ship Power System
Research," Proceedings of IEEE Electric Ship Technologies Symposium
(ESTS) 2009, Baltimore, pp. 560-567, 2009.
[9] A. Wachter and L.T.Biegler, “On the Implementation of an InteriorPoint Filter Line-Search Algorithm for Large-Scale Nonlinear
Programming,” Mathematical Programming, Vol. 106 (2), pp. 25-57,
2006.
[10] R. Ghaemi, J. Sun, and I. Kolamanovsky, “An Integrated Perturbation
Analysis and Sequential Quadratic Programming Approach for Model
Predictive Control,” Automatica, Vol. 45, No. 6, pp. 2412-2418, 2009.
[11] H. Park, J. Sun, S. Pekarek, P. Stone, D.F. Opila, R. Meyer, I.
Kolmanovsky, R. DeCarlo, “Real-Time Model Predictive Control for
Shipboard Power Management Using the IPA-SQP Approach,” IEEE
Transactions on Control Systems Technology, Preprint, Vol. PP (99),
2015.