Shipboard Microgrid Optimization

Tom Trapp
PhD Defense
April 23, 2015
1

Committee Chair & Thesis Advisor
Franz Hover Assoc. Prof. MechE MIT
Committee Members
Joe Harbour Prof. of Pract. MechE MIT
Jim Kirtley Prof. ElecE MIT
Mark Thomas CAPT USN (retired)
Ed Zivi Prof. SystemsE USNA
2

Background & Problem Statement
Contributions
Previous Work
Network Optimization / IEP Modeling
Demonstrations
Conclusions & Recommendations
3

Contributions
Previous Work
Demonstrations
4

Objective
IEP Survivability Performance
Cost
B
C
B
B
C
A
C
B
6

Shipboard IEP design for survivability
is a complex, iterative process that does
not guarantee a minimum cost solution.
The process is not well matched for the
Pareto-optimal tradeoff process used to
support cost-as-an-independent-
variable (CAIV) DoD policy.
7

Contributions
Previous Work
Demonstrations
8

IEP Network
Optimization
Modeling
Survivability
& Operating
Condition
Specifications
Guaranteed
Minimum Cost
Survivable IEP
Solver
9

Electrical & Cooling Interdependence
Detailed Modeling
Flexibility to add
domains
Fischer Panda
10

Integral design of minimum
cost stored energy
Accounting for casualty &
operating conditions
Outback Power
11

1. Direct Design of Minimum Cost
Survivable IEP
2. Detailed Modeling of Interdependent
Domains with Flexibility to Add
Domains
3. Stored Energy Design at Minimum
Cost
12

Contributions
Previous Work
Demonstrations
13

Petry & Rumberg – Electrical Distribution
Topology
Doerry – Survivability, QoS, Definitions
– Zonal Elec. Distribution (ZED)
– Integrated Power System
Chalfant – Breaker-and-a-Half Topology
NAVSEA – Acquisition Strategy
14

Cramer, Zivi, Sudhoff – IEP Dynamic
Modeling & Survivability Metrics
Chan - Stored Energy Allocation
Marden, Chryssosstomidis – Model of
Purdue MVDC plant
15

Labbé – Network Synthesis NSMCF
Woungang – Survivable Mesh
Networks
Grover – Survivable Mesh-Based
Transport Networks
Taylor – Convex Optimization of Power
Systems
16

Contributions
Previous Work
Demonstrations
17

Formulation Example
Minimize:
Subject to:
2 f1 - f2 + 4 f3
f1 + f2 £ 2
3f2 - f3 = 5
f1 - 3f3 ³ 3
f1 ³ 0
f3 £ 0
Cost Function (Objective)
Constraints
18

Global
Minimum
Simplex
Method
Solver – IBM CPLEX®
19

Demand
Demand
Supply
Supply
Distribution
Distribution
Cost, Capacity
20

Laws
Conservation:
Sum of flow in and out of node = supply or
demand (Continuity)
Direction:
If flows have physical restrictions
Capacity:
Flow cannot exceed limitations of edges
21

Problem:
Minimize total
cost of flow
s = supply
d = demand
(Cost, Capacity)
22

Capacity relates to the flow limitation of the
roadway
Speed limit, Number of lanes
Rate of goods/time
Cost relates to how much it costs to transport on
the roadway
Mileage, Tolls, Wear & Tear
$/flowrate
23

Minimize flow cost:
5f12 + 2f13 + f34 + 2f42 + f46 + f53 + 10f56
Subject to:
Flow continuities at each node
Capacities
|f12| ≤ 15
|f13| ≤ 8
:
|f56| ≤ 15
24

Objective (cost):
(1,2) 25
(3,4) + 8
(5,3) + 8
(4,6) + 8
(5,6) + 20
= 69
(5,15)
(1,15) (1,10)
(2,15)
(10,15)
(1,8)
(2,15)
d=5
d=10
s=5
s=10
5
2
8
8
8
00
25

Can optimize anything that can be
modeled as flow:
Commodity Distribution
Transportation (Rail, Airlines, etc.)
Financial Investment
Electrical Power Flow
Cooling Mass Flow
26

Applied Mathematician
Correct, Efficient Solver Algorithms
Engineer
Model Accurately
Solver Format
Formulation Tricks
27

Now minimize cost of roadways. Account for
contingencies.
1. Minimize Capacity (instead of flow cost).
2. Roadway (1,2) could be lost sometime in future
3. Two unique set of constraints – (1) for normal
operations, (2) for the loss of roadway (1,2).
4. Find the minimum capacity (roadway limitation)
needed.
28

Problem:
1. Minimize total
Capacity of
the network
2. Account for
the possible loss
of path (1,2)
1
6
2
5
43
d=5
d=10
s=5
s=15
X
29

Solution:
d=5
d=10
s=5
s=15
0
10
0
5
0
5U=5
1
6
2
5
43
30

Specification: Survive the loss of all roadways,
any one roadway at a time (M-1 survivability).
Make a unique set of constraints for each loss
condition.
Let the capacity variable Uij take the value of the
largest of all flow conditions.
31

Minimize capacity:
U12 + U13 + U34 + U42 + U46 + U53 + U56
Subject to:
– f0
12 – f0
13 + 5 = 0
: : :
f0
56 + f0
46 = 10
-----------------------------
– f7
12 – f7
13 + 5 = 0
: : :
f7
56 + f7
46 = 10
-----------------------------
f1
12 = 0 … f7
56 = 0 (losses)
f0
12 <= U12 rollup capacities
:
f7
12 <= U12
d=5
d=10
s=5
s=15
10
10
10
5
5
5
1
6
2
5
43
32

Loss f12 f13 f34 f35 f42 f46 f56
(1,2) -- 5 5 5 10
(1,3) 5 -- 10
(3,4) 5 -- 10
(3,5) 5 -- 10
(4,2) 5 -- 10
(4,6) 5 -- 10
(5,6) 5 10 10 10 --
Maximum
= Uij
5 5 10 10 5 10 10
If we added a casualty for simultaneous loss of (1,2) and (5,6), then all flow
Would detour through (3,4) and U34 = 15.
33

Minimize:
Σ(aij Fij+ cij Uij)
Subject to:
Flow continuities
Casualty constraints
Uij ≤ M aij
M is large
d=5
d=10
s=5
s=15
15
15
10
10
1
6
2
5
43
34

Minimize:
U12 + … + U56 + C72xk
72
d=5
d=10
s=15
s=15
5
10
10
10
10
5U=5
1
6
2
5
43
7
35

Example 1: Network flow cost minimization
Example 2: Design a minimum cost network, with
contingencies for loss of roadways.
Requires unique variables for each casualty
Design output is minimum cost survivable network.
“Non-Simultaneous Multicommodity Flow”
NSMCF
36

GENERATOR
1 2
3 4
5
PUMP MOTOR
6
7 8
9
10
PROPULSION
MOTOR
11
GENERATOR
12 13
14 15
16
PUMP MOTOR
17
18 19
20
21
PROPULSION
MOTOR
22
STORED ENERGY23
1
PUMP
2 3
45
COOLER
6 7
COOLER
8 9
10
11
12
PUMP
1314
1516
COOLER
17 18
COOLER
1920
21
22
23 24
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25 26
1
2
3
456
7
8
9
10 11
12
13
14
15
16
17
18
1920 21 22 23
24
25 26
27
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
IEP Candidate Topology
38

1. Flow Continuity
a. Electrical Power
b. Cooling Mass Flow
2. Fixed & Variable Cost
a. Fixed cost (of installation, etc.)
b. Variable cost (of material purchase)
3. Stored Energy
39

4. Constitutive Relationships
a. Cooling mass flow vs. Electrical Heat Load
b. Pump electrical power vs. Cooling mass flow
5. Casualty & Operating Conditions
a. Unique flow variables for each condition
b. “Sets” of constraints
6. Global Capacity Rollup
a. Min Edge Capacity = Max Edge Flows
40

GENERATOR
1 2
3 4
5
PUMP MOTOR
6
7 8
9
10
PROPULSION
MOTOR
11
GENERATOR
12 13
14 15
16
PUMP MOTOR
17
18 19
20
21
PROPULSION
MOTOR
22
STORED ENERGY23
1
PUMP
2 3
45
COOLER
6 7
COOLER
8 9
10
11
12
PUMP
1314
1516
COOLER
17 18
COOLER
1920
21
22
23 24
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25 26
1
2
3
456
7
8
9
10 11
12
13
14
15
16
17
18
1920 21 22 23
24
25 26
27
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
41

• Each Node Conservation Equations
• Flow in – Flow out = Supply (or Demand)
GENERATOR
1 2
3 4
5
PUMP MOTOR
6
7 8
9
10
STORED ENERGY23
1
PUMP
2 3
45
COOLER
6 711
1
2
3
4
5
6
7
8
9
10
11
12
25 26
1
2
3
456
7
8 10
42

• Fixed Cost - The cost of existence of an edge in
the network
– Design
– Installation
– Maintenance
• Variable Cost – cost that varies with capacity
– Material cost
• Fixed cost is generally much higher than
variable cost
43

• Modeling objectives
– Allow the solver the option to delete the edge
using a binary variable
– When the solver deletes the edge, make sure
both fixed and variable costs are zeroed in the
solution
44

Minimize:
a12 x F12 + c12 x U12 + … … + a56 x F56 + c56 x
U56
Subject To:
U12 ≤ M x a12
aij = binary variable “on” or “off” aij = {0 or 1}
Fij = fixed cost of edge (i,j)
cij = variable cost (per unit capacity of edge (i,j))
Uij = capacity of edge (i,j)
M = very large number
GENERATOR
1 2
3
6
1
PUMP
2
5
COOLER
611
1
2
3
4
525
1
2
456
7
45

• Modeling objectives:
– Should only be used in emergency or in
specific instances. Otherwise, use a
conventional power source
– When turned on, the power flow will be
captured by the power flow capacity variable
– The capacity will be the minimum power flow
required for the design
– Multiply capacity by time = minimum energy
46

Minimize:
a12 x F12 + … + c56 x U56 + Σ (ζij x fk
ij)
ζij = “cost” of stored energy power flow (large number)
fk
ij = stored energy power flow (casualty & op condition
k)
If ζij is large enough, stored energy will only be used
when all normal power is lost and demand is not met.
Uij will equal the minimum power flow
required.
Otherwise, all fk
ij = 0 and stored energy not required
GENERATOR
1 2
5
PUMP MOTOR
6
GENERATOR
12 13
14 15
16
PU
1
18
STORED ENERGY23
PUMP
2 3
45
COOLER
611
1
PUMP
114
1516
COOLER
1720
21
23
1
4
5
7
13
14
15
16
17
18
19
20
25 26
1
2
3
456
7
8
14
15
16
17
18
1920 21
24
25
27
47

• Loss of Edges
– Flow set to zero
• Loss of Nodes
– All flow into/out of node set to zero
• Operating Conditions
– Unique load variables
50

• The capacity of an edge must meet or exceed
the highest of any flow condition experienced by
that edge.
• Uij ≤ max (fij)
51

Contributions
Previous Work
Demonstrations
52

• 2 Domain (electrical & seawater cooling)
• Generators (SMs) rating 30 MW
• 2 Propulsion Motors (PMs) rating 20 MW
• 2 Seawater Pumps (SWPs)
• 1 Stored Energy Device (SED)
• Candidate Topology
• M-1 survivability plus loss of all normal
power to seawater pump #1
53

GENERATOR
1 2
3 4
5
PUMP MOTOR
6
7 8
9
10
PROPULSION
MOTOR
11
GENERATOR
12 13
14 15
16
PUMP MOTOR
17
18 19
20
21
PROPULSION
MOTOR
22
STORED ENERGY23
1
PUMP
2 3
45
COOLER
6 7
COOLER
8 9
10
11
12
PUMP
1314
1516
COOLER
17 18
COOLER
1920
21
22
23 24
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25 26
1
2
3
456
7
8
9
10 11
12
13
14
15
16
17
18
1920 21 22 23
24
25 26
27
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
55

GENERATOR
1 2
3 4
5
PUMP MOTOR
6
7 8
9
10
PROPULSION
MOTOR
11
GENERATOR
12 13
14 15
16
PUMP MOTOR
17
18 19
20
21
PROPULSION
MOTOR
22
STORED ENERGY23
1
PUMP
2 3
45
COOLER
6 7
COOLER
8 9
10
11
12
PUMP
1314
1516
COOLER
17 18
COOLER
1920
21
22
23 24
1
20.33
2 20.33
3
20.33
4 0.33
5
0.33
6
20
7 0
8
20
9 20
10
20
11
0
12 0
13
20.33
14 20.33
15
20.33
16 0
17
20.33
18 0.33
19
0.33
20
20
21 0
22
20
23 20
24
20
25 0 26
0.32
1 4.03
2
4.03
3 4.03
4
2.03
5
2.03
6
2.03
7 2.03
8
2
9 0
10
2
11
2
12 4.03
13 2.03
14 4.03
15
4.03
16 4.03
17
2.03
18 0
19
2.03
20
2.03
21
2
22
2
23
2
24 4.03
25 2 26 2
27
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
Capacities
56

Minimize:
Sum of capacity costs (fixed & variable - both domains)
Subject to (for all casualty & operating conditions):
Continuity both domains
Capacity/flow min-max
Constitutive relationships
Electrical heat load vs. cooling mass flow
Pump mass flow vs. electrical power
Edge “choosing” for both domains
Using binary variables
Casualty & operating conditions
57

GENERATOR
1 2
3 4
5
PUMP MOTOR
6
7 8
9
10
PROPULSION
MOTOR
11
GENERATOR
12 13
14 15
16
PUMP MOTOR
17
18 19
20
21
PROPULSION
MOTOR
22
STORED ENERGY23
1
PUMP
2 3
45
COOLER
6 7
COOLER
8 9
10
11
12
PUMP
1314
1516
COOLER
17 18
COOLER
1920
21
22
23 24
1
20.33
2 20.33
3
20.33
4 0.33
5
0.33
6
20
7 0
8
20
9 20
10
20
11
0
12 0
13
0.33
14 0.33
15
0.33
16 0
17
0.33
18 -0.33
19
0.33
20
0
21 0
22
0
23 0
24
0
25 0 26
0
1 4.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
6 Lost Electrical Arc
2 Lost Cooling Arc
2
4.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
3 4.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
4
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
5
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
6
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
7 2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
8
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
9 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
10
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
11
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
12 4.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
13 -2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
14 0.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
15
0.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
16 0.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc17
0.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
18 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
24 0.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
25 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
26 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
27
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
Casualty #0 (Showing Flow)
58

GENERATOR
1 2
3 4
5
PUMP MOTOR
6
7 8
9
10
PROPULSION
MOTOR
11
GENERATOR
12 13
14 15
16
PUMP MOTOR
17
18 19
20
21
PROPULSION
MOTOR
22
STORED ENERGY23
1
PUMP
2 3
45
COOLER
6 7
COOLER
8 9
10
11
12
PUMP
1314
1516
COOLER
17 18
COOLER
1920
21
22
23 24
11
0
2 0
3
0
4 0
5
0
6
0
7 0
8
0
9 0
10
0
11
0
12 0
13
20.33
14 20.33
15
20.33
16 0
17
20.33
18 -0.33
19
0.33
20
20
21 0
22
20
23 -20
24
20
25 0 26
0
1 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
2
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
3 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
4
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
5
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
6
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
7 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
8
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
9 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
10
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
11
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
12 2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
13 -2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
14 4.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
15
4.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
16 4.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
18 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
24 2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
25 0.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
26 2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
27
0.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
59

GENERATOR
1 2
3 4
5
PUMP MOTOR
6
7 8
9
10
PROPULSION
MOTOR
11
GENERATOR
12 13
14 15
16
PUMP MOTOR
17
18 19
20
21
PROPULSION
MOTOR
22
STORED ENERGY23
1
PUMP
2 3
45
COOLER
6 7
COOLER
8 9
10
11
12
PUMP
1314
1516
COOLER
17 18
COOLER
1920
21
22
23 24
1
20.33
2 20.33
3
20.33
4 0.33
5
0.33
6
20
7 0
8
20
9 20
10
20
11
0
12 0
13
0
14 0
15
0
16 0
17
0
18 0
19
0
20
0
21 0
22
0
23 0
24
0
25 0 26
0
1 4.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
2
4.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
3 4.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
4
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
5
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
6
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
7 2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
8
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
9 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
10
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
11
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
12 4.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
13 -2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
1414 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
15
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
16 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
18 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
24 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
25 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
26 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
27
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
60

GENERATOR
1 2
3 4
5
PUMP MOTOR
6
7 8
9
10
PROPULSION
MOTOR
11
GENERATOR
12 13
14 15
16
PUMP MOTOR
17
18 19
20
21
PROPULSION
MOTOR
22
STORED ENERGY23
1
PUMP
2 3
45
COOLER
6 7
COOLER
8 9
10
11
12
PUMP
1314
1516
COOLER
17 18
COOLER
1920
21
22
23 24
1
20.33
2 20.33
3
20.33
4 0.33
5
0.33
6
20
7 0
8
20
9 20
10
20
11
0
12 0
13
0
14 0
15
0
16 0
17
0
18 0
19
0
20
0
21 0
22
0
23 0
24
0
25 0 26
0
1 4.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
2
4.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
3 4.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
4
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
5
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
6
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
7 2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
8
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
9 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
10
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
11
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
12 2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
13 -0.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
14 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
15
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
16 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
18 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
24 2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
25 -2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
26 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
27
0.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
61

GENERATOR
1 2
3 4
5
PUMP MOTOR
6
7 8
9
10
PROPULSION
MOTOR
11
GENERATOR
12 13
14 15
16
PUMP MOTOR
17
18 19
20
21
PROPULSION
MOTOR
22
STORED ENERGY23
1
PUMP
2 3
45
COOLER
6 7
COOLER
8 9
10
11
12
PUMP
1314
1516
COOLER
17 18
COOLER
1920
21
22
23 24
1
20.33
2 20.33
3
20.33
4 0.33
5
0.33
6
20
7 0
8
20
9 20
10
20
11
0
12 0
13
0
14 0
15
0
16 0
17
0
18 0
19
0
20
0
21 0
22
0
23 0
24
0
25 0 26
0
1 4.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
2
4.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
3 4.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
4
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
5
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
6
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
7 2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
8
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
9 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
10
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
11
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
12 2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
13 -0.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
14 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
15
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
16 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
18 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
24 2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
25 -2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
26 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
27
0.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
62

GENERATOR
1 2
3 4
5
PUMP MOTOR
6
7 8
9
10
PROPULSION
MOTOR
11
GENERATOR
12 13
14 15
16
PUMP MOTOR
17
18 19
20
21
PROPULSION
MOTOR
22
STORED ENERGY23
1
PUMP
2 3
45
COOLER
6 7
COOLER
8 9
10
11
12
PUMP
1314
1516
COOLER
17 18
COOLER
1920
21
22
23 24
1
20
2 20
3
20
44 0
5
0.32
6
20
77 0
8
20
9 20
10
20
11
0
12 0
13
0
14 0
15
0
1616 0
17
0
1818 0
19
0
20
0
21 0
22
0
23 0
24
0
25 0 26
-0.32
1 4
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
2
4
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
3 4
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
4
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
5
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
6
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
7 2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
8
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
9 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
10
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
11
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
12 4
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
13 -2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
14 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
15
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
16 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
18 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
24 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
25 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
26 0
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
27
2
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
2 Lost Cooling Arc
63

• 2 Synchronous Machines
• 2 Propulsion Drives
• 3 Seawater Pumps
• 3 Fresh Water Pumps
• 2 Power Supplies (AC - DC)
• 6 Converter Modules (DC – DC)
• 3 Inverter Modules (DC – AC)
64

SWP
1
SWP
2
SWP
3
Cramer 2007
65

110
100
CM3
90
80
IM3
FHX3
X (m)
70
PD1
SM2
CM6
PS2
60
SWP3
CM2
50
SWP0
40
PD2
FHX2
IM2
SM1
CM1
-6
SWP1
CM5
Freshwater Heat Exchanger (FHX)
-4
FHX1
PS1
Syncronous Machine (SM)
-2
Converter Module (CM)
Seawater Pump (SWP)
Propulsion Drive (PD)
IM1
Inverter Module (IM)
Power Supply (PS)
0
Freshwater Arc
Electrical Arc
Seawater Arc
Y (m)
2
CM4
468101214
4
6
8
10
12
14
16
18
20
Z(m)
68

Contributions
Previous Work
Demonstration
70

Notional IEP Purdue NCST
Candidate Edges 53 146
Solution Edges 45 75
Edge Savings 15.1% 48.6%
Candidate Cost $93,531 $323,647
Solution Cost $86,031 $201,648
Cost Savings 8.0% 37.7%
No. Constraints ~16,000 ~68,000
Computation Time 0.72 sec 2 hr 9 min
GENERATOR
1 2
3 4
5
PUMP MOTOR
6
7 8
9
10
PROPULSION
MOTOR
11
GENERATOR
12 13
14 15
16
PUMP MOTOR
17
18 19
20
21
PROPULSION
MOTOR
22
STORED ENERGY23
1
PUMP
2 3
45
COOLER
6 7
COOLER
8 9
10
11
12
PUMP
1314
1516
COOLER
17 18
COOLER
1920
21
22
23 24
1
20.33
2 20.33
3
20.33
4 0.33
5
0.33
6
20
7 0
8
20
9 20
10
20
11
0
12 0
13
20.33
14 20.33
15
20.33
16 0
17
20.33
18 0.33
19
0.33
20
20
21 0
22
20
23 20
24
20
25 0 26
0.32
1 4.03
2
4.03
3 4.03
4
2.03
5
2.03
6
2.03
7 2.03
8
2
9 0
10
2
11
2
12 4.03
13 2.03
14 4.03
15
4.03
16 4.03
17
2.03
18 0
19
2.03
20
2.03
21
2
22
2
23
2
24 4.03
25 2 26 2
27
2.03
LEGEND
10
Electrical Node
12 Electrical Arc
9
Cooling Node
13 Cooling Arc
Capacities
71

• Minimizes Cost Survivable IEP
– Supports CAIV Pareto-Optimal
– Fixed Cost consideration
– Direct Design Method for Survivability
– Scalable for Nodes, Edges, domains
• Minimum Stored Energy Design
72

• Stored Energy Placement
• Standard Edge Components
• Optimal Edge Routing
• Spatial Layer
• Optimal Generator Size, Placement
• Hydrodynamic Layer
73

Tom Trapp
PhD Defense
April 23, 2015
74

• University of Wisconsin–
Milwaukee 88 BSEE
• Navy Nuclear Propulsion
Program 89-95
• MIT 95-98 NavEng, SM
ME
• Navy EDO 95-
• MIT 09-15 –PhD ME
75

Shipboard Small scale
IEP Domain interdependent
Survivable Reserve capacity
Network Linear programming
Optimization Minimize cost
76

Centrifugal Pump
Affinity Laws
qµn
h = Dpµn2
P µhq = n2
n( ) = n3
q = pump volumetric flow rate
n = pump speed (angular velocity)
Δp = pump head or pressure
P = pump power
78

Continuity 0
– x0
12 – x0
13 + 5 = 0
: : :
x0
56 + x0
46 = 10
Continuity 1
– x1
12 – x1
13 + 5 = 0
: : :
x1
56 + x1
46 = 10
Continuity 2
– x2
12 – x2
13 + 5 = 0
: : :
x2
56 + x2
46 = 10
Continuity 3
– x3
12 – x3
13 + 5 = 0
: : :
x3
56 + x3
46 = 10
Continuity 4
– x4
12 – x4
13 + 5 = 0
: : :
x4
56 + x4
46 = 10
Continuity 5
– x5
12 – x5
13 + 5 = 0
: : :
x5
56 + x5
46 = 10
Continuity 6
– x6
12 – x6
13 + 5 = 0
: : :
x6
56 + x6
46 = 10
Continuity 7
– x7
12 – x7
13 + 5 = 0
: : :
x7
56 + x7
46 = 10
79

Minimize capacity:
U12 + U13 + U34 + U42 + U46 + U53 + U56
Subject to:
– x0
12 – x0
13 + 5 = 0
: : :
x0
56 + x0
46 = 10
-----------------------------
– x1
12 – x1
13 + 5 = 0
: : :
x1
56 + x1
46 = 10
-----------------------------
x1
12 = 0 loss of path (1,2)
x0
12 <= U12 rollup U12
x1
12 <= U12
d=5
d=10
s=5
s=10
0
U=10
0
U=5
0
U=5U=5
1
6
2
5
43
80

Minimize capacity:
U12 + U13 + U34 + U42 + U46 + U53 + U56
Subject to:
– x0
12 – x0
13 + 5 = 0
: : :
x0
56 + x0
46 = 10
-----------------------------
– x1
12 – x1
13 + 5 = 0
: : :
x1
56 + x1
46 = 10
-----------------------------
x1
12 = 0 loss of path (1,2)
x0
12 <= U12 rollup U12
x1
12 <= U12
d=5
d=10
s=15
s=15
10
0
5
0
55
1
6
2
5
43
81

Cost/unit Flow Capacity
Continuity
Edge
Capacities
N nodes
M edges
K casualties
e – electrical
t - thermal
H cooled
S powered
e – electrical
t – thermal
d, g – demand
cooling, powering
Constitutive relationships 82

Electrical
Capacity
Cost
pij =
$
l
æ
è
ç
ö
ø
÷
Pij max
Lij
85

Cooling
Capacity
Cost
qlm =
$
l
æ
è
ç
ö
ø
÷
Qlmmax
Llm
$
l
æ
è
ç
ö
ø
÷
rwVmax
Llm
86

Electrical Power
Continuity
Equations
p3
p2
p1
-p12 + p13 + p14 = d1
d1
87

Cooling Mass Flow
Continuity
Equations
q3
q2
q1
-q12 +q13 +q14 = g1
g1
88

Electrical
Capacity
“Rollup”
89

Electrical
Capacity
“Rollup”
Pij is the maximum power flow edge (i,j)
experiences during all casualty and
pij
k are unique variables for each casop.
Pij are global variables (no k)
90

Cooling
Capacity
“Rollup”
Qlm is the maximum mass flow edge (l,m)
experiences during all casualty and
qlm
k are unique variables for each casop.
Qlm are global variables (no k)
91

Redundant
Loads,
Such as
Propulsion
Motors
Allows for two PMs, for example
To share the load for the ordered
Ship speed. If one PM is unavailable
Due to casualty, the other PM can
Provide the power required
92

Fixed Costs
aij & blm
Are binary variables
aij,blm Î {0,1}
Pij £ Maij
Qlm £ Mblm
M is a large number
Large enough to allow
P, Q to take values needed
To meet power, flow requirements
If edge associated with them is necessary
F, G are fixed costs associated with the
Existence of the edge
93

Stored
Energy
ζ is a large number
Penalizes the solver for
Using power flow from node
n. ζ is sufficiently large
Such that solver will only use
When all normal power is lost
94

NOT SHOWN:
CASUALTY
CONSTRAINTS
95

• Edge capacity becomes decision variable
• Allows multiple casualties & operating
conditions
• Solves for optimal with casualties &
operating conditions in the formulation
104

(5,15)
(10,15)(1,15)
(1,8)
(2,15)(2,15)
(1,10)
1
6
2
5
43
d=5
d=10
s=5
s=10
106

Shipboard Microgrid Optimization

Recommended

Recommended

More Related Content

Similar to Shipboard Microgrid Optimization

Similar to Shipboard Microgrid Optimization (20)

Recently uploaded

Recently uploaded (20)

Shipboard Microgrid Optimization