Dynamic Optimal Generation Scheduling of Shipboard Power Systems

1
Dynamic Optimal Generation Scheduling of
Shipboard Power Systems

• Wei Wu, Kent Davey and Ari Arapostathis
• The University of Texas at Austin
• ESRDC Purdue Controls Workshop
• Aug. 17-18, 2006

2
Schematic of Power Train of Electric Ship
3
Motivation

• Turbine-generator design and control
• Key for power density and efficiency
• Design of Turbine-generator
• Granularity number, size, maximum power capacity
• Fuel how much is needed for different missions?
• Storage how much power storage is beneficial to
  have in a warship?
• Dynamic scheduling of turbine-generator
• Status ON or OFF
• Generation scheduling how much each generator
  generates?
• Storage control how to use the storage
  dynamically

4
Specific Fuel Consumption

• Efficiency of power generator
• Maximum power is efficient for power generation
• Choice of the set of generators
• Max power 80MW destroyer
• Mission profile
• Fuel efficiency

5
Mission Profiles

• Mission profile Distribution of speed and power
  for specific mission
• ?k the probability at speed vk
• Mission profile alone is not sufficient for
  controls
• Frequency how fast the power demand changes?
• Switching cost of turbine-generator from OFF to
  ON
• Mission profile ? Load profile

6
Static Scheduling Formulation Fuel Consumption
Minimization

• Objective minimizing the total fuel consumption
• The optimization problem is non-convex
• Static Scheduling Davey 2004

Fuel consumed by Generator n at speed vk
Power demand for speed vk
7
Dynamic vs. Static Scheduling

• Static Scheduling suboptimal
• Generation scheduling depends only on power
  demands
• Switching fuel consumption fuel to restart
  generators
• Impact of power storage
• Dynamic scheduling
• Depends on power demands, generator status,
  storage level
• Capture performance impact by the intensity of
  load fluctuations of the ship
• Dimensioning the power storage

8
Dynamic Generation Scheduling Modeling (I)

• Speed transition S Markov chain, state s
• Transition probability parameterized by ?,
  denoting the intensity of load fluctuations
• Power demand P(s) at speed state s
• Generator state G how many generators are ON

Typical power profile for a navy frigate Max
Power 72MW, Hotel Power8 MW
9
Objective function Approximation

• Assumption convexized fuel consumption rate
• Nonconvex optimization
• Use a convex approximating function to model fuel
  consumption rate

10
Modeling without Power Storage

• Model Markov decision process (MDP)
• State space (sn an-1) ? S G
• Action space (an Pn,s) ? G P
• Cost function power generation fuel switching
  fuel
• Transition probability
• Optimal policy dynamic programming equation
• Algorithm value iteration

11
Numerical Results (I)

• As intensity of load fluctuations increases, the
  additional fuel consumption increases
• The mission profile is not enough to design
  control the turbine-generators
• Max additional fuel 2.8 or 40 m3

420MW turbine-generators (4LM2500)
12
Numerical Results (II)

• Max additional fuel 10 or 135 m3
• Save 200 m3 fuel in comparison with 4LM2500
• Need to optimize the system design based on
  dynamic scheduling (power storage!)
• Adaptive control for intensity of load
  fluctuations?

6 13.5 MW turbine-generators (6 13.5 MW
Alstom)
13
Preliminary Result (I) Modeling with Power
Storage
xn
d(s)
Turbine-generators
Switch Logic

• A queueing model
• Server power demand, Markov chain controlled
• Arrival generators, control the number of
  generator
• Queue power in storage
• Objective minimize fuel consumption
• Difference from the queueing model
• Storage leakage (e.g., flywheel) xn1?xn, ?lt1

14
Preliminary Result (II) Modeling with Power
Storage

• Model still MDP, but with constraints
• State space (xn sn an-1) ? XSG
• Action space (an Pn,s) ? GP
• Constraint xn ? 0
• System dynamics xn1 ?xnP-d(s)
• Optimal policy characterized by
  Hamilton-Jocobi-Bellman equation
• Solution
• Much higher computational complexity due to the
  continuous variable xn
• More intuitive results need to be further
  explored

15
Conclusion and Future Work

• Address the question of dynamic power generation
• Control data need refined mission profiles
• Static scheduling is conservative
• Dynamic generation scheduling
• Symmetric turbine generators
• Long-time average cost
• Account for fuel penalty for generator startup
• Future work
• Structure results for scheduling with power
  storage
• Designing an algorithm to find the optimal
  combinations of turbine-generators for given ship
  configuration and missions