A fast current response control strategy for flywheel peak power capability under DC bus voltage constraint L. Xu and S. Li Department of Electrical Engineering The Ohio State University Grainger Center for Electric Machinery and - PowerPoint PPT Presentation

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A fast current response control strategy for flywheel peak power capability under DC bus voltage constraint L. Xu and S. Li Department of Electrical Engineering The Ohio State University Grainger Center for Electric Machinery and

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Title: A fast current response control strategy for flywheel peak power capability under DC bus voltage constraint L. Xu and S. Li Department of Electrical Engineering The Ohio State University Grainger Center for Electric Machinery and


1
A fast current response control strategy for
flywheel peak power capability under DC bus
voltage constraintL. Xu and S. Li Department
of Electrical Engineering The Ohio State
UniversityGrainger Center for Electric
Machinery and ElectromechanicsUniversity of
Illinois at Urbana-ChampaignDec. 2001
2
Presentation Outline
  1. Introduction
  2. Problem Formulation
  3. Prerequisite Case of Disk Voltage Constraint
  4. Feedback Time-Optimal Design under Hexagonal
    Voltage Constraint
  5. Application in Flywheel Energy Storage Systems
  6. Conclusion

3
Introduction
  • Literature Review
  • General concept of minimum-time current
    transition at DC bus voltage constraint, Choi
    Sul 2.
  • PMSM application, torque patching and current
    regulator conditioning, Xu 3, 4.
  • Motivations
  • Peak power delivery of flywheels as energy
    storage devices
  • Disk constraint V.S.
    Hexagonal constraint
  • Feedback solution is preferable

4
II. Problem Formulation
  • Efficient DC bus utilization for high speed PMSM
    operation for fast peak power delivery
  • Synchronous reference frame model of PMSM,
  • Denote
  • Then with stator resistance neglected,
  • Now define the state as
  • Then, where

5
The Equivalent Circuit Representation in
Synchronous Reference Frame
  • Synchronous
  • Reference Frame
  • is assumed

6
Voltage Constraints
  • In stationary reference frame
  • Voltage Constraint
  • Case of Disk Voltage Constraint
  • Hexagonal Voltage Constraint

7
III. Prerequisite Case of Disk Voltage
Constraint
  • Geometrical explanation
  • Given,
  • Solution,

8
IV. Feedback Time-Optimal Design under Hexagonal
Voltage Constraint
  • Dynamic equation
  • Define the Hamiltonian
  • By Pontryagins maximum principle, necessary
    conditions

9
Some Theoretical Implications
  • Assumption consider the regulator problem
  • System is normal, i.e.,
  • are all controllable,
  • so, the optimal control is unique and is
    determined by the necessary conditions.
  • The co-state is a rotating vector.

10
  • Under the hexagonal voltage constraint, solutions
    to are
  • almost everywhere in time t.
  • Due to the nature of maximization problem and the
    special form of the co-state

11
  • With a constant voltage input ,
  • solution to
  • is actually an angular transformation
    of a clockwise angle

12
  • Local optimal path at the origin

13
Construction of a global feedback switching
diagram
  • For autonomous system, theoretically we can
    integrate backwards to find the solution
  • Our case is very special
  • The co-state is a rotating vector.
  • The maximization problem is
  • So, sequencing and voltage vector impress
  • Compare with the solution to the case of the disk
    voltage constraint

14
Feedback Switching Diagram under the Hexagonal
Constraint
  • Consider the case where
  • General case can be similarly treated
  • The example

15
Applications in Flywheel Energy Storage Systems
  • 10kw flywheel energy storage system
  • PMSM parameters

16
  • At 21000RPM

17
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18
V. Conclusion
  • New current control for flywheel energy storage
    applications
  • Solved the feedback control design problem of the
    time-optimal current transition
  • Reduced computational requirements in practical
    implementations
  • Laboratory implementation is under way
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