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
1A 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
2Presentation Outline
- Introduction
- Problem Formulation
- Prerequisite Case of Disk Voltage Constraint
- Feedback Time-Optimal Design under Hexagonal
Voltage Constraint - Application in Flywheel Energy Storage Systems
- Conclusion
3Introduction
- 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
4II. 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
5The Equivalent Circuit Representation in
Synchronous Reference Frame
- Synchronous
- Reference Frame
- is assumed
6Voltage Constraints
- In stationary reference frame
- Voltage Constraint
- Case of Disk Voltage Constraint
- Hexagonal Voltage Constraint
7III. Prerequisite Case of Disk Voltage
Constraint
8IV. Feedback Time-Optimal Design under Hexagonal
Voltage Constraint
- Dynamic equation
- Define the Hamiltonian
- By Pontryagins maximum principle, necessary
conditions -
-
9Some 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
13Construction 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
14Feedback Switching Diagram under the Hexagonal
Constraint
- Consider the case where
- General case can be similarly treated
- The example
15Applications in Flywheel Energy Storage Systems
- 10kw flywheel energy storage system
- PMSM parameters
-
16 17(No Transcript)
18V. 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