1. Multi-phase Synchronous Motors
Star and Delta Complex
Dynamic Models of
Multi-phase Synchronous Motors
R. Zanasi, M.Fei
Computer Science Engineering Department (DII)
University of Modena and Reggio Emilia
Italy

2. Outlines POG Modeling Technique Multi-Phase Synchronous Motors model
Star and Delta connected Motors
Vectorial Control
Simulations in Matlab/Simulink
Conclusions
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 2

3. Outlines POG Modeling Technique Multi-Phase Synchronous Motors model
Star and Delta connected Motors
Vectorial Control
Simulations in Matlab/Simulink
Conclusions
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 3

4. Power-Oriented Graphs
The Power-Oriented Graphs (POG) are ''block diagrams'' with a ''modular'' structure based on two main blocks:
Elaboration block
Connection block
Stores and dissipates or generates energy
Only transforms energy
Direct correspondence between dashed sections and real power sections:
Direct correspondence between POG scheme and state space equations
Direct implementation of the POG scheme in Simulink
Scalar product of two variables = power flowing through that section
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 4

5. Outlines POG Modeling Technique Multi-Phase Synchronous Motors model
Star and Delta connected Motors
Vectorial Control
Simulations in Matlab/Simulink
Conclusions
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 5

6. Direct correspondence between dashed sections and real power sections:
POG scheme
The POG scheme of the motors in the reduce complex reference frame:
Torque Vector
Mechanical part
Electrical part
Transformations
Direct correspondence between dashed sections and real power sections:
The structure of the POG model is the same whatever the type of stator connection is.
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 6

7. Transformations
The connection blocks used to transform the current and the voltage vectors are :
The Connection matrix is the only block of the POG scheme that is modified by the type of stator connection:
Terminal vectors
Phase vectors
Transformed vectors
The Complex transformations from fixed frame to rotaitng fame:
it reduces the number of dynamic equations:
complex subspaces
it is power invariant:
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 7

8. Transformed Dynamic equations
The dynamic equations of the system can be directly obtained from the POG scheme:
Electrical equations
Torque Vector
Mechanical equation
Introducing the vectorial notation one obtains:
Disadvantage: Notation quite difficult
Advantage: The POG dynamic models can be directly implemented in Simulink whatever the number of phases is
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 8

9. Transformed Torque Vector
The motor torque is:
Each component is characterized by specific harmonics
constant torque
torque ripple
If the rotor flux is characterized by the first odd harmonics:
constant torque
Considering also the th harmonic:
const. torque
torque ripple
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 9

10. Outlines POG Modeling Technique Multi-Phase Synchronous Motors model
Star and Delta connected Motors
Vectorial Control
Simulations in Matlab/Simulink
Conclusions
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 10

11. Star-connected motor When the multi-phase motor is star-connected:
The Connection matrix is the identity matrix:
The last component of the transformed current vector is zero:
The last differential equation of the transformed system becomes:
The dynamic dimension of the system is:
The generated motor torque is constant regardless the last component of
const. torque
torque ripple
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 11

12. The dynamic behavior is related to the type of rotor flux
Delta connected-motor
When the multi-phase motor is delta-connected
The Connection matrix is singular:
The last component of the transformed voltage vector is zero:
The last differential equation of the transformed system becomes:
The dynamic behavior is related to the type of rotor flux
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 12

13. Delta connected-motor
When the rotor flux is characterized by the first odd harmonics:
The dynamic dimension is
An undesired ripple torque with a negative mean value is generated:
When the rotor flux is characterized by the first odd harmonics:
The dynamic dimension is in steady state condition
The torque is constant:
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 13

14. Outlines POG Modeling Technique Multi-Phase Synchronous Motors model
Star and Delta connected Motors
Vectorial Control
Simulations in Matlab/Simulink
Conclusions
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 14

15. Vectorial Control: equations
The Vectorial control law:
The phase complex current vector is obtained from the terminal current vector.
The optimal complex current reference vector minimizing the dissipation
Problem: The connection matrix is singular in delta-connected motor.
Solution: Diagonalize the connection matrix by the transformation matrix.
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 15

16. Vectorial Control: block diagram
Block diagram of a vectorial controlled Multi-Phase Synchronous Motor:
Control law:
feed-forward
feed-back
complex reference vector
complex phase vector
The POG scheme of the motors:
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 16

17. Outlines POG Modeling Technique Multi-Phase Synchronous Motors model
Star and Delta connected Motors
Vectorial Control
Simulations in Matlab/Simulink
Conclusions
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 17

18. Matlab-Simulink vectorial controlled Multi-Phase Synchronous Motor:
Simulink scheme
Matlab-Simulink vectorial controlled Multi-Phase Synchronous Motor:
direct correspondence
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 18

19. Simulations Three different 5-phase motors have been compared:
1) star-connected motor with
2) delta-connected motor with
3) delta-connected motor with 2 3
1-2 3 1
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 19

20. Conclusion General vectorial approach
The model and the control are independent of the number of stator phases and the type of stator connection
Effectiveness of the vectorial control in the case of 5-phase star and delta connected motors
R.Zanasi, M.Fei Star and Delta Complex Dynamic Models of Multi-phase Synchronous Motors 20