Modeling And Simulation Of Switched Reluctance Machine2
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Modeling and Simulation of Switched Reluctance Machine
Dr.V.Kamaraj Asst. Professor Sri Venkateswara College of Engineering Sriperumbudur
Page: 1
Introduction The features of Switched Reluctance Machine SRM Poles, Phases and windings The principle of operation Torque equation Structure of the converter Simulation for performance evaluation Conclusions
Page: 2
Features of SRM –
The Switched Reluctance Motor ■ ■ ■ ■ ■
–
Doubly-Salient, Singly-Excited motor Poles on both rotor and stator Only stator carries windings The rotor has no windings, magnets,or cage winding Rotor is simply a stack of salient pole laminations
Advantage ■
■ ■
■
The rotor is simple, requires relatively few manufacturing steps and tends to have a low inertia. The stator is simple to wind The bulk of the losses occur in the stator part and is easy to cool down Because there are no magnets the maximum permissible rotor temperature may be higher than in PM macines Page: 3
Continued»
»
» » »
»
–
The torque is independent of the polarity of phase current. This permits a reduction in the number of power semiconductor switches needed in the controller Under fault conditions the open circuit voltage and short circuit current are zero or very small Without excessive inrush current high starting current is possible Extremely high speeds are possible The toque/speed characteristics can be tailored to the application requirement Low material cost
Disadvantages » »
Per unit copper loss high Torque ripple and acoustic noise
Page: 4
Poles,Phases and windings »
»
The basic rules constraining the choice of number of poles,pole arcs and phase numbers were expounded by Lawrensen (1980) The relationship between speed and fundamental frequency f 1= n N r = rpm/60 Nr Hz
N - speed in rev/sec N r - the number of rotor poles If q-number of phases then q Nr steps per revolution and the step angle is ε
= 360 / q Nr
Page: 5
Constraints on the pole The number of stator poles exceeds the number of stator poles. Let βr –rotor pole arcβs –stator pole arc. min{βr, βs}= β To produce unidirectional torque β > ε In order to get the largest possible variation of phase inductance with rotor position, the inter polar arc of the rotor must exceed the stator pole arc. This Leads to the condition 2π / Nr- βr > βs . The stator pole arc is made slightly smaller than the rotor pole arc.
Page: 6
Lawrensen Feasible Triangle –
The constraints on the pole arcs can be expressed by Lawrensen feasible Triangle
Page: 7
Torque Equation Consider the primitive SRM. When current is passed through the phase winding the rotor tends to align with the stator poles. Produces a torque that tends to move the rotor to a minimum reluctance position. The instantaneous torque is T= {∂W’/∂θ}I=constant Where W’ is the coenergy defined as in figure An equivalent expression is T= -{∂W/∂θ}ψ=constant Page: 8
Continued
If magnetic saturation is negligible, then the relationship between flux linkage and current at instantaneous rotor position θ is a straight line whose slope is instantaneous inductance L.
–
Thus ψ = L I
–
And W’=Wf =1/2 Li 2
–
Therefore T=1/2 i 2 d L/dθ
Page: 9
Inductance Profile –
The value of the inductance per phase is depending on the rotor position in the SRM
Lu LPH =
θ≤0 0≤ θ ≤ βs
Lu + kθ
β s ≤ θ ≤ βr
La Lu-k(θ-βr -βs)
Page: 10
βs ≤ θ ≤ β r - βs
Continued– –
Where k= (La -Lu )/β s
Page: 11
Energy Conversion Loop
Page: 12
Continued – – –
–
–
The average torque can be estimated from the energy conversion loop. The electromagnetic energy that is available to be converted into mechanical work is equal to the area W. In one revolution each phase conducts as many strokes as there are rotor poles so that there are there are q N r strokes or steps per revolution. The average torque therefore is given by Ta = W * q N r /2π The average electromagnetic power converted is Pe = ω Ta
Page: 13
Converter Circuits » » » » »
» »
»
The torque is independent of the direction of the current Phase current is unidirectioinal Unipolar controller circuit. The phases are independent The upper and lower phase leg are switched on together at the start of each conduction period At the commutation point both are switched off During the conduction period either or both of them may be chopped At the end of the conduction period when both switches are turned off any stored magnetic energy that has not been converted to mechanical work is returned to the supply by the current free wheeling through the diodes
Page: 14
The Need for Computer Modeling » »
» » » » » » »
The switched reluctance motor does not have steady state CAD package must incorporate both design and simulation cpability Percentage structure to be modeled The Stator Model The Rotor Model Airgap discretization Simulation of rotation Boundary Conditions Pre-processing and post-processing
Page: 15
SRM MODEL
Page: 16
Page: 17
Page: 18
SRM With Skewed Rotor
Page: 19
SRM 3-D
Page: 20
Dr.V.Kamaraj Asst. Professor Sri Venkateswara College of Engineering Sriperumbudur
Page: 1
Introduction The features of Switched Reluctance Machine SRM Poles, Phases and windings The principle of operation Torque equation Structure of the converter Simulation for performance evaluation Conclusions
Page: 2
Features of SRM –
The Switched Reluctance Motor ■ ■ ■ ■ ■
–
Doubly-Salient, Singly-Excited motor Poles on both rotor and stator Only stator carries windings The rotor has no windings, magnets,or cage winding Rotor is simply a stack of salient pole laminations
Advantage ■
■ ■
■
The rotor is simple, requires relatively few manufacturing steps and tends to have a low inertia. The stator is simple to wind The bulk of the losses occur in the stator part and is easy to cool down Because there are no magnets the maximum permissible rotor temperature may be higher than in PM macines Page: 3
Continued»
»
» » »
»
–
The torque is independent of the polarity of phase current. This permits a reduction in the number of power semiconductor switches needed in the controller Under fault conditions the open circuit voltage and short circuit current are zero or very small Without excessive inrush current high starting current is possible Extremely high speeds are possible The toque/speed characteristics can be tailored to the application requirement Low material cost
Disadvantages » »
Per unit copper loss high Torque ripple and acoustic noise
Page: 4
Poles,Phases and windings »
»
The basic rules constraining the choice of number of poles,pole arcs and phase numbers were expounded by Lawrensen (1980) The relationship between speed and fundamental frequency f 1= n N r = rpm/60 Nr Hz
N - speed in rev/sec N r - the number of rotor poles If q-number of phases then q Nr steps per revolution and the step angle is ε
= 360 / q Nr
Page: 5
Constraints on the pole The number of stator poles exceeds the number of stator poles. Let βr –rotor pole arcβs –stator pole arc. min{βr, βs}= β To produce unidirectional torque β > ε In order to get the largest possible variation of phase inductance with rotor position, the inter polar arc of the rotor must exceed the stator pole arc. This Leads to the condition 2π / Nr- βr > βs . The stator pole arc is made slightly smaller than the rotor pole arc.
Page: 6
Lawrensen Feasible Triangle –
The constraints on the pole arcs can be expressed by Lawrensen feasible Triangle
Page: 7
Torque Equation Consider the primitive SRM. When current is passed through the phase winding the rotor tends to align with the stator poles. Produces a torque that tends to move the rotor to a minimum reluctance position. The instantaneous torque is T= {∂W’/∂θ}I=constant Where W’ is the coenergy defined as in figure An equivalent expression is T= -{∂W/∂θ}ψ=constant Page: 8
Continued
If magnetic saturation is negligible, then the relationship between flux linkage and current at instantaneous rotor position θ is a straight line whose slope is instantaneous inductance L.
–
Thus ψ = L I
–
And W’=Wf =1/2 Li 2
–
Therefore T=1/2 i 2 d L/dθ
Page: 9
Inductance Profile –
The value of the inductance per phase is depending on the rotor position in the SRM
Lu LPH =
θ≤0 0≤ θ ≤ βs
Lu + kθ
β s ≤ θ ≤ βr
La Lu-k(θ-βr -βs)
Page: 10
βs ≤ θ ≤ β r - βs
Continued– –
Where k= (La -Lu )/β s
Page: 11
Energy Conversion Loop
Page: 12
Continued – – –
–
–
The average torque can be estimated from the energy conversion loop. The electromagnetic energy that is available to be converted into mechanical work is equal to the area W. In one revolution each phase conducts as many strokes as there are rotor poles so that there are there are q N r strokes or steps per revolution. The average torque therefore is given by Ta = W * q N r /2π The average electromagnetic power converted is Pe = ω Ta
Page: 13
Converter Circuits » » » » »
» »
»
The torque is independent of the direction of the current Phase current is unidirectioinal Unipolar controller circuit. The phases are independent The upper and lower phase leg are switched on together at the start of each conduction period At the commutation point both are switched off During the conduction period either or both of them may be chopped At the end of the conduction period when both switches are turned off any stored magnetic energy that has not been converted to mechanical work is returned to the supply by the current free wheeling through the diodes
Page: 14
The Need for Computer Modeling » »
» » » » » » »
The switched reluctance motor does not have steady state CAD package must incorporate both design and simulation cpability Percentage structure to be modeled The Stator Model The Rotor Model Airgap discretization Simulation of rotation Boundary Conditions Pre-processing and post-processing
Page: 15
SRM MODEL
Page: 16
Page: 17
Page: 18
SRM With Skewed Rotor
Page: 19
SRM 3-D
Page: 20
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