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Special topic of rotor position estimation of permanent magnet synchronous motor -- fundamental wave model and rotor position angle
2022-07-06 20:07:00 【Explain the motor in simple terms】
Preface
The topic of rotor position estimation of permanent magnet synchronous motor will be written as a series , The commonly used motor position estimation method of permanent magnet synchronous motor is decomposed into several subcategories , Then write the specific principles one by one . The style of the article is consistent with other articles , Keep it easy to understand , Without losing depth .
This is the opening work of this topic , First understand what angle the rotor position angle refers to , And connect it with the mathematical model .
List of articles
One 、 Rotor position angle of permanent magnet synchronous motor
This article wants to explain how to estimate the rotor position angle , This is a big topic , In order to make this problem clear , First of all, understand what is the rotor position angle .
First, I want to add the basic knowledge of permanent magnet synchronous motor , When doing permanent magnet synchronous motor control , We are concerned with the interaction between the stator and the rotor , This force is generated by the interaction of stator magnetic field and rotor magnetic field . The rotor of permanent magnet synchronous motor is a permanent magnet , After being produced , Its magnetic field is fixed , Its direction is rotor N The direction of the pole . The stator magnetic field is generated by current , The greater the current , The stronger the magnetic field generated , The magnitude of the magnetic field generated by each phase current is proportional to the current at the current moment , The direction is the direction of the phase in space . The total stator magnetic field is the vector sum of the magnetic field generated by the three-phase current .
Take a pair of pole permanent magnet synchronous motor as an example , The simplified model is shown in the figure above .
In order to illustrate the spatial relationship of rotor position angle , Here, it is analyzed to use the pre positioning method to drag the rotor to 0° The process of .
Make i d = 10 A , i q = 0 , f o c A n g l e = 0 ; id = 10A,iq = 0,focAngle = 0; id=10A,iq=0,focAngle=0;
Carry out counter-measures park Transformation and inversion clark Transformation
[ i α i β ] = [ c o s θ s i n θ − s i n θ c o s θ ] [ i d i q ] (1) \left[\begin{array}{c} i_{\alpha }\\ i_{\beta } \end{array}\right] = \left[\begin{array}{c} cos\theta&sin\theta\\ -sin\theta & cos\theta \end{array}\right] \left[\begin{array}{c} i_{d }\\ i_{q } \end{array}\right] \tag{1} [iαiβ]=[cosθ−sinθsinθcosθ][idiq](1)
back park Transformation
[ i a i b i c ] = 2 3 [ 1 0 − 1 2 3 2 − 1 2 − 3 2 ] [ i α i β ] (2) \left[\begin{array}{c} i_{a}\\ i_{b} \\ i{c} \end{array}\right] = \frac{2}{3} \left[\begin{array}{c} 1 & 0\\ -\frac{1}{2} & \frac{\sqrt3}{2} \\ -\frac{1}{2} & -\frac{\sqrt3}{2} \end{array}\right] \left[\begin{array}{c} i_{\alpha }\\ i_{\beta } \end{array}\right] \tag{2} ⎣⎡iaibic⎦⎤=32⎣⎢⎡1−21−21023−23⎦⎥⎤[iαiβ](2)
back clark Transformation
Into the Make i d = 10 A , i q = 0 , f o c A n g l e = 0 id = 10A,iq = 0,focAngle = 0 id=10A,iq=0,focAngle=0, Yes i α = 10 A , i β = 0 ; i a = 6.67 A , i b = − 3.3 A , i c = − 3.3 A i_{\alpha} = 10A, i_{\beta} = 0; i_a = 6.67A,i_b = - 3.3A,i_c = -3.3A iα=10A,iβ=0;ia=6.67A,ib=−3.3A,ic=−3.3A
Put it in the picture above , Vector synthesis , No matter in α β \alpha \beta αβ Coordinate system , Still a b c abc abc Coordinate system , The same conclusion can be reached , The direction and of the composite vector a Axis coincidence , The size is 10A;
So when the position angle of the pre positioned rotor is 0 When the degree of , Get one Direction and a Stator magnetic field with coincident shafts , Pull the rotor to a Axis direction . It can also be said that the rotor position angle is 0 When the degree of , rotor N Pole position and a Phase stator coils coincide , Here we are , The following statement has been verified : The rotor position angle refers to the rotor in space N Pole and stator a Electrical included angle of phase winding .
Rotor position angle here , Also called vector angle , Pole position angle , Different industries have different customary names .
Two 、 Where does the rotor position angle react
To estimate the rotor position , You must know when the rotor position is in different positions , How will you react . stay abc Coordinate system , Three phase voltage 、 electric current 、 flux linkage , Coupled with each other , The mathematical model is complex , Common rotor position estimation methods are α β \alpha \beta αβ Coordinate system .
2.1 α β \alpha \beta αβ Mathematical model in coordinate system
Let's first look at the voltage equation
[ v α v β ] = [ i α i β ] R s + d d t [ ϕ α ϕ β ] (3) \left[\begin{array}{c} v_{\alpha }\\ v_{\beta } \end{array}\right] = \left[\begin{array}{c} i_{\alpha }\\ i_{\beta } \end{array}\right] R_s + \frac{d}{dt} \left[\begin{array}{c} \phi_{\alpha }\\ \phi_{\beta } \end{array}\right] \tag{3} [vαvβ]=[iαiβ]Rs+dtd[ϕαϕβ](3)
among ϕ α ϕ β \phi_{\alpha} \phi_{\beta} ϕαϕβ Express α β \alpha \beta αβ Axial flux linkage
[ ϕ α ϕ β ] = [ c o s θ s i n θ − s i n θ c o s θ ] [ L s i d + ϕ f L s i q ] (4) \left[\begin{array}{c} \phi_{\alpha }\\ \phi_{\beta } \end{array}\right] = \left[\begin{array}{c} cos\theta&sin\theta\\ -sin\theta & cos\theta \end{array}\right] \left[\begin{array}{c} L_s i_{d } + \phi_f\\ L_s i_{q } \end{array}\right] \tag{4} [ϕαϕβ]=[cosθ−sinθsinθcosθ][Lsid+ϕfLsiq](4)
hold d q dq dq The axis flux linkage changes to α β \alpha \beta αβ Axis
[ ϕ α ϕ β ] = [ i α i β ] L s + [ ϕ f c o s θ ϕ f s i n θ ] (5) \left[\begin{array}{c} \phi_{\alpha }\\ \phi_{\beta } \end{array}\right] = \left[\begin{array}{c} i_{\alpha }\\ i_{\beta } \end{array}\right]L_s+ \left[\begin{array}{c} \phi_{f }cos\theta\\ \phi_{f}sin\theta \end{array}\right] \tag{5} [ϕαϕβ]=[iαiβ]Ls+[ϕfcosθϕfsinθ](5)
among ϕ f \phi_f ϕf Indicates permanent magnet flux linkage .
Relative to the above form of voltage equation , I think more friends are more familiar with the following forms
[ v α v β ] = [ i α i β ] R s + d d t [ L s i α L s i β ] + [ − ω e ϕ f s i n θ ω e ϕ f c o s θ ] (6) \left[\begin{array}{c} v_{\alpha }\\ v_{\beta } \end{array}\right] = \left[\begin{array}{c} i_{\alpha }\\ i_{\beta } \end{array}\right] R_s + \frac{d}{dt} \left[\begin{array}{c}L_s i_{\alpha }\\L_s i_{\beta } \end{array}\right] + \left[\begin{array}{c}- \omega_e \phi_{f } sin\theta \\ \omega_e\phi_{f}cos\theta \end{array}\right] \tag{6} [vαvβ]=[iαiβ]Rs+dtd[LsiαLsiβ]+[−ωeϕfsinθωeϕfcosθ](6)
among ω e \omega_e ωe Is the electrical angular velocity .
But compared to (6),(4) and (5) Easier to explain
2.2 α β \alpha \beta αβ The rotor flux linkage component of the shaft contains position information
(4) in , α β \alpha \beta αβ The flux linkage of the shaft is composed of d q dq dq Axial flux linkage ipark transformation , among , d d d The axis flux linkage is composed of L s i d L_s i_{d } Lsid and ϕ f \phi_f ϕf Two parts , I said before. , d d d The position of the shaft is defined as a permanent magnet N N N The direction of the pole , So permanent magnet flux linkage ϕ f \phi_f ϕf Is only found in d d d Axis , The other part is the current flowing d d d Stator flux linkage generated by shaft inductance L s i d L_s i_{d } Lsid ; q q q The shaft has only stator flux L s i q L_s i_{q } Lsiq.
take (4) Medium ipark Transform expansion , Get the formula (5)
You can see ,** The flux linkage in the air gap of permanent magnet synchronous motor is composed of two parts , One part is stator flux [ i α i β ] L s \left[\begin{array}{c} i_{\alpha }\\ i_{\beta } \end{array}\right]L_s [iαiβ]Ls, It is generated by the current flowing through the stator coil , The other part is rotor flux [ ϕ f c o s θ ϕ f s i n θ ] \left[\begin{array}{c} \phi_{f }cos\theta\\ \phi_{f}sin\theta \end{array}\right] [ϕfcosθϕfsinθ], Produced by the rotor permanent magnet .
α β \alpha \beta αβ The rotor flux linkage component in the coordinate system contains the rotor angle information .
2.3 α β \alpha \beta αβ The back EMF voltage component of the shaft contains position information
take (5) Plug in (3) obtain (6), This formula is common α β \alpha \beta αβ Expression of voltage equation in coordinate system . We know that changes in the magnetic field produce an electric field , In permanent magnet synchronous motor , The stator coil of each phase is wound around the stator core to form a closed space , In this space , Flux linkage changes , Voltage is formed at both ends of the coil , The faster the flux linkage changes , The greater the voltage generated . [ − ω e ϕ f s i n θ ω e ϕ f c o s θ ] \left[\begin{array}{c}- \omega_e \phi_{f } sin\theta \\ \omega_e\phi_{f}cos\theta \end{array}\right] [−ωeϕfsinθωeϕfcosθ] Describes the voltage generated by the rotation of the rotor magnetic field , Relationship with rotor speed and current rotor angle , This part of voltage is also called back EMF ; [ L s i α L s i β ] \left[\begin{array}{c}L_s i_{\alpha }\\L_s i_{\beta } \end{array}\right] [LsiαLsiβ] The relationship between voltage and current caused by the change of stator magnetic field is described .
α β \alpha \beta αβ The back EMF voltage component in the coordinate system contains the rotor angle information .
3、 ... and 、 Summary
This paper is the first article on the topic of rotor position estimation of permanent magnet synchronous motor , To ensure that the length of each article is not too long , End here . The common methods of rotor position estimation are decomposed into , α β \alpha \beta αβ Location estimation of fundamental wave model in coordinate system 、 d q dq dq Location estimation of fundamental wave model in coordinate system 、 Position estimation of injection signal class , Wait for multiple directions , Specific decomposition .
Like my article , Remember to pay attention .
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