MORAWIEC, Marcin (ul. Reja 7, Myszkόw, PL-42-300, PL)
KRZEMINSKI, Zbigniew (ul. Czecha 2/21, Gdansk, PL-80-288, PL)
MORAWIEC, Marcin (ul. Reja 7, Myszkόw, PL-42-300, PL)
Claim A method for the estimation of variables of permanent magnet motor state, consisting on stator velocity vector component signal x and y measurement and stator current vector signal x and y measurement, where x and y indicate, that the vector components are determined in rectangular coordinate system - immobile towards stator, determining x and y component reproduced signals of stator current vector and comparing their values with measured x and y component reproduced signals of stator current vector, determining x and y component reproduced signals of stator flux vector, determining x and y component reproduced signals of disturbance vector, where disturbance vector is a product of stator flux vector and motor rotational speed, determining signal of reproduced angular speed of disturbance vector converting the motor rotational reproduced speed signal and disturbance and stator flux vectors x and y component estimated signals, transformation of component signals of stator estimated current x and y vector and transformation of component signals of stator voltage x and y vector to a system connected with permanent magnet flux vector, determining the mark of rotor estimated angular speed consisting of, that variables of permanent magnet motor are estimated by the following relations: di SX = a_{11}z_{y}-ai2-cs-i_{(}j+a_{1}3-sn-i_{q}+a_{11} -cs-Ud -ai_{4}-sn-u_{q} + Iq (i_{sx} - i_{sx} ) + T_{1} dτ di ^{l}sy = -^{a}HZχ-ai2-sn-i_{d}-a_{1}3-cs-i_{q} + a_{11}-sn-u_{d}+a_{1}4-cs-u_{q}+k_{1}(i_{sy}-i_{sy}) + T_{2} dτ - ^{sx}- = -a_{21}z_{y} - a_{22}ω(Loi2q - L_{2}i_{sy} J - a_{23} (-R_{s}i2d + «2d j + T_{3} dτ dψsy d_{χ} ^{•} = ^{a}2l^{Z}χ+a22ω(Loi2d^{+L}2^{i}sx) + a23(-^{R}s^{i}2q+^{u}2q) + ^{T}4 — dz_{x} — = Δώ m „ _. — dτ Δτ ψ_{s}__{x}-a2iώz_{y}-a22ώ^{2}(LoΪ2q-L_{2}ϊ_{sy})-a_{23}ώ(-R_{s}i2d+^{U}2d) + k6(isy-isy) " QZZyy " \ - ^{"}Jdτ^{L~} "^{1}Sx j dθ _{A} , / _{Λ} - \ - = ω _{+} k_{7} (ψ_{rq} -a_{311q}) where component signals of stator current vector and stator flux are determined fromm current estimated element and OPS stator flux, components of stator current vector /_{rf},ζ,4r_{f}Λ_{9} ^d stator voltage vector are transformed in a BT transformation block, disturbance vector signals ( Z_{x} , z_{y} ) are obtained from OZ disturbance estimation block, suppressive signals V_{5}T_{15}T_{25}T_{35}T_{4} are determined in OST suppressive signals estimation block, signal of motor rotational estimated speed (ω_{r}) is determined by transformation of conjugate signal (V ) to factor signal (V ) and signals of stator flux vector estimated components ( ψ_{sx} , ψ_{sy} ) in rotational speed estimation block (OP), signal of rotor estimated positional angle is determined in OK estimation angle block. Where: Δ - constant factor k_{ls} k_{2}, k_{35} k4, k_{5}, k_{6}— signal amplification factors a_{l5} a_{2}, a_{3}, a_{4}, a_{5}, a_{$} - motor parameter dependent factors V 2 _ L_{d} -L_{q} L_{2} : 2 1 R R 1 ai l ^{a}12 = ^{a}13 ^{=} a_{14} = — Ld ' ^{1} Lq ' ^{L}q ^{a}21 a22 = 7^ -l ) a_{2}3 = l - ^ ^{a}31 ^{= L}q - ^{L}d ' ^{L}d ^{L}d R_{s} - stator resistance ; L_{d},L_{q} - stator inductances. ^{~} - rotor positional cosine and sinus angle estimation blocks sn = sin θ — is a speed gain to relative time Δτ i_{d},i_{g},i_{2d>}h_{q} ~ components of stator voltage vector transformed do dq system in transformation block u_{d},u_{q},u_{2d},u_{2q} - components of stator currnet vector transformed do dq system in transformation block ψ_{rq} - component of flux estimated vector transformed do (dq) system in transformation block i_{sx} , i_{sy} - components of stator current vector in coordinate system connected with stator (xy) z_{x} , Z_{y} - components of disturbance vector |
The subject of the invention is a method of the estimation of variables of permanent magnet motor state. The invention is applicable in control systems of permanent magnet motors.
Permanent magnet motors are broadly applied in electrical power transmission systems of regulated rotational speed. The input variables for regulation system are among others, angular velocity of rotor and it's orientation towards immobile stator.
The need of receiving a hardly measurable stator flux signal or permanent magnet signal, can occur.
The easiest method of receiving a rotational speed signal of permanent magnet motor is it's direct measurement with help of proper speed sensor, and subsequently integration of this signal for the purpose of obtaining the position of rotor towards immobile stator. The measurement systems with speed sensors are, however, sensitive for disturbances, and their cost in some applications can exceed the cost of a motor.
The rotational speed signal of permanent magnet motor can be reproduced in proper systems on the base of measured signals of stator current and permanent magnet motor stator voltage. Simultaneous estimation of remaining variables of motor state is possible in these systems. Because of the electric machine theory, the motor state can be described by the spatial vectors representing, correspondingly, currents in particular stator phases and electromagnetic fluxes associated with particular rotor phases, the variables of motor state are corresponding, correspondingly, to rotational speed and to vectors component of stator current and associated stator flux.
Estimation of all signals of variables of permanent magnet motor state gives possibility to implement high-quality regulation system of a motor powered by a voltage inverter or current inverter.
From the publicatio [Zawurski K. "Control of permanent magnet synchronous motor" Politechnika Poznanska, Poznan 2005] the methods of estimation of rotational speed and position of rotor, consisting on signal measurement, corresponding to velocity vectors components and motor stator current, examined in rectangular coordinate system — immobile towards stator, estimation of signals corresponding to vector components of stator current, comparing them with the measured values and reproducing, on that base, the components of interference vectors — which are, electromotive forces induced in phase windings of stator, interference vector components signals are therefore used to specify the angular speed and position of permanent magnet motor rotor, are known. The methods of estimation of angular speed and position of rotor given in publication [Zawurski K. "Control of permanent magnet synchronous motor" Politechnika Poznanska, Poznan 2005] based on magnetic symmetry in a motor model assumption, that is equality of synchronous reactance in longitudinal and lateral axis Xd, Xq assumption. The methods of angular speed estimation and rotor position suggested in publication [Zawurski K. "Control of permanent magnet synchronous motor" Politechnika Poznanska, Poznan 2005] may be also used in a magnetic asymmetry ( X _{d } ≠ X _{q } ) case, but they will cause the estimation of angular speed and position of permanent magnet motor rotor with large speed and rotor position in stationery and transient state errors.
Solutions proposed in publication [Zawurski K. " Control of permanent magnet synchronous motor" Politechnika Poznanska, Poznan 2005] are not applicable in permanent magnet motors with magnetic asymmetry precise driving systems. A method for the estimation of variables of permanent magnet motor state, consisting on stator velocity vector component signal x and y measurement and stator current vector signal x and y measurement, where x and y indicate, that the vector components are determined in rectangular coordinate system - immobile towards stator, determining x and y component reproduced signals of stator current vector and comparing their values with measured x and y component reproduced signals of stator current vector, determining x and y component reproduced signals of stator flux vector, determining x and y component reproduced signals of disturbance vector, where disturbance vector is a product of stator flux vector and motor rotational speed, determining signal of reproduced angular speed of disturbance vector converting the motor rotational reproduced speed signal and disturbance and stator flux vectors x and y component estimated signals, transformation of component signals of stator estimated current x and y vector and transformation of component signals of stator voltage x and y vector to a system connected with permanent magnet flux vector, determining the mark of rotor estimated angular speed is characterized according to the present invention that variables of permanent magnet motor are estimated by the following relations:
di
= aπz _{y }-a _{12 }-cs-i _{( }i+a _{1 }3-sn-i _{q }+a _{11 } -cs-Ud -a _{14 }-sn-u _{q }+ki(i _{sx }-i _{sx }j + Ti
-r- = - ^{a }llZχ ~ ^{a }12 -sn-i _{d } -a _{13 } -cs-i _{q } +a _{π } -sn-u _{d } + a _{14 } -cs-u _{q } + k^i _{sy } - i _{sy } j + T _{2 }
^ ^{/ }^ = -a _{2 }iZ _{y }-a _{2 }2ώ(LoΪ2q-L2isy) ^{~a }23(- ^{R }s ^{i }2d+ ^{u }2d) ^{+ τ }3 dτ +a22ώ(L _{0 }Ϊ2d+L2isx) + a _{2 }3(- ^{R }si2q + ^{U }2q) + ^{T }4
-|^ = -^Ψsx - a21» ^{Z }y - a22∞ ^{2 } (L _{0 }i2q - L2>sy ) ^{~ a }23 ^{ώ }( ^{~R }si2d + ^{U }2d ) + ^{k }6 (isy ^{~ } W ) — =— Ψsy +a _{21 }ωz _{x } +a _{22 }ω ^L _{0 }i _{2 }d ÷I^sx j + a _{2 }3ω(-R _{s }i _{2 }q +u _{2q } )-k _{6 }(i _{S }χ ~hx J dθ _{Λ } / _{A } ? \
— = ω _{+ } k _{7 } (ψ _{rq } -a _{31 }i _{q })
where component signals of stator current vector and stator flux are determined fromm current estimated element and OPS stator flux, components of stator current vector i _{d },i _{q },i _{2d> }h _{q } ^{anc }^ stator voltage vector are transformed in a BT transformation block, disturbance vector signals ( Z _{x } , z _{y } ) are obtained from OZ disturbance estimation block, suppressive signals V _{5 }T _{15 }T _{25 }T _{35 }T _{4 } are determined in OST suppressive signals estimation block, signal of motor rotational estimated speed (ω _{r }) is determined by transformation of conjugate signal (V ) to factor signal (V ) and signals of stator flux vector estimated components (ψ _{sx } , ψ _{sy } ) in rotational speed estimation block (OP) _{5 } signal of rotor estimated positional angle is determined in OK estimation angle block.
Where:
Δ - constant factor k _{l5 } k _{2 }, k _{3 }, Ic _{4 }, k _{5 }, kβ- signal amplification factors ai, a _{2 }, a _{3 }, a^ a _{5 }, a$ - motor parameter dependent factors
_ L _{d } +L _{q }
Lo 2 '
L _{2 } _ L _{d } -L _{q }
2 '
1 R R 1 all ^{a }12 ^{a }13
^{" } Ld ' ^{= }v ^{a }14 = ^{ L }q
»21 ^{a }22 ^{a }23 1 ^{L }d ^{a }31 = L _{q }
^{L }d ^{L }d
R _{s }- stator resistance ; L _{d },L _{q } - stator inductances.
- rotor positional cosine and sinus angle estimation blocks sn = sinθ — is a speed gain to relative time
Δτ and i _{d },i _{q }j _{2d> }h _{q } components of stator voltage vector transformed do dq system in transformation block u _{d },u _{q },u _{2d },u _{2(l } components of stator currnet vector transformed do dq system in transformation block ψ _{f } component of flux estimated vector transformed do (dq) system in transformation block
hx ■ _{> } h _{y } " components of stator current vector in coordinate system connected with stator (xy)
Z _{x } , z _{y } - components of disturbance vector
The usage of the method according to the present invention enables estimation of variables of permanent magnet motor state in a wide range. Determination and transformation of suppressing signals influences the improvement of estimation quality of stator flux vector component signals and motor rotational low-speed disturbances. The usage of the method according to the present invention provides the simplification of variables estimation of permanent magnet motor state for the use of regulation system because the method doesn't require additional estimation of motor rotational estimated speed mark signal, and on it's basis the direction of permanent magnet motor rotation is determined, and it is beneficial especially for permanent magnet motor rotational speed near zero.
The aim of the present invention is more closely explained in the implementation example and drawing, in where the schematic method of procedure is presented.
Signals of stator estimated current vector components i _{sx } , i _{sy } obtained from OPS unit of current and flux estimation are being subtracted in OUP current deviation calculating unit from signals of stator current vector components i _{sx }, i _{sy } obtained from PI current measure converter as well as transforming in BT block to i _{d }J _{q }J _{2d }'h _{q } signals, signals of stator voltage vector components u _{sx }, u _{sy } obtained from PU voltage measure converter, are transformed in BT to u _{d },u _{q },u _{2d },u _{2q } , signals of current component deviation obtained by the result of subtraction as well as signal of ω disturbance vector rotational angular estimated speed obtained from OP speed estimation unit is processed in OZ disturbance estimation unit according to following relations:
-^- = — Ψ _{s }x - a _{2 }iωz _{y } - a _{22 }ω ^L _{0 }i _{2q } - L _{2 }i _{sy } J - a _{23 }ω (-R _{s }i _{2d } + u _{2d } J + k _{6 } ^i _{sy } - i _{sy } J
^{" }dT ^{= } Δ^ ^{Ψsy + a2iωZχ + a22 } ^ ^{L }° ^{i2d + L2isx } / ^{+ a23C0 } i ^{""Rsi2(i + U2q } ) ^{~ kβ } l ^{isx ~ isx } ) as a result signals of disturbance vector estimated components z _{x } , z _{y } are obtained.
Signals of disturbance vector estimated components Z _{x } , z _{y } obtained from
OZ disturbance estimation unit as well as deviation signals obtained from OUP current deviation calculating unit and signals of stator voltage vector components u _{S }χ _{, } u _{sy } obtained from PU voltage measure converter, transformed in BT into u _{d },u _{q },u _{2d }, u _{2q } components, are processed in OPS unit of current and flux estimation according to following relations:
d ^{i }sx _ = ai _{1 }Zy - ai2 - cs - i _{( }i + ai3 -sn - i _{q } +aii - cs -u _{( }j -a _{1 }4 -sn -Uq +ki (i _{sx } - i _{sx } ) + T _{1 } dτ dϊ 'sy
= -aiiz _{x } -a _{12 } -sn- id -a _{1 }3 -cs-i _{q } +a _{11 } -sn -u _{d } +a _{14 } -cs-u _{q } + Iq (i _{sy } - i _{sy } ) + T _{2 } dτ
as a result signals of stator current vector components i _{SX; } i _{sy } are obtained.
Z _{x } , z _{y } Signals of estimated components of disturbance vector, obtained from
OZ disturbance estimation unit as well as ψ _{sx } , ψ _{sy } signals of stator flux vector estimated components obtained from OPS unit of current and flux estimation are processed in OST suppressive signals estimation block according to following relations:
V = z _{x }ψ _{sy } -z _{y }ψ _{sx }
T _{1 } =k _{2 }Vψ _{sx } -k _{3 }S _{ψ }Vψ _{sy } T _{2 } = k _{2 }Vψ _{sy } +k _{3 }S _{ψ }Vψ _{sx } T3 = k _{4 }Vψ _{sx } -k _{5 }SψVψ _{sy } T _{4 } = k _{4 }Vψ _{sy } +k _{5 }S _{ψ }Vψ _{sx } as a result V _{5 }T _{15 }T _{25 }T _{35 }T _{4 } suppressive signals are obtained. i _{SXj } i _{S }y signals of stator current vector components obtained from OPS unit of current and flux estimation and z _{x } , z _{y } signals of estimated components of disturbance vector obtained from OZ disturbance estimation unit and T _{3 } and T _{4 } suppressive signals obtained from OST unit are processed in OPS unit of current and flux estimation according to following relations:
-~- = ^{~a }2l ^{Z }y - a22 ^{ώ }(L _{O }i2q - L _{2 }^y ) ~ ^{a }23 (-R _{8 }Ϊ2d + ^{U }2d ) + ^{T }3 dψ _{sy Λ } / „ _{Λ } v , x
—fø- = ^{a }21 ^{z }x + ^{a }22 ^{ω }( ^{L }θ ^{! }2d + ^{L }2 ^{1 }sx J + ^{a }23 ( ^{" }R _{8 }^q + ^{U }2q J + ^{T }4 as a result ψ _{sx } , ψ _{sy } signals of stator flux vector estimated components are obtained.
V coupled signal to V suppressive signal obtained from OST suppressive signal estimation unit and ψ _{sx } , ψ _{sy } signals of stator flux vector estimated components obtained from OPS unit of current and flux estimation are processed in OP rotational speed estimation unit according to following relations:
Ψ 'sS ^{s }y"V ^{≥ Δ } < Δ as a result ω signal of permanent magnet motor rotational estimated speed is obtained.
S _{ψ } signal is defined as following:
S _{ψ } = sign(ω _{r }) . ώ _{r } signal of rotor angular estimated speed and signals of stator flux and stator current estimated components obtained from BT transformation block are processed in rotor angle position estimation unit according to following relations:
dθ
— = ω + k _{7 } (ψ _{rq } -R _{31 }Iq)
Where:
Δ - constant factor, ki, k _{2 }, k _{3 }, Ic _{4 }, k _{5 }, k _{6 }- signal amplification factors, ai, a _{2 }, a _{3 }, 3 _{4 }, a _{5 }, aβ - motor parameter dependent factors, q
Lo 2
L _{d } -L _{q }
L _{2 } 2
1 R R al l ^{a }13 =^— ^{a }14 = - ~ Ld ^{L }d ' Lq ' R _{s } - stator resistance ; L _{d },L _{q } - stator inductances.
- rotor positional cosine and sinus angle estimation blocks sn = sinθ
Transformation block is realized according to following relations: x _{d } = x _{x } cos(<9) + y _{y } sin(<9) y = -X _{x } sin(6>) + y cos(6>) ' and x _{2d } = X _{x } cos(2(9) + y _{y } sin(26>) y _{2q } = -x _{x } sin(2<9) + y _{y } cos(2(9) ' where: x _{n } means an input signal to BT transformation block s
— means speed gam to relative time
Δτ
' _{. }'V^ _{> }V components of stator voltage vector transformed do dq system in transformation block u _{d },u _{g },u _{2d },u _{2g } - components of stator currnet vector transformed do dq system in transformation block ψrq - component of flux estimated vector transformed do (dq) system in transformation block i _{sx } , i _{sy } - components of stator current vector in coordinate system connected with stator (xy)
Z _{x } , z _{y } - components of disturbance vector