The 6th International Power Electronics Drive Systems and Technologies Conference (PEDSTC2015)
3-4 February 2015, Shahid Beheshti University, Tehran, Iran
Improved Predictive Torque Control of a Permanent Magnet Synchronous Motor fed by a Matrix Converter
Mohsen Siami, D. A. Khaburi
Department of Electrical Engineering Iran University of Science and Technology Tehran, Iran
[email protected],
[email protected]
Mosayeb Yousefi
Faculty of Electr. & Comput. Eng Shahid Beheshti University Tehran, Iran
Abstract- This paper presents a new predictive direct torque
drives in [3]. The main advantage of DTC in comparison with FOC is a faster dynamic torque response. Furthermore, DTC is independent of motor parameters except for stator resistance. In DTC, the appropriate inverter configuration is selected from a switching table according to the signs of the errors between the references of torque and stator flux and their actual values to keep torque and stator flux within a hysteresis band. There are some disadvantages such as torque ripple, current distortion and mainly needing a high sampling frequency for digital implementation. Some studies have been done to solve these problems [4]-[5]. Predictive control is a control theory that was developed at the end of the 1970s [6]. Due to the technique'S qualities such as fast dynamic torque response, low torque ripple, and reduced switching frequency, the application of this control techniques for torque and flux control of induction machines (IMs) and PMSM, has received attention from researchers [7] [10]. In [11] different approaches of predictive method were used for current control of PMSM. An alternative technique for control of the torque and flux of a PMSM based on fixed torque ripple has also been investigated [12]. A Comparative study between DTC and predictive method was done in [13]. The limited number of voltage vectors from traditional inverters makes the torque ripple problem more challenging. So, a number of researchers tum to utilization of multilevel inverters that develop a higher number of voltage vectors [14],[15]. Recently, Matrix Converters (MCs) due to the higher number of voltage vectors have received considerable attention as an attractive alternative to the conventional voltage-source inverter (VSI) [16],[17]. The absence of large capacitors or inductances allows the MC to give a compact design. Modulation strategies for MCs are reviewed in [17]. These can be classified into two main groups: scalar and space vector methods. The use of MCs in DTC for induction machines (IMs) was proposed in [18]. The approach was implemented for PMSMs in [19]. They adapted the lookup table of DTC for MCs. In [20],[21], a predictive method was introduced that directly controls the torque and flux of an 1M fed by a MC. In this model the selection of the switching state of the MC is performed by means of a quality function which is evaluated
and stator flux control of a permanent magnet synchronous machine
by
a
matrix
converter.
Unlike
conventional
direct
torque control for permanent magnet machine that only
18
actives voltage vectors of matrix converter with fix direction are
used, in the proposed predictive control all 27 possible switching
states including fixed direction voltage vectors, zero voltage vectors and also rotational voltage vectors are used to control the machine. So, the number of voltage vectors to control increases that leads to faster dynamic torque response and lower ripple of torque and flux. Furthermore, an extension of the predictive control is proposed to make it more efficient. Simulation results which confirm the good performance of the proposed methods are presented.
Keywords-permanent
converter; predictive control
magnet
synchronous
motor;
matrix
NOMENCLATURE V
IX ,v
j3
i IX' i j3
stator voltage on
a
and
fJ axes;
stator current on d and q axes;
R,
stator armature resistance,
Ls
stator armature inductance, H;
Q ;
OJ
rotor speed in electrical rad/s; electromagnetic torque, N.m;
p
pole pairs; rotor magnet flux linkage.
Te CfJm
qJSIX' rp'j3 stator flux linkage on a and e
fJ axes
rotor position angle I.
INTRODUCTION
Recently, permanent magnet synchronous machines (PMSM) due to the advantages such as small size with high efficiency and high reliability have been receiving much attention. These machines are widely used for electrical motor drives when fast torque responses are required [1]. Two widely used control schemes in commercial are field oriented control (FOC) and direct torque control (DTC). DTC technique was developed for induction motor drivers in the middle of 1980s [2]. It was applied to permanent magnet
978-1-4799-7653-9/15/$31.00 ©2015 IEEE
Jose Rodriguez
Departamento de Electr6nica Universidad Federico Santa Maria Casilla IIO-V, Valparaiso, Chile
369
Considering the equations (4), (6) there are 27 valid switching states for a 3x3MC. In accordance with the kind of output voltage vector, these 27 switching configurations can be grouped into three groups as follows: 1) All three output phases are linked to the one input phase. 2) Two output phases are linked to one input phase, and the other output phase is linked to a different input phase. 3) Each output phase is connected to a different input phase. These vectors have constant amplitudes, but their angles change at the source frequency. In Fig. 1, the output voltage and the input current space vectors of MC can be expressed as (4) and (5), respectively.
for each of 27 valid switching states of the converter based on predictions obtained from the discrete time model of the system. This approach was implemented on a PMSM fed by a YSI in [22]. The objective of this paper is to direct control of torque and flux of a surface mounted PMSM fed by a matrix converter using predictive method. The approach is based on the evaluation of an objective function including errors of torque and flux, developed according to discrete time model of the machine, for all valid switching states. Furthermore, an extension of the predictive control is proposed to make it more efficient. Simulation results which confirm the good performance of the proposed methods are presented. II.
Zero vectors: directioSn:pace vectors with varying amplitude and fixed Rotational space vectors:
MATRIX CONVERTER
A Matrix Converter (MC) is an ac-ac single-stage power converter with m x n bidirectional switches, which connects a m-phase voltage source to a n-phase load. The most widely used configuration is the three-phase MC, 3 x 3-switches, shown in Fig. 2. It connects a three-phase voltage source to a three-phase load directly without using any intermediate dc link circuit. The input filter attenuates the high-frequency switching components in the input current. The corresponding switching function of each nine bidirectional switches is xy with E {A, B, and
YE {a, b,
Where
Bb
VSA
Input Filter
and
+
B
a2·I.C ) Vc v,s
(5)
+
and
are output phase
are input phase currents of the MC.
io . i
III.
PREDICTIVE CONTROL
Predictive control comprise of selecting one of the 27 possible switching configurations of the MC, at fixed time intervals, based on minimization of a cost function Actually, the cost function defines the evaluation criteria to choose the best switching configuration for the next time interval. For the computation of the input current
(CF).
vector
i"
the electromagnetic torque
CF,Te
, and the stator flux
CPs on the next time interval are predicted, supposing the application of each valid switching configuration in next time interval, by a mathematical discrete-time model of the PMSM. These predicted values are compared with their reference values in
(2)
A.
(3)
CF. Cost Function (CF)
The evaluation criteria used to determine which switching configuration is the best to be applied in next time interval, are defmed by the cost function. The cost function is made-up of the absolute error of the predicted torque and the absolute error of the predicted stator flux magnitude as follows
Matrix Converter
i!:;:4 Lf
A
and
=
voltages and
The state of the converter switches can be represented by means of the following matrix:
=
3
A similar expression can be defined for the source current vector s , the source voltage vector and the output current
operation of the converter, two basic rules must be observed. Normally the matrix converter is fed by a voltage source and therefore the input terminals should not be short circuited. The load has typically an inductive nature and for this reason output phase must never be opened. Considering these rules, switching functions should fulfill, at all times, the following equation: \lYE { , b, } (1) Where
2
=
, as shown in Fig. 2. In order to achieve the safe
ac iiss clopoense [T S" Ab,"C(tt)l SSHa((tt)) SC"""bC(tt))] SAc(t) SHe t) Scc(t)
e - (I. a·I. I a eJiaC2,:r!i3h) icva' vh .
x C}
S
c}
(4)
CF
=re* -T/ I +AV' l qJ�I - I � 1 1
(6)
Where predicted values have been shown by the superscript "p" and the references values are shown by the superscript "*". A is a weighting factor that manages the relationship tp
CF
between torque and stator flux situations. To maintain as a magnitude without a physic interpretation, A is in Weber tp
Fig. l. 3
x
inverse. The cost function must be computed for each of the 27 possible switching states. The state that produces the minimum value will be selected and exerted during the next time interval. A proportional-integral (PI) controller is used to
3 MC
produce the reference torque
370
Te* for the predictive algorithm.
B.
Models Used to Obtain Predictions 1) Model of Matrix Converter: Due to the instantaneous power transfer of MCs, voltages and currents at any moment in one side may depend on the voltages and currents in the other side. Because the MC is connected to the source, the input line-to-neutral voltages are known; therefore, the output line-to-neutral output voltages are obtained as follows [20]:
[vVah ] [SSAaAb SBSBba Sse(ba] . [VVBA] Vc ,SAC Sec Sec, VI' =
ia(k+1)
..•••••.••• _-_ ••••••.•••_-_._-
-
i.(� + � [v. R,i. +"'9'm sin(e)] !:!. ... __ ._-_... __ ._-
•••••• __ .• __ .•
(7) :.. ---- T,
r
.. ! -.'
---
Fig. 2. Current ia during a switching interval.
So the output voltages applied to the load are dependent on the switching functions, reflected in matrix T, and the input voltages. The output currents are resulted from applying these output voltages to a given load. By measuring the output currents, the input currents can be easily found as
qJs jJ(k + 1) = qJs jJ(k) + jJ(k)Ts
V
-
f
Rs ijJdt
(16)
The current within a switching interval has the trajectory shown in Fig. 2. So ia and ijJ during time interval [t(k) t(k + 1) ] are
(8)
r
(17) (18)
1
2) Model ofLoad: To predict the response of the system for every switching state, a mathematical discrete-time model is obtained on the basis of the dynamic equations of a PMSM. The stator flux linkage of a PMSM in the stationary reference frame can be expressed as qJs
f
= (v, -RJs )dt
Resolving for the derivative of ia and ijJ in (22) and (23),
(9)
f
,2
R,T . -'-' [vP - R,lp(k) + OJ
