Analysis and Control of Excitation, Field Weakening and Stability in Direct Torque Controlled Electrically Excited Synchronous Motor Drives

Lappeenrannan teknillinen korkeakoulu Lappeenranta University of Technology

Olli Pyrhönen

ANALYSIS AND CONTROL OF EXCITATION, FIELD WEAKENING AND STABILITY IN DIRECT TORQUE CONTROLLED ELECTRICALLY EXCITED SYNCHRONOUS MOTOR DRIVES

Tieteellisiä julkaisuja Research papers

74

ABSTRACT

Lappeenranta University of Technology Research papers 74

Olli Pyrhönen

Analysis and Control of Excitation, Field Weakening and Stability in Direct Torque Controlled Electrically Excited Synchronous Motor Drives

Lappeenranta 1998

ISBN 951-764-274-1 UDK 621.313.32 : 621.3.077

Key words: synchronous machines, synchronous motor drives, direct torque control, excitation, field weakening, stability control

Direct torque control (DTC) is a new control method for rotating field electrical machines. DTC controls directly the motor stator flux linkage with the stator voltage, and no stator current controllers are used. With the DTC method very good torque dynamics can be achieved. Until now, DTC has been applied to asynchronous motor drives.

The purpose of this work is to analyse the applicability of DTC to electrically excited synchronous motor drives. Compared with asynchronous motor drives, electrically excited synchronous motor drives require an additional control for the rotor field current. The field current control is called excitation control in this study. The dependence of the static and dynamic performance of DTC synchronous motor drives on the excitation control has been analysed and a straightforward excitation control method has been developed and tested.

In the field weakening range the stator flux linkage modulus must be reduced in order to keep the electro motive force of the synchronous motor smaller than the stator voltage and in order to maintain a sufficient voltage reserve. The dynamic performance of the DTC synchronous motor drive depends on the stator flux linkage modulus. Another important factor for the dynamic performance in the field weakening range is the excitation control. The field weakening analysis considers both dependencies. A modified excitation control method, which maximises the dynamic performance in the field weakening range, has been developed.

In synchronous motor drives the load angle must be kept in a stabile working area in order to avoid loss of synchronism. The traditional vector control methods allow to adjust the load angle of the synchronous motor directly by the stator current control. In the DTC synchronous motor drive the load angle is not a directly controllable variable, but it is formed freely according to the motor’s electromagnetic state and load. The load angle can be limited indirectly by limiting the torque reference. This method is however parameter sensitive and requires a safety margin between the theoretical torque maximum and the actual torque limit. The DTC modulation principle allows however a direct load angle adjustment without any current control. In this work a direct load angle control method has been developed. The method keeps the drive stabile and allows the maximal utilisation of the drive without a safety margin in the torque limitation.

ACKNOWLEDGEMENTS

I took special interest in electrical drives and in the DTC method already during the years 1990 and 1993, when I was working at the research department in ABB Industry Oy. These years of working experience turned out to be very valuable for all later research work, because during that time the DTC method has been intensively developed for asynchronous motor drives by the company’s research team. Additionally, my working in the industry branch gave me a good general survey of the large application area of electrical drives.

The research work of this study has been carried out during the years 1995 and 1998 in the Laboratory of Electrical Engineering at Lappeenranta University of Technology, where I have worked as a laboratory manager and senior researcher. The research work introduced in this thesis is part of a larger research project, in which the different aspects of the DTC method for synchronous motor drives are studied.

I would like to thank professor Jarmo Partanen, the head of the Institute of Electrical Engineering and the supervisor of this work. It was his activity and enthusiasm, which made this research project possible in the first place. His has encouraged and helped throughout the work.

Special thanks are due to professor Juha Pyrhönen, my brother, whose knowledge of electrical machines has been extremely valuable also for this project. His contribution to the revision of the manuscript has been of immense importance.

I wish to express my sincere thanks to the pre-examiners of this work, professor Mats Alaküla, Lund Institute of Technology, Sweden and docent Janne Väänänen, Tellabs Oy, for their valuable comments and corrections.

The “red pen boutique” of professor Pekka Eskelinen has given an important contribution to the scientific style of the manuscript. He revised the text not only once, but twice. I am most grateful to him for his valuable help as well as for his encouragement. I also would like to thank Mrs Julia Parkkila for her contribution to improve the English language of the manuscript.

The good working atmosphere in the synchronous motor drive research team has been of great importance to me. I would like to thank the members of the team as well as the other staff in the Laboratory of Electrical Engineering. I wish also to express my thanks to my former boss, professor Martti Harmoinen, and to my former colleagues at the research team in ABB Industry Oy, for giving me an interesting career start.

I am obliged to the IVO Foundation, the Lauri ja Lahja Hotisen Rahasto and the Sähköinsinööriliitto for the financial support. I also thank ABB Industry Oy for helping our research team to construct the test equipments for the laboratory tests.

My parents, Raili and Jorma, have given me all the best for a good start in life, they have encouraged and supported me also during the recent years. They deserve my special thanks.

Most of all, I am indebted to my wife Kaisa for her love and patience, and to my children, Aino, Lauri and Eeva, for giving me strength and motivation for this work.

Lappeenranta, December 1998 Olli Pyrhönen

CONTENTS

ABSTRACT... 1

ACKNOWLEDGEMENTS ... 2

CONTENTS... 3

NOMENCLATURE... 5

1 INTRODUCTION... 9

1.1 History of speed controlled AC motor drives... 9

1.2 Functional principle of DTC... 10

1.3 DTC for electrically excited synchronous motors... 16

1.4 Outline of the thesis... 20

2 ANALYSIS OF STATIC AND DYNAMIC PERFORMANCE... 21

2.1 Maximal static torque ... 21

2.2 Maximal dynamic torque... 25

2.2.1 Stator current, stator flux linkage and field current during a torque step ... 26

2.2.2 Maximal dynamic torque in the theoretical case of a fast transient... 29

2.2.3 Transient analysis with derived operator inductances ... 32

3 EXCITATION CONTROL OF DTC SYNCHRONOUS MOTOR DRIVES ... 43

3.1 Reactive power compensation ... 43

3.2 Effect of magnetic saturation on the calculation of the excitation curve ... 44

3.3 Combined open loop and feedback control ... 47

3.4 Reaction excitation control in DTC... 50

4 FIELD WEAKENING CONTROL OF DTC SYNCHRONOUS MOTOR DRIVES... 54

4.1 Voltage Reserve in field weakening... 55

4.2 Relation between voltage reserve and excitation voltage... 58

4.3 DTC modulation in field weakening range ... 61

4.4 DTC stability control in field weakening range ... 69

4.4.1 Indirect load angle control ... 69

4.4.2 Direct load angle control... 72

5 SIMULATION AND TEST RESULTS... 75

5.1 Description of the simulation method ... 75

5.2 Simulation results of excitation control... 77

5.2.1 Combined excitation control in the nominal speed range... 77

5.2.2 Excitation control in the field weakening range ... 84

5.3 Simulation results of flux control in the field weakening range... 91

5.3.1 Voltage reserve and dynamic performance... 91

5.3.2 Results of modulation modification in the field weakening range ... 94

5.4 Simulation results of stability control in the field weakening range ... 96

5.5 Results of laboratory tests... 99

5.5.1 Description of the laboratory test drive... 99

5.5.2 Measurements of excitation control ... 101

5.5.3 Measurements of field weakening control... 103

5.5.4 Measurements of stability control ... 105

5.6 Discussion of the results ... 106

6 SUMMARY ... 108

7 REFERENCES... 110

APPENDIX A, Reference motor parameters used in the simulation ... 113

APPENDIX B, Excitation curve calculation for the salient pole synchronous motor... 114

APPENDIX C, Description of the PC-based C-language DTC-Simulator ... 116

NOMENCLATURE

C value of cost function e electro motive force vector, pu

ef electro motive force component produced by ψ_f, pu fb basic frequency for per unit system

fC cost function fM motor modelling function i stator voltage vector index id d-axis stator current, pu

iD d-axis damper winding current, pu id,sum d-axis current sum, pu

if field current, pu

if,corr field current reference for power factor correction, pu if,sat field current corresponding saturated excitation curve, pu if,us field current corresponding unsaturated excitation curve, pu im magnetising current of non salient pole machine, pu imf rotor component of magnetising current im, pu ims stator component of magnetising current im, pu is current vector, pu

is,P active stator current component, pu is,Q reactive stator current component, pu

isx x-axis stator current component in stator reference frame, pu isy y-axis stator current component in stator reference frame, pu iq q-axis stator current component in rotor reference frame, pu iQ q-axis damper winding current, pu

iq,sum q-axis current sum, pu

it torque stator current component, pu i1..3 phase current, pu

iψ flux linkage stator current component, pu If,m Measured field current

If,e field current used by digital control system

I1..3 phase current

j complex operator, time step index k discrete time instant

kex over excitation coefficient

kd d-axis transient coefficient in Eq.(2.12) kD(k) inverse inductance matrix component, pu kdD(k) inverse inductance matrix component, pu kdf(k) inverse inductance matrix component, pu kf(k) inverse inductance matrix component, pu kfD(k) inverse inductance matrix component, pu km d-axis transient coefficient in Eq.(2.12) kq q-axis transient coefficient in Eq.(2.12) kq2 q-axis inductance coefficient in Eq.(2.12) kQ(k) inverse inductance matrix component, pu

kpsi cost function coefficient for flux linkage amplitude error kD inductance coefficient for d-axis damper winding kQ inductance coefficient for q-axis damper winding

kres voltage reserve coefficient, which includes resistive voltage drop kres1 voltage reserve coefficient, which excludes resistive voltage drop ksd(k) inverse inductance matrix component, pu

ksq(k) inverse inductance matrix component, pu kqQ(k) inverse inductance matrix component, pu kQ(k) inverse inductance matrix component, pu k0..4 coefficient in general

lD d-axis damper winding inductance, pu ld,tr d-axis transient inductance, pu

lDσ d-axis damper winding leakage inductance, pu lf field winding inductance, pu

lfD mutual inductance between field winding and d-axis damper winding, pu lfσ field winding leakage inductance, pu

lkσ field winding and d-axis damper winding common leakage inductance, pu lm magnetising inductance of non salient pole machine, pu

lmd d-axis magnetising inductance, pu

lmd,sat saturated d-axis magnetising inductance, pu lmq q-axis magnetising inductance, pu

lmq,sat saturated q-axis magnetising inductance, pu lQ q-axis damper winding inductance, pu lq,tr q-axis transient inductance, pu

lQσ q-axis damper winding leakage inductance, pu lsd d-axis stator inductance, pu

lsq q-axis stator inductance, pu lsσ stator leakage inductance, pu n rotating speed, pu

N rotating speed

Pex proportional gain for feedback excitation controller rf field winding resistance, pu

rs stator resistance, pu

rD d-axis damper winding resistance, pu rQ q-axis damper winding resistance, pu

s Laplace operator

S1..3 switching commands for three phase inverter

t time

te electrical torque vector, pu

|te| electrical torque vector modulus, positive (+|te|) for anticlockwice torque, negative (-|te|) for clockwice torque, referred as torque in text, pu

|te|cosϕ1 torque for unity power factor, pu

|te|d,max maximal dynamic torque, pu

|te|max maximal torque, pu T simulation step time

Te electrical torque vector (see also |te| for modulus and sign definition) T^’d d-axis transient time constant

T^’’d d-axis subtransient time constant Td0 field winding time constant

TD d-axis damper winding time constant Tex ramp time constant for excitation Tf filter time constant

Tm mechanical torque vector (see also |te| for modulus and sign definition) TQ q-axis damper winding time constant

T^’q q-axis transient time constant

Tramp ramp time constant

Ttr load transient time constant ud d-axis stator voltage component, pu

ud,DTC d-axis stator voltage component produced by DTC modulation, pu

ud,res d-axis voltage reserve component, pu

uf excitation voltage, pu

uf,res excitation unit voltage reserve, pu

u0..7 discrete voltage vector of a two level inverter, pu u1..3 instantaneous phase voltage, pu

uq q-axis stator voltage component, pu

uq,DTC q-axis stator voltage component produced by DTC modulation, pu

uq,res q-axis voltage reserve component, pu ures voltage reserve, pu

u_res,i internal voltage reserve which does not include resistive voltage drop, pu ures voltage reserve vector, pu

u^rres Voltage reserve vector in rotor reference frame, pu us stator voltage vector, pu

u_s,i internal stator voltage vector which does not include resistive voltage drop, pu usx x-axis stator voltage component in stator reference frame, pu

usy y-axis stator voltage component in stator reference frame, pu u0..7 Discrete voltage vectors of three phase inverter, pu

UDC DC link voltage of voltage source inverter Us stator voltage vector

U_1..3 instantaneous phase voltage xd d-axis synchronous reactance x^’d d-axis transient reactance x^’’d d-axis subtransient reactance xq q-axis synchronous reactance x^’q q-axis transient reactance x^’’q q-axis subtransient reactance

β direction of voltage vector in switching sector

β_1,2 angles between stator flux linkage vector and discrete voltage vector γ angle between air gap and stator flux linkage vectors

δ stator flux linkage load angle δcosϕ1 load angle for unity power factor

δ_d,max load angle for maximal dynamic torque

δlim,high higher load angle limit in load angle hysteresis control δ_lim,low lower load angle limit in load angle hysteresis control δ_m air gap flux linkage load angle

δorth load angle, for which triangle in Fig. (2.1) is orthogonal

δ_t,max load angle for maximal torque

ε error signal for feedback excitation control ε_1,2 modulation modification angles

ϑ rotor position angle in stator reference frame

θ position angle of stator flux linkage vector in stator reference frame κ1..6 swithing sectors of DTC

τ dimensionless time, τ = ω_b⋅t

τtr load transient time constant, dimensionless

ϕ phase shift angle between stator current and stator voltage ψ_D d-axis damper winding flux linkage component, pu

ψ_f flux linkage component created by field current, ψ_f =if lmd, pu ψ_m air gap flux linkage vector, pu

ψs stator flux linkage vector, pu

ψ_Q q-axis damper winding flux linkage component, pu ψsd d-axis stator flux linkage component, pu

ψ_s,est stator flux linkage vector estimate, pu ψ_s,motor real stator flux linkage in motor, pu ψ_sq q-axis stator flux linkage component, pu

ψsx x-axis stator flux linkage component in stator reference frame, pu ψ_sy y-axis stator flux linkage component in stator reference frame, pu ω stator flux linkage vector angular speed, pu

ω_b basic angular speed for per unit system ω_m mechanical angular speed, pu

Symbols, Laplace domain

Gq(s) transfer function between q-axis stator current and voltage reserve Id(s) d-axis stator current

ID(s) d-axis damper winding current If(s) field current

Iq(s) q-axis stator current

IQ(s) q-axis damper winding current Ld(s) d-axis operator inductance Lq(s) q-axis operator inductance Uq,res(s) q-axis voltage reserve

Ψd(s) d-axis stator flux linkage reference Ψ_q(s) q-axis stator flux linkage

Subscripts

act actual value

av avarage value

b basic value of per unit system cosϕ1 unity power factor condition d,max dynamic maximal torque condition d,q rotor reference frame, stator quantities

D,Q rotor reference frame, damper winding quantities est estimated value

i current model

max maximal min minimal opt optimal pr previous ref reference value ref,d dynamic reference

s stator quantity

sat magnetic saturation tr transient

u voltage model

x,y Stator reference frame

0 Initial value

Superscript

(k) Order of derivative r Rotor reference frame R slope limited with ramp

* Final working point

Operators

RE{ } Real part IM{ } Imaginary part

Acronyms

emf electromotive force mmf magneto motive force pu per unit value

AC Alternate Current DFLC Direct Flux Linkage Control DC Direct Current

DTC Direct Torque Control

IGBT Insulated Gate Bipolar Transistor IGCT Integrated Gate Commutated Thyristor LPF Low Pass Filter

LUT Lappeenranta University of Technology PWM Pulse Width Modulation

VSI Voltage Source Inverter

1 INTRODUCTION

1.1 History of speed controlled AC motor drives

The idea of vector controlled AC motor drives is based on the excellent control properties of DC motors, where torque and motor magnetic flux can be separately controlled. In the development of vector controlled AC technology the first theoretical problem was to model a three phase AC coil system in a way, that separation between torque and flux control could be done.

Extensive research work of synchronous machine theory was done in the 1920s mainly in the United States. Motivation for synchronous motor modelling that time was not vector control development, but the increasing importance of synchronous machines in power systems. Improved models for synchronous machines were required particularly for the analysis of abnormal situations in power networks.

One of the most thorough researches on synchronous machine theory has been done by R.E.Doherty and C.A.Nickle, who represented their results in a four paper series at the end of 1920s (Doherty & Nickle 1926, 1927, 1928 and 1930). These papers already included the two-axis modelling of synchronous machine. The more detailed mathematical analysis of the two-axis model was presented by Park (1929). Park’s two axis mathematical analysis was a success, and that is the reason why the synchronous motor two-axis model carries his name. Park’s two-axis model includes indirectly one basic element of vector control; the actual measurable phase quantities were replaced by calculatory elements in a different reference frame.

The next major steps in AC machine modelling were taken in the 1950s, when the space vector theory was developed for multi-phase AC machines in Hungary. The theory was published in German at the end of 1950s by Kovács & Rácz (1959). The space vector theory made it possible to combine motor phase quantities into a single complex vector variable in any reference frame. This was a breakthrough, which made the final vector control innovation possible.

An important factor, which made controlled electrical drives more interesting on a practical level, was the intensive development of semiconductor devices in the middle of this century. The first breakthrough was the development of the transistor in 1948. The introduction of the first commercial thyristor ten years later was the second discovery. This thyristor was the first controllable semiconductor power switch, which made the true electronic control of power electric circuits possible.

In the 1960s, the new semiconductor technology was intensively applied in controlled DC motor drives, and thyristor bridge supplied drives gained popularity in industrial and traction applications.

At the same time, intensive research work has been done to develop AC drive systems with variable frequency. The first variable frequency AC drives were based on the pulsewidth modulation (PWM), (Stemmler 1994).

At the end of 1960s, German engineer Felix Blaschke made an innovation, which lead to the development of the first field oriented vector controlled AC motor drive. He represented the principle of field orientation and the separate control of motor magnetic flux linkage and torque, the so called transvector control, (Blaschke 1972). This method made it possible for the first time to control AC motors like DC motors. Siemens applied the transvector control for large synchronous motors (Bayer et al. 1971).

At the same time, intensive research work was going on in the Finnish company Strömberg to develop the asynchronous motor speed control. Asynchronous motors were one of the company’s main products, and they suited very well for traction drives and industrial applications due to their robustness and competitive price. The solution was not a vector control, but a PWM based variable frequency control, which was named scalar control. The main designer of the new technology was Finnish engineer Martti Harmoinen. As a result, the first world wide AC motor traction drive was introduced in the underground of Helsinki at the beginning of 1980s. Another important application area, where Strömberg used for the first time world wide AC motor technology, was the sector of the paper machine speed controlled drives.

In 1980s, AC motor drive technology was getting more popular in the different application areas.

Because of the growing demand for high dynamic performance the Blaschke's idea of field oriented vector control was introduced into the field of asynchronous machines as well. During the whole decade the vector controlled asynchronous motor has been an object for intensive research work as well as product development. The wide survey of the vector control methods for AC drive systems has been represented e.g. by Leonhard (1996) and Vas (1992).

In the middle of 1980s, a new principle for asynchronous motor control has been developed in Germany and in Japan almost simultaneously by Depenbrock (1985) and by Takahashi and Noguchi (1986). Depenbrock named his new method the Direct Self Control. A name, which better describes the method, is Direct Flux Linkage Control - DFLC. The name points out, that the stator flux linkage of the AC motor is directly controlled with the stator voltage vector and no current vector control is necessary. Again, the essential tool for the new control method was the space vector theory. The first industrial application, which used the DFLC method, was introduced in Finland by the company ABB Industry Oy, previously Strömberg Oy (Tiitinen et al 1995). There DFLC is combined with a current model, which keeps the stator flux linkage estimate accurate also at low frequencies. The method was named Direct Torque Control, called later DTC.

1.2 Functional principle of DTC

The understanding of DTC or other field oriented vector control methods requires the presentation of the space vector. If a three phase symmetrical coil system is assumed, scalar valued electrical quantities in different coils, like current, voltage or flux linkage, can be combined into one complex vector variable, where different coil magneto motive force (mmf) directions are defining the directions for each coil quantities. The stator voltage vector Us is defined as

( ) ( ) ( ) ( )

U_s t = e U t^j +e^j U t +e^j U t

 

 2

3

0 1

2

3 2

4

3 3

π π

. (1.1)

In Eq. (1.1) the voltage space vector is introduced. The voltages U1(t), U2(t) and U3(t) represent the instantaneous phase voltage values and the angles 0, 2π/3 and 4π/3 represent the mmf directions of the respective coils in a symmetrical three phase system. The length of the voltage vector is reduced by the factor 2/3 in order to make the vector length equal to the amplitude of the sinusoidally varying phase voltage of the three phase symmetrical system. Per unit (pu) quantities will be used this work throughout and thus pu stator voltage vector us is defined using pu phase voltages u1(t), u2(t) and u3(t) as

( ) ( ) ( ) ( )

u_s t = e u t^j +e^j u t +e^j u t

 

 2

3

0 1

2

3 2

4

3 3

π π

. (1.2)

The stator current pu space vector is is defined respectively using pu phase currents i1(t), i2(t) and i3(t) as

( ) ( ) ( ) ( )

i_s t = e i t^j +e^j i t +e^j i t

 

 2

3

0 1

2 3 2

4 3 3

π π

. (1.3)

With a three phase two level inverter in conjunction with a three phase winding six different non zero voltage vectors can be produced. Faraday’s induction law gives a connection between the stator voltage vector us and the stator flux linkage vector ψs. When the basic angular speed of the pu system ωb and the stator resistance rs are known, the relation between ψs and us is

( )

ψ_s =^ω_b

∫

This will later be called the voltage model. The pu electromagnetic torque te can be calculated as the cross product of the flux linkage space vector and the current space vector

t_e =ψ_s×i_s. (1.5)

Later torque modulust_e will be named torque for simplicity. According to Eq. (1.4) it is possible to drive the stator flux linkage to any position with the available six voltage vectors of a three phase two level inverter. It has been proved e.g. by Takahashi and Noguchi (1986), that the increase of slip frequency immediately increases the motor torque in an asynchronous motor. From the motor point of view, it is advantageous to keep the stator flux linkage modulus at its nominal value. These two conditions together with the field orientation give all necessary information to control the power stage transistors in order to meet the required flux linkage modulus and the requested torque.

Besides the voltage model, Eq. (1.4), and the torque estimation law, Eq. (1.5), the third essential part of DFLC is the optimal switching table. The name optimal switching table is given by the Japanese inventors Takahashi and Noguchi (1986). The optimal switching table selects at every modulation instant the most suitable voltage vector in order to meet the flux linkage and the torque control requirements. The selection is done according to the stator flux linkage orientation.

U_DC u₁

u₂ u₀

u₆ u₅

u₄ u₃

u₇

Figure 1.1 Three phase two level voltage source inverter (VSI) in conjunction with a three phase winding. Six non zero voltage vectors u1..u6 and two zero voltage vectors u0 and u7 are available.

DC link voltage UDC.

The optimal switching table is a logic array, which has three logical input variables. The logical input for the torque and flux linkage modulus is done by supplying the error signals

ψ_{s ref} −ψ_{s act}and t_{e ref} − t_{e act}into hysteresis comparators. The third input is the position angle θ for ψs, which is converted to a discrete variable κ. The discrete variable κ describes six different switching sectors κ1..κ6, where different voltage vectors are used for the certain combination of the flux linkage and torque logical variables, Figs. (1.2) and (1.3).

θ κ

0

optimal switching table

S

S

S

COMP

COMP

| |ts_ref−| |ts_act

κ₂ κ₁ κ₆ κ₅ κ₄

κ₃

ψ_{s ref}−ψ_{s act}

0

Figure 1.2 The functional principle of the optimal switching table of DFLC is based on the three multi valued logical variables; the torque error t_{e ref} − t_{e act}, the flux linkage modulus error

ψ_{s ref} −ψ_{s act}and the position angle θ for ψs. The actual switching commands S1, S2, S3 are available in the output. κ - discrete valued field orientation, ↑ - increase ψ_s , ↓ - decreaseψ_s ,

- increaset_s to positive direction, - increase t_s to negative direction, 0 - no torque or flux linkage modulus chance.

The optimal switching table is an ideal modulator. Every switching, that occurs, transfers the stator flux linkage towards the desired direction. No unnecessary switching takes place and the dynamic response is good. Since DFLC uses the voltage model, Eq. (1.4), for the stator flux linkage estimation, the only necessary parameter is the stator resistance. DFLC controls directly the torque of the motor by using the voltage and no stator current controllers are required. In principle DFLC suits well for the different types of rotating field machines. The represented parts of DFLC - the voltage model, the torque estimation law and the optimal switching table - are valid without modifications for asynchronous and synchronous motors.

The principal assumption of DFLC is, that the stator flux linkage can be estimated by using the voltage model alone. In practice this is not possible. The transistor switches cause nonlinearly current dependent voltage drops. The power switches require a certain time to switch on or off, and during that time the voltage is difficult to estimate. The resistive voltage drop in the motor cable and in the stator winding causes further uncertainty. The voltage model is based on the integration, and errors are integrated, too. Even with quite accurate estimates for all these voltage drops the pure voltage integral based estimate is erroneous. The DFLC method keeps the stator flux linkage

estimate origin centred. If it contains a cumulative error, the real motor stator flux linkage drifts erroneous, as is shown in Fig. (1.4).

ψ

ψ

|

ψ

ψ

ω

θ γ

y

x

|t_e|_min

|t_e|_max q

d

δ

Figure 1.3 A stator flux linkage vector trajectory as the result of DFLC. No unnecessary switching occurs in the DFLC method. The voltage vector is selected according to the hysteresis limits of torque (|te|min, |te|max) and stator flux linkage modulus (|ψs|min, |ψs|max). DFLC works in the x-y stator reference frame. Also rotor oriented d-q reference frame is shown. It is used later by the Park’s two axis model.

Symbols in the figure: is - Stator current vector ψs - Stator flux linkage vector ψm - Air gap flux linkage vector

θ - Position angle of ψs in stator reference frame γ - Angle between ψm and ψs

δ - Stator flux linkage load angle

ω - Angular speed of stator flux linkage vector

ψ_s,est ψ_s,motor

Figure 1.4 The controlled stator flux linkage estimate ψs,est and the real flux linkage in the motor ψs,motor, when the voltage model is used alone.

The voltage model requires some feedback to be able to estimate the stator flux linkage correctly.

Since current measurements are required for the torque estimation, they are available also for the stator flux linkage estimation. The stator flux linkage can be calculated with the so called current model, which uses the measured stator currents and motor inductance parameters. Here DTC is defined as a vector control method, which uses the DFLC principle, but includes also some current feedback correction to keep the stator flux linkage estimate accurate.

Fig. (1.5) compares the control structures of DTC and a traditional field oriented control method.

Most traditional vector control methods are based on the idea of field oriented control (Blaschke 1972), where torque and flux linkage can be separately controlled like in DC motors. Thus the basic difference between DTC and earlier methods is, that DTC combines torque and flux linkage control, whereas previous methods have separate control paths for torque and flux linkage. Further the control structure of DTC is simpler, since stator current controllers are not required. It is possible to control the flux linkage directly also in the traditional field oriented concept, like proposed by Alaküla (1993). However, when compared to DTC, control structure is more complicated also in that case.

The structural simplicity of DTC core, where torque and flux linkage control are combined directly with the voltage modulation, enables better dynamic response than traditional field oriented control methods. The voltage model can estimate the stator flux linkage with good accuracy in torque steps.

The long term accuracy for the stator flux linkage estimate is achieved by using feedback currents and some current model. Since every switching in DTC requires a controller decision, high computation power is required. Modern microcontrollers, however, offer good alternatives for high speed real time control.

Torque and Flux Control

AC- motor

Motor Model:

U-Model + I-Model

i2

i₃

| ψs| ref

S₁ S₂ S₃

| te|ref

| te|act

| ψs| act

ϑ

Converter S1

S2

S₃

Figure 1.5 a

Torque Controller

FluxController i_{t, ref}

i_{ψ, ref}

Coordinate Transformation

i_1,ref i_2,ref i_3,ref

Converter with current control

Coordinate Transformation

AC- motor

Motor Model

i₂

i₃

| t_e|_ref

ϑ

| t_e|_act

| ψ_s| _act

| ψ_s| _ref

i_t

i_ψ

Figure 1.5 b

Figure 1.5 Control structure in DTC (a) and one example of traditional field oriented control of an AC motor (b). DTC combines torque and flux linkage control with voltage modulation and no current controllers are needed. In traditional field oriented control methods separate control paths are used for flux linkage control and torque control. Also separate current controllers are often used.

The field current control has been left intentionally away from the figure.

Symbols in figure: |te|ref, |te|act - Torque reference and actual value

|ψs|ref, |ψs|act - Stator flux linkage modulus reference and actual value i2,i3 - Phase current actual values

i1..3,ref - Phase current reference values

i_ψ,ref, i_ψ - Reference and actual values for flux current component it,ref, it - Reference and actual values for torque current component ϑ - Rotor position

1.3 DTC for electrically excited synchronous motors

DTC was originally designed for asynchronous motors, but its robustness and simplicity has encouraged researchers to investigate other motor drives with DTC as well. The papers at the EPE conference in Norway 1997 were among the first international publications about the general features of DTC electrically excited synchronous motor drives (Pyrhönen, J. et al 1997), (Zolghardi, M.R. et al, 1997).

In an asynchronous motor, there is a natural feedback between the rotor current and the load of the machine due to the increasing slip frequency. In a synchronous motor, the stator generates currents into rotor only during transients, when the damper windings are resisting the change of the air gap flux linkage. Despite of this functional difference, the torque can be changed in both machine types in the same way, by accelerating the stator flux linkage vector rotating speed. The idea of torque production by using the stator flux linkage vector acceleration becomes more evident, if the torque is expressed with the stator flux linkage vector ψ_s and the air gap flux linkage vector ψ_m. When the stator leakage inductance lsσ is known, the torque can be expressed as

t_e

= l1 ×

s

s m

σ

ψ ψ . (1.6)

The air gap flux linkage ψ_m has quite a long time constant due to different damping effects in the air gap region, typically in the range of 10..100 ms. The angular acceleration of the stator flux linkage is, according to Eq. (1.4), dependent only on the voltage available. A large torque step can be achieved by accelerating the rotational speed of the stator flux linkage ψ_s in a fast way, so that the angle γ between ψ_s and the air gap flux linkage ψ_m increasesrapidly (Pyrhönen, J. et al 1997).

The functional difference of DTC applied to asynchronous or synchronous motors becomes evident during a load step. While in asynchronous motors the increase of slip frequency is permanent, in synchronous motors the angular speed difference between the stator flux linkage vector and the rotor disappears after the transient, and the induced damper winding currents decay to zero.

The electrically excited synchronous motor has typically quite large synchronous inductance values. Therefore, the armature reaction of the stator current is large as well. The large armature reaction and the lack of the natural rotor current increase will cause a large increase in the load angle and possible loss of synchronism, if the rotor field current is not increased along with the electrical torque. The most important differences between the asynchronous motor and synchronous motor DTC control appear thus in the field current control, later called the excitation control, and in the stability control. The term excitation control, familiar in generator applications, is used here, even though it is known, that in the case of a synchronous motor the stator voltage defines the machine’s magnetic condition.

Synchronous motors have, in principle, a stable working area approximately within the load angle δ

between -π/2…π/2. According to the basic theory of DTC the angular acceleration of ψ_s is assumed to increase the torque in all cases. DTC does not recognise the unstable working area, but tries to accelerate the stator flux linkage vector ψ_s as long as the actual value less than the torque reference. It is thus obvious, that DTC causes a very fast torque breakdown for the synchronous machine, if the load angle leaves the stable working area.

Variable frequency rotating field AC motor drives have a linear frequency dependent connection between the produced electro motive force e (emf) and the stator flux linkage modulus, defined by the angular speed ω of the stator flux linkage vector

e =ω ψ_s . (1.7)

If the motor uses the nominal flux linkage, the maximal available voltage will be reached with a certain angular speed. This particular speed is called the field weakening point, since the rotating speed cannot be increased above it without decreasing the flux linkage modulus. The speed range above the field weakening point is called the field weakening range, whereas the speed range below it is called the nominal speed range. The difference between the maximal available voltage modulus

|us| and the electromotive force e is defined as the voltage reserve ures,

u_res = u_s − e_s = u_s −ω ψ_s . (1.8)

In the field weakening range only a small voltage reserve is available, and thus the drive dynamics is reduced. Also the armature reaction is stronger, since the currents are larger in relation to the stator flux linkage, than in the nominal flux range. Field weakening is thus a special drive mode, which should be examined separately.

It was found earlier, that DTC requires feedback for the stator flux linkage estimate correction, since the voltage model alone is not stable. The current model of the salient pole synchronous machine is based on the Park’s two axis model. The salient pole motor is unsymmetric, and thus it is advantageous to examine the motor separately on the direct axis (d-axis) and on the quadrature axis (q-axis). The dependence between the currents and the flux linkages is then

ψ ψ ψ ψ ψ

sd sq D Q f

sd md md

sq mq

md D fD

mq Q

md fD f

d q D Q f





















=





















⋅





















l l l

l l

l l l

l l

l l l

i i i i i

0 0

0 0 0

0 0

0 0 0

0 0

(1.9) where

ψsd - d-axis stator flux linkage component, ψsq - q-axis stator flux linkage component,

ψD - d-axis damper winding flux linkage component, ψQ - q-axis damper winding flux linkage component, ψf - field winding flux linkage component,

id - d-axis stator current component, iq - q-axis stator current component, iD - d-axis damper winding current, iQ - q-axis damper winding current, if - field winding current.

The inductance parameters in Eq. (1.8) are

l l l

l l l

l l l l

sd md s

sq mq s

D md D k

, ,

,

= +

= +

= + +

σ σ

σ σ

l l l

l l l l

l l l

Q mq Q

f md f k

fD md k

, , ,

= +

= + +

= +

σ

σ σ

σ

where inductance components are

lmd - d-axis magnetising inductance, lmq - q-axis magnetising inductance, lsσ - stator leakage inductance,

lDσ - d-axis damper winding leakage inductance, lQσ - q-axis damper winding leakage inductance, lfσ - field winding leakage inductance,

l_kσ - common leakage inductance for field winding and d-axis damper winding.

The voltage equations in the two-axis model are u i r

t u i r

t

i r t

i r t

u i r

t

d d s

b sd

sq

q q s

b sq

sd

D D b

D

Q Q b

Q

f f f

b f

, , ,

, ,

= + −

= + +

= +

= +

= +

1 1

0 1

0 1

1 ω

∂ψ

∂ ωψ ω

∂ψ

∂ ωψ ω

∂ψ

∂ ω

∂ψ

∂ ω

∂ψ

∂

(1.10)

where

ud - d-axis stator voltage component, uq - q-axis stator voltage component, rD - d-axis damper winding resistance, rQ - q-axis damper winding resistance, uf - excitation voltage.

The two-axis mode of a salien pole synchronous machine has been shown in Fig. (1.6).

l_sσ

l_md

l_Dσ l_fσ

r_f l_kσ

r_s

i_f i_D

i_d

i_d+i_D+i_f

r_D u_f

ωψ_sq u_d

l_sσ

l_mq

l_Qσ r_s

i_D i_q

i_q+i_Q

r_Q

ωψ_sd u_q

Figure 1.6 Equivalent circuits for the salient pole synchronous machine two-axis model.

With the known inductance parameters and measured currents and rotor position the current model of Eq. (1.9) can produce an estimate for the stator flux linkage. DTC for a synchronous motor requires thus the rotor position feedback and the knowledge of the motor inductance parameters and does not differ in this sense from traditional synchronous motor field oriented control methods.

However, the essential difference between DTC and earlier control methods is still valid; the DTC control is based on the accurate physical connection between the voltage and the flux linkage, Eq.

(1.4), and the control principle is simple and avoids unnecessary switching events. The drifting of the voltage integral is slow, and the current model of the motor is just needed to prevent that slow drifting. In fast transients, the voltage model is superior compared to the current model, where more specific the accurate damper winding modelling is the most demanding task. By combining the best parts of the voltage and the current model, a good stator flux linkage estimate can be achieved (Pyrhönen, J. et al, 1997).

The block diagram of a DTC synchronous motor drive is shown in Fig. (1.7). The main control blocks are: the torque and flux linkage hysteresis control including the optimal switching table, the motor model calculating the actual values for the stator flux linkage and for the torque, the flux linkage controller for the field weakening range, the load angle limitter to keep the drive in the stable working area and the excitation control, which controls the power factor and reacts fast to the load changes in order to improve the drive stability and dynamic performance.

i₂ i3

i_f motor model

hysteresis

0

ψ_s = ∫u_s-i_sr_s dt ψ_sx,u

load angle limitation

| t_e| _ref

| ψ_s| _ref

torque and flux linkage hysteresis control flux linkage

correction and torque calcualtion

optimal switching table

motor parameter estimation parameter

initialisation identification run

voltage model current model

S1,S2,S3 U_DC

position sensor θ

i1

excitation control

| te|

| ψ_s|

| te| ref - | te|

| ψ_s| _ref-| ψ_s|

ψ_sy,u ψ_sx,i ψ_sy,i

ϑ field

weakening

2 3

isx

i_sy S1,S2,S3

U_DC

κ 0

Figure 1.7 Functional control block diagram of DTC electrically excited synchronous motor drive.

Following symbols are introduced in the figure for the first time:

ψsx,u, ψsy,u - stator flux components of the voltage model in xy-reference frame ψsx,i, ψsy,i - stator flux components of the current model in xy-reference frame isx,isy - stator current components in xy-reference frame

if - rotor field current

1.4 Outline of the thesis

The research work introduced here is a part of a larger research project, where the different aspects of the DTC method for salient pole synchronous motors have been studied. The starting point for the project was a DTC drive for asynchronous motors, and the goal was to convert and enlarge it to be suitable for the control of salient pole synchronous motors. The main topics in the project have been

- flux linkage modelling

- parameter identification and estimation

- sensorless control without rotor position feedback - field current control (later called excitation control) - field weakening control

- stability of the drive

The last three topics were studied by the author and are introduced in this work.

In traditional synchronous motor field oriented control methods, excitation control is usually related to stator current controllers. Thus the electromagnetic state of the machine is actually defined by the stator current controllers as well. In DTC the primary control variable is the stator flux linkage vector instead of the stator current. Since DTC lets the stator current to be formed freely, excitation control can not be related to stator current controllers. On the contrary, the field current control is needed in DTC to be able to adjust the stator current, like in synchronous generators. Thus a new concept for the excitation control is needed in DTC synchronous motor drives.

In the field weakening control there is a contradiction between the dynamic performance, motor losses and stability. A sufficient voltage reserve is essential for the dynamic performance, since the voltage reserve is the actual means of increasing the motor torque. On the other hand a reduced flux linkage increases the stator and rotor currents as well as the load angle for the certain level of torque. Also the maximal available torque will be reduced. The effects of the voltage reserve to the drive dynamics and stability have been studied in the field weakening range. Also an enhanced excitation method has been developed and analysed to improve both dynamic performance and stability.

The stability of a DTC synchronous motor drive is an important question because of the basic control principle, where it is assumed, that the rotational acceleration of the stator flux linkage vector always increases torque. This assumption is not valid in the unstable working area of the synchronous motor. The traditional method to assure synchronous motor drive stability is to limit the maximal torque below the assumed breakdown torque. The drawback is, that the utilisation of the motor is reduced, since some safety margin must be left between the maximal torque and the breakdown torque. In current controlled drives, the instantaneous overswing of the maximal load angle in a transient can be accepted, since the current controllers will reduce the load angle to the stable value, when the transient has been dampened. In DTC, such a recovery is not possible. Thus, if safety margin is used for DTC, it should be selected larger than in the previous case. In this work, an alternative method for DTC stability control was studied. In the alternative method the load angle can be controlled directly and no safety margin is necessary. This improves the usability and reliability of DTC synchronous motor drive especially in the field weakening range.