A basic study of electrical drives is fundamental to an electrical engineering curriculum, and, today, gaining a better academic understanding of the theory and application of controlled-velocity electrical drive technologies is increasingly important. Electrical drives provide superior control properties for a wide variety of processes, and the number of applications for precision-controlled motor drives is increasing. A modern electrical drive accurately controls motor torque and speed with relatively high electromechanical conversion efficiencies, making it possible to considerably reduce energy consumption. Because of the present pervasive use of electric machinery and the associated large energy flows, the introduction of more effective and efficient electrical drives promises significant environmental benefit, and electrical engineers are responding by introducing new and more efficient electrical drives to a myriad of industrial processes.

A controlled-velocity electrical drive combines power electronics, electric machinery, a control system, and drive mechanisms to apply force or torque to execute any number of desired functions. The term electric machinery refers primarily to the electromagnetic mechanical devices that convert electricity to mechanical power or mechanical power to electricity—that is, to electric motors or generators. The term control system refers to the control electronics, instrumentation, and coding that monitor the condition of the electric machinery and adjust operating speed and/or match force or torque to load.

With a rigorous introduction to theoretical principles and techniques, this academic reference and research book offers the master of science or doctoral student in electrical engineering a textbook that provides the background needed to carry out detailed analyses with respect to controlled-velocity electrical drives. At the same time, for engineers in general, the text can serve as a guide to understanding the main phenomena associated with electrical machine drives. The edition includes up-to-date theory and design guidelines, taking into account the most recent advances in the field. The years of scientific research activity and the extensive pedagogical skill of the authors have combined to produce this comprehensive approach to the subject matter. The considered electric machinery consists of not only classic rotating machines, such as direct current, asynchronous, and synchronous motors and generators, but also new electric machine architectures that have resulted as the controller and power electronics have continued to develop and as new materials, such as permanent magnets, have been introduced. Examples covered include permanent magnet synchronous machines, switched reluctance machines, and synchronous reluctance machines.

The text is comprehensive in its analysis of existing and emerging electrical drive technologies, and it thoroughly covers the variety of drive control methods. In comparison to other books in the field, this treatment is unique. The authors are experts in the theory and design of electric machinery. They clearly define the most basic electrical drive concepts and go on to explain the critical details while maintaining a solid connection to theory and design of the associated electric machinery. Addressing a number of industrial applications, the authors take their investigation of electrical drives beyond theory to examine a number of practical aspects of control and application. Scalar, vector, and direct torque control methods are thoroughly covered with the nonidealities of direct torque control being given particular focus.

The expert body of knowledge that makes up this book has been built up over a number of years with contributions from numerous colleagues from both the Lappeenranta University of Technology and the University of Žilina in Slovakia. The authors are grateful for their help.

In particular, the authors would like to thank Professor Tapani Jokinen for his extensive contributions in general, Professor Olli Pyrhönen for his expert guidance on the control of synchronous electrical machine drives, Dr. Pasi Peltoniemi for the detailed and valuable example on tuning the control of an electrically excited synchronous machine, and M.Sc. Juho Montonen for his permanent magnet machine analysis. The authors would also like to specifically thank Dr. Hanna Niemelä, who translated some of the included text from its original Finnish. Finally, we give our warmest thanks to our families, who accommodated our long hours of writing, editing, and manuscript preparation.

This academic reference and research book uniquely provides comprehensive materials concerning all aspects of controlled-velocity electrical drive technology including control and operation. The treatise is based on the authors' extensive expertise in the theory and design of electric machinery, and in contrast to existing publications, its handling of electrical drives is solidly linked to the theory and design of the associated electric machinery.

A	magnetic vector potential [Vs/m], linear current density [A/m]
AC	alternating current
AM	asynchronous machine
ASIC	application-specific integrated circuit
A1–A2	armature winding terminals of a DC machine
AlNiCo	aluminium nickel cobalt permanent magnet
A	transmission ratio
B	magnetic flux density, vector [T] [Vs/m2]
B	magnetic flux density, scalar [T] [Vs/m2]
BLDC	brushless DC motor
B1–B2	commutating pole winding of a DC machine
C	capacitance [F], machine constant, speed of light [m/s]
CE	constant, function of machine construction
CT	torque producing dimensionless factor
C1–C2	compensating winding of a DC machine
Cio,i	outer or inner capacitance between the ball and the race in the ball bearing [F]
Cg	capacitance between the races of the ball bearing [F]
C01, C02	capacitance of the filter [F]
Cwf	capacitance between the stator winding and the stator frame [F]
Cwr	capacitance between the stator winding and the rotor core [F]
Csr	capacitance between the stator and rotor cores [F]
c	experimentally determined coefficient, distributed capacitance [F/m]
c/h	duty cycles per hour
c′	capacitance per unit length [F/m]
CENELEC	Comité Européen de Normalisation Electrotechnique
CHP	combined heat and power
CSI	current source inverter
D	diameter [m], friction coefficient, code (drive end)
D1, D2	diode 1, diode 2
DΩ	viscous friction, frictional torque
DC	direct current
DFIG	doubly fed induction generator
DFIM	doubly fed induction motor
DFLC	direct flux linkage control
DTC	direct torque control
D1–D2	series magnetizing winding terminals of a DC machine
d	thickness [m], axis
DOL	Direct On Line
DSC	Direct Self Control
E	electromotive force (emf) [V], RMS, electric field strength [V/m], scalar
EPMph	phase value of emf induced by PM [V]
emf	electromotive force [V]
E	electric field strength, vector [V/m]
ESR	equivalent series resistance [Ω]
e	electromotive force [V], instantaneous value e(t) or per-unit value
es	back electromotive force vector induced by the stator flux linkage ψs [V] or per-unit value
em	back electromotive force induced by the air gap flux linkage ψm [V] or per-unit value
F	force [N], scalar
F	force [N], vector
F1, F2	terminals of field winding
FEA	finite element analysis
FLC	flux linkage control
FOC	field oriented control
FPGA	field programmable gate array
Fm	magnetomotive force [A], (mmf)
FPGA	field-programmable gate array
f	frequency, characteristic oscillation frequency [Hz], or per-unit value
fsw	switching frequency [Hz] or per-unit value
g	distributed conductance [S/m]
Gm	transfer function
Gce	closed loop transfer function
GTO	gate turn-off thyristor
H	magnetic field strength [A/m]
hPM	height of permanent magnet material [m]
I	electric current [A], RMS
IE1, 2, 3, 4	efficiency classes
IC	cooling methods
IGBT	insulated-gate bipolar transistor
IGCT	integrated gate-commutated thyristor, integrated gate controlled thyristor
IEC	International Electrotechnical Commission
IEEE	Institute of Electrical and Electronics Engineers
IM	induction motor
Im	imaginary part
IP	enclosure class
i(t)	instantaneous value of current [A]
iB	base value for current [A]
Ik, Is	starting current [A]
Ist	locked rotor current (starting) [A]
Ief	effective load current [A]
ia	armature current [A]
icom	common current linkage [A]
if	field current [A]
im	magnetizing current space vector [A] or per-unit value
iPM	PM represented by a current source in the rotor [A] or per-unit value
iPE	current in the protective earth wire of the motor cable [A] or per-unit value
imPE	earthing current [A] or per-unit value
J	moment of inertia [kgm2], inertia, current density [A/m2], magnetic polarization [Vs/m2]
Jm	moment of inertia of the motor [kgm2]
Jload	load moment of inertia [kgm2]
Jtot	total moment of inertia [kgm2]
j	imaginary unit
K	kelvin, transformation ratio, constant
Kp	amplification
k	coupling factor
kC	Carter factor
kd	distribution factor
kgain	gain coefficient
kp	pitch factor
kri	reduction factor (current ratio of synchronous machine)
kriav	ratio of magnitudes of the current space vectors
krs	transformation ratio between stator and rotor
ksq,ksk	skewing factor
kw	winding factor
kwN	effective number of turns
L	inductance [H]
Lc	choke
LCI	load commutated inverter
LD	total inductance of the direct damper winding [H] or per-unit value
LDσ	leakage inductance of the direct damper winding [H] or per-unit value
Ld	direct axis synchronous inductance [H] or per-unit value
LdD	mutual inductance between the stator equivalent winding on the d-axis and the direct equivalent damper winding [H] or per-unit value
LdF	mutual inductance between the stator equivalent winding on the d-axis and the field winding (in practice Lmd) [H] or per-unit value
	transient inductance [H] or per-unit value
	direct axis transient inductance [H] or per-unit value
	direct axis subtransient inductance [H] or per-unit value
Lf	total inductance of the field winding [H] or per-unit value
LF	inductance of the DC field winding [H] or per-unit value
Lfσ	leakage inductance of the field winding [H] or per-unit value
Lk	short-circuit inductance [H] or per-unit value
Lkσ	mutual leakage inductance between the field winding and the direct damper winding, i.e., the Canay inductance [H] or per-unit value
Lm	magnetizing inductance [H] or per-unit value
Lmd	magnetizing inductance of an m-phase synchronous machine, in d-axis [H] or per-unit value
Lmn	mutual inductance [H] or per-unit value
Lmq	quadrature magnetizing inductance [H] or per-unit value
LQ	total inductance of the quadrature damper winding [H] or per-unit value
LQσ	leakage inductance of the quadrature damper winding [H] or per-unit value
Lpd	main inductance of a single phase [H] or per-unit value
Lp	main inductance of a single phase [H] or per-unit value
Lq	quadrature axis synchronous inductance [H] or per-unit value
	quadrature axis subtransient inductance [H] or per-unit value
LqQ	mutual inductance between the stator equivalent winding on the q-axis and the quadrature equivalent damper winding (in practice Lmq) [H] or per-unit value
L0	equivalent inductance [H] or per-unit value
Lm0	magnetizing inductance at no load at the rated stator flux level or per-unit value
LSRM	linear switched reluctance machine
Ls	stator synchronous inductance [H] or per-unit value
Lsσ	stator leakage inductance [H] or per-unit value
L01, L02	inductance of the filter [H] or per-unit value
L′	transient inductance [H] or per-unit value
L″	subtransient inductance [H] or per-unit value
L1, L2, L3	network phases
l	length [m], magnetizing route [m], distance [m], relative inductance, distributed inductance [H/m]
lcr	critical cable length [m]
le	effective core length [m]
l′	equivalent core length, effective machine length [m], inductance per unit length [H/m]
M	mutual inductance [H], or per-unit value
M	modulation index
MMF	magnetomotive force [A]
m	number of phases, mass [kg]
ma	amplitude modulation ratio
mf	frequency modulation ratio
m′	phase number of the reduced system
m0	constant
N	number of turns in a winding, magnetic north pole, code (nondrive end)
Np	number of turns of one pole pair
NdFeB	neodymium iron boron permanent magnet
NEMA	National Electrical Manufacturers Association
NPC	neutral point clamped (inverter)
n	normal unit vector of the surface
n	number of teeth, number of units determined by the subscript
pu	per unit
P	power, losses [W] or per-unit value
Pef	effective power [W]
Pe	electrical power [W] or per-unit value
Pel	electrical power [W] or per-unit value
Pin	input power [W] or per-unit value
Pmec	mechanical power [W] or per-unit value
PE	protective earth wire of the motor cable
PID	proportional-integrating-differentiating controller
PMSM	permanent magnet synchronous motor (or machine)
PWM	pulse-width-modulation
PM	permanent magnet
PMaSynRM	permanent magnet assisted synchronous reluctance motor
MTPV	maximum torque per volt
MTPA	maximum torque per ampere
Pρ	friction loss [W] or per-unit value
p	number of pole pairs
Q	electric charge [C], number of slots
q	number of slots per pole and phase, instantaneous charge, q(t) [C]
R	resistance [Ω] or per-unit value
Rball	resistance of the ball of the ball bearing [Ω]
Rri	resistance of the inner race of the ball bearing [Ω]
Rro	resistance of the outer race of the ball bearing [Ω]
RD	resistance of the direct damper winding [Ω] or per-unit value
	representing the part of mechanical power associated with Rr
Rf	resistance of the field winding [Ω] or per-unit value
RF	resistance of the field winding [Ω] or per-unit value
RM	reluctance machine
RMS	root mean square
Rs	stator resistance [Ω]
RQ	resistance of the quadrature damper winding [Ω] or per-unit value
R01,R02	resistance of the filter [Ω] or per-unit value
r	radius [m], distributed resistance [Ω/m]
r	radius unit vector
S1–S9	duty types of electrical machines
S	apparent power [VA], or per-unit value, surface [m2]
S	switch, magnetic south pole
SM	synchronous motor
SR	switched reluctance
SRM	switched reluctance motor
SynRM	synchronous reluctance motor
SVM	space vector modulated inverters
Sst	maximum permitted starting apparent power [VA] or per-unit value
SPE	power processing ability required by power electronics [VA] or per-unit value
SU, SV, SW	switching function variables
SmCo	samarium cobalt permanent magnet
SynRM	synchronous reluctance machine
s,	slip, Laplace domains operator
sb	slip at Tb
s0	base slip value
T	temperature [K] [°C], duration [s], torque [Nm], cycle time of the oscillation [s]
T1, T2	transistor 1, transistor 2
TEFC	totally enclosed fan cooled
Tsub	duration of the subsequent of the modulation [s]
ΔT	temperature rise [K] [°C]
T	torque space vector [Nm] or per-unit value
Tb	pull out torque, breakdown torque [Nm] or per-unit value
Tem	electromagnetic torque [Nm] or per-unit value
Te	electromagnetic torque [Nm] or per-unit value
TL	load torque [Nm] or per-unit value
Tmax	maximal torque [Nm] or per-unit value
TN	nominal, rated torque [Nm] or per-unit value
Tpull-in	synchronizing torque [Nm] or per-unit value
Ts	starting torque [Nm] or per-unit value
TwL	working torque of the load [Nm] or per-unit value
t0	operating period [s]
tc	commutation period [s]
tcef	effective cooling period [s]
T1	starting torque, locked rotor torque [Nm] or per-unit value
Tu	minimum torque [Nm] or per-unit value
TI	integrating time constant [s]
TD	differentiating time constant [s]
t	time [s]
t	tangential unit vector
tj	cycle time [s]
tp	time of pulse propagation (wave propagation time) [s]
tr	rise time, duration of converter pulse [s]
U	voltage [V], RMS
Ud	supply voltage [V]
UDC,meas	measured intermediate voltage [V]
U	depiction of a phase
u	voltage, instantaneous value u(t), incoming voltage [V] or per-unit value
ucm	common mode voltage (star point voltage) [V] or per-unit value
ur	reflected voltage [V] or per-unit value
udrop	voltage drop estimation error [V] or per-unit value
u2	forward travelling voltage [V] or per-unit value
uDCmE	voltage from DC link midpoint to PE [V] or per-unit value
Δu	voltage drop [V] or per-unit value
ΔUDC,offs	offset voltage [V] or per-unit value
V	depiction of a phase
VDE	Verband Deutscher Elektroingenieure
VRM	variable reluctance motor
VSI	voltage source inverter
v	speed, velocity, wave velocity, propagation speed of the voltage pulse [m/s]
v	vector
W	energy [J], coil span (width) [m]
W	depiction of a phase
W*, Wx	magnetic co-energy [J]
We	magnetic energy (energy stored in magnetic field) [J]
Wmec	mechanical work [J]
Wmt	energy converted into mechanical work when the transistor is conducting [J]
Wmd	mechanical work when the diode is conducting [J]
Wfc	energy stored in the magnetic field [J]
WR	energy returning to the voltage source [J]
Wd	energy returned through the diode to the voltage source [J]
wins	thickness of the insulation layer,[m]
wFe	thickness of the iron layer,[m]
X	reactance [Ω]
x	coordinate, axis
Y	admittance [S]
y	axis
Z	impedance, nonlinear impedance of the ball bearing [Ω]
Zm	characteristic impedance of the motor cable [Ω]
Zs	characteristic impedance of the filter [Ω]
Zs01, Zs02	impedance of the filter [Ω]
Z0	characteristic impedance [Ω]
z	coordinate, length [m]
zQ	number of conductors in a slot
α	angle [rad] [°], coefficient, temperature coefficient, relative pole width of the pole shoe
αi	factor of the arithmetical average of the flux density
αPM	relative permanent magnet width
αSM	relative pole width coefficient for synchronous machines
β	angle [rad] [°]
Γ	energy ratio, cylinder that confines the rotor, integration route
γ	angle, rotor angle [rad] [°], coefficient
γc	commutation angle [rad] [°]
γD	switch conducting angle, dwelling angle [rad] [°]
γ0	turn on switching angle [rad] [°]
δ	air gap (length) [m], load angle [rad] [°]
δde	equivalent air gap (slotting taken into account) in the d-axis [m]
δe	equivalent air gap (slotting taken into account) [m]
δef	effective air gap (influence of iron taken into account) [m]
δ′, δ0	minimum air gap, (air gap in the middle of the pole shoe) [m]
	minimum air gap, influence of slotting is taken into account [m]
	equivalent direct axis air gap [m]
	equivalent quadrature axis air gap [m]
δs	load angle [rad] [°]
δm	load angle [rad] [°]
Δδef	additional effective air gap caused by PM [m]
ɛ	permittivity [F/m], stroke angle [rad] [°], angle, correction term
ɛr	relative permittivity
ɛ0	permittivity of vacuum 8.854·10−12 [F/m]
η	efficiency
Θ	current linkage vector [A] or per-unit value
Θ	current linkage [A], angle [rad] [°]
θ	angle [rad] [°]
ϑ	angle [rad] [°]
κ	angle, current angle [rad] [°], vector position in a sector
λ	angle [rad] [°],
μ	permeability [Vs/Am],
μr	relative permeability
μ0	permeability of vacuum, 4 · π · 10–7 [Vs/Am] [H/m]
ν	pulse velocity [m/s], ordinal of harmonic
П	surface [m2]
ρ	resistivity [Ωm], reflection factor (coefficient)
ρν	transformation ratio for IM impedance, resistance, inductance
σ	leakage factor, ratio of the leakage flux to the main flux, Maxwell stress [N/m2]
σF	tension, tension force [Pa]
σFn	normal tension [Pa]
σFtan	tangential tension [Pa]
σmec	mechanical stress [Pa]
τ	relative time, transmission coefficient, control bit (torque or flux linkage)
	direct axis transient time constant with an open-circuit stator winding [s]
	direct axis transient time constant [s]
	direct axis subtransient time constant [s]
	quadrature axis subtransient time constant [s]
	quadrature axis subtransient time constant with open-circuit stator winding [s]
τp	pole pitch [m]
τv	phase zone distribution
τA	armature time constant [s]
τmec	mechanical time constant [s]
Φ	magnetic flux space vector [Wb] [Vs] or per-unit value
Φ	magnetic flux [Wb] [Vs]
Φδ	air gap flux [Wb] [Vs]
Φh	main magnetic flux [Wb] [Vs]
ϕ	magnetic flux, instantaneous value ϕ(t) [Wb] [Vs],
φ	phase shift angle, power factor angle [rad] [°]
ψ	magnetic flux linkage [Vs] or per-unit value
ψh	flux linkage of a single phase [Vs] or per-unit value
ψm	air-gap flux linkage [Vs] or per-unit value
ψs,u	stator flux linkage integrated from the converter voltages [Vs] or per-unit value
ψs,i	stator flux linkage calculated from the current model [Vs] or per-unit value
ψs0	initial flux linkage (∼ψPM) [Vs] or per-unit value
ψA	armature reaction flux linkage [Vs] or per-unit value
ψC	compensating winding flux linkage [Vs] or per-unit value
ψB	commutating pole winding flux linkage [Vs] or per-unit value
ψF	field winding flux linkage [Vs] or per-unit value
ψPM	permanent magnet flux linkage [Vs] or per-unit value
ψtot	total flux linkage of the machine [Vs] or per-unit value
Ω	mechanical angular speed [rad/s] or per-unit value
Ωhs	speed of high speed area starts at Ωhs or per-unit value
ω	electric angular velocity [rad/s], angular frequency [rad/s] or per-unit value

Subscripts

Superscripts

Boldface symbols are used for space vectors