Object of the present invention is a process for measuring the speed
of an induction motor when the applied frequency is null in a control of the Sensorless
type.

The application type to which the process is usefully applied regards
all uses in which the load is able to turn the motor moving meanwhile the control
is released.

The terms "control is released" mean the zeroing of every current
in stator phases. The main (but not only) application to which reference will be
made is the traction of an electric vehicle on steep paths: abandoning the vehicle
on a ramp, with released accelerator, a torque is produced that tends to drag the
vehicle along the descent. When a vehicle or car is dealt with, this will mean the
one handled by the motor.

The definition null applied frequency means any situation in which
a non-null triad of direct currents is applied to stator phases to produce a non-null
current phasor (herein below called stationing phasor or stationing current) whose
spatial orientation is fixed and could be any one within the electric 360° range.

Sensorless control methods are known for induction motors based on
the estimation of magnetic flux components.

It is also known that, under the null applied frequency status, said
methods fail due to the zeroing of electromotive forces in stator phases from whose
measure the flux components are obtained.

The difficulties in measuring the flux with null applied frequency
can be ignored if a speed measure is available as an alternative. The herein below
described idea is a process for measuring the vehicle speed starting from the null
applied frequency status.

The null applied frequency status supplies in the motor a torque that
opposes the motion (stationing torque Tstand). This stationing torque will
be useful for preventing the free vehicle rotation once having ended any deceleration
manoeuvre towards the vehicle stop. Invariably, zero deceleration operations of
the vehicle will end with the application of a stationing phasor. If the vehicle
is on a descent path, the stationing phasor will not completely stop it, but will
brake its descent according to the herein below described mode. By providing the
general expression of the Torque (2.9) in case of null applied frequency, for
Tstand an expression is found whose qualitative behaviour (as function of
electric motor speed ωr and for two different widths of the stationing
phasor Idc), is shown on the curve in FIG. 2 and refers to a Motor with Rated
Power Pn = 1250W, Vphase=16Veff, a corner frequency
fc=75 Hz and Rotor Time Constant Tr = 62 msec.

It can be demonstrated, and it is also pointed out in FIG. 2, that
at low speeds the stationing torque is proportional to the product between speed
(ωr) and square of stationing phasor width.

It can further be seen that, for a load torque less than
Tsmax (maximum stationing torque), the vehicle will be braked and its descent
will occur at a low and controlled speed (it can be demonstrated that it will be
ωr<1/Tr: in the example shown, ωr<1/Tr=2π2.6Hz).

If the dragging torque towards the descent exceeded Tsmax,
the working point would go into the torque collapsed range with consequent uncontrolled
vehicle acceleration along the descent.

If there is an Encoder on the motor shaft, this difficulty is easily
solved by increasing the control frequency and limiting the slip in the motor at
values that are able to guarantee everywhere the production of the maximum torque.

In a Sensorless control, it is rather obvious to use a management
of the feedforward type (i.e open loop) for the stationing torque: it will be convenient
to apply an high stationing phasor width (at least as much high as the motor saturates),
in order to minimise the risk the load exceeds the maximum torque (Tsmax).

Since, under operating conditions, the vehicle will mainly travel
on plane courses and with partial loads, the application of high stationing currents
will bring about very high energy wastes as inconvenience.

It must be added that, due to the incapability of measuring the magnetic
flux in the machine, it will not be possible to estimate the actual stationing torque
that would allow cancelling the currents if superfluous.

Object of the present invention is therefore providing a process for
deciding whether the stationing current phasor is useful and adequate. An intervention
mode will then be discussed in one case or the other.

This object is fully obtained in the process for measuring the motor
speed starting from an applied null frequency status, object of the present invention,
that is characterised by what is included in the below listed claims and in particular
in that it allows activating a motor speed monitoring function by overlapping in
stator phases a particular sampling signal (a step transition of the stationing
phasor) and the measure of produced effects.

The process will now be shown, merely as a non-limiting example, with
reference to the enclosed drawings, in which:

FIG. 1 shows a particular configuration of the applied null frequency status,
characterised by injecting a current idc in phase a and by extracting
two currents idc/2 from phases b and c.

FIG. 2 shows the behaviour of the stationing torque Tstand depending
on motor speed ωr and when the stationing phasor width (idc)
changes. The curve refers to a simulation for a motor with Pn=1250W Vphase=16Vac
fc=75Hz p=2 Tr=62msec.

FIG. 3 shows the effects of a double step transition of the stationing current
phasor (ids=idc from 0 to 50Adc and afterwards to 100Adc) on quadrature voltage
(vqs); it is the result of a simulation involving the same motor as above,
rotating at an electric speed ωr=100rd/sec.

FIG. 4 shows the effects of a double step transition of the stationing current
phasor (ids=idc from 0 to 50Adc and afterwards to 100Adc) on quadrature voltage
(vqs); it is the result of a simulation involving the same motor as above,
rotating at an electric speed ωr=-100rd/sec.

FIG. 5 shows the effects of a double step transition of the stationing current
phasor (ids=idc from 0 to 50Adc and afterwards to 100Adc) on quadrature voltage
(vqs); it is the result of a simulation involving the same motor as above,
rotating at an electric speed ωr=400rd/sec.

FIG. 6 shows the oscilloscope response of a real motor (Pn=1250W wound
for Vfase=16Vac fc=75Hz and rotating at a speed of ωr=-100rd/sec)
at a step transition of idc from 100Adc to 0; the upper trace
is vb-vc (2V/div); the lower trace is the stimulus and stationing
current ias=idc (50 A/div).

FIG. 7 shows the response of the same motor in FIG. 6 (rotating at a speed of
ωr=100rd/sec) at a step transition of idc from
100Adc to 0.

FIG. 8 shows the response of the same motor in FIG. 6 (rotating at a speed of
ωr=-240rd/sec) at the step transition of idc from
100Adc to 0.

The above process must be justified at theoretical level starting
from the general dynamic model for an induction motor (from 2.1 to 2.9).
ϕqs=L_{S} iqs+L_{m} iQsϕds=L_{S} ids+L_{m} iDsϕQs=L_{R} iQs+L_{m} iqsϕDs=L_{R} iDs+L_{m} idsvqs =R_{S} iqs+ d/dt ϕqs+ω
ϕdsvds=R_{S} ids+ d/dt ϕds- ω
ϕqs0=R_{R} iQs+ d/dt ϕQs+
ω_{R} ϕDs0=R_{R} iDs+ d/dt ϕDs-
ω_{R} ϕQsC_{m}=3 / (2)p(iqs ϕds- ids ϕqs)
Where:

ϕqs, ϕds: stator flux components

ϕQs, ϕDs: rotor flux components

iqs, ids: stator current components

iQs, iDs: rotor current components

vqs, vds: stator voltage components

ω: electric rotation angular speed of the reference system with
respect to the stator

ω_{R}: electric rotation angular speed of the reference
system with respect to the rotor (ω_{R} = ω
- ωr), with ωr electric rotor angular speed

ωr: (electric) rotor angular speed ωr = pΩr

Ωr: rotor shaft speed

p: poles pair number

Ls: stator inductance

Rs: stator resistance

Lm: magnetization inductance

Lr: rotor inductance

Rr: rotor resistance

Tr: rotor time constant Lr/Rr

(2.9) is the general expression of the instantaneous torque developed by the motor.

For an obvious analysis simplification, and without affecting its
generality, reference has been made to the equivalent two-phase model of the three-phase
motor, which is obtained through the well-known Clarke transform (3.1,3.2).

and vice versa
Where:

iqs, ids: quadrature and direct components of the stator current phasor
in the equivalent two-phase system whose axis ds is along the as direction.

ias, ibs: currents in phases as and bs of the three-phase
motor.

For our purposes, it is interesting to note how the general dynamic
representation (from 2.1 to 2.8) is modified when applying a stator current phasor
fixed in space. To simplify the analysis, without affecting its generality, such
phasor will be identified with a three-phase triad composed of a current
idc entering phase a and two currents idc/2 going out
of phases b and c (FIG. 1). Such current (idc) will be considered
time depending.

By applying the Clarke transforming formulae (3.1) to the thereby
defined triad, the equivalent two-phase model components are obtained.
ids = idciqs = 0

By replacing iqs and ids with their values, the general
dynamic model (from 2.1 to 2.8) for the null frequency status (ω =
0) is simplified into:
ϕqs=L_{m} iQsϕds=L_{S} ids+L_{m} iDsϕQs=L_{R} iQsϕDs=L_{R} iDs+L_{m} idsvqs=d/dt ϕqsvds=R_{S} ids+ d/dt ϕds0=R_{R} iQs+ d/dt ϕQs-
ωr ϕDs0=R_{R} iDs+ d/dt ϕDs+
ωr ϕQsC_{m}=-3 / (2)p ids ϕqs

By processing the above model (from 4.1 to 4.8), a linear second-order
differential equation is obtained, that expresses the functional dependency of quadrature
voltage (vqs) from current ids in direct phase (ids =
idc) with iqs = 0:

To complete, the similar functional relationship vds=f(ids)
could be determined. Its analysis however will be more complex and worsely readable.
Therefore, only relationship (5) will be studied.

Transforming relationship (5) from zero-state, namely from null initial
conditions (vqs(0+)=0, ϕqs(0+)=0), the representation (6) in
the Laplace domain is obtained:
Vqs(s) = ωrLm^{2} / (RrTr^{2})s / ((s+1/Tr)^{2}
+ ωr^{2})Ids(s)

Relationship (6) manages the reply (vqs) of our motor to the
application of any current ids(t) (provided that it is null ∀t<0)
at iqs = 0.

In particular, it is interesting to study the effect on
vqs of the step transition of ids(t).

In order to point out how the present measuring procedure can be repeated
after a short time without necessarily starting from zero-state, we will in practice
analyse a double step transition of ids (t).

We will apply a first step by going from zero to value Idc0
at time t0=0; afterwards, we will move towards the final value
Idc1 applied at time t=t1. Theids transform then becomes:
Ids(s) = Idc0 / (s)+Idc1-Idc0 / (s)e^{-st1}

By replacing (7) in transfer function (6) and by antitransforming,
the expression in the time domain of the response (vqs) to the step transition
of ids will be obtained:

The second line of (8) is the initial step response with which
ids transits from 0 to Idc0. The third line of (8) provides
the response to the following step with which, at time t1, ids moves
from Idc0 to Idc1.

In both cases, vqs reacts with a dampened oscillation at a
frequency equal to electric rotor speed (ωr) and enveloped by an exponential
with time constant τ=Tr (FIG. 3).

It can further be seen how the transient following the first step
transition of ids is already exhausting at time t1 and the
vqs response for the following transition from Idc0 to 2Idc0
resembles the previous one though the starting state it not the initial zero-state
any more. It will then be enough to store a fixed value of ids(t)=Idc0 for
a duration corresponding to some rotor time constants (in the example a bit more
than two) to restore a new steady-state configuration of the pair vqs, ϕqs
that is suitable for a new step transition of ids; and this without necessarily
passing from the zero-state.

Such initial state, compatible with the application of the present
process, can be generalised in the one for which vqs is simply zeroed (while
flux ϕqs can assume any value, not necessarily null) and it is easy
to check that it is restored as steady-state solution of every previous step transition
of ids. Relationship (8) can further be simplified by approximating the
Lm/Lr ratio to unit:

Relationship (9) points out the extreme readability of response (vqs) to
the step transition of ids. In particular:

the starting width of vqs envelope (RrΔIdc) does not depend
(or depends very little) on speed (ωr), on slip (ωslip),
on machine saturation level (namely on magnetic flux Φ).

the starting width of vqs envelope (RrΔIdc) depends only
on the discontinuity amount on ids and on rotor resistance.

It follows that the potential width of the useful signal does not
change with operating motor conditions. Only at low speed, the meaningful
vqs lobes will reach their maximum when the exponential envelope will already
be degraded. Speeds can therefore be measured starting from an order of magnitude
comparable with the rotor time constant inverse (1/2πTr = few hertz)
and over.

Moreover, it can be seen from (9) that, if speed direction is reversed,
also the first vqs lobe of the step response has an inverted sign (FIG. 4).

From the vqs signal analysis, effect of the step modification
of ids, the electric rotor speed measure (with sign) can be obtained as inverse
of period T of the sinusoid enveloped by the exponential (ωr=2π/T).
See FIG. 3, FIG. 4, FIG. 5.

The described analysis, referring to a two-phase model, must be generalised
by examining four of its aspects in more detail:

The first current level (Idc0) can be interpreted as the one corresponding
to the stationing phasor proper that afterwards is made temporarily transit towards
a different width (Idc1) to induce effects documented on vqs. It is
as well obvious that also the new current level (as a not necessarily undesired
consequence) will produce its own stationing torque value.

The same results can be immediately applied to a three-phase motor (applying
the Clark transform (3.1)). In this context the transition effect on the stationing
current will have to be monitored on the triangle linked voltage vqs = vbc =
vbs-vcs (FIG. 1).

If it is still not clear, the step modification of the stationing current
ids must be meant as instantaneous transition between two different levels
of any direct current; the transition from one direct current level to zero is only
its more intuitive particular case. The width of the step transition establishes
the amount of the effect produced on vqs.

A simplified approach has been proposed that identifies the stationing and stimulus
current with ids = ias and the effects with the behaviour of
vqs =vb - vc (FIG. 1). It will be justified how this is not a limit
to generality. Let us see it.

The scalar components of the two-phase representation, that so far
have been identified with the electric quantities values in motor phases, in a wider
interpretation represent the projections of space phasors produced by the motor
on any two-phase reference system and whose axes are not necessarily overlapped
to stator phase orientations.

Therefore, axis d can always be identified with the stationing
phasor orientation and axis q with the direction in quadrature thereto whichever
they are (namely, the configuration in FIG. 1 with ids=ias=Idc and
iqs=0 is only a particular, not a constraining choice for orienting the stationing
phasor).

This and other results will more easily be understood from the following
description of a preferred, but not exclusive embodiment, shown merely as a non-limiting
example in the text that follows.

The above described measuring process has been really implemented
on a three-phase induction motor with Pn=1250W p=2 poles pair Vphase=16V
comer frequency fc=75Hz Tr=63msec. Using a microprocessor power inverter,
a stationing current of Idc=100A has been injected in the configuration described
in Fig. 1 (Idc entering in a and Idc/2 going out of
b and c). The motor rotor has been forced to move at a known speed
ωr = -100rd/sec.

The sudden stationing current interruption stimulates in the motor,
according to the above described theory, a concatenated voltage vqs=vb-vc
shown in FIG. 6. The periodicity measure of this voltage, following the step application,
provides the searched speed information. The first lobe (main lobe) sign after the
ids transition to 0 provides the speed sign.

The modes for determining the vqs period and the main lobe
sign can be several. In the current embodiment, and merely as a non-limiting example,
the following measuring dynamics has been chosen.

A quick processing unit (microcontroller) checks the injection level
of the stationing current (Idc) and takes care of suddenly interrupting the
current by opening the inverter half bridges. This operation approximates in a simple
way a step transition of a stationing phasor. The sudden opening of power devices
implies a very short transient in which the stator currents, sustained only by stator
leakage inductances (Ls-Lm), discharge their energy, through inverter freewheeling
diodes, on the supply line (in this case a 24V battery).

Immediately after the stator currents reset, at a 125µs interrupt,
vqs=vb-vc is read. Every reading is numbered with an increasing index and
its absolute value is compared with the relative maximum previously determined,
having the same sign. The width of the greater of the two compared elements (current
sample and previous relative maximum) and the related index are stored in a continuous
search for the absolute maximum. The same process is applied both to the search
for a maximum for positive lobes and to the search for a maximum of negative lobes
of vqs.

Reasonably, the process will end after a survey time that will have,
as order of magnitude, the rotor time constant (Tr). After that, a stationing
phasor can again be applied and it could be, for example, the same phasor preceding
the measure or the same phasor used for measuring, waiting that the analysis result
on vqs allows deciding about the adequacy and usefulness of the stationing
phasor itself.

After the survey transient for the step response of vqs elapses,
a positive maximum will have been stored with its succession number (index_p)
together with a negative maximum with its succession number (index_n). The
sinusoid period on vqs will then be computed as:
T=2 abs(index_p-index_n) 125µs
from which:
abs(ωr)=2π/T
Moreover, if:
index_p<index_n ⇒ ωr<0
Instead, if:
index_p>index_n ⇒ ωr>0

After having computed ωr with related sign, it is decided
whether the stationing current is enough or not. If the stationing current is enough
(ωr close to 0), its proportional reduction can be carried out, at
the same time performing further speed monitoring operations and till the final
deletion of the current itself.

If, instead, the ωr measure detects a moving motor, a
control recovery procedure will have to be carried out. Also for the recovery procedure,
merely as a non-limiting information, an execution mode is provided.

After having measured the motor descent speed, the processing unit
in a quick ramp will increase the frequency from zero to the value with sign of
the detected speed (control re-tuning).

This frequency ramp can be carried out, for example, with a fixed
width of the stator current. Once having tuned the frequency on the measured speed,
the Sensorless control, that is able to control the motor at a non-zero frequency
(line control), will be reactivated. The frequency will then be decreased at very
low (not null) values to accompany the motor at very slow speed along the descent
with line control and till a new travel request or until the torque produced in
line is converted from braking torque to motive torque. (The torque estimating methods
in an induction motor are known in literature.) This torque sign transition from
braking torque to motive torque testifies that the descent is ended. Then, the frequency
will be reduced to zero by applying the stationing current and restarting the timed
monitoring procedure.

From what has been stated, the described process can be applied to
a more general system re-tuning context (namely the application of a frequency that
is next to the electric motor speed once known) every time a control loss occurs.
A situation with a lack in the stationing torque along a descent is only a particular
case of control loss. More generally, every time and for any reason the system goes
to work with an inadequate slip (i.e. too high: for example due to a sudden deceleration
due to an obstacle along the trajectory or following a start-up with running motor)
with following motion torque collapse, the on line recovery procedure can be activated
and exploits the herein described speed measuring and recovering process. A direct
current phasor will be applied, then will be made step-transit towards a different
value and the effects on stator voltages will be analysed.

Finally, it must be underlined that the above-described control recovery
modes, must be deemed merely as a non-limiting example and the recognition criteria
for a control loss status are outside the current scope but are known or can be
easily determined if the applied frequency is not null.

Anspruch[en]

Process for measuring a speed of an induction motor operating under an applied
null frequency status and under sensorless control, characterised in that
it exploits a step transition between two levels of a static stator current phasor
to induce electric effects on phase voltages and from whose analysis the rotor speed
is obtained.

Process according to claim 1 under a control loss status, characterised in
that it provides passing firstly from a frequency in which control has been
lost, to the applied null frequency status (namely to the application of a stator
current phasor unmoving in space), and then exploiting a following step transition
towards a different stator current phasor width in order to induce electric effects
on phase voltages and from whose analysis the rotor speed can be obtained.

Process for controlling an electric vehicle, actuated by an induction motor,
placed on a ramp with released accelerator and characterised in that, starting
from an applied null frequency status, it activates a cyclic check procedure of
adequacy and usefulness of the stationing phasor by time repeatedly measuring the
motor speed with the process according to claim 1.

Process for controlling an electric vehicle according to claim 3,
characterised in that it degrades a stationing current with a slow ramp by
cyclically verifying adequacy and usefulness of decreasing current levels by repeatedly
measuring the motor speed with the process of claim 1.

Process for controlling an electric vehicle, actuated by an induction motor,
placed on a ramp with released accelerator according to claim 4 and that, when the
stationing current results not adequte, recovers the motor control by applying a
frequency that is next to the measured speed and makes it ramp-degrade towards a
low frequency value to accompany the motor along the descent.

Process for controlling an electric vehicle, actuated by an induction motor,
placed on a ramp with released accelerator according to claim 5 with which it is
possible to go to the applied null frequency status when the sign of the torque
developed during the low-frequency controlled descent goes from negative (braking)
to positive (motive) for the descent end.

Process for controlling an electric vehicle, actuated by an induction motor
under the control loss status (high slip and low motion torques) according to claim
2 and that recovers the motor control by applying a frequency that is next to the
measured speed and then delivers the control to a line algorithm that modulates
the re-tuning value frequency towards a value controlled by the accelerator.