METHOD F ~ R-SC HEDULING THE, OPERATION OF ENERGY
DISTRIBUTION DEVICES, AND INSTALLATION IMPLEMENTING SAME
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5 The present invention relates to the optimization of the energy supply of an
installation equipped with energy distribution devices operating in all or nothing
mode and in operating duration modulation mode. The energy distribution
devices may especially be burners or electrical resistors.
10 The invention relates more particdlarly to industrial furnaces equipped with
burners as energy distribution devices. Patent FR 2853959 describes an
exemplary furnace at which the invention is particularly aimed.
For an onloff mode of operation, each burner is supplied with oxidant and fuel
15 through individual automatic isolating valves. Each valve is equipped with
position detectors, for example with an end of opening travel sensor and an end
of closing travel sensor.
Two or more energy distribution devices can operate in a synchronous manner
20 so that they are always turned on and turned off at the same time. In this case,
the synchronous devices are considered to be the parts of one8 and the same
energy distributipn device.
1
Hereinafter, we will consider that the oxidant is air and the fuel is gas, knowing
25 that all types of oxi&nt and fuel are possible according to the invention.
The furnace is driven by means of a command-control system which, on the
basis of the requirements needed for heating the products, determines the
thermal energy demand that must be delivered by each burner, especially as a
30 ), function of its position in the furnace.
The thermal energy demands are refreshed periodically on the basis of a time
interval I, of duration D, an integer multiple of a time measurement unit T,
typically a second. The duration D of the time interval is dependent especially
35 on the size of the burners, the isolating valves and the furnace. For example
defined at- 60 seconds, it is thereafter adjusted during commissioning, for
example between 30 and 120 seconds.
The burners operating in all or nothing mode, the thermal energy demand
translates into a duration of ignition. Thus, during the time interval I, the opening
time Ai and closing time of the air and gas valves of each burner is proportional
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to the thermal energy demand for the, relevant burner. The opening time Ai is
lower than, or at most equal to, the duration D of the time interval I.
The opening and the closing of the air and/or gas valves disturb the equilibrium
of the pressures in the pipelines, in the furnace and in the duct for evacuating
the combustion products. The disturbances thus created are all the more
considerable the more often and sidnificantly the number of open valves varies
during the time interval. The various control loops of the installation are not able
to stabilize the pressures if the scheduling of the ignition of the burners is not
chosen in an optimal manner. The term "scheduling" designates the temporal
allotment of the durations of operation of the burners over the time interval I.
Moreover, for burners of significant powers, the air and gas supply valves are of
large dimensions. It follows from this that full openings and closings of the
valves are not immediate and require a certain time span which must be taken
into account before actuating the valves again. During these transient regimes,
combustion is not optimal in terms of energy efficiency and pollution. Thus,
when the energy demand is too low, the duration of ignition of these burn&rs is
not sufficient for; combustion to be correct.
I
Likewise, frequent changes of state, corresponding to the ignition or to the
shutdown of a buraer, are the source of mechanical fatigue of the valves and
burners. Reducing the frequency of these changes of state makes it possible to
increase their lifetime.
Moreover, when the energy demands are too great, there is a risk of exceeding
the capacity of the furnace which may translate into a situation in which there is
a dearth of air and/or gas. The capacity of the furnace depends on the initial
design, but also on the running state of the various equipment. For safety
reasons, the exceeding of capacity generally triggers a shutdown in the
operation of the furnace.
As we have just seen, numerous problems may result from poor scheduling of
the ignition of the burners.
Patent FR2853959 describes a method of controlling a steel-making reheating
furnace characterized in that the order of ignition of the burners is chosen so as
to reduce the pressure variations in the furnace and in the circuits supplying fuel
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and oxidant for the burners. According to this method, the position of the
5 operating sequence of a burner in the time interval T is chosen as a function of
that of the other burners. This solution exhibits limits especially when numerous
burners have an operating sequence of a duration greater than half the duration
of the time interval T.
10. Tq defneYP4gLunal scheduling, t ~ feirst constraint with which it is necessary
to cope is that of the time required by a computer or calcl;;Sator which dispatches
the opening and closing instructions to the burner supply valves. It is clear that
in an operational framework we have only a few seconds to find a scheduling
which addresses all the criteria stated above, thereby excluding the use of the
15 usual approaches of exhaustive search type which may require considerable
calculation time.
:i Thus, the invention consists mainly of a method for optimizing the energy
supply, over a time interval I of duration D, of an installation equipped with N
energy distribution devices operating in all or nothing mode and in duration
20 modulation mode, a duration of operation Ai, less than or equal to D, being
allocated to each of the N energy distribution devices over the time interval I,
8
the durations Ai being deduced from the energy demand of the installation and
provided by a command-control system of the installation, characterized in that: ,
CC
- the duration of operation Ai of an energy distribution device either consists of a
25 single operating sequence of duration Ai, or is divided into several sequences of
partial durations, whose sum is equal to Ai,
- a scheduling is defined over the time interval I by a temporal allotment of the
. set of operating sequences of the N energy distribution devices, I ,
- and the scheduling is calculated before the start of the time interval I by taking
30 account of the desired durations Ai of operation of each energy distribution
device.
Moreover, according to the invention, the scheduling is calculated as follows:
a/ any arbitrary initial scheduling is chosen,
bl an order number from 1 to N is associated with each distribution device,
i, 3
c/ for the distribution device of order number 1, a search is conducted for the
number, the duiation or durations and the position or positions over the time
interval I of the operating sequence br sequences of this distribution device
5 which make it possible to minimize a function U representative of the
fluctuations of the energy throughput over the time interval, the sequences of
the other devices maintaining the positions of the initial scheduling,
and a resulting scheduling is obtained with the number, the duration or
durations and the optimal position or positions retaineg.for the sequence or
10 sequences of the device of order number 1,
d) step c) is repeated on the basis of the scheduling resulting from step c) by
successively considering the distribution devices of higher order number up to
the distribution device of order number N.
, I Advantageously, the method for optimizing the energy supply comprises the i $ 15 following additional steps:
e) by using as initial scheduling the scheduling retained in step d), a new order
8 number from I to N is associated with each distribution device and steps c) and
d) are repeated,
I
f) step e) is repeated a number of times compatible with the calculation time ,
20 available before thastart of the time interval.
According to a particularly advantageous variant of the invention, the order
number allocated to each distribution device is dependent on the desired
durations of operation, the device of order number 1 is that whose desired
duration of operation is the longest and the device of order number N is that '
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25 ' whose desired duration of operation is the shortest. ' ,
The function U to be minimized may be the sum of the absolute value of the
fluctuations of the energy throughput Qj about a mean value Qmean during the
time interval I:
The scheduling which minimizes a function U taking into account not only the
fluctuation of the energy throughput during the time interval I, but also the
variation of the energy throughput between the instant preceding the start of the
time interval and the instant following fhe start of the time interval, can also be
5 retained as scheduling. The function U is then the sum of the absolute value of
the fluctuations of the energy throughput about a mean value during the time
interval I and of the variation of the total energy throughput between the instant
preceding the start of the time interval and the instant following the start of the
time interval.
t
10 Another exemplary function U to be minimized consists of the sum of the
squares of the deviations with respect to the arithmetic m%:
I According to another example, the function U to be minimized consists of the
sum of the absolute value of the variations of the energy throughput between
15 two successive subdivisions during the time interval I:
b
According to yet a~othere xample, the function U to be minimized consists of
the sum of the square of the variations of the energy throughput between two
. . successive subdivisions during the time interval I:
The function U to be minimized may be supplemented with additional terms.
According to another possibility, the scheduling for which the total energy
throughput engendered does not exceed a defined threshold is retained as
scheduling:
Advantageously, it is ensured that the total energy throughput engendered by
the scheduling bbtained does not exceed a defined threshold.
Preferably, the desired durations of operation of the energy distribution devices
are reduced if they lead to a total energy throughput which exceeds the defined
5 threshold.
Advantageously, for each energy distribution device, the gap between the
duration of operation over a time interval I and the desired duration of operation
of the device is limited by a maximum gap, especially 5% of the duration of the
time interval. --
10 Preferably the sequences for each energy distribution device correspond at
most to three changes of state of the device over a time interval I.
Advantageously, two successive changes of state of each energy distribution
device are spaced apart by a minimum time gap which corresponds for example
I to the time required for the establishment of a steady regime of the energy
? 3 15 distribution device, especially so as to take into account the opening or closing
time for the valves. The minimum time gap may be at least equal to a twentieth
of the duration D of the time interval, i.e. D/20.
I
For each energy distribution device, the last change of state during the time
interval I is preferably spaced apart by a minimum time gap from the end of the
20 interval, especially at least equal to a twentieth of the duration D of the time ,
interval, i.e. D/20. 'C
I
The search for the operating sequence or sequences of an energy distribution
device which make it possible to minimize the function U may be performed in a
defined subset of the set of possible sequences.
t
25 ' Preferably, the defined subset of the set of possible sequences consists of
-sequences comprising at most three changes of state of an energy distribution
device over a time interval I.
According to an exemplary embodiment of the invention, an initial scheduling is
that where all the energy distribution hevices are off during the time interval I.
30 The order number allocated to each distribution device after the first iteration
may be chosen in a random manner.
The time interval I is advantageously divided into a number M of temporal
subdivisions of not necessarily equal duratjons. The changes of state of the
distribution devices take place between two successive temporal subdivisions.
1 -
According to an exemplary embodiment of the invention, the states of the
5 distribution devices are coded according to a binary matrix Z of size N x M (N
rows x M columns), each of the N rows of which codes the state of the various
distribution devices during the M successive temporal subdivisions and each
column of which corresponds to a temporal subdivision.
According to another exemplary embodiment of the invention, the function U is
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10 expressed in the form Ci Cj G, yi N, which is the weighted sum of the products of
the pairs of components yiy, of a vector Y, with i and j integer indices between 1
and N x M, and q, are weighting coefficients.
The total energy throughput resulting from the scheduling is, at each instant of
the time interval I, the sum of the throughputs engendered by the distribution
I 15 devices that are on at this instant.
According to the invention, the objective of the optimization is also aimed at the
energy throughput being monotonic, increasing or else decreasing, during the
t
time interval.
8
According to the invention, the energy throughput variation, between two
20 successive temporal subdivisions, engendered by the choice of scheduling of ,
each energy distribution device must not be greater than a maximum value
determined as a function of the characteristics and reactivities of the various
parts of the system. For burners, these are especially the characteristics and
reactivities of the isolating valves, of the combustion air fan, of the pressure
25 regulator on the gas network, of the smoke exhauster and of the dimensions of
, the air, gas and smoke circuits. The maximum value of the variation is
preferably less than or equal to half the value of the energy throughput before
variation.
Moreover, the optimization is aimed at ensuring that the total energy throughput
30 engendered does not exceed a defined threshold. This threshold may be
different according to the time interval I considered. It may for example result
from the maximum energy throughput Qma corresponding to the capacity of the
furnace. It may also be dependent on the energy throughput of the previous
time interval, for example so as to limit the throughput variations between two
successive timd intervals. . 3
Thus, the desired durations of operation of the energy distribution devices, as a
function of the demand of the command-control system, are reduced if they lead
5 to a total throughput which exceeds the defined threshold.
According to a variant embodiment of the invention, the search for a solution, at
each refreshing of the energy demands, proceeds in two steps, the objective
being always to propose a scheduliqg for each time interval of duration D which
best delivers the energy demands without ever causing shutdown of the
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10 furnace:
11 Search for a first scheduling where, for each burner, ignition will be chosen in
such a way that there are no more than three changes of state, that the
durations of establishment and of extinguishing of the flame are complied with
and that there are no changes of state at the end of the time interval,
15 21 Adjustment of the solution in accordance with the principle of the simulated
'$ annealing scheme which consists in favoring the best schedulings without
however excluding the worst. The process stops after a fixed number of
iterations or else on completion of a fixed time span and thq best solution
obtained is kept.
8
20 The list of energy distribution devices is traversed in a defined order and for
each device of the list the scheduling of the ignition of this device is chosen
within the subset ofbossible values which complies with the desired duration of ,
ignition and which minimizes the function U, having regard to the scheduling
choices already performed for the previous energy distribution devices and by.
25 considering that the following energy distribution devices are shut down.
, According to a variant embodiment of the invention, the list of energy
' ,
distribution devices is traversed in a random order and for each device of the
list, the scheduling of the ignition of this device is chosen within the subset of
possible values which complies with the desired duration of ignition and which
30 minimizes the function U, having regard to the schedulings already performed
for the other energy distribution devices.
The traversal of the list of energy distribution devices is repeated a fixed
number of times, in particular about a hundred, or else for a limited duration, in
particular one to two seconds, and on completion, the best scheduling obtained
is maintained. ' . 9
According to an"exemplary embodiment of the invention, the energy distribution
devices are burners and the energy thfoughput of the installation is proportional
5 to the fuel supply throughput for the burners. .The energy distribution devices
can also consist of electrical resistors.
The method defined above is advantageously implemented for the driving of a
reheating furnace whose energy distribution devices consist of burners or
electrical resistors. .-
The invention also relates to an installation equipped with energy distribution
devices operating in all or nothing mode and in operating duration modulation
mode, characterized in that it comprises a computer or calculator programmed
to control the energy distribution devices in accordance with a method such as
I
' j 15 definedabove.
The installation advantageously consists of an industrial furnace.
The invention consists, apart.from the provisions set forth herbinabove, of a
certain number of other provisions which will be more explicitly dealt with
20 hereinafter in r6gard to exemplary embodiments, described with reference ,to
the appended drawings, but which are wholly non-limiting. In these drawings: b
fig. 1 is &simplified schematic view of an industrial furnace equipped
with burners constituting the energy distribution devices.
fig. 2 comprises two simplified charts illustrating, as a function of the
25 time plotted as abscissa, the e'nergy throughput Q plotted as ordinate for a first
scheduling of the durations of operation of four burners.
> fig. 3 shows, similarly to fig. 2, the energy throughput for a different '
' scheduling of the same durations of operation of the four burners, only the
position of the duration of operation of a burner being modified.
30 fig. 4 is a chart illustrating a curve of the energy throughput Q plotted
as ordinate, as a function of the time plotted as abscissa.
fig. 5 shows similarly to fig. 4 a curve of the energy throughput Q as a
function of-time, with a significant drop in the energy throughput over a reduced
temporal segment.
3 5 fig. 6 is a chart schematically illustrating a slope of variation of the
energy throughput as a function of time.
fig. '7 is a schematic representation of a time interval with
subdivisions.
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fig. 8 is a schematic view of the time interval of fig. 7 in which the "off'
state of an energy distribution device is represented by a thick line coincident
with the abscissa axis (0 value).
fig. 8 is a schematic view of the time interval of fig. 7 in which the
"on" state of the energy distribution device is represented in the form of a thick
line of ordinate 1.
fig. 10 represents, similaAy to fig. 9, a change of state of the energy
distribution device over the time interval. --
fig. 11 shows, similarly to fig. 10, another change of state of the
energy distribution device.
fig. 12 represents, similarly to fig. 10, two changes of state of the
energy distribution device over the time interval considered.
fig. 13 shows, similarly to fig. 12, two other changes of state of the
energy distribution device.
fig. 14 shows, similarly to fig. 12, three changes of state of the energy
distribution device.
fig. 15 shows, similarly to fig. 14, three other changes of state of the
energy distribution device, and, I
fig. lfi is a schematic representation of the coding of the state of the
energy distribution devices in the form of a binary matrix. I
L
The description wnich follows relates to the particular case of an industrial
I furnace equipped with several burners constituting the energy distribution I
devices, but the invention applies to any installation equipped with energy
distribution devices, especially electrical resistors, operating in all or nothing .
mode, and in operating duration modulation mode.
' ,
Referring to fig. 1, it is possible to see, represented schematically, an industrial
furnace 1, especially for the heating of iron and steel products which travel
continuously in the direction of the arrows 2, entering on the left of the furnace 1
and exiting on the right according to the example drawn. The furnace is
equipped with burners B1, B2. .. BN which operate in all or nothing (onloff) mode
and in duration modulation mode. The number N of burners Bl, 92 ... may be
several tens, these burners being allotted, during design, over the length of the
furnace, according to the processing operations for which this furnace is
intended.
1',
i,
Each burner B1, B2 ... is supplied with fuel on the basis of a common pipeline
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3a, 3b, common to several burners,, by an automatic isolating valve 4b1,
4b2 ... The pipelines 3a, 3b constitute bypass branches of a pipeline 3 generally
equipped with a flowmeter 3c upstream of the branches 3a, 3b.
Likewise, the supply of oxidant, especially air or oxygen, for each .burner, 'is
ensured by a general pipeline 5 and by bypasses with individual valves 6bl,
t 6b2.. . for each burner.
4.-
The valves 4b1, 4b2 ... 6b1, 6b2 ... are controlled by a computer or calculator 7.
The furnace is driven, on the basis of the requirements needed for heating the
products which will travel along this furnace, with the aid of a program installed
in the computer 7. The program is suited to the type of products, to their speed
of travel, to the desired processing. This program determines, for each burner
B1, B2 ... BN, the amount of thermal energy that it must deliver over a time
interval I of duration D. This amount of energy corresponds, for a burner Bi, to a
duration of operation Ai, less than or equal to the duration D of the time interval
I. This duration of operation is specific to each burner and depends especially
I
on its power, its position and the thermal regime that it is desired to obtain in the
furnace. The tiwe intervals D have a limited duration, for example of 30 to 120
seconds, and the computer 7 calculates for each successive time intedal
values Ai for each burner. b
ZC
I The invention is aimed at optimizing the provision of energy by the set of ,
burners Bi over the time interyals I and at limiting the pressure fluctuations in
the furnace and in the oxidant and fuel supply networks.
30 ). fig. 2 comprises two simplified charts. The chart 2.1 represents, for four burners
' ,
B1, B2, B3, B4 with a random possible scheduling, durations of operation A1,
62, 63, A4 allocated to each of the four burners over the time interval I. The
slots CBI, CB2, CB3, CB4 on the chart 2.1 illustrate the on state of the burner.
The chart 2.2 represents the energy throughput Q delivered by the burners,
35 plotted as ordinate, as a function of time plotted as abscissa. In this example,
the four burners have one and the same unit power.
The chart 2.2, reveals a zone of overlap of the durations of operation of the
burners B1, 821 83, 84, thereby leading to a peak in the total energy tJhroughput
at a level Q4. In a general way, fig. 2 reveals a considerable variation in the
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energy throughput over the time interval I which is not favorable to good
conditions of operation and of distribution of the pressures in the furnace 1.
fig. 3 illustrates a different scheduling of the durations of operation of the four
burners B1, B2, B3, B4 of fig. 2. Only the operation of the burner B1. has been
modified with respect to fig.2. This has been split into two distinct operating
sequences A1 .I,61 .2 correspondinb to two slots CB1. Ia nd CB1.2. The chart
3.2 reveals a zone of overlap of the durations of operati6n of the burners B2,
83, 84, but no longer of the burner B1, thereby leading to a peak in the total
energy throughput at a level Q3 which is less than Q4. The scheduling of fig. 3
for the durations of operation of the four burners makes it possible, with respect
to that of fig.2, to reduce the variation in energy throughput, and therefore the
pressure fluctuations in the supply pipelines, as well as in the furnace, and to
improve the operating conditions.
It is appreciated that, for a larger number of burners, especially several tens,
optimization of the temporal allotment of the durations of operation will be
I
advantageous for the behavior of the installation as a whole.
8
It should be noted that the duration of operation Ai can consist of a single
operating sequence (of duration Ai), or may be divided as explained in regard to b
fig. 7-15 into seveal sequences of partial durations of less than Ail but whose
sum is equal to Ai.
To optimize the energy supply over the time interval I of duration Dl a
scheduling of the durations of operation Ai of each of the N burners B1,
B2,. . . BN is determined by proceeding according to the following steps:
I
Step a) any arbitrary initial scheduling is chosen,
- Step b) an order number from 1 to N is associated with each burner
B1 ... BN,
Step c) a search is conducted, for the burner B1 (of order number I),
for the optimal position or positions of the duration of operation CB1 over the
time interval I which make it possible to minimize a function U representative of
the fluctuations of the energy throughput over the time interval I, the durations
of operation of the other burners B2 ... BN maintaining the positions of the initial
scheduling, 3
and an improved resulting scheduling is obtained with the optimal
>
position or positions retained for the sequences of the burner B1.
A simplified example of this result is provided by the scheduling of
fig. 3: the modified position of the duration CB1 in CB1.l and CB1.2, whereas
the durations CB2, CB3 and CB4 have maintained the positions offig. 2, has
led to a decrease in the amplitude of the throughput variation.
t
The function U can take various forms. .-.. .-
In fig. 4 the energy throughput Q, plotted as ordinate, has been represented by
a curve 9 as a function of time, plotted as abscissa, over the time interval I of
duration D, for a determined scheduling of the burners B1 .. . BN. The area
included between the curve 9 and the abscissa axis represents the amount of
energy provided over the time interval I and corresponds to the energy provision
global instruction given in a known manner by the computer 7. The curve 9
portrays fluctuations on either side of the mean value Q,,,, of the throughput
over the interval I represented by the straight line 10, parallel to the abscissa
I axis. The curve 9 also illustrates the fluctuations in fuel throughput at the level
of the flowmeter 3c. The straight line 10 determines, with the curve 9, equal
areas above and below the line 10. 1
b
The curve 9 may 6k established by the computer 7 which performs a sampling
1
of n samples, with sufficiently reduced time increments, especially of the order
of a hundredth of 0, i.e. DllOO, and which determines for each of the n samples
the energy throughput Qj according to the burners which will be turned on at this
instant.
A first exemplary function U that one seeks to minimize is the sum of the '
.absolute value of the fluctuations of the energy throughput Qj about a mean
value Qmean during the time interval I:
Another exemplary function U to be minimized consists of the sum of the
squares of the beviations with respect to the arithmetic mean:
5 The program installed in the computer 7 ensures this minimization processing
which translates into an optimal scheduling of the durations of operation of the
burners.
t
Another criterion that can be taken into account for the optimization of the
scheduling is illustrated schematically by the chart of 5. The curve 11 of
10 throughput as a function of time ensures a total amount of energy over the
interval I that is equal to that of fig.4, corresponding to the mean value Qmean
represented by the straight line 12 parallel to the abscissa axis. The energy
provided during the interval I corresponds to the area delimited, over the interval
I, between the line 12 and the abscissa axis. Because the areas situated above
15 and below the line 12 between the curve 11 and the line 12 are equal, the
+ i scheduling corresponding to the curve 11 yields a global energy provided over
the interval I corresponding to the desired value but a negative peak 13 occurs,
corresponding to a drop in the throughput over a reduced tipe. It may be
desirable to avoid such abrupt drops in throughput although the objective of
20 energy provision desired over the time interval I is ensured.
1
In this case, the function U will be able to take into account a determined limit, '
ZC
especially equal to half Qmeani,. e. Qmean/ 2, SO as to keep the absolute value of ,
the gap between the various values Qj of the curve representative of the
25 throughput over the interval Ia nd the mean value Qmeanb elow this-determined
limit.
. '. The function U can furthermore take into consideration the difference in energy ,
.throughput (fig. 5) between the end of the previous interval and the start of the
30 new interval, corresponding to the vertical segment 14, so as to minimize this
difference in energy throughput.
The scheduling which minimizes a function U taking into account not only the
fluctuation- of the energy throughput during the time interval I, but also the
variation of the energy throughput between the instant preceding the start of the
35 time interval and the instant following the start of the time interval may be
1 retained as optimal scheduling. The function U can then be the sum of the
absolute value'of the fluctuations (Qj-Q,,,,,~ of the energy throughput about a
mean value Qmtan during the time interval I and of the variation 14 of the total
energy throughput between the instant preceding the start of the time interval
5 and the instant following the start of the time interval
fig. 6 is a chart revealing the taking into account of the slope of the variation
(plotted as ordinate) of the energy throughput as a function of time,-plotted as
abscissa, in the search for optiqization. The optimal scheduling may be
10 determined as being that which makes it possible to obtain an angle 15 of
inclination of the throughput variation curve, over the mean line 16, which is as
small as possible. The function U to be minimized can then be defined as the
slope of the tangent to the throughput curve at a point.
15 After having determined a scheduling with an optimal position, or optimal
positions in the case of a splitting, retained for the duration of operation of the
I burner B1 of order number I , step c) is repeated on the basis of this scheduling , * $ by successively considering the burners of higher order number up to the
burner of order number N.
At each repetition, only the position of the duration of operation of the burner
whose order number is taken into consideration is displaced over the interval I,
the other sequences not being displaced over the interval I.
b
3
25 Step e) Using as initial scheduling that retained in step d), a new order number ,
from 1 to N is associated with each burner and steps c and, d/are repeated.
Step 5) step e) is repeated a number of times compatible with the calculation
time available before the start of the following time interval I; this number of
30 '. repetitions depends on the calculation speed of the computer 7. b ,
According to an advantageous embodiment, corresponding to figs.7-15, the
time interval I is divided into a number M of temporal subdivisions of not
necessarily equal durations. The changes of state of the burners, or more
35 generally of the energy distribution devices, take place between two successive
temporal subdivisions.
For an onloff, representation, it is possible, as illustrated in figs. 7-15, to
disregard the pbwer and to represent solely the on or off state of the burner by a
binary magnitude 1 or 0. To involve the power of the burner, a weighting
1 -
coefficient qi assigned to this .burner and representative of its power is then
5 introduced.
Referring to fig. 7, it is possible to see, represented schematically, a grid of a
time interval I divided into ten temporal subdivisions 17. The dashed-horizontal
lines 18a and 18b represent states of the energy distribution device. To
10 comment on the figures, we consider that the energy distribution device is a
burner. At the level 18a ("1" state), the burner is turnect-an, whilst at the level
18b ("0 state"), the burner is turned off.
Referring to fig. 8 of the drawings, it is possible to see, represented
15 schematically, the grid of a time interval of fig. 7. In this grid, the evolution of the
state of the burner is represented as a thick line 19. In this time interval, the
burner is permanently off.
Referring to fig. 9 of the drawings, it is possible to see, represented
20 schematically, the grid of a time interval of fig. 7. In this grid, the evolution of the
t state of a burner is represented as a thick line 20. In this time interval, the
burner is permapently on.
1
In the examples represented in fig.8 and fig.9, there is no change of state of the
25 burner. %
Referring to fig. 10 of the drawings, it is possible to see, represented
schematically, the grid of a time interval of fig. 7. In this time interval, the burner
is alight over the stretch 21. Between the 5th and the 6th temporal subdivision,
30 ). the burner is extinguished and kept off over the stretch 22.
' .
Referring to fig. 11 of the drawings, it is possible to see, 'represented
schematically, the grid of a time interval of fig.7. In this time interval, the burner
is extinguished over the stretch 23. Between the 5th and the 6th temporal
35 subdivision, the burner is alight and kept on over the stretch 24.
In the examples represented in fig.10 and fig.1 I , there is therefore a single
change of state of the burner.
Referring to fig. 12 of the drawings, it iis possible to see, represented
schematically, the grid of a time interval of fig. 7. In this time interval, the burner
\ -
is extinguished over the stretch 25. ,Between the 3rd and the 4th temporal
5 subdivision, the burner is alight and kept on over the stretch 26. Between the 6th
and the 7" temporal subdivision, the burner is extinguished and kept off over
the stretch 27.
This fig. 12 represents a time interval comprising a single possible operating
sequence according to the invention: with a first change of state between the 3rd
10 and the 4th temporal subdivision, and a second change &state between the 6th
and the 7th temporal subdivision. A sequence similar to that of fig. 12 but with a
first change of state between the znd and the 3rd temporal subdivision, and a
second change of state between the 7th and the 8th temporal subdivision also
forms part of the subset of possible sequences according to the invention.
15
I
,{ Referring to fig.13 of the drawings, it is possible to see, represented
schematically, the grid of a time interval of fig. 7. In this time interval, the burner
is in operation over the stretch 28. Between the 3rd and the 4th temporal
subdivision, the burner is extinguished and kept off over the stretch 29.
20 Between the 6th and the 7th temporal subdivision, the burner is alight and kept
on over the strefch 30. I
In the examples @presented in fig.12 and fig.13, there are therefore two
changes of state of the burner.
25
Referring to fig. 14 of the 'drawings, it is possible to see, represented
schematically, the grid of a time interval of fig. 7. In this time interval, the burner
is in operation over the stretch 31. Between the 3d and the 4th temporal '
. ' subdivision, the burner is extinguished and kept off over the stretch 32.
30 Between the 5th and the 6th temporal subdivision, the burner is alight and kept
on ove-r .th e stretch 33. Between the 6'h and the 7th temporal subdivision, the
burner is extinguished and kept off over the stretch 34.
Referring to fig. 15 of the drawings, it is possible to see, represented
35 schematically, the grid of a time interval of fig. 7. In this time interval, the burner
is off over the stretch 35. Between the 3'C' and the 4th temporal subdivision, the
burner is alight and kept on over the stretch 36. Between the 5th and the 6th
temporal subdibision, the burner is extinguished and kept off over the stretch
37. Between the 6th and the 7th temporal subdivision, the burner is alright and
8 -
kept in operation over the stretch 38. ,
In the examples represented in fig.14 and fig.15, there are therefore three
changes of state of the burner.
The profiles of change of state of an energy distribution device represented .in
figs. 10 to 15 are given by way of hon~imi t ine~xa mple, each change of state
being able to occur at the end of another temporal subdivision.
The time gap between two changes of state, that is to say the horizontal
distance between two successive vertical segments in figs.12 to 15, is greater
than a determined limit, in particular than a twentieth of the duration D of the
interval, i.e. greater than D/20.
The last change of state over the interval I is separated from the end of this
interval I by a minimum time gap, in particular at least equal to a twentieth of the
duration D of the interval, i.e. D/20.
8
According to an,exemplary embodiment, represented in fig. 16, of the invention,
the states of the distribution devices are coded according to a binary matrix Z of
size N x M, having N rows and M columns, each of the N rows of which codes
the state of the varaus burners during the M successive temporal subdivisions,
each column corresponding to a temporal subdivision.
The burners have different powers and are advantageously assigned a
weighting coefficient qi representative of the power of the relevant burner. In ,
practice q, does not depend on the temporal subdivision since the power of the
' i
burner is constant.
Each element of the matrix Z is designated by yk with k an integer index varying
between 1 and NxM, in accordance with a row numbering as represented in
fig. 16. The elements yk have the value 0 or 1.
35 For a temporal subdivision j corresponding to a column of the matrix Z, the total
energy throughput Q, during this subdivision is equal to:
The function U to be minimized may be the sum of the absolute value of the
fluctuations of the energy throughput for a subdivision about a mean value
Qmeand uring the time interval I.T his function U may be written:
According to another embodiment of the invention, theyuiction. U may be the
sum of the square of the fluctuations of the energy throughput for a subdivision
about a mean value Qmeand uring the time interval I.I t may then be written:
According to another embodiment of the invention, the function U to be
minimized may be the sum of the absolute value of the variations of the energy
throughput between two successive subdivisions during the time interval I. his
function U may ,be written:
According to another embodiment of the invention, the function U to be
minimized may be the sum of the square of the variations of the energy
throughput between two successive subdivisions during the time interval I. This
function U may be written ? a
It should be noted that the function U can also take one of the forms described
previously and which would be supplemented with additional terms, for example
the variation between the first temporal subdivision of a time interval and the
last temporal sbbdivision of the previous time interval.
According to aqother exemplary embodiment of the invention, the function U
can be expressed in the form C, C, ad y, y, which is the weighted sum of the
5 products of the pairs of components of a vector Y, with i and j integer indices
between 1 and Nx M, and c l a~ r e weighting coefficients.
The invention makes it possible to obtain optimal efficiency of a furnace with
burners operating in all or nothing mode, and in duration modulation mode. The
invention ensures a drop in the thrdughput fluctuations, better combustion, and
10 a decrease in polluting waste. When a furnace is ~t a r t d :~utph,e best running
conditions are obtained very rapidly and automatically, and are maintained.
By way of example, on a reheating furnace with a capacity of 400 tlh, switching
from a method for scheduling the ignition of the burners according to
FR2853959 to that according to the invention makes it possible to reduce the
15 fluctuations in throughputs of oxidant and of fuel by about 30%.

CLAIMS?
1. A method for optimizing the energy supply, over a time interval / of duration
5 D, of an installation equipped with A/ energy distribution devices operating in all
or nothing mode and in duration modulation mode, a duration of operation Ai,
less than or equal to D, being allocated to each of the N energy distribution
devices over the time interval /, the durations Ai being deduced from the energy
demand of the installation and pro\?ided by a command-control system of the
10 installation, characterized in that: —-
- the duration of operation Ai of an energy distribution device (B1,B2...BN)
either consists of a single operating sequence of duration Ai, or is divided into
several sequences of partial durations, whose sum is equal to Ai,
- a scheduling is defined over the time interval / by a temporal allotment of the
\ 15 set of operating sequences of the N energy distribution devices,
- and the scheduling is calculated before the start of the time interval / by taking
account of the desired durations Ai of operation of each energy distribution
device.
2. The method as claimed in claim 1, characterized in that the scheduling'is
20 calculated as follows: •
a/ any arbitrary initial scheduling is chosen, * '
b/ an order number from 1 to N is associated with each distribution device,
c/ for the distribution device of order number 1, a search is conducted for the •
• number, the duration or durations and the position or positions over the time
25 interval / of the operating sequence or sequences of this distribution device
which make it possible to minimize a function U representative of the
fluctuations of the energy throughput over the time interval, the sequences of
the other devices maintaining the positions of the initial scheduling,
and a resulting scheduling is obtained with the number, the duration or
30 durations and the optimal position or positions retained for the sequences of the
device of order number 1,
wo 2012/004686 PCT/IB20ri/05d899
^ 22
d/ step (c) is repeated on the basis of the scheduling resulting from step (c) by
successively considering the distribution devices of higher order number up to
the distribution device of order number N.
3. The method as claimed in claims 1 and 2, characterized in that it comprises
5 the following additional steps:
e/ by using as initial scheduling the scheduling retained in step (d), a new order
number from 1 to N is associated with each distribution device and steps (c)
and (d) are repeated, »
g/ step (e) is repeated a number of times compatible with the calculation time
10 available before the start of the time interval.
4. The method as claimed in claim 2, characterized in that the order number
allocated to each distribution device is dependent on the desired durations of
operation Ai, the device of order number 1 being that whose desired duration of
"> operation A1 is the longest and the device of order number N being that whose
' I 15 desired duration of operation AN is the shortest.
5. The method as claimed in any one of the preceding claims, characterized in
that the time interval / is divided into a number M of temporal subdivisions (17)
of not necessarijy equal durations.
6. The method as claimed in claim 5, characterized in that the states of the ^
20 distribution devices»are coded according to a binary matrix Z of size N x M {N
rows and M columns), each of the N rows of which codes the state of the '
various distribution devices during the successive temporal subdivisions and
each column of which corresponds to a temporal subdivision.
7. The method as claimed in any one of the preceding claims, characterized in '
> , •
25 that the function U to be minimized is the sum of the absolute value of the
fluctuations of the energy throughput Qj about a mean value Qmean during the
time inten/al I:
. M
U=Z|QJ Q™.„
j-1 ^_
' wo 2012/004686 PCT/IB20Il/oi0899
23
8. The method as claimed in any one of claims 1 to 6, characterized in that the
function U to b6 minimized consists of the si^m of the squares of the deviations
with respect to the arithmetic mean:
r i
5 9. The method as claimed in any one of claims 1 to 6, characterized in that the
function U to be minimized consists of the sum of the absolute value of the
variations of the energy throughput between two successive subdivisions during
the time interval /;
M-L
'^ 10 10. The method as claimed in any one of claims 1 to 6, characterized in that the
function U to be minimized consists of the sum of the square of the variations of
the energy throughput between two successive subdivisions during the time
interval I:
M-1/ Vp '
J=l
1
15 11. The method as claimed in one of claims 7 to 10, characterized in that the
function U to be minimized is supplemented with additional terms.
12. The method as claimed in claim 2, characterized in that the function U to be
'minimized takes into account not only the fluctuation of the energy throughput
during the time interval /, but also the variation (14) of the energy throughput
20 between the instant preceding the start of the. time interval and the instant
following the start of the time interval, the function U being the sum of the
absolute value of the fluctuations of the energy throughput about a mean value
during the time interval / and of the variation (14) of the total energy throughput
between the instant preceding the start of the time interval and the instant
25 following the start of the time interval.
' wo 2012/004686 PCT/IB2011/050899
24
13. The method as claimed in any one of the preceding claims, characterized in
that it is ensure'Gl that the total energy througlpput engendered by the scheduling
obtained does not exceed a defined threshold.
14. The method as claimed in any one'of the preceding claims, characterized in
5 that the desired durations of operation of the energy distribution devices are
reduced if they lead to a total throughput which exceeds a defined threshold.
15. The method as claimed in any one of the preceding claims, characterized in
that, for each energy distribution flevice, the gap between the duration of
operation over a time interval / and the desired duration is limited by a
10 maximum gap, in particular of 5% of the duration of the time interval.
16. The method as claimed in any one of the preceding claims, characterized in
that the sequences for each energy distribution device correspond at most to
three changes of state of the device over a time interval /.
; 17. The method as claimed in any one of the preceding claims, characterized in
'/ 15 that two successive changes of state of each energy distribution device are
spaced apart by a minimum time gap, in particular at least equal to a twentieth
of the duration D of the time inten/al, i.e. D/20.
I
18. The method as claimed in any one of the preceding claims, characterized in
that, for each energy distribution device, the last change of state during the time
20 interval / is spaced apart by a minimum time gap from the end of the interval, in ,
particular at least equal to a twentieth of the duration D of the time interval, i.e.
D/20. ;
19. The method as claimed in any one of the preceding claims, characterized in'
that the initial scheduling is that where all the energy distribution devices are off
25 during the time interval.
20. The method as claimed in any one of the preceding claims, characterized in
that the order number allocated to each distribution device after the first iteration
is random.
21. The method as claimed in'claim 5, characterized in that the changes of state
30 of the distribution devices take place between two successive temporal
subdivisions.
j
•
> wo 2012/004686 PCT/IB2011/050899
2 5 . .• ~- •••- •
22. The method as claimed in any one of the preceding claims, characterized in
that the energy distribution devices are burners and in that the throughput of the
energy supply of the installation is proportion-al to the fuel supply throughput for
the burners. ,v : .
5 23. The method as claimed in claim 2, characterized in that the function L/ is
expressed in the form S,Sy or/^y/yy, which is the weighted sum of the products of
the pairs of components of a vector Y, with / and; integer indices between 1 and
A/X M, and or//are weighting coefficients.
24. The method as claimed in any ohe of the preceding claims for the driving of
10 a reheating furnace whose energy distribution devicesIxSnsist of burners or
electrical resistors.
25. An installation equipped with energy distribution devices operating in all or
nothing mode and in operating duration modulation mode, characterized in that
15 it comprises a computer or calculator programmed to control the energy
•i distribution devices in accordance with a method as claimed in any one of the
• t .
d preceding claims.
26. The installation as claimed in claim 25, consisting of an indus^ial furnace.