FR2970579A1 - Device i.e. fixed or portable computer for calculation of lengths of sections of electric cables for electric line of aircraft, has calculating unit determining optimal length for each of cable sections from theoretical mass of each section - Google Patents

Abstract

The device has a calculation unit (MC1) arranged to determine, for each of cable sections (T11-T13) of a line (L1), a theoretical minimum mass and a voltage drop less than or equal to a preset maximum voltage drop. The calculation unit determines a theoretical mass for an upper section and a lower section from a set of available predefined sections. Another calculating unit (MC2) determines an optimal length for each of the sections from the determined theoretical mass, so that the line has a minimum optimum mass and a voltage drop less than or equal to the preset maximum voltage drop. An independent claim is also included for a method for calculation of length of sections of electric cables.

Description

DEVICE AND METHOD FOR CALCULATING OPTIMUM SECTION SECTIONS OF AT LEAST ONE ELECTRIC LINE BASED ON THE MAXIMUM VOLTAGE DROP AUTHORIZED ON THIS LINE The invention relates to electrical lines which consist of several (at least two) cable sections ( or electric wire), and more specifically the determination of the sections of such sections. In some areas, such as vehicles or the aeronautics, the number of electrical devices that equip the same system or device continues to increase. However, to power these electrical organs must be connected to power lines that are very often consist of several (at least two) sections of cable (or wire) electrical. It will therefore be understood that the more we increase the number of power lines within a system (or device or device), the more we increase the mass of the latter, and therefore more he will have to consume energy to move. It is therefore important to optimize the weight of each line (electric) when we want to limit energy consumption and costs.

To do this, we can play on two parameters: the section of the line sections and the length of the line sections. The optimization of the length is a relatively simple operation because it is done in the presence of few constraints. On the other hand, the optimization of the sections is a much more complex operation, in particular because each line must withstand at least one thermal stress (of heating) while presenting a voltage drop that is greater than a voltage drop (maximum ) predefined so that the electrical member that it supplies has a voltage at least equal to a predetermined minimum voltage. It is recalled that the voltage drop imposed by a section of line depends directly on its resistance R, which is given by the relation R _ (pmax * L) / S, where Pmax is the worst resistivity of the section, L is the length of the section and S is the section of the section. It follows from the preceding formula that the smaller the section S of a section (of fixed Pmax and L), the higher the resistance R and the voltage drop of this section, and the smaller the mass of this section. It will therefore be understood that the stress relating to the voltage drop of a line opposes the constraint relating to the reduction of the mass of this line. At least two line optimization methods have been proposed. A first method has been proposed by the PSA PEUGEOT CITROËN group. It is implemented in particular by a beam sizing software called OPHELIE. This first method proposes starting from minimum sections of sections of a line and then incrementing all these sections as long as the cumulative voltage drop of this line remains less than or equal to the predefined voltage drop (maximum). It will be understood that, thanks to this first method, the stress relating to the voltage drop is well respected, but, not at all, each section section is optimized in order to tend towards a minimum line mass. In other words, at least some of the section sections determined by this first method could be reduced without affecting the proper functioning of the line. A second method has been proposed by the company AIRBUS, in particular in the patent document FR 2868573. It consists in globally treating a line with all its parameters, and in particular the lengths and sections of its sections. The problem of optimizing sections is here treated globally as a parameter among a set of parameters, without any precision. Consequently, this second method does not make it possible to optimize the section sections of a line independently of the other parameters of this line. The invention therefore aims to propose an alternative solution that optimizes the sections of electric cable sections constituting at least one (electric) line, connecting a source of electric current to an electrical member (or load), in order to minimize the mass of this line while ensuring that it has a voltage drop less than or equal to a predefined voltage drop (maximum). The invention proposes more precisely, and in particular, a computing device comprising: first calculation means arranged to determine for each of the sections of a line respective theoretical sections suitable for allowing this line to present a theoretical minimum mass and a voltage drop less than or equal to a predefined (maximum) voltage drop, then for determining for each section at least a first section smaller than its determined theoretical section and at least a second section greater than its determined theoretical section, from a set of predefined available sections, and second calculation means arranged to determine for each section a so-called optimum section among its first and second determined sections, so that the line has a minimum (quasi) optimal mass and a voltage drop less than or equal to the predefined voltage drop.

The computing device according to the invention may comprise other characteristics that can be taken separately or in combination, and in particular: its first calculation means can be arranged to determine the theoretical sections within a subset of sections; which all support at least one predefined thermal criterion, specific to the line; its first calculation means can be arranged to constitute the subset with sections which are each between a minimum section and a maximum section supporting the predefined thermal criterion; its first calculation means can be arranged to determine the theoretical sections by means of a function which satisfies predefined conditions and which has as parameters at least the respective lengths of the sections, the set of predefined available sections, the maximum resistivity of the sections, the nominal currents to flow respectively in the sections, and the minimum operating voltage across the line; its first calculation means can be arranged to determine the maximum resistivity of the sections according to the predefined thermal criterion supported by the line; its first calculation means can be arranged to use predefined conditions of Kuhn-Tucker type; its first calculation means may be arranged to determine for each section a single first section smaller than its determined theoretical section and a single second section greater than its theoretical section determined from the set of predefined available sections; its second calculation means can be arranged to determine for each section an optimum section among its first and second determined sections, by means of a tree construction technique whose base is defined by a first section of the line which is connected to the electric power source and for which a second section associated with its theoretical section (determined by the first calculation means) is chosen, and in which each constructed branch represents a possible combination of segments of line; its second calculation means can be arranged to determine each optimal section by means of a so-called "separation and evaluation" technique (or "branch and bound"); its second calculation means can be arranged to interrupt the construction of a branch as soon as it has a voltage drop greater than or equal to the predefined voltage drop; its second calculation means can be arranged, in the presence of several complete branches, to select the one which has the smallest mass; its second calculation means can be arranged, after having selected the branch having the smallest mass, to determine the difference between the predefined (maximum) voltage drop and the voltage drop presented by this selected branch, and then to replace at least one optimum section determined for a section by an available section of the predefined set that is smaller than this optimum section while having a voltage drop less than or equal to this determined difference.

The invention also proposes a method, dedicated to the calculation of sections of sections of electric cables constituting at least one line, connecting a source of electric current to an electrical member and supporting a predefined voltage drop, and comprising the following steps: determining respective theoretical sections for each of the sections of this line, in order to allow this line to present a theoretical minimum mass and a voltage drop that is lower than or equal to the predefined voltage drop, and then to determine for each section at least a first section less than its determined theoretical section and at least a second section greater than its determined theoretical section, from among a set of predefined available sections, and b) determining for each section a so-called optimum section among its first (s) and second (s) sections determined, so that the line has a minimum mass (quasi) opt imale and a voltage drop less than or equal to the predefined voltage drop. The invention is well adapted to, although not limited to, power lines which are intended to equip a vehicle, possibly of automobile type. Other features and advantages of the invention will appear on examining the detailed description below, and the accompanying drawings, in which: FIG. 1 diagrammatically and functionally illustrates an example of an electrical circuit comprising a battery connected to three electrical members via three electric lines having common sections, and an exemplary embodiment of a computing device according to the invention, and - Figures 2A and 2B schematically illustrate, functionally and respectively an example of a set of theoretical sections (circles black) respectively framed respectively by first (gray circle) and second (circle white) associated sections, obtained through the first step of the method according to the invention, and a branch selected from the first and second sections of the example of FIG. 2A, obtained thanks to the second step of the method according to the invention. The attached drawings may not only serve to complete the invention, but also contribute to its definition, if any. The aim of the invention is to provide a computing device (D), and an associated method, for optimally calculating the sections of electrical cable sections (or wires) (Tij) constituting at least one electrical line ( Li) which connects an electric power source (BA) to an electrical component (or load) (Oi). In the following, we consider, by way of non-limiting example, that the electric lines (Li) are intended to equip a motor vehicle, such as a car. But, the invention is not limited to this application. It concerns indeed any type of system or apparatus or device comprising at least one electrical line comprising at least two sections (of electric cable) and whose mass must be minimized. FIG. 1 schematically shows a non-limiting example of an electrical circuit for which a calculation of sections Sij of sections Tij of line Li must be carried out by means of a computing device D according to the invention. This example of an electric circuit comprises a battery BA, possibly connected to an alternator (not represented), and connected to three electric members 01 to 03 (i = 1 to 3) via three (electrical) lines L1 to L3 respectively, which have, here , sections (of cable or electric wire) Tij common. More precisely, in this nonlimiting example, the first line L1 consists of the sections T11, T12 and T13 (i = 1 and j = 1 to 3), the second line L2 consists of the sections T21, T22 and T23 (i = 2 and j = 1 to 3), and the third line L3 consists of the sections T31 and T32 (i = 3 and j = 1 or 2), the sections T11, T21 and T31 being common and the sections T12 and T22 being common. . It should be noted that the invention can also make it possible to calculate the sections of the sections of a single line or of several lines independent of each other (that is to say without common sections).

As illustrated non-limitatively in FIG. 1, a computing device D according to the invention comprises at least first MC1 and second MC2 calculation means coupled together. Such a (computing) device D may, for example, be implanted in a fixed or portable computer. It may possibly be part of a more complete device dedicated, for example, to the sizing of the electrical harnesses of a system, such as for example and not only the OPHELIE software of the PSA PEUGEOT CITROËN group. Consequently, the computing device D is preferably implemented in the form of software (or computer) modules. But, it could also be realized in the form of a combination of electronic circuits and software modules. The first calculation means MC1, of the device D, are arranged (or designed) to determine, for each of the sections Tij of a line Li, the respective theoretical sections STij, which are suitable for allowing this line Li to present a theoretical minimum mass and a voltage drop CT i which is less than or equal to a predefined voltage drop (maximum) CT max. It is recalled that this predetermined (maximum) voltage drop CTmax depends on the voltage VBA, which is supplied by the electric power source BA (here a battery) which is connected to the first section Tif of the line Li, and the minimum voltage Vmin whose member Oi, which is connected to the last section TiN (j = 1 to N) of the line Li, needs to function properly. More precisely, one must have CTi CTmax = VBA-Vmin, or VBA-CTi Vmin, or else CTmax -N Pal * LOij * Inomij> 0 (where LOij is the length of a section Tij, pij is the resistivity of the section Tij, Inomij is the nominal current to flow in the section Tij, and Sij is the section of the section Tij). The first calculation means MC1, of the device D, are also arranged, after having determined the theoretical sections STij, to determine for each section Tij at least a first section PSij less than its determined theoretical section STij and at least a second section SSij greater than its theoretical section determined STij, among a set of predefined available sections. Here is meant by "set of predefined available sections" the 30 sections that are in stock and that can actually be used in practice to form lines Li. It will be understood that only a certain number of number of sections of different (or "discrete") values while the theoretical sections can take any value (from a "continuous" set). It will be noted that it is advantageous if it is desired to reduce the calculation times, that the first calculation means MC1 determine the theoretical sections STij within a subset of sections that support at least one predefined thermal criterion, which is specific to the considered Li line. It will be understood that it is useless to perform a calculation for a set which includes sections which are known in advance that they can not be used because they do not satisfy at least one criterion. (here thermal). The objective of this thermal criterion is to determine the sections that will not allow their respective sections to withstand a certain limit temperature when they are traversed by known nominal currents Inomij. To do this, one can use any electrothermal model known to those skilled in the art, and in particular that described in the patent application FR 0853413. It will also be noted that the first calculation means MC1 can be arranged to form the subset with sections which are each between a minimum section Sminij and a maximum section Smaxij supporting the predefined thermal criterion. It will also be noted that the first calculation means MC1 can be arranged to determine the theoretical sections STij by means of a function which respects predefined conditions and which has as parameters at least the respective lengths LOij of the sections Tij, the set of sections predefined available values (and preferably the subset defined above), the maximum resistivity pmax of the sections Tij, the nominal currents Inomij to flow respectively in the sections Tij, and the minimum operating voltage Vm; n at the terminals of the line Li. For example, the first calculation means MC1 can determine the maximum resistivity pmax of the sections Tij as a function of the predefined thermal criterion which must be supported by the line Li. Here, the term "maximum resistivity pmax" is used to denote the worst of the resistivities that can be present a section Tij of a line Li which supports the predefined thermal criterion. It is recalled that the resistivity pij of a section Tij is related to the resistance Rij of this section Tij by the relation Rij = (pij * Lij) / Sij, where Lij is the length of the section Tij and Sij is the section of the section Tij. Consequently, when all the lengths Lij of the sections Tij of a line Li and the smallest section making it possible to support the predefined thermal criterion are known, it is possible to deduce the worst of the resistivities pmax of this line Li. It will also be noted that the first calculation means MC1 can be arranged to use predefined conditions of the Kuhn-Tucker type. These conditions are notably described in the document by W.

Karush (1939): "Minima of Functions of Several Variables with Inequalities as Side Constraints", M.Sc. Dissertation Dept. of Mathematics, Univ. of Chicago, Chicago, Illinois. These conditions are well adapted to the minimization of a function of n type f (Sil, ..., SiN) = ~ LOij *, which represents here the cumulated volume (and therefore = 1 the cumulative mass) of a line Li that the device D has the ultimate goal of minimizing. As known to those skilled in the art, this minimization can be done by means of a Lagrangian: .l * J) * (~~ zj * LOiJ * Inomi.) - ~ (y (J)) L = LOi If - ~, CTmax- ~. Sj i = Sma ~ 'Sij N - ~ (eld (Smir1j) -Slj). j = 1 It should be noted that this minimization can be facilitated when it is considered when calculating the Lagrangian L gradient that the resistivity pij is constant, which is a good approximation here. It will also be noted that the first calculation means MC1 can be arranged to determine for each section Tij only a single first section PSij less than its determined theoretical section STij and that a single second section SSij greater than its theoretical section determines STij among the set of predefined available sections (and preferably among the determined subset). This is particularly the case in the non-limiting example which is illustrated in FIG. 2A. More precisely, in FIG. 2A is illustrated the result of the calculations carried out by the first calculation means MC1 (or first step), in the case of a line Li comprising six sections Tif to Ti6 (j = 1 to 6). In this example, each black circle represents a theoretical section STij calculated for a section Tij, each gray circle represents a first section PSij determined for a section Tij (it is therefore the available section which is the closest, by a lower value , of the theoretical section STij of the section Tij), and each white circle represents a second section SSij determined for a section Tij (it is therefore the available section which is the closest, by higher value, of the theoretical section STij of the 1 st section Tij). Consequently, each theoretical section STij of a section Tij is framed here by a first section PSij and a second section SSij (this does not prevent a theoretical section STij of a section Tij from being equal to a first section PSij or a second section SSij). It should be noted that one could consider associating with each theoretical section STij several (at least two) first sections PSij and / or several (at least two) second sections SSij. However, this substantially increases the computation time for a final result that is not significantly different from that which can be obtained with a single first section PSij and a single second section SSij. The second calculation means MC2, of the device D, are arranged (or designed) to determine for each section Tij a so-called optimum section SOij (taking into account availability) among its first PSij and second SSij determined sections. by the first calculation means MC1. These optimal sections SOij are determined so that the line Li 25 has an optimal minimum mass and a voltage drop (cumulative) CTi less than or equal to the predetermined (maximum) voltage drop CTmax. To determine these optimal sections SOij the second calculation means may, for example, use a construction technique of a tree structure. The term "tree" here means an element comprising branches consisting of different possible combinations of sections Tij of a line Li and having a base (or a first link) common to and defined by the first section. Tif of the line Li (connected to the battery BA) and for which one chooses a (or the) second section SSi1 which is Il associated with its determined theoretical section STi1. By way of example, the second calculation means MC2 can use the so-called "branch and bound" tree technique. This technique is particularly described in the document by A. H. Land and A. G. Doig (July 1960): "An automatic method of solving discrete programming problems", Econometrica 28 (3): pp. 497-520. This tree technique consists in building each link branch after link, checking after each addition of a new link if the branch verifies a criterion (here a voltage drop CTi less than or equal to the predetermined (maximum) voltage drop CTmax), and if the branch (then a priori partial) does not check this criterion it is removed from the tree (or not taken into account). Here, the second calculation means MC2 will therefore interrupt the construction of a branch (and possibly delete it) as soon as it presents a voltage drop CTi greater than or equal to the predetermined (maximum) voltage drop CTmax. Once all possible combinations have been tested, one can end up with several complete branches that satisfy the criterion relating to the voltage drop. In this case, the second calculation means MC2 can determine the masses of the lines Li which are represented by these complete branches, then they can select the complete branch which represents the line whose mass is the smallest. It will be noted that instead of determining the masses, it may be simpler to determine the volumes (defined by the lengths Lij and the optimal sections SOij) when all the sections are made of the same material.

It will also be noted that in some cases it may still be possible to further optimize the mass (or volume) of a line Li (represented by the selected branch). This situation can arise when the difference between the predetermined (maximum) voltage drop CTmax and the voltage drop CTi presented by the selected branch is non-zero (CTmax - CTi> 0). In this case, the second calculation means MC2 can be arranged to determine the difference CTmax-CTi between the predetermined (maximum) voltage drop CTmax and the voltage drop CTi presented by the selected branch, and, if this difference is not zero (> 0), to replace at least one optimal section SOij which has been determined for a section Tij (and thus which is part of the selected branch) by another available section of the predefined set whose value is lower than that of this optimal section SOij and which has a voltage drop that is less than or equal to the determined difference CTmax - CTi. It should be noted that this additional and optional final optimization can sometimes make it possible to replace several optimal sections SOij. It will also be noted that other techniques for determining optimal sections SOij can be used, and in particular heuristic or metaheuristic techniques (such as for example those called "genetic" or "simulated annealing"). It is important to note that the invention can also be considered from the angle of a calculation method, which can be implemented in particular by means of a computing device D of the type of that presented above. The functionalities offered by the implementation of the method according to the invention being identical to those offered by the computing device D presented above, only the combination of main features offered by the method is presented below.

This calculation method comprises two steps (a) and (b). Step (a) consists in determining, for each of the sections Tij of a line Li, theoretical sections STij respectively, suitable for allowing this line Li to have a theoretical minimum mass and a voltage drop CTi less than or equal to a fall. of predetermined (maximum) tension CTmax, then to be determined for each section Tij at least a first section PSij less than its determined theoretical section STij and at least a second section SSij greater than its determined theoretical section STij, from among a set of predefined available sections . Step (b) consists in determining for each section Tij an optimal section SOij among its first (s) PSij and second (s) SSij determined sections, so that the line Li has a minimum (quasi) optimal mass and a fall of voltage CTi less than or equal to the predetermined (maximum) voltage drop CTmax.

The invention is not limited to the embodiments of calculation device and calculation method described above, only by way of example, but it encompasses all the variants that can be considered by those skilled in the art in the the scope of the claims below.

Claims (14)

REVENDICATIONS1. Device (D) for calculating the sections of electrical cable sections (Tij) constituting at least one line (Li) connecting a source of electric current (BA) to an electrical component (Oi) and supporting a predefined voltage drop, characterized in it comprises i) first calculation means (MC1) arranged for determining for each of said sections (Tij) of said line (Li) respective theoretical sections to allow this line (Li) to have a theoretical minimum mass and a voltage drop less than or equal to said predefined voltage drop, then for determining for each section (Tij) at least a first section less than its determined theoretical section and at least a second section greater than its determined theoretical section, from a set of predefined available sections, and ii) second calculation means (MC2) arranged to determine for each section (Tij) an optimum section called pa rmi its first (s) and second (s) determined sections, so that said line (Li) has an optimal minimum mass and a voltage drop less than or equal to said predefined voltage drop. 2. Device according to claim 1, characterized in that said first calculation means (MC1) are arranged to determine the theoretical sections within a subset of sections supporting at least one predefined thermal criterion specific to said line ( Li). 3. Device according to claim 2, characterized in that said first calculation means (MC1) are arranged to form said subset with sections each between a minimum section and a maximum section supporting said predefined thermal criterion. 4. Device according to one of claims 1 to 3, characterized in that said first calculation means (MC1) are arranged to determine the theoretical sections by means of a function respecting predefined conditions and having as parameters at least lengths respective said sections (Tij), said set of predefined available sections, maximum unerésistivity of said sections (Tij), nominal currents to flow respectively in said sections (Tij), and the minimum operating voltage across said line (Li). 5. Device according to one of claims 2 and 3 in combination with claim 4, characterized in that said first calculation means (MC1) are arranged to determine said maximum resistivity of said sections (Tij) according to said predefined thermal criterion supported by said line (Li). 6. Device according to one of claims 4 and 5, characterized in that said first calculation means (MC1) are arranged to use predefined Kuhn-Tucker type conditions. 7. Device according to one of claims 1 to 6, characterized in that said first calculation means (MC1) are arranged to determine for each section (Tij) a single first section lower than its theoretical section determined and a single second section greater than its theoretical section of said set of predefined available sections. 8. Device according to one of claims 1 to 7, characterized in that said second calculation means (MC2) are arranged to determine for each section (Tij) an optimum section among its first (s) and second (s) sections determined by means of a construction technique of a tree whose base is defined by a first section (Ti1) of said line (Li) which is connected to said source of electric current (BA) and for which a second section associated with its theoretical section, determined by said first calculation means (MC1), and wherein each branch constructed represents a possible combination of sections (Tij) of said line (Li). 9. Device according to claim 8, characterized in that said second calculation means (MC2) are arranged to determine each optimum section by means of a so-called "separation and evaluation" technique. 10. Device according to claim 9, characterized in that said second calculation means (MC2) are arranged to interrupt the construction of a branch as soon as it has a voltage drop greater than or equal to said predefined voltage drop. 11. Device according to one of claims 8 to 10, characterized in that said second calculation means (MC2) are arranged, in the presence of several complete branches, to select the one having the smallest mass. 12. Device according to claim 11, characterized in that said second calculation means (MC2) are arranged, after selecting the branch having the smallest mass, to determine the difference between said predefined voltage drop and the fall of voltage presented by the selected branch, then to replace at least one optimal section determined for a section (Tij) by an available section of said predefined set below this optimum section while having a voltage drop less than or equal to said determined difference. 13. A method of calculating sections of sections of electrical cables (Tij) constituting at least one line (Li) connecting a source of electric current (BA) to an electrical member (Oi) and supporting a predefined voltage drop, characterized in that it comprises the following steps: a) determining for each of said sections (Tij) of said line (Li) respective theoretical sections, to allow this line (Li) to have a minimum theoretical mass and a lower voltage drop or equal to said predefined voltage drop, then determining for each section (Tij) at least a first section smaller than its determined theoretical section and at least a second section greater than its determined theoretical section, from among a set of predefined available sections, and b) determining for each section (Tij) a so-called optimal section among its first (s) and second (s) determined sections, so that said ligand ne (Li) has an optimum minimum mass and a voltage drop less than or equal to said predefined voltage drop. 14. Use of the computing device (D) according to one of claims 1 to 12 and the calculation method according to claim 13 for electric lines (Li) of a vehicle.