Method for evaluating a model describing an energy system

Abstract

One aspect of the invention relates to a computer-implemented method of evaluating an aggregated model describing an energy system, the energy system comprising a plurality of energy networks, each energy network comprising a plurality of energy entities, each energy entity being associated with a respective energy production for each energy network, each energy network being associated with a respective energy demand. Figure to be published with the abstract: Figure 2

Description

Title of the invention: Method for evaluating a model describing an energy system TECHNICAL FIELD OF THE INVENTION

[0001] The technical field of the invention is that of energy production and modeling of energy systems, in particular large-scale multi-vector energy systems.

[0002] In particular, the invention relates to the evaluation of the quality of a model of an energy system with respect to the local constraints of the different energy networks making up the energy system. TECHNOLOGICAL BACKGROUND OF THE INVENTION

[0003] Modeling energy systems across multiple regions or countries has become a major issue at a time when energy management and efficiency are at the heart of concerns at national, community and international levels.

[0004] Such models should ideally take into account the structural complexity of energy systems, in particular the fact that they are "multi-vector", in the sense that they bring together different types of networks, including electricity networks, gas networks and heat networks, and that the different networks may be located in different places (two different cities or even two different countries). The objective is to study the coupling between these different networks to optimize the energy system as a whole. Indeed, there are interactions between these networks, via components such as co- and trigeneration systems, heat pumps, fuel cells, electrolysers, etc. The interaction between these networks can increase their flexibility, in particular thanks to the storage systems in place. Each network can therefore benefit from the storage of the other networks thanks to the coupling.

[0005] Ideally, each network should first be modeled in a fine and independent manner, and then the overall model should integrate the interactions between the different networks. This approach is not feasible in practice, due to the complexity of the underlying optimization problem, linked to the large number of networks to be considered. It is therefore necessary to opt for problem simplification methods, for example aggregation methods.

[0006] There are currently models of energy systems at national or European scale, which take into account the coupling between different networks, and which are based on aggregated models. For example, in the context of network modeling In Europe, the different energy networks of each country can be grouped into nodes, one node representing one country. The energy production associated with all the energy networks of a country is modeled by an aggregated production, as is the energy demand. The size of the associated optimization problem is thus reduced, making its solution computationally feasible.

[0007] However, these models are not satisfactory when they integrate heat networks, because they do not necessarily take into account the limitations associated with such networks. A first limitation lies in the multiplicity of heat production means (by combustion of gas, fuel oil, biomass, solar thermal technology, geothermal energy, via heat pumps, etc.), which must be represented and differentiated in the energy model. A second limitation lies in the fact that a heat network is a network that is not distributed (not interconnected) on a national scale. In other words, the production means of a heat network are specific to this heat network and cannot necessarily meet the demand of other heat networks.For example, a means of production located in one city cannot supply heat to another city if the two cities are geographically distant, because there is no means of transporting heat over long distances.

[0008] These limitations have already been noted in different articles using such aggregated models, but no solution has been proposed so far.

[0009] There is therefore a need for a modeling of heat networks which is more faithful to reality and which integrates the technical constraints linked to such networks. Summary of the invention

[0010] The invention provides a solution to the problems mentioned above, by making it possible to evaluate an aggregated model associated with an energy system, and in particular to evaluate the deviations between energy distribution profiles obtained from the aggregated model and local constraints of the energy production units.

[0011] One aspect of the invention thus relates to a computer-implemented method for evaluating an aggregated model describing an energy system, the energy system comprising a plurality of energy networks, each energy network comprising a plurality of energy entities, each energy entity being associated with a respective energy production for at least one energy network, each energy network being associated with a respective energy demand, the method comprising:

[0012] - for each energy network of the plurality of energy networks, receive a respective model associated with said energy network, said model describing a relationship between an energy demand of said energy network and energy production energy entities for said energy network;

[0013] - receive the aggregated model associated with the energy system, the aggregated model comprising at least one relationship between at least one aggregated energy production associated with the energy system and the energy productions of the energy entities;

[0014] - build an evaluation model of the aggregated model from:

[0015] relationships between energy demands and energy productions of energy entities for the plurality of energy networks;

[0016] of the at least one relationship between the at least one aggregated energy production associated with the energy system and the energy productions of the energy entities for the plurality of energy networks, modified to integrate at least one adjustment variable representing a difference between the at least one aggregated energy production associated with the energy system and the energy productions of the energy entities;

[0017] said evaluation model being associated with an objective function dependent on at least one adjustment variable;

[0018] - for a subset of energy networks among the plurality of energy networks getics, receive:

[0019] for each energy network of the subset of energy networks, a respective energy demand value associated with said each energy network;

[0020] at least one aggregated energy production value associated with the subset of energy networks;

[0021] - determine, from the received values ​​of energy demands and production aggregated energy, values ​​of energy production of energy entities and at least one adjustment variable which optimize the objective function;

[0022] - evaluate a quality of the aggregated model from a value of the objective function calculated for the values ​​of the energy production of the energy entities and at least one determined adjustment variable.

[0023] By "energy entity" is meant an entity capable of providing energy to the energy system, and more precisely to one or more energy networks of the energy system. By "energy production" is meant a parameter measuring the energy production capacity of an energy entity.

[0024] Each energy network is associated with a model translating an optimization problem between the energy demand of the energy network and the energy production of the energy entities capable of providing energy to the energy network considered. Each energy network is thus subject to “local” constraints (i.e. at the scale of the energy network) which are part of the model associated with the energy network.

[0025] By "aggregate model" is meant a model associated with the entire energy system, parameterized by data (for example an aggregated demand, a production aggregated, ...) determined from data associated with energy networks. In other words, the energy system is represented by a set of so-called aggregated parameters, which are determined from the parameters of the energy networks. For example, the energy demand of the aggregated model can be equal to the sum of the energy demands of all the energy networks. Similarly, the energy production of the aggregated model can be equal to the sum of the energy productions of the energy networks.

[0026] The aggregated model therefore makes it possible to model a large energy system from aggregated data. The idea is to use a smaller approximate model, where it would not be possible to model the system exactly (because the problem would be impossible to solve).

[0027] The use of aggregated models for large-scale systems is conventional and makes it possible in particular to determine a distribution of energy between the different entities of the system (optimization of the energy mix), or to determine the energy production needs for a given geographical area (for example, district, city, region, country or continent). The quality of the distribution and its use in practice for large-scale systems is therefore directly linked to the quality of the aggregated model.

[0028] Data aggregation is inevitably accompanied by a loss of information, which becomes problematic when the resolution of the aggregated model provides a solution that is not feasible in practice, due to certain local constraints that are not reflected in the aggregated model. The aim of the invention is precisely to evaluate the quality of the aggregated model in terms of feasibility and applicability of the solution obtained. The invention also makes it possible to determine where the gaps between the aggregated model and the local constraints are located, which allows an expert to analyze these locations more precisely and to deduce constraints, which can then be reinjected into the aggregated model in order to improve it.

[0029] The evaluation of the aggregated model is carried out by means of an evaluation model constructed from the parameters of the “local” models (i.e. models associated with the energy networks) and the parameters of the aggregated model, and which integrates one or more adjustment variables guaranteeing the obtaining of a solution.

[0030] This evaluation model is solved on a restricted set of networks (its large-scale resolution would not be feasible). The adjustment variables thus obtained make it possible to determine the quality of the aggregated model.

[0031] For example, the models associated with the plurality of energy networks, the aggregate model and the evaluation model are MILP models.

[0032] In embodiments, the energy networks are heat networks, the energy entities are heat generating entities, the energy demands Getics are heat demands, and energy productions are thermal powers.

[0033] It is understood that the use of the invention for heat networks is one of the possible applications of the invention, but that the invention is not limited to this application.

[0034] For example, each energy entity may be associated with one of a set of entity types, and the at least one aggregated energy output associated with the energy system may include an aggregated energy output for each of the set of entity types.

[0035] The types of entities can be for example: heat pump, electric boiler, biomass boiler, etc.

[0036] In one embodiment, for each energy network, the relationship, in the model associated with the energy network, between the energy demand Drdc of said energy network and the energy productions Pi dr of the energy entities i^rdc for said energy network rdc is, for each time step 1 among a plurality of time steps time : 100371

[0038] where S is an index representing the entity type, and is an index representing an energy entity of type S in the energy network rdc.

[0039] It is therefore understood that all these quantities vary as a function of the time step considered.

[0040] Further, the at least one aggregated energy production value associated with the received energy network subset may comprise a set of aggregated energy production values ​​each associated with a respective entity type 8 from the set of entity types; wherein the at least one adjustment variable comprises, for each energy entity î^c, a respective positive adjustment variable $ and a negative adjustment variable Ô, , {g,rdc ^.c respective. For each energy network rdc and for each time step f, the values ​​Pi„rdr of the energy productions of the determined energy entities can be such that, for each time step 1 among the plurality of time steps: 100411 VT=ZUÆw [ ++]

[0042] The optimization of the objective function can be a minimization, and the objective function can correspond to the sum, over all time steps of the quantities: [00431 p=EÆX [ÿ,-ÆJ-

[0044] In this embodiment, the higher the value of the objective function calculated for the The higher the values ​​of the energy production of the energy entities and of at least one determined adjustment variable, the worse the quality of the aggregated model.

[0045] Of course, the invention is not limited to the above application, and can be applied to any energy system requiring aggregated modeling.

[0046] In particular, in embodiments, the energy networks are fleets of electric vehicles, the energy entities are electric batteries, the energy demands are electricity demands and the energy productions are electric powers.

[0047] Another aspect of the invention relates to a method for optimizing an aggregated model describing an energy system, the energy system comprising a plurality of energy networks, each energy network comprising a plurality of energy entities, each energy entity being associated with a respective energy production for at least one energy network, each energy network being associated with a respective energy demand, the method comprising:

[0048] - implement the method of evaluating the aggregated model describing the system energy defined above;

[0049] - use the values ​​of energy productions of energy entities and of the at least one adjustment variable that optimizes the objective function to determine an additional relationship between the at least one aggregate energy production associated with the energy system and the energy productions of the energy entities for the plurality of energy networks;

[0050] - update the aggregated model associated with the energy system with the sup relation additional determined.

[0051] The determination of the additional relationship (i.e. the local constraint) can be made by an expert, from the analysis of the results obtained during the resolution of the evaluation model.

[0052] Another aspect of the invention relates to a device for evaluating an aggregated model describing an energy system, the energy system comprising a plurality of energy networks, each energy network comprising a plurality of energy entities, each energy entity being associated with a respective energy production for at least one energy network, each energy network being associated with a respective energy demand, the device being configured to implement the method for evaluating a model of the energy system above.

[0053] A computer program, implementing all or part of the method described above, installed on pre-existing equipment, is in itself advantageous.

[0054] Thus, the present invention also relates to a computer program comprising instructions for implementing certain steps of the method for evaluating a model of an energy system previously described, when this program is executed by a processor.

[0055] This program may use any programming language (for example, an object-oriented language or other), and be in the form of interpretable source code, partially compiled code or fully compiled code.

[0056] The [Fig.2] described in detail below can form the flowchart of the general algorithm of such a computer program.

[0057] The invention and its various applications will be better understood upon reading the following description and examining the accompanying figures. BRIEF DESCRIPTION OF THE FIGURES

[0058] Other characteristics and advantages of the invention will appear on reading the description, which can be read in conjunction with the figures. These figures are presented for information purposes only and are in no way limiting of the invention.

[0059] [Fig.l] [Fig.l] illustrates an example of aggregated modeling of a plurality of heat networks located in different geographical areas, which themselves interact with each other via electrical networks.

[0060] [Fig.2] [Fig.2] represents an example of a flowchart of an evaluation method of a model describing an energy system, according to one embodiment of the invention.

[0061] [Fig.3] [Fig.3] represents models of heat networks and an aggregated model.

[0062] [Fig.4] [Fig.4] illustrates production profiles obtained when solving a aggregate model.

[0063] [Fig.5a] [Fig.5a] illustrates an example of variations of the penalty variable of the MILP time evaluation problem in one embodiment of the invention.

[0064] [Fig.5b] [Fig.5b] represents an example of variation curves, hour by hour, on a particular day, the penalty variable and the adjustment variables.

[0065] [Fig.6a] [Fig.6a] illustrates an improvement of the aggregated model with the addition of a constraint determined from the invention evaluation model.

[0066] [Fig.6b] [Fig.6b] represents the variation curves, hour by hour, on a particular day, the penalty variable and the adjustment variables after adding a constraint determined from the invention evaluation model.

[0067] [Fig.7] [Fig.7] represents a device for evaluating an aggregated model describing an energy system, according to one embodiment of the invention. DETAILED DESCRIPTION

[0068] The present invention has applications in several fields requiring simplification of an optimization problem using aggregated models.

[0069] [Fig. 1] illustrates an example of an application for which the present invention can be used. [Fig. 1] thus illustrates an example of aggregated modeling of a plurality of heat networks located in different geographical areas.

[0070] For example, in the context of modeling an energy system on a European scale, the different geographical zones 11, 12 may represent different European countries (such as France, Germany, etc.). Each geographical zone 11, 12 comprises a respective plurality of heat networks 21, 22, 23. The number of heat networks 21, 22, 23 may vary from one geographical zone 11, 12 to another, and may range from several tens to several hundreds, or even several thousands. For example, in France, there are approximately 700 heat networks.

[0071] To model the energy system on a European scale, it is possible, for each geographical area 11, 12, to aggregate all the heat networks 21, 22, 23 of this geographical area 11, 12, to create a node 11', 12', each node 11', 12' therefore being associated with a respective geographical area 11, 12 and representing the heat networks of the respective geographical area 11, 12. A model 30 is thus obtained comprising as many nodes 11', 12' as there are geographical areas 11, 12. The lines connecting the nodes 11', 12' represent the infrastructures (typically electricity and gas networks) between the different geographical areas 11, 12.

[0072] In this example, only the heat networks are represented within zones 11 and 12, but the energy model can integrate other types of networks, for example electricity and / or gas networks.

[0073] Each heat network 21, 22, 23 is represented by a respective model that links the heat production by the heat network with the heat demand in the heat network. The model can integrate other parameters, such as the storage capacity of the heat network. For example, each heat network can be modeled by a MILP model (for “Mixed-Integer Linear Programming” in English, or “partially integer linear programming” in French). This type of model is based on an optimization of a cost function with linear constraints and in which and in which a part of the variables are integer variables.

[0074] For each heat network, the associated MILP model makes it possible to solve an optimization problem within the heat network between heat production and heat demand. In the invention, the MILP model is assumed to be known for each heat network.

[0075] As mentioned below, the aggregation of the heat networks 21, 22, 23 by geographical zone 11, 12 is necessary to make the problem of optimizing the energy system on the scale of several geographical zones 11, 12 solvable.

[0076] To carry out the aggregation of the Nrdc heat networks 21, 22, 23 of a geographical area- graph 11, 12 data:

[0077] - the Nrdc heat demands of the Nrdc heat networks are represented by a only heat demand;

[0078] - the Nrdc heat production plants of the Nrdc heat networks are re presented by a single heat production plant;

[0079] - the Nrdc heat storage capacities (if applicable) of the Nrdc heat networks are represented by a single storage capacity.

[0080] The objective is thus to represent all the Nrdc heat networks, modeled by Nrdc respective MILP models, by a single aggregated MILP optimization model.

[0081] The invention aims to evaluate an aggregated MILP model with respect to a set of physical constraints inherent to the heat networks considered (in particular the constraints inherent to the heat networks, such as the absence of interconnection), using adjustment variables, or "slack" variables in English. The temporal variation of these slack variables also indicates which variables, in the aggregated MILP model, are not correctly described. A study by an expert of these variables can then make it possible to determine constraints which are then reinjected into the aggregated model, and thus to obtain an updated aggregated MILP model, which is more faithful to physical reality, and which can in turn itself be evaluated and possibly updated by the same strategy.

[0082] It is noted that [Fig.l] represents an example of application among others. The invention can be applied to any system involving a plurality of entities distributed into several groups. For example, the invention can be applied to a modeling of a fleet of electric vehicles by an equivalent (aggregated) electric battery model.

[0083] [Fig.2] represents an example of a flowchart of a method for evaluating a model describing an energy system, according to an embodiment of the invention.

[0084] The energy system comprises a plurality of energy entities. For the sake of simplification, [Fig.2] is described in the case where the energy entities are heat networks, but it is understood that the invention can be applied to any type of energy entity, in particular electric vehicle batteries.

[0085] During a step 210, a plurality of MILP models are received, each MILP model being associated with a respective heat network and representing a link between a heat demand of a heat network and a heat production capacity of the heat network.

[0086] For example, the plurality of Nrdc (Nrdc being a non-zero natural integer) heat networks may comprise a plurality of thermal generators, each thermal generator being associated with a certain type ^2' ' ' ' ' ^G- For example, types of thermal generators may be: heat pump, electric boiler, boiler biomass, etc.

[0087] Each heat network rdc comprises a number G of thermal generators of type Sh where Gj rdc is a natural integer (which can be zero).

[0088] The MILP model associated with each ground floor heating network can be associated with the following optimization problem:

[0089] VA vr <fc W

[0090] VI, VrJ<; V#, Vlft„,„ (2)

[0091] v / .VrÆ-, (3)

[0092] where:

[0093] - rdc designates a heat network among all the Nrdc heat networks,

[0094] - p [ pp pl denotes a type of thermal generator,

[0095] ■ G.rdc denotes the index of the production unit i of the thermal generator 8 in the ground floor network,

[0096] - Pi.,rdc[ t] denotes the thermal power sent by the production unit i of the generator thermal generator 8 of the ground floor network at the moment,

[0097] - Drdc[t ] denotes the heat demand of the rdc network at time f

[0098] - designates the nominal power of the thermal generator 8 in the ground floor network,

[0099] - designates the minimum power of the thermal generator 8 in the ground floor network,

[0100] - denotes a binary variable indicating whether the generator's production unit i lg,rdc thermal 8 of the ground floor network is in operation or not.

[0101] ! represents time, which is usually a discrete variable. For example fE {tj, G ... ] °where two successive instants 6, can be separated by a constant time step, for example 1 hour.

[0102] Equation (1) above reflects the fact that at each instant z, the heat demand in the ground floor network is equal to the sum of all the thermal powers sent by all the production units i of all the thermal generators 8 of the ground floor network. In other words, equation (1) above reflects a balance between the heat demand of the ground floor network and the heat production capacity of the ground floor heating network.

[0103] Equation (2) reflects the fact that, for each production unit i of each thermal generator 8 of each heat network rdc, the thermal power sent at each instant? is less than or equal to the nominal power (maximum power) of the generator 8. Equation (3) reflects the fact that, for each production unit i of each thermal generator 8 of each heat network rdc, the thermal power sent at each instant? is, when the production unit i is in operation operation, greater than or equal to the minimum power of the generator S (which can be equal for example to the minimum of all the powers associated with the different production units i of the thermal generator &).

[0104] It is noted that equations (1)-(3) represent a MILP model of the rdc network "simple", in which we seek to achieve a balance between heat supply and demand, without additional constraints (ramps, minimum time during which a generator is switched on or off, etc.). It is noted that other, more complex models incorporating additional constraints can be used. The example MILP model (1)-(3) indicated above is provided to show that such a model is always available.

[0105] Returning to Figure 2, at step 220, an aggregated MILP model representing all N ground floor heating networks is obtained.

[0106] In the aggregated MILP model, the N rdc heat networks are grouped into a single aggregated network associated with an aggregated heat demand Dagieg, an energy ^fsres contained in the storage of the aggregated network and a power set p^g,es representing the thermal powers of the aggregated S-type generators.

[0107] A representation of the MILP models of the heat networks and the aggregated MILP model is provided in Figure 3. Each MILP model 310a, 310b is associated with a respective heat network. In the example of Figure 3, the different types of heat generators are denoted ^i, ^2, ^3. It is assumed that there are Gi r^c generators of type Sj in the ground floor network.

[0108] The MILP model 310a, 310b models the link between the thermal powers t ] sent from unit j of the generator of the rdc network at each instant1 and the heat demand Drdc [ t ] of the rdc network at each instantr.

[0109] The MILP models 310a, 310b are aggregated into an aggregated MILP model 320. In this aggregated model 320, the 8j type generators of all the heat networks are grouped into one or more units of an aggregated generator of type ^j, noted , each associated with an aggregate thermal power], and the demand for heat t] of the aggregated network at each instant f is determined from the Nrdc heat demands / | of the different rdc networks at each instant f. By example, the heat demand Da8>e8[ t] of the aggregated network is equal to the sum of the Nrdc heat demands t\ of the different rdc networks.

[0110] Ideally, the aggregated MILP model perfectly represents all networks of modeled heat. Thus, the aggregated power can be distributed across all S generators in all rdc networks. In other words, if local constraints are not taken into account, the aggregated power f ] of each S-type generator aggregated at any time1 can be written: [Olin vz, w

[0112] However, in practice, equality (4) cannot be verified due to existing local constraints. For this reason, during a step 230, an evaluation model is introduced, to take these local constraints into account. Thus, during step 230, a MILP model called "evaluation model" or "evaluation MILP model" is constructed. This model groups together a smaller number Neval < Nrdc of heat networks in order to find a decomposition of the aggregated power] into several local generators from each ground floor heat network, and respecting certain local constraints: the local heat demand Drdc and technical constraints on the local generators if,^-

[0113] The MILP evaluation model can thus be written (with the variables in bold representing optimization variables): 101141 (1)

[0115] v t. V rdc, V g, V i.^,, P,-, Jz] < pjï. (2)

[0116] vt, V rdc, V g, V PW[Z] 1 (3) far] vi. (*)

[0118] where g^ pj denotes a positive adjustment variable, or “slack” variable, [ ?] denotes a negative slack variable, g^ tj takes real values positive or zero and ôignic [ / ] takes negative or zero values.

[0119] As mentioned above, equations (1)-(3) above are provided as an example and represent a "simple" model, but other constraints can be introduced into the above model.

[0120] The objective is to seek a decomposition of the power of an aggregated generator p“8>eg into a sum of powers of local generators (actually present on the heat networks) Pi (equation 4, transformed into 4' to take into account the fact that a “perfect” decomposition is not always possible), and which respect a set of local constraints: technical constraints on the generators (maximum power by equation 2, minimum power by equation 3) and constraint of satisfaction of the heat demand at the local scale (equation 1).

[0121] From the slack variables rf [?], , it is possible to define a function "penalty" / ?[ which represents the sum of the penalties, that is to say the sum of the deviations between the aggregated model and the local constraints at each moment: [heard] vz, (5)

[0123] The optimization problem to be solved is a problem of minimizing the penalty function, that is to say that the optimization problem is associated with the objective function:

[0124] = min^2 J ODJ J

[0125] The variables slack / J, 11 are introduced so that the problem optimization above always has a solution. These slack variables quantify a deviation and a power adjustment on the aggregate powers so that the local constraints (1), (2) and (3) can be respected

[0126] The quantity corresponds to a positive deviation: the aggregated power, from the aggregated MILP model, is too large for local constraints to be respected (for example maximum power). In this case, a positive quantity is added to the local power (which is subject to maximum power) in order to obtain the quantity pafre8.

[0127] Conversely, the quantity <5,- corresponds to a negative deviation, for example in the case of a local minimum power greater than the imposed aggregate power: in this case, the adequate quantity is subtracted from the local power to obtain the imposed aggregate quantity.

[0128] The variables in bold in the above equations correspond to the optimization variables, i.e. the variables whose values ​​are determined during optimization. Thus, the optimization problem above amounts to determining, for values ​​PJ^dc ct r 1 ^x^es' 'cs values ​​of the variables

[0129] This optimization problem is therefore solved, in step 235 of Figure 2, on a number Ni;val of heat networks smaller than the total number Nrdc of heat networks. For example, the number Neval can be of the order of a few units to a few tens, preferably of the order of tens (for example between 3 and 10). This makes it possible to quickly obtain a solution to the problem and to draw conclusions. If too large a number of networks to be aggregated is chosen, the risk is to have a long convergence towards a solution, or even no convergence at all. The objective here is to quantify infeasibilities which arise from the aggregated formulation, and these infeasibilities already exist for a small number of networks.

[0130] In a step 240, the solutions obtained in step 235, in particular the temporal variation of the slack variables, are analyzed for each time step. Non-zero values ​​of the slack variables reflect an adjustment of the aggregated powers so that the local constraints are respected. In other words, when the slack variables are non-zero, this means that the aggregated model is not compatible with the

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137] - if the objective function n), this means that the solutions of the local constraints, from the models obtained in step 210. Thus, in step 240, the analysis of the slack variables makes it possible to evaluate whether the aggregated model is compatible with the local constraints (and therefore the physical constraints at the scale of the heat networks) or whether, on the contrary, it is not feasible in practice. The advantage is that these slack variables are associated with a type of generator, allowing for a detailed analysis. The value of the objective function of the optimization problem associated with the MILP evaluation model can thus be seen as a quantifier of the quality of the aggregated solution obtained (and therefore of the aggregated model): is zero (£fp[t] = aggregated model (aggregate demand and aggregate generator power) are perfectly decomposed in the Neval heat networks considered. This therefore means that the aggregated MILP model correctly describes the behavior of the Neval heat networks; - if this objective function is not zero, this means that there is no decomposition of the power of the aggregated generators in the heat networks, respecting the local constraints (minimum power, maximum power and / or local demand). The value of the objective function then corresponds to the difference between a feasible solution and the aggregated solution tested. Furthermore, on time steps where the slack variable(s) are non-zero, a specific analysis of the behavior of the aggregated problem can be performed, with the aim of establishing new constraints to be added to the aggregated optimization problem. Thus, at step 250, an expert can determine one or more new constraints by analyzing more precisely the time steps over which the slack variables take non-zero values. This analysis can also be carried out using real operating data from the heat networks, for example the effective values ​​of the powers Pû)yj,c [ / ] during the analyzed time steps (historical operating data). These constraints, obtained from a limited number of heat networks, can then be reinjected into the aggregated MILP model, to obtain an improved aggregated MILP model (arrow connecting step 250 to step 220 in [Fig.2]). It is indeed noted that, even if the constraints are determined from the analysis of a limited number of heat networks, they are valid in a general manner, on all heat networks. The new constraints determined can therefore be added to the aggregated model, which can be solved on a large number of heat networks. It is thus possible to iterate between the aggregate problem, the MILP solution qualification problem and the detection / addition of constraints to improve the model aggregated, and move closer to non-aggregated modeling, more in line with physical reality.

[0138] It is noted that the modeling of an energy system is useful, for example, to determine a distribution of energy production between different energy generators of the energy system. For example, an aggregated MILP model of the plurality of heat networks over a geographical territory (for example at the scale of a country) thus makes it possible to determine, as a function of the energy demands, storage and production capacities of the different generators present in the territory, an optimal distribution of energy production between the different generators. The closer the aggregated MILP model is to the local MILP models, the more the distribution obtained is applicable in reality.

[0139] The invention is now illustrated by an example of application in which the energy system comprises three heat networks denoted H1, H2 and H3. These three heat networks correspond respectively to three cities: Strasbourg, Bordeaux and Montpellier. It is assumed that each heat network H1, H2, H3 is composed of three heat pumps (PAC), two electric boilers (PtH), two biomass power plants (B 10) and a sensible heat storage, the characteristics of which are presented in the table below: Network Hl Network H2 Network H3 Heat pumps (HP) Number of PACs 3 3 3 Pmax PAC [MW] 20 15 10 Pmin PAC [MW] 4 3 2 Efficiency PAC [-] 3.5 3.6 3.6 Electric boilers (PtH) Number of PtH 2 2 2 Pmax PtH [MW] 40 40 40 Pmin PtH [MW] 2 2 2 Efficiency PtH [-] 0.99 0.99 0.99 Biomass boilers (BIO) Number of bio 2 2 2 Pmax bio [MW] 75 60 45 Pmin bio [MW] 30 24 18 Efficiency BIO [-] 0.97 0.96 0.95 Sensible heat storage (STO) Max energy [MWh] 200 180 150 Pmax [MW] 10 9 8

[0140] In the table above, Pmax denotes the nominal power in megawatts (MW), Pmin the minimum power in megawatts (MW), the efficiency of a heat pump is defined by its coefficient of performance (COP), which corresponds to the ratio between the useful energy (heat returned for heating) and the energy consumed to operate the heat pump, and the efficiency of a PtH or a BIO is defined by its efficiency, i.e. the ratio between the heat produced and the energy consumed to ensure this production. “Max energy” represents the maximum energy stored, expressed in megawatt hours.

[0141] In this example, an aggregated model is chosen in which the production plants are aggregated by technology, whose “intensive” type parameterization corresponds to the average parameterization of the H2 network. Thus, it is considered that the aggregated model includes 9 “aggregated” H2 type PAC generator units, 6 “aggregated” H2 type PtH generator units and 6 “aggregated” H2 type BIO generator units. The aggregated demand corresponds to the sum of the demands of the three networks H1, H2, H3 and the aggregated storage corresponds to the sum of the storages of the three networks H1, H2 and H3. The values ​​thus obtained are presented in the table below: Aggregate demand Sum of the 3 demands Aggregate PAC Pmin: 3 MW Pmax: 15 MW Aggregate PtH Pmin: 2 MW Pmax: 40 MW Aggregate BIO Pmin: 24 MW Pmax: 60 MW Aggregate STO Emax: 530 MWh Pmax: 27 MW

[0142] It is understood that other settings could be used for the aggregated model.

[0143] The resolution of the above aggregated model is then implemented, and the production profiles of the aggregated generators allowing to minimize the cost function associated with the optimization problem are determined. [Fig.4] illustrates some production profiles thus obtained. In particular, Figure 4a represents the production profile obtained for the aggregated electric boiler Figure 4b represents the profile production profile obtained for the aggregated biomass boiler and Figure 4c represents the production profile obtained by the aggregated heat pump. These profiles correspond to the hourly production, in megawatts, of each aggregated generator to obtain the aggregated heat demand.

[0144] These results do not allow us to directly establish whether they are physically feasible at the local scale of independent heat networks. This is why the invention proposes to reinject the production profiles obtained into the MILP evaluation model, and to analyze the values ​​of the penalty variable over time.

[0145] [Fig.5a] represents the variations of the penalty variable of the MILP evaluation problem over time. [Fig.5b] represents the variations of several slack variables and the penalty variable (sum of the slack variables) on a particular day.

[0146] In [Fig.5a], each "peak" of the curve represents a time step over which the penalty variable has a value that corresponds to a local maximum and therefore represents a problem of adequacy between the aggregated model and the physical constraints of the different generators. For example, the curve of the penalty variable has a peak at the value t = 2500 h, which corresponds to a particular day, shown in more detail in [Fig.5b].

[0147] [Fig.5b] thus represents the variation curves, hour by hour, on a particular day, of the penalty variable (in solid lines), of the positive slack variable associated with the aggregated biomass boiler (in dotted lines), of the positive slack variable associated with the aggregated electric boiler (in dashes), and of the negative slack variable associated with the aggregated heat pump (in dashes separated by points).

[0148] It is clear from [Fig.5b] that:

[0149] - the positive slack variable associated with the aggregated biomass boiler takes values ​​which are strictly positive over almost all time steps of the day studied;

[0150] - the positive slack variable associated with the aggregated electric boiler takes values ​​that are strictly positive over certain time steps during the day studied; and

[0151] - the negative slack variable associated with the aggregated heat pump takes values which are strictly negative only over certain time steps of the day studied (and zero the rest of the time).

[0152] This means that heat pumps are favored, in the aggregated model, because of their efficiency, and that certain heat pumps in a network actually supply, according to the aggregated model, another network (which is physically impossible), to the detriment of biomass and electric boilers.

[0153] By analyzing the solution of the aggregate problem (represented in [Fig.4]) and the data complementary data relating to the different networks (in particular the heat demands on the day in question), it can be seen that the PAC generator group is at its maximum power, i.e. 135 MW, while the heat demands of the three networks are respectively 68 MW, 23 MW and 50 MW. Locally on the H2 network, the power of the PACs is broken down into 3x15=45 MW which is greater than 23+9 MW, i.e. the local demand plus the quantity of energy storable over a time step in the H2 network.

[0154] This information allows an expert to identify a maximum power constraint to be added to the aggregated problem. This constraint consists of limiting the power of an aggregated generator relative to its maximum locally available power and the local thermal demand, taking into account a quantity of storable energy, which can be translated mathematically as:

[0155] v& Vf, (Cl)

[0156] Adding this new constraint to the aggregated MILP model makes it possible to improve the latter, making it more consistent with the constraints associated with the different heat networks. This improvement can be seen in Figures 6a and 6b. [Fig.6a] represents the variation in power of the aggregated PAC generator over the day considered above, without the Cl constraint (in solid line with dots above) and with the Cl constraint (in solid line with crosses above). It can be seen that the power is no longer equal to the maximum power over all time steps, but that it fluctuates.

[0157] [Fig.6b] represents the variation curves, hour by hour, on the same day as in [Fig.5b], of the penalty variable (in solid line), of the positive slack variable associated with the aggregated biomass boiler (in dotted line), of the positive slack variable associated with the aggregated electric boiler (in dashed line), and of the negative slack variable associated with the aggregated heat pump (in dashed line separated by dots), after the addition of the CL constraint

[0158] We see in [Fig.6b] that the value of the penalty variable is generally lower with the addition of the Cl constraint in the model, than in [Fig.5b], which means that the aggregated model with the new Cl constraint allows a better representation of the physical constraints inherent in the different heat networks.

[0159] It can also be seen in [Fig.6b] that the values ​​of the slack variables are globally closer to zero than in [Fig.5b], which also illustrates the fact that the aggregated model integrating the new constraint is thus improved.

[0160] Here again, the analysis of the solution to the new aggregated problem and of additional data relating to the different networks can make it possible to further refine the model with new constraints, for example a C2 constraint taking into account the behavior of aggregated storage (and no longer only at the local scale, as in Cl), or a constraint C3 taking into account the fact that certain generators are necessarily called upon at a local scale if the maximum power of the other local generators is not sufficient to satisfy the local heat demand. Such constraints can for example be written:

[0161] vj, v,, + (cg

[0162] vS VI, (es)

[0163] Several aggregated models were compared, depending on whether or not they integrate certain constraints. In particular, the following four scenarios (A, B, C, D) were compared: A Without additional constraints B With Cl C With C1+C2 D With C1+C2+C3

[0164] The quality of the different models is evaluated by comparing the square roots of the root mean square error (RMSE) of the penalty variable over the different time steps normalized by its maximum value. Fobj [MW] Normalized Fobj Average penalties [MW] Max penalties [MW] Normalized RMSE A 26121 100% 3 74 0.2360 B 16093 62% 1.84 56 0.2238 C 14801 57% 1.7 56 0.2235 D 14315 55% 1.64 56 0.2237

[0165] These results confirm the effect of adding the new constraints identified in the aggregated model: the objective function (i.e. the sum of the penalties) of the MILP solution qualification problem decreases by almost 50% thanks to the addition of the constraints, and the costs of the aggregated system thus approach the costs of the non-aggregated system.

[0166] [Fig.7] represents a device for evaluating an aggregated model describing a energy system, according to one or more embodiments of the invention.

[0167] In these embodiments, the device comprises a computer 700, comprising a memory 701 for storing instructions allowing the implementation of the method, the parameters of the different models and possibly additional operating data, and temporary data for carrying out different steps of the method described previously.

[0168] The computer 700 further comprises a circuit 702. This circuit may be, for example, a processor capable of interpreting instructions in the form of a computer program, an electronic card whose steps of the method of the invention are described in the silicon, or even a programmable electronic chip such as an FPGA chip (for “Field-Programmable Gate Array” in English).

[0169] The computer 700 comprises an input interface 703 for receiving different MILP models associated with the different electrical networks and an aggregated MILP model, and an output interface 704 for providing the values ​​of the slack variables. Finally, the computer may comprise, to allow easy interaction with a user, a screen 705 and a keyboard 706. Of course, the keyboard is optional, particularly in the context of a computer having the form of a touch pad, for example.

[0170] Furthermore, the functional diagram presented in [Fig.2] is a typical example of a program of which certain instructions can be carried out using the device described. In this respect, [Fig.2] can correspond to the flowchart of the general algorithm of a computer program within the meaning of the invention.

[0171] Of course, the present invention is not limited to the embodiments described above as examples. It extends to other variants and other applications. For example, as mentioned above, the invention can be applied to other energy systems, such as fleets of electric vehicles and the use of individual batteries for services to the electricity grid. The large number of electric vehicles makes the problem complex. For this reason, the fleet of electric vehicles can be modeled by an equivalent battery model, with maximum and minimum charge and discharge profiles, depending on the behavior of each individual battery. The method described above makes it possible in particular to validate the modeling of an aggregated battery or, where appropriate, to quantify the differences in solutions between an aggregated battery modeling and individual batteries.

Claims

Claims

1. A computer-implemented method of evaluating an aggregated model describing an energy system, the energy system comprising a plurality of energy networks (21, 22, 23), each energy network comprising a plurality of energy entities, each energy entity being associated with a respective energy production for at least one energy network, each energy network being associated with a respective energy demand, the method comprising: - for each energy network of the plurality of energy networks (21, 22, 23), receiving (210) a respective model (310a, 310b) associated with said energy network, said model describing a relationship between an energy demand of said energy network and the energy productions of the energy entities for said energy network; - receiving (220) the aggregated model (320) associated with the energy system, the aggregated model comprising at least one relationship between at least one aggregated energy production associated with the energy system and the energy productions of the energy entities; - construct (230) an evaluation model of the aggregated model from: the relationships between the energy demands and the energy productions of the energy entities for the plurality of energy networks (21, 22, 23); of the at least one relationship between the at least one aggregated energy production associated with the energy system and the energy productions of the energy entities for the plurality of energy networks (21, 22, 23); said evaluation model integrating at least one adjustment variable representing a difference between the at least one aggregated energy production associated with the energy system and the energy production of the energy entities; said evaluation model being associated with an objective function dependent on at least one adjustment variable; - for a subset of energy networks among the plurality of energy networks (21, 22, 23), receiving: for each energy network of the subset of energy networks, a respective energy demand value associated with said each energy network; at least one aggregated energy production value associated with the sub- set of energy networks; - determining (235), from the received values ​​of energy demands and aggregated energy production, values ​​of the energy productions of the energy entities and of the at least one adjustment variable which optimize the objective function; - evaluating (240) a quality of the aggregated model from a value of the objective function calculated for the values ​​of the energy productions of the energy entities and of the at least one determined adjustment variable.

2. The method of claim 1, wherein the models (310a, 310b) associated with the plurality of energy networks (21, 22, 23), the aggregated model (320) and the evaluation model are MILP models.

3. Method according to claim 1 or 2, in which the energy networks (21, 22, 23) are heat networks, the energy entities are heat generating entities, the energy demands are heat demands and the energy productions are thermal powers.

4. The method of claim 3, wherein each energy entity is associated with one of a set of entity types, wherein the at least one aggregated energy output associated with the energy system comprises an aggregated energy output for each of the set of entity types.

5. Method according to claim 4, in which, for each energy network, the relationship, in the model (310a, 310b) associated with the energy network, between the energy demand Drdc of said energy network and the energy productions Pigrdc of the energy entities ig^ for said energy network rdc is, for each time step 1 among a plurality of time steps: r\ yy p. rdc where S is an index representing the type of entity, and is an index re representing an energy entity of type S in the energy network rdc.

6. The method of claim 5, wherein the at least one aggregated energy production value associated with the received subset of energy networks (21, 22, 23) comprises a set of aggregated energy production values ​​each associated with a respective entity type * from the set of entity types; ... least one adjustment variable comprises, for each energy entity, a respective positive adjustment variable ÿ and a respective negative adjustment variable ôi„rdr; in which, for each energy network rdc and for each time step \ the values ​​Pi dc of the energy productions of the determined energy entities are such that, for each time step 1 among the plurality of time steps: pa / res^ yr 1^, +<5î , / 1 in which the optimization of the objective function is a minimization, and the objective function corresponds to the sum, over all the time steps 1 , of the quantities:

7. Method according to the preceding claim, in which the higher the value of the objective function calculated for the values ​​of the energy productions of the energy entities and of the at least one determined adjustment variable, the worse the quality of the aggregated model (320).

8. A method according to claim 1 or 2, wherein the energy networks (21, 22, 23) are fleets of electric vehicles, the energy entities are electric batteries, the energy demands are electricity demands and the energy productions are electric powers.

9. A method for optimizing an aggregated model (320) describing an energy system, the energy system comprising a plurality of energy networks (21, 22, 23), each energy network comprising a plurality of energy entities, each energy entity being associated with a respective energy production for at least one energy network, each energy network being associated with a respective energy demand, the method comprising: - implementing the method for evaluating the aggregated model (320) describing the energy system according to one of claims 1 to 8; - using the values ​​of the energy productions of the energy entities and the at least one adjustment variable which optimize the objective function to determine a further relationship between the at least one aggregated energy production associated with the energy system and the energy productions of the energy entities for the plurality of energy networks (21, 22, 23); - updating the aggregated model (320) associated with the energy system with the determined additional relationship.

10. Device for evaluating an aggregated model describing an energy system, the energy system comprising a plurality of energy networks (21, 22, 23), each energy network comprising a plurality of energy entities, each energy entity being associated with a respective energy production for at least one energy network, each energy network being associated with a respective energy demand, the device being configured to implement the method according to one of claims 1 to 8.

11. Computer program product comprising instructions for implementing the method according to one of claims 1 to 8 when this program is executed by a processor.

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