Method for evaluating a model describing an energy system

Abstract

One aspect of the invention relates to a computer-implemented method for evaluating an aggregate 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 composing the energy system. TECHNOLOGICAL BACKGROUND OF THE INVENTION

[0003] The modelling of energy systems on the scale of several regions or several countries has become a major issue at a time when energy management and efficiency are at the heart of concerns at the national, community and international level.

[0004] Such models should ideally take into account the structural complexity of energy systems, particularly their "multi-vector" nature, meaning they encompass different types of networks, including electricity, gas, and heat networks, which 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 cogeneration and trigeneration systems, heat pumps, fuel cells, electrolyzers, etc. The interaction between these networks can enhance their flexibility, especially through existing storage systems. Each network can then benefit from the storage capacity of the other networks thanks to this coupling.

[0005] Ideally, each network should first be modeled in detail and independently, 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 the national or European level, which take into account the coupling between different networks, and which are based on aggregated models. For example, within the framework of network modeling In Europe, the various energy networks of each country can be grouped into nodes, with each node representing a country. The energy production associated with all the energy networks of a country is modeled by an aggregate 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 incorporate district heating networks, as they do not necessarily take into account the limitations associated with such networks. A first limitation lies in the multiplicity of heat production methods (gas, fuel oil, biomass combustion, solar thermal technology, geothermal energy, heat pumps, etc.), which must be represented and differentiated in the energy model. A second limitation lies in the fact that a district heating network is a non-distributed (non-interconnected) network at the national level. In other words, the production methods of a district heating network are specific to that network and cannot necessarily meet the demand of other district heating 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 various articles using such aggregated models, but no solution has been proposed so far.

[0009] There is therefore a need for a model of heat networks that is more faithful to reality and that incorporates the technical constraints related to such networks. Summary of the invention

[0010] The invention offers a solution to the problems mentioned above, by allowing the evaluation of an aggregate model associated with an energy system, and in particular the evaluation of the discrepancies between energy distribution profiles obtained from the aggregate model and the local constraints of the energy production units.

[0011] One aspect of the invention thus relates to a computer-implemented method for evaluating an aggregate 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 aggregate model associated with the energy system, the aggregate model including at least one relationship between at least one aggregate energy production associated with the energy system and the energy productions of the energy entities;

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

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

[0016] of at least one relationship between 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, modified to incorporate at least one adjustment variable representing a difference between at least one aggregate 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 depending 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 aggregate energy production value associated with the subset of energy networks;

[0021] - determine, from the received values ​​of energy demand and production aggregate energy, the values ​​of energy production of energy entities and at least one adjustment variable that optimizes the objective function;

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

[0023] The term "energy entity" means an entity capable of supplying energy to the energy system, and more specifically to one or more energy networks of the energy system. "Energy production" means a parameter measuring the energy production capacity of an energy entity.

[0024] Each energy network is associated with a model that represents an optimization problem between the energy demand of the energy network and the energy production of the energy entities capable of supplying energy to the energy network in question. 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, aggregate demand, production aggregated, ...) determined from data associated with energy networks. In other words, the energy system is represented by a set of so-called aggregate parameters, which are determined from the parameters of the energy networks. For example, the energy demand of the aggregate model can be equal to the sum of the energy demands of all the energy networks. Similarly, the energy production of the aggregate model can be equal to the sum of the energy productions of the energy networks.

[0026] The aggregate model thus 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 aggregate models for large-scale systems is common and allows, in particular, the determination of energy allocation among the different entities of the system (optimization of the energy mix), or the determination of energy production needs for a given geographical area (e.g., neighborhood, city, region, country, or continent). The quality of the allocation and its practical application for large-scale systems is therefore directly linked to the quality of the aggregate model.

[0028] Data aggregation inevitably involves a loss of information, which becomes problematic when solving the aggregated model yields a solution that is not practically feasible due to certain local constraints that are not reflected in the aggregated model. The purpose of the invention is precisely to evaluate the quality of the aggregated model in terms of the feasibility and applicability of the resulting solution. Furthermore, the invention makes it possible to determine where the discrepancies lie between the aggregated model and the local constraints, allowing an expert to analyze these discrepancies in greater detail and deduce constraints that can then be incorporated back into the aggregated model to improve it.

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

[0030] This evaluation model is solved on a limited set of networks (its large-scale solution would not be feasible). The adjustment variables thus obtained make it possible to determine the quality of the aggregate 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 some embodiments, the energy networks are heat networks, the energy entities are heat-generating entities, and the energy demands Energy demands are heat demands, and energy productions are thermal power.

[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 can be associated with one type of entity from a set of entity types, and the at least one aggregate energy production associated with the energy system can include an aggregate energy production for each type of entity from 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 steps of time : 100371

[0038] where S is an index representing the type of entity, 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 according to the time step considered.

[0040] Furthermore, the at least one aggregate energy production value associated with the received energy network subset may comprise a set of aggregate 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 respective negative adjustment variable Ô, , {g,rdc ^.c respective. For each energy network rdc and for each time step f, the Pi„rdr values ​​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 energy production of energy entities and at least one determined adjustment variable, the worse the quality of the aggregate model.

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

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

[0047] Another aspect of the invention relates to a method for optimizing an aggregate 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 for evaluating the aggregate model describing the system energy defined above;

[0049] - use the energy production values ​​of the energy entities and the less one adjustment variable that optimizes the objective function to determine an additional relationship between 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 aggregate 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 done 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 aggregate 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 above energy system.

[0053] A computer program, implementing all or part of the process 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 in the process of evaluating a model of an energy system described earlier, 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 may 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 by reading the following description and examining the accompanying figures. BRIEF DESCRIPTION OF THE FIGURES

[0058] Other features and advantages of the invention will become apparent from the description, which can be read in conjunction with the figures. These figures are provided for illustrative purposes only and are not in any way limiting of the invention.

[0059] [Fig.1] Fig.1 illustrates an example of aggregate modeling of a plurality of heat networks located in different geographical areas, which themselves interact with each other through electrical networks.

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

[0061] [Fig.3] Fig.3 represents heat network models and an aggregate model.

[0062] [Fig.4] Fig.4 illustrates production profiles obtained during the resolution of a aggregate model.

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

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

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

[0066] [Fig. 6b] Fig. 6b represents the hourly variation curves over 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 an evaluation device for an aggregate model describing an energy system, according to one embodiment of the invention. DETAILED DESCRIPTION

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

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

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

[0071] To model the energy system at the European scale, it is possible, for each geographical area 11, 12, to aggregate all the heat networks 21, 22, 23 of that geographical area 11, 12, to create a node 11', 12', each node 11', 12' being thus 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 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 of the heat network with the heat demand in the heat network. The model may incorporate other parameters, such as the storage capacity of the heat network. For example, each heat network may be modeled by a MILP model (for "Mixed-Integer Linear Programming"). This type of model is based on the optimization of a cost function with linear constraints, in which some of the variables are integers.

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

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

[0076] To perform the aggregation of the Nrdc heat networks 21, 22, 23 of a geo- zone 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 (where 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 respective Nrdc MILP models, by a single aggregated MILP optimization model.

[0081] The invention aims to evaluate an aggregate MILP model against a set of physical constraints inherent to the heat networks under consideration (in particular, constraints inherent to heat networks, such as the lack of interconnection), using adjustment variables, or "slack" variables. The temporal variation of these slack variables further indicates which variables in the aggregate MILP model are not accurately described. An expert analysis of these variables can then identify constraints that are subsequently reintroduced into the aggregate model, thus yielding an updated aggregate MILP model that more closely reflects physical reality and can, in turn, be evaluated and potentially updated using the same strategy.

[0082] It is noted that [Fig. 1] represents one example of application among others. The invention can be applied to any system involving a plurality of entities distributed in several groups. For example, the invention can be applied to modeling a fleet of electric vehicles using an equivalent (aggregated) electric battery model.

[0083] Figure 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 simplicity, [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 number) heat networks may comprise a plurality of heat generators, each heat generator being associated with a certain type ^2' ' ' ' ' ^G- For example, types of heat generators may be: heat pump, electric boiler, boiler biomass, etc.

[0087] Each ground floor heating network comprises a number G of thermal generators of type Sh where Gj ground floor is a natural number (which may 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] designates a type of thermal generator,

[0095] ■ G.rdc designates the index of the production unit i of the thermal generator 8 in the DRC network,

[0096] - Pi.,rdc[ t] denotes the thermal power sent by the production unit i of the ge Thermal neutron 8 of the ground floor network at this instant,

[0097] - Drdc[t] denotes the heat demand of the ground floor 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] - designates a binary variable indicating whether the production unit i of the generator lg,rdc Thermal unit 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 any given time z, the heat demand in the rdc 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 rdc network. In other words, equation (1) above reflects a balance between the heat demand of the rdc network and the heat production capacity of the rdc heating network.

[0103] Equation (2) expresses the fact that, for each production unit i of each thermal generator 8 of each district heating network rdc, the thermal power delivered at each instant θ is less than or equal to the rated power (maximum power) of the generator 8. Equation (3) expresses the fact that, for each production unit i of each thermal generator 8 of each district heating network rdc, the thermal power delivered at each instant θ 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" refers to the model in which the goal is to achieve a balance between heat supply and demand, without additional constraints (ramps, minimum time a generator is on or off, etc.). It should be noted that other, more complex models incorporating additional constraints can be used. The MILP (1)-(3) model example shown above is provided to demonstrate that such a model is always available.

[0105] Returning to Figure 2, at step 220, an aggregated MILP model representing the set of N ground floor heat networks is obtained.

[0106] In the aggregated MILP model, the N rdc heat networks are grouped into a single aggregated network associated with an aggregate heat demand Dagieg, an energy ^fsres contained in the storage of the aggregated network and a set of power p^g,es representing the thermal powers of the aggregated type S 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 in Figure 3, the different types of heat generators are denoted ^1, ^2, ^3. It is assumed that there are Gi r^c heat generators of type Sj in the rdc network.

[0108] The MILP 310a, 310b model 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 Nmodels 310a, 310b are aggregated into an aggregated MILP model 320. In this aggregated model 320, the type 8j generators of all the heat networks are grouped into one or more units of an aggregated generator of type ^j, denoted , each associated with an aggregate thermal power ], and the demand for The 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 aggregate 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 heat modeled. Thus, the aggregate power can be distributed across all S-type generators in all ground floor networks. In other words, if local constraints are disregarded, the aggregate power f of each S-type generator aggregated at any given moment1 can be written: [Olin vz, w

[0112] However, in practice, equality (4) cannot be verified due to existing local constraints. For this reason, in step 230, an evaluation model is introduced to take these local constraints into account. Thus, in step 230, a MILP model, referred to as the "evaluation model" or "MILP evaluation model," is constructed. This model groups a smaller number of heat networks (Neval < Nrdc) in order to find a decomposition of the aggregate power into several local generators for each district heating network, respecting certain local constraints: local heat demand and technical constraints on the local generators.

[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 by way of example and represent a "simple" model, but other constraints may be introduced into the above model.

[0120] The objective is to find a decomposition of the power of an aggregate 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 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 satisfying 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, the sum of the differences between the aggregate model and the local constraints at each instant: [ouï] vz, (5)

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

[0124] = min^2 J ODJ J

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

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

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

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

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

[0130] In step 240, the solutions obtained in step 235, in particular the time variation of the slack variables, are analyzed for each time step. Non-zero values ​​of the slack variables indicate an adjustment of the aggregate powers to ensure that the local constraints are met. In other words, when the slack variables are non-zero, it means that the aggregate 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, derived from the models obtained in step 210, are considered. Thus, in step 240, the analysis of the slack variables allows us to assess 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 practical. The advantage is that these slack variables are associated with a generator type, 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] = The aggregate model (aggregate demand and aggregate generator power) decomposes perfectly in the Neval heat networks considered. This therefore means that the aggregate MILP model correctly describes the behavior of the Neval heat networks; - If this objective function is not zero, it means that there is no power decomposition of the aggregated generators in the heating networks that respects 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 tested aggregated solution. Furthermore, on the time steps where the slack variable(s) are non-zero, a specific analysis of the behavior of the aggregate problem can be carried out, with the aim of establishing new constraints to be added to the aggregate optimization problem. Thus, at step 250, an expert can determine one or more new constraints by more precisely analyzing the time steps at which the slack variables take non-zero values. This analysis can also be performed using real operating data from the heat networks, for example, the actual power values ​​Pû)yj,c [ / ] during the analyzed time steps (historical operating data). These constraints, obtained from a limited number of heat networks, can then be fed back into the aggregated MILP model to obtain an improved aggregated MILP model (arrow connecting step 250 to step 220 in [Fig. 2]). It is noted that, even though the constraints are determined from the analysis of a limited number of heat networks, they are generally valid across all heat networks. The newly determined constraints can therefore be added to the aggregated model, which can then be solved for a large number of heat networks. It is therefore possible to iterate between the aggregated problem, the MILP solution qualification problem, and the detection / addition of constraints to improve the model. aggregated, and move closer to a non-aggregated model, which is more in line with physical reality.

[0138] It is noted that modeling an energy system is useful, for example, for determining the distribution of energy production among different energy generators within the energy system. For example, an aggregated MILP model of the plurality of heat networks over a geographical area (e.g., at the national level) makes it possible to determine, based on energy demands and the storage and production capacities of the various generators present in the area, an optimal distribution of energy production among the different generators. The closer the aggregated MILP model is to the local MILP models, the more applicable the resulting distribution is in reality.

[0139] The invention is now illustrated by an application example 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 consists of three heat pumps (HP), two electric boilers (EV), two biomass power plants (B10), and a sensible heat storage unit, the characteristics of which are presented in the table below: Network H1 Network H2 Network H3 Heat Pumps (HP) Number of HPs 3 3 3 Pmax HP [MW] 20 15 10 Pmin HP [MW] 4 3 2 HP Efficiency [-] 3.5 3.6 3.6 Electric Boilers (PtH) Number of PtHs 2 2 2 Pmax PtH [MW] 40 40 40 Pmin PtH [MW] 2 2 2 PtH Efficiency [-] 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 BIO Efficiency [-] 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 delivered 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 stored energy, expressed in megawatt-hours.

[0141] In this example, an aggregate model is chosen in which the power plants are grouped by technology, with an "intensive" type parameterization corresponding to the average parameterization of the H2 network. Thus, the aggregate model is considered to comprise 9 H2-type "aggregated" heat pump generator units, 6 H2-type "aggregated" phosphate-to-hydropower (PtH) generator units, and 6 H2-type "aggregated" bio-hydropower (BIO) generator units. The aggregate demand corresponds to the sum of the demands of the three networks H1, H2, and H3, and the aggregate storage corresponds to the sum of the storage capacities of the three networks H1, H2, and H3. The values ​​thus obtained are presented in the table below: Aggregate demand Sum of the 3 aggregated PAC demands Pmin: 3 MW Pmax: 15 MW Aggregated PtH Pmin: 2 MW Pmax: 40 MW Aggregated BIO Pmin: 24 MW Pmax: 60 MW Aggregated STO Emax: 530 MWh Pmax: 27 MW

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

[0143] The solution of the aggregate model above is then implemented, and the production profiles of the aggregate generators that minimize the cost function associated with the optimization problem are determined. Figure 4 illustrates some of the production profiles thus obtained. In particular, Figure 4a represents the production profile obtained for the aggregate electric boiler, and Figure 4b represents the profile Figure 4c shows the production profile obtained for the aggregate biomass boiler and the production profile obtained for the aggregate heat pump. These profiles correspond to the hourly production, in megawatts, of each aggregate generator to meet the aggregate 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. Therefore, the invention proposes to reintroduce the production profiles obtained into the MILP evaluation model and to analyze the values ​​of the penalty variable over time.

[0145] Figure 5a represents the variations of the penalty variable in the MILP evaluation problem over time. Figure 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 on which the penalty variable has a value that corresponds to a local maximum and therefore represents a problem of fit between the aggregate 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 hourly variation curves on a particular day of the penalty variable (solid line), the positive slack variable associated with the aggregate biomass boiler (dotted line), the positive slack variable associated with the aggregate electric boiler (dashed line), and the negative slack variable associated with the aggregate heat pump (dashed line separated by dots).

[0148] It appears from [Fig.5b] that:

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

[0150] - the positive slack variable associated with the aggregate electric boiler takes on values ​​that are strictly positive over certain time intervals during the day under study; and

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

[0152] This means that heat pumps are favoured, in the aggregate model, because of their efficiency, and that some heat pumps in one network actually supply, according to the aggregate 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 Based on additional data relating to the different networks (particularly the heat demands on the day in question), it can be observed that the heat pump 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 network H2, the heat pump power is broken down into 3 x 15 = 45 MW, which is greater than 23 + 9 MW, i.e., the local demand plus the amount of energy that can be stored over a given time period in network H2.

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

[0155] v& Vf, (Cl)

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

[0157] Figure 6b shows the hourly variation curves, over the same day as Figure 5b, of the penalty variable (solid line), the positive slack variable associated with the aggregate biomass boiler (dashed line), the positive slack variable associated with the aggregate electric boiler (dashed line), and the negative slack variable associated with the aggregate heat pump (dashed line separated by dots), after the addition of the CL constraint

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

[0159] It can also be seen on [Fig.6b] that the values ​​of the slack variables are generally closer to zero than on [Fig.5b], which also illustrates the fact that the aggregate model incorporating 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 aggregate storage (and no longer just at the local scale, as in Cl), or a C3 constraint taking into account the fact that some generators are necessarily called upon at a local scale if the maximum power of the other local generators is insufficient to meet the local heat demand. Such constraints can, for example, be written as:

[0161] vj, v,, + (cg

[0162] vS VI, (es)

[0163] Several aggregate models were compared, depending on whether or not they incorporate 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 mean squared error (MSE) of the penalty variable over the different time steps normalized by its maximum value. Fobj [MW] Normalized Fobj Average Penalty [MW] Maximum Penalty [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 penalties) of the MILP problem of qualifying solutions 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] Figure 7 represents an evaluation device for an aggregate model describing a energy system, according to one or more embodiments of the invention.

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

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

[0169] The computer 700 includes an input interface 703 for receiving various MILP models associated with 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 include, to allow easy interaction with a user, a screen 705 and a keyboard 706. Of course, the keyboard is optional, particularly in the case of a computer in the form of a touch tablet, for example.

[0170] Furthermore, the functional diagram shown in [Fig. 2] is a typical example of a program in which certain instructions can be executed using the described device. As such, [Fig. 2] can be considered 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 by way of example. It extends to other variations 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 grid services. 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 aggregate battery or, where appropriate, to quantify the differences in solutions between an aggregate battery model 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 of 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.

Images