Distributed robust optimization scheduling method and device for port energy system

Abstract

The invention discloses a distributed robust optimization scheduling method and device for a port energy system, and belongs to the field of energy system operation scheduling. The method comprises the following steps: establishing a port energy system coupling model comprising a productivity system and an energy storage system; wherein the energy production system comprises a renewable energy subsystem, a gas energy subsystem and an urban power grid subsystem, and the energy storage system comprises a hydrogen production subsystem and an ammonia production subsystem; according to the prediction error of the renewable energy subsystem, calculating to obtain an output probability distribution set of the renewable energy subsystem; and establishing a distributed robust optimization scheduling model of the port energy system with the stage cost as an objective function and the system balance as a constraint condition, and solving the distributed robust optimization scheduling model of the port energy system according to the output probability distribution set to obtain an optimal scheduling scheme of the port energy system. According to the method, the problem of uncertainty risk caused by intermittency and volatility of renewable energy to a port energy system can be solved.

Description

Technical Field

[0001] The present invention relates to the technical field of energy system operation scheduling, and in particular to a distributed robust optimization scheduling method and device for a port energy system. Background Art

[0002] The emissions caused by global port transportation tasks have an adverse impact on the global environment. In order to promote the construction of green and low-carbon ports, by building rooftop distributed photovoltaics and offshore wind power, a port multi-energy complementary integrated energy system with renewable energy as the main source, natural gas distributed energy as the auxiliary source, and coordinated with urban power grids is formed to improve the comprehensive energy utilization efficiency.

[0003] Ammonia, as a low-carbon and clean secondary energy, is a green energy that promotes the low-carbon transformation of ports. However, there is still a lack of research on the scheduling capacity of electric ammonia systems under uncertain conditions in related technologies. At the same time, the traditional single optimization scheduling method is difficult to cope with the impact of the intermittent and volatile nature of large-scale renewable energy on the reliable operation of port energy systems.

[0004] Based on this, there is an urgent need for a distributed robust optimization scheduling method and device for a port energy system to solve the above technical problems. Summary of the invention

[0005] The present invention provides a distributed robust optimization scheduling method and device for a port energy system, which can effectively improve the port's ability to absorb renewable energy and solve the uncertainty risk problem caused by the intermittent and volatile renewable energy to the port energy system. The technical solution is as follows:

[0006] On the one hand, a distributed robust optimization scheduling method for a port energy system is provided, the method comprising:

[0007] Establish a port energy system coupling model including a power generation system and an energy storage system; wherein the power generation system includes a renewable energy subsystem, a gas energy subsystem and an urban power grid subsystem, and the energy storage system includes a hydrogen production subsystem and an ammonia production subsystem;

[0008] Calculating an output probability distribution set of the renewable energy subsystem according to the prediction error of the renewable energy subsystem;

[0009] A distributed robust optimization scheduling model for the port energy system is established with stage cost as the objective function and system balance as the constraint condition, and the distributed robust optimization scheduling model for the port energy system is solved according to the output probability distribution set to obtain the optimal scheduling plan for the port energy system.

[0010] On the other hand, a distributed robust optimization scheduling device for a port energy system is provided, the device comprising:

[0011] The first modeling module is used to establish a port energy system coupling model including a power generation system and an energy storage system; wherein the power generation system includes a renewable energy subsystem, a gas energy subsystem and an urban power grid subsystem, and the energy storage system includes a hydrogen production subsystem and an ammonia production subsystem;

[0012] A calculation module, configured to calculate an output probability distribution set of the renewable energy subsystem according to a prediction error of the renewable energy subsystem;

[0013] The second modeling module is used to establish a distributed robust optimization scheduling model for the port energy system with stage cost as the objective function and system balance as the constraint condition, and to solve the distributed robust optimization scheduling model for the port energy system according to the output probability distribution set to obtain the optimal scheduling plan for the port energy system.

[0014] On the other hand, a computer device is provided, which includes a memory and a processor, wherein the memory is used to store computer programs, and the processor is used to execute the computer programs stored in the memory to implement the steps of the above-mentioned distributed robust optimization scheduling method for the port energy system.

[0015] On the other hand, a computer-readable storage medium is provided, wherein a computer program is stored in the storage medium, and when the computer program is executed by a processor, the steps of the above-mentioned distributed robust optimization scheduling method for the port energy system are implemented.

[0016] The technical solution provided by the present invention can at least bring the following beneficial effects: First, the overall architecture of the green chemical port energy system is built, and the electric ammonia model takes into account the load regulation characteristics of renewable energy power generation, hydrogen production, and synthetic ammonia chemical processes. Secondly, the set of renewable energy power generation output scenarios under different confidence levels can be constructed using the Wasserstein measure. Then, taking into account the two stages of pre-planning and dynamic adjustment, a distributed robust optimization scheduling model for the green chemical port energy system based on the randomness of renewable energy power generation output is constructed. The strategy proposed in the present invention can significantly improve the low-carbon flexibility of the port energy system, taking into account the economy and robustness of the port energy system scheduling plan, while improving the port energy system's ability to absorb and its flexibility in absorbing renewable energy. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0018] Figure 1 It is a flow chart of a distributed robust optimization scheduling method for a port energy system provided by an embodiment of the present invention;

[0019] Figure 2 This is a schematic diagram of the port energy system architecture provided by an embodiment of the present invention;

[0020] Figure 3 is a structural diagram of an electric ammonia production system provided by an embodiment of the present invention;

[0021] Figure 4 This is a schematic diagram of energy purchase and sale prices at a port provided by an embodiment of the present invention;

[0022] Figure 5 is a schematic diagram of prediction error probability distribution provided by an embodiment of the present invention;

[0023] Figure 6 is a schematic diagram of a system scheduling result based on distributed robust optimization provided by an embodiment of the present invention;

[0024] Figure 7 is a schematic diagram of the relationship between the scheduling cost and the radius of the Wasserstein sphere provided by an embodiment of the present invention;

[0025] Figure 8 is a schematic diagram of total scheduling costs under different scenarios provided by an embodiment of the present invention;

[0026] Fig. 9 This is a structural diagram of a distributed robust optimization scheduling device for a port energy system provided by an embodiment of the present invention;

[0027] Fig.10 It is a hardware architecture diagram of a computer device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0028] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0029] As mentioned above, the optimization methods commonly used in relevant technologies are difficult to cope with the uncertain risks caused by the intermittent nature of renewable energy consumption and grid connection, making it difficult for the port energy system to maintain a safe operating state.

[0030] Based on this, the concept of the present invention is to construct a green port energy system including an electric ammonia system, and establish a distributed robust optimization scheduling model to flexibly adjust the port energy system's renewable energy absorption plan, improve the renewable energy absorption capacity, and thus ensure the safe operation of the port energy system.

[0031] The specific implementation of the above concept is described below.

[0032] Please refer to Figure 1 , an embodiment of the present invention provides a distributed robust optimization scheduling method for a port energy system, the method comprising:

[0033] Step 100, establishing a port energy system coupling model including a power generation system and an energy storage system; wherein the power generation system includes a renewable energy subsystem, a gas energy subsystem and an urban power grid subsystem, and the energy storage system includes a hydrogen production subsystem and an ammonia production subsystem;

[0034] Step 102, calculating an output probability distribution set of the renewable energy subsystem according to the prediction error of the renewable energy subsystem;

[0035] Step 104, establish a distributed robust optimization scheduling model for the port energy system with stage cost as the objective function and system balance as the constraint condition, and solve the distributed robust optimization scheduling model for the port energy system according to the output probability distribution set to obtain the optimal scheduling plan for the port energy system.

[0036] In the embodiment of the present invention, firstly, the overall architecture of the green chemical port energy system is constructed, and the electric ammonia model takes into account the load regulation characteristics of renewable energy power generation, hydrogen production, and synthetic ammonia chemical processes. Secondly, the set of renewable energy power generation output scenarios at different confidence levels can be constructed using the Wasserstein measure. Then, taking into account the two stages of pre-planning and dynamic adjustment, a distributed robust optimization scheduling model of the green chemical port energy system based on the randomness of renewable energy power generation output is constructed. The strategy proposed in the present invention can significantly improve the low-carbon flexibility of the port energy system, taking into account the economy and robustness of the port energy system scheduling plan, while improving the port energy system's ability to absorb and flexibility of renewable energy.

[0037] Described below Figure 1 How the various steps are performed.

[0038] First, with respect to step 100, a port energy system coupling model including a production capacity system and an energy storage system is established.

[0039] The electric ammonia system has the ability to flexibly adjust loads, and can provide large-capacity flexible resources for the port energy system to adapt to fluctuations in renewable energy power generation output. Therefore, the "electricity-green hydrogen-chemical" coupling technology has become a research hotspot.

[0040] The embodiment of the present invention establishes a coupled model of the port energy system including electric ammonia production, wherein the energy production system includes a renewable energy subsystem, a gas energy subsystem and an urban power grid subsystem, and the energy storage system includes a hydrogen production subsystem and an ammonia production subsystem. The renewable energy and other energy sources are converted and stored through the two technologies of electric hydrogen production and electric ammonia production for subsequent use.

[0041] like Figure 2 As shown, in the port energy system coupling model constructed in this embodiment, the system energy sources include urban power grid, photovoltaic power generation, wind power generation, and gas source. The energy coupling equipment includes an electric ammonia system, an electric refrigerator, an absorption refrigerator, a gas turbine, and a gas boiler. The electric ammonia system consists of an electrolyzer, an air separation nitrogen production equipment, a hydrogen storage tank, and a synthetic ammonia tower. In addition, the system also includes a heat storage tank, cold / heat / electric loads, and liquid ammonia output.

[0042] Specifically, the electric ammonia system involves the deep coupling of the power system and the chemical system, and is closely related to various links such as renewable energy, hydrogen production and ammonia synthesis. Through reasonable regulation, it can effectively absorb renewable energy power generation. The principle of ammonia synthesis reaction is shown in the following formula:

[0043] N 2 (g)+3H 2 (g) → 2NH 3 (g)

[0044] The structure of the electric ammonia system is as follows: Figure 3 As shown. T and p represent the temperature and pressure of each link respectively. 2 It can be obtained by electrolyzing water to produce hydrogen, N 2 It can be obtained through air separation. After the two react in the synthetic ammonia tower, liquid ammonia products can be obtained through ammonia separation equipment, and the remaining gas will re-enter the synthetic ammonia tower for reaction.

[0045] The hydrogen production process usually uses alkaline water electrolysis technology. The power of water electrolysis hydrogen production usually includes the power of the electrolyzer and the power of the supporting auxiliary equipment. The load rate constraint of a single electrolyzer is [0.2,1], but after combining multiple electrolyzers, the load rate constraint can be expanded to [0.05,1]. Therefore, the function of water electrolysis hydrogen production power with respect to hydrogen output is as follows:

[0046]

[0047] Where: P t P2His the hydrogen production power at time t; is the upper limit of hydrogen production power; P P2H,0 To match the auxiliary equipment power, take 0.01; c P2H is the electrolyzer power factor, which is 0.0048MWh / Nm 3 ; is the hydrogen production at time t; The upper limit of the ramp rate of hydrogen production is 0.5

[0048] The mature Harbor-Bosch process is usually used in the synthetic ammonia process, and the ammonia production can be appropriately adjusted to adapt to the fluctuation of hydrogen production. The constraints that ammonia production should meet are as follows:

[0049]

[0050] Where: is the ammonia production at time t; and are the upper and lower limits of ammonia production, Pick 0.2; and Take separately of 0.15 and -0.25.

[0051] Considering the ammonia separation equipment and the power supply required in the circulation process, the power consumption of synthetic ammonia as a function of ammonia production is as follows:

[0052]

[0053] In the formula, is a fixed power; is a constant coefficient.

[0054] Affected by the fluctuation of renewable energy generation, hydrogen production is volatile. Hydrogen production fluctuations can be smoothly adjusted through hydrogen storage tanks to meet the stability requirements of hydrogen used in synthetic ammonia. And hydrogen compressor power The expression is as follows:

[0055]

[0056] Where: is the outlet flow rate of the hydrogen storage tank; η HST The hydrogen storage / desorption efficiency of the hydrogen storage tank; VOL HST The installed capacity of hydrogen storage tanks; and They are the upper and lower limits of the SOC of the hydrogen storage tank respectively; is the upper limit of the hydrogen storage tank flow rate; R is the ideal gas constant; T 1 is the hydrogen temperature of the input hydrogen storage tank; is the molar mass of hydrogen; p 1 and p 2 are the pressure of hydrogen gas input into the hydrogen storage tank and output from the hydrogen storage tank respectively; η c is the compressor working efficiency, take 0.55.

[0057] The nitrogen required for ammonia synthesis can be obtained by air separation. Considering the compressor power consumption in the process of obtaining nitrogen, the power of air separation equipment P t AS As shown below:

[0058]

[0059] Where: is the air flow rate at time t; M Air is the molar mass of air. 4 and p 4 is the air temperature and pressure of the input air separation equipment; p 3 The pressure of nitrogen output for air separation equipment

[0060] According to the material balance relationship of the synthetic ammonia reaction, the ammonia yield Hydrogen tank outlet flow The relationship is as follows:

[0061]

[0062] Considering that thermal energy storage is similar to hydrogen storage tanks, the thermal energy storage model is briefly described as follows:

[0063]

[0064] Where: is the SOC of the heat storage tank at time t; are the heat storage / release power of the heat storage tank at time t; η HES is the heat storage / release efficiency of the heat storage tank; VOL HES The installed capacity of the heat storage tank; The upper and lower limits of SOC of the heat storage tank; The upper limit of the heat storage tank power.

[0065] The electric refrigerator model is shown below:

[0066]

[0067] The absorption refrigerant model is shown below:

[0068]

[0069] The gas boiler model is shown below:

[0070]

[0071] The gas turbine model is shown below:

[0072]

[0073] In the above model, P is the cooling power of the electric refrigerator at time t; t EC is the electric power of the electric refrigerator at time t; η EC is the cooling efficiency of the electric refrigerator; is the upper limit of the cooling power of the electric refrigerator; is the cooling power of the absorption refrigerator at time t; P t AC is the electrical power of the absorption refrigerator at time t; η AC is the refrigeration efficiency of the absorption chiller; is the upper limit of the cooling power of the absorption chiller; is the thermal power of the gas boiler at time t; is the gas consumption of the gas boiler at time t; η GB is the heating efficiency of the gas boiler; is the upper limit of thermal power of gas boiler; P t GT , are the electric power and thermal power of the gas turbine at time t respectively; η GT,p , η GT,h are the electrical efficiency and thermal efficiency of the gas turbine respectively; are the upper and lower limits of the gas turbine's electrical power; is the upper limit of the ramp rate of the gas turbine; Indicates the on / off status of the gas turbine at time t. When the value is 1, it indicates on, and when the value is 0, it indicates off; It is the lower limit of the on / off time of the gas turbine.

[0074] Then, for step 102, the output probability distribution set of the renewable energy subsystem is calculated according to the prediction error of the renewable energy subsystem.

[0075] Although the coupling model used to ensure the normal operation of the port energy system has been constructed through the above steps, in actual application, the power generation output of renewable energy is a random resource with great intermittency and volatility, that is, the output results predicted in advance may not be the same as the actual output results. This gap becomes a prediction error. For example, offshore wind power generation generates more power when the wind is strong and less power when the wind is low. If the prediction is made according to the situation of low wind speed, and strong winds occur temporarily during actual operation, this will cause the output of renewable energy to increase, which will lead to the production fluctuation of hydrogen and ammonia production equipment used to store renewable energy power generation. The emergence of this situation will bring risks to the safe operation of the entire port energy system. Therefore, in order to solve this problem, it is necessary to find a suitable scheduling method to keep the system in a safe operating state.

[0076] In an embodiment of the present invention, taking into account the randomness of renewable energy, the output probability distribution set of renewable energy is determined based on historical output data, including: calculating the difference between the observed distribution and the sample distribution of the prediction error based on the Wasserstein distance algorithm, and establishing a soft set containing all prediction error distributions of the renewable energy output; wherein the sample distribution is determined by a sample set composed of historical prediction error data of the renewable energy output; and calculating the support set of the soft set based on the standardized sample set to determine the output probability distribution set.

[0077] Specifically, according to stochastic optimization theory, the uncertainty of renewable energy power generation follows the sample distribution extracted from historical forecast error data. Based on stochastic optimization theory and combined with robust optimization theory, the uncertainty of renewable energy can be modeled:

[0078] For example, suppose D e is a sample distribution, and the sample set consists of M prediction error samples of renewable energy random variables It is determined that the sample distribution can be used in subsequent steps to estimate the observed distribution of the prediction error, that is, the distribution of the true error.

[0079] Then, the difference between the empirical distribution and the true distribution of the prediction error is quantified by introducing the Wasserstein distance:

[0080]

[0081] Among them, inf(·) is the infimum function; is the randomness parameter that obeys the sample distribution of the prediction error; ω ti is the randomness parameter that follows the distribution of forecast error observations; D eis the sample distribution; D is the observation distribution; M is the number of elements in the sample set; Π(·) is the joint distribution of the sample distribution and the observation distribution.

[0082] Furthermore, a soft set containing the observed distribution is constructed based on the sample distribution

[0083]

[0084] Where: Ξ is the support set; L(Ξ) is the probability distribution of the support set; W(D e ,D) is a sample distribution D e is a Wasserstein sphere with centered ε(M) and radius ε(M).

[0085] The set can be adjusted conservatively by ε(M), as shown in the following formula:

[0086]

[0087] Where: α is the confidence level; F M is a constant; μ ti is the sample data mean; is the uncertainty parameter.

[0088] After the soft set is obtained, it is necessary to calculate the support set of the soft set according to the sample set after the normalization process to determine the output probability distribution set.

[0089] Specifically, the sample set The standardized form of is calculated by the following formula:

[0090]

[0091] Calculate the support set Φ of the sample set through the standardized sample set:

[0092]

[0093] In the formula, Γ ti is the variance of the sample set; is the mth sample data in the sample set; is θ u The mth element in θ u is the sample of the randomness parameter after standardization; l is The border

[0094] The optimal value of the boundary l can be calculated by the following formula:

[0095]

[0096] Then the support set of the soft set is calculated by the following formula:

[0097] Ξ=(Γ ti ) 0.5 Φ+μ ti

[0098] Among them, sup(·) is the supremum function; l max for The upper boundary of p std is θ u The probability distribution of is θ u is a soft set; φ is the confidence level; and the support set Ξ is used as the output probability distribution set of the renewable energy subsystem.

[0099] It is worth noting that the support set is used to describe the "non-zero" or "meaningful" part of a function, measure or distribution on its domain. The support set in this embodiment is used to characterize the non-random parts of renewable energy output, thereby avoiding the uncontrollable scheduling model caused by the uncertainty of output.

[0100] For step 104, a distributed robust optimization scheduling model for the port energy system is established with stage cost as the objective function and system balance as the constraint condition, and the optimization scheduling model is solved according to the output probability distribution set to obtain the optimal scheduling plan for the port energy system.

[0101] After determining the output of renewable energy, the corresponding port energy system scheduling model can be established. Specifically, combining the advantages of stochastic optimization and robust optimization, the objective function of the scheduling cost of the port energy system in the pre-planning stage and the dynamic adjustment stage is proposed as follows:

[0102]

[0103] Where x is the scheduling decision variable in the pre-planning stage; c is the coefficient column vector corresponding to x; X is the set of scheduling decision variables in the pre-planning stage; sup(·) is the supremum function; Q(x,ω u ) is the adjustment cost caused by the forecast error of renewable energy output based on the pre-planning stage; u is the forecast error of renewable energy output; E D (·) is the expected function of the bad scenario

[0104] Among them, Q(x,ω u ) is a soft set. The expectation of the worst distribution in is:

[0105] Q(x,ω u )=min(dT y(x,ω u )),Zy(x,ω u )≤g(ω u )

[0106] Among them, y(x,ω u ) is the scheduling decision variable in the dynamic adjustment stage; d is the coefficient vector of y; Z and g(ω u ) are the coefficient matrix and parameter vector of the constraints in the dynamic adjustment stage respectively; X is the set of scheduling decision variables in the pre-planning stage; A and b are the coefficient matrix and parameter vector of the constraints in the pre-planning stage respectively.

[0107] Specifically, the pre-planning stage needs to ensure the consumption of renewable energy and the reliable supply of load. Therefore, the scheduling in the pre-planning stage does not consider wind and solar power abandonment and load reduction. The scheduling cost in the pre-planning stage is c T x includes the cost of buying and selling energy at time t Carbon emissions costs and grid power fluctuation penalty costs

[0108]

[0109] Where: is the selling price of ammonia; and P are the pre-planned prices for selling and purchasing electricity from the port to the city power grid; t sell and P t buy They are the power sold and purchased by the port from the city power grid; is the gas price; c pr,CO2 is the carbon tax price; δ g,CO2 and δ p,CO2 are the carbon emission coefficients of gas and urban power grid respectively; c vary P is the penalty coefficient for power fluctuation of the main power grid; t vary is the power fluctuation of the urban power grid at time t.

[0110] Furthermore, when there is a forecast error ω in the renewable energy power generation output u The dynamic adjustment stage needs to smooth out its adverse effects. By adjusting the scheduling strategy of the pre-planning stage through dynamic adjustment stage scheduling, wind and solar abandonment, and load reduction, the dynamic adjustment stage will generate adjustment costs Q(x,ω u ). Therefore, the goal of the dynamic adjustment stage is to minimize the expected value of the dynamic adjustment stage adjustment cost under severe scenarios. The scheduling cost of the dynamic adjustment stage is Including purchase and sale of energy to dynamically adjust scheduling costs Dynamic adjustment of carbon emissions scheduling costs Cost of curtailment of wind and solar power and penalty for load shedding

[0111]

[0112] Where: is the adjustment value of ammonia production at time t; and Dynamically adjust prices for the port to sell electricity to and purchase electricity from the municipal power grid; and They are the adjustment values ​​of the power sold and purchased by the port from the municipal power grid; and are the adjustment values ​​of gas consumption of gas turbine and gas boiler respectively; c pr,re 、c pr,load P is the penalty coefficient for wind and solar power abandonment and load reduction; t cut,wt , P t cut,pv , P t cut,load It refers to the wind and solar power abandonment and load power reduction during period t.

[0113] After determining the objective function, it is also necessary to determine the constraints corresponding to the two stages of the port energy system.

[0114] Firstly, according to the port energy system coupling model, the first system balance constraint in the pre-planning stage is established to enable the system to maintain a stable operating state; wherein, the first system balance constraint includes system equipment constraints, urban power grid operation constraints and system power balance constraints, and the system equipment constraints are the production capacity and energy storage constraints of each equipment in the above-mentioned port energy system coupling model.

[0115] Specifically, the urban power grid operation constraints are:

[0116]

[0117]

[0118] Where: Indicates the status of the port purchasing / selling electricity from the municipal power grid. When the value is 1, it means that the port purchases electricity from the municipal power grid, and when the value is 0, it means that the port sells electricity to the municipal power grid; The upper limit of the power that the port can purchase / sell from the municipal power grid.

[0119] System power balance constraints:

[0120]

[0121] Where: P t WT and Pt PV are the output of wind turbines and photovoltaic power generation respectively; P t load,e , is the power of electricity, heating and cooling load in period t.

[0122] Then, according to the first system balance constraint, a second system balance constraint in the dynamic adjustment phase is established; wherein the second system balance constraint includes wind and solar power abandonment and load reduction constraints, as well as system power balance constraints;

[0123] Specifically, wind and solar curtailment and load reduction constraints include:

[0124] 0≤P t cut,i ≤P t i +ω u ,i={WT,PV}

[0125] 0≤P t cut,load ≤P t load,e

[0126] Where: P t cut,i and P t cut,load are renewable energy generation and load reduction respectively; ω u Forecast error of renewable energy power generation output

[0127] System power balance constraints include:

[0128]

[0129] In summary, based on the objective function and constraints constructed above, we can get the distributed robust optimization scheduling model of the port energy system:

[0130]

[0131] Since the model contains D And ω u ∈Ξ, its constraints become infinite constraints because they contain prediction error random variables. Therefore, the constructed two-stage optimization scheduling model belongs to a semi-infinite three-level programming model that is difficult to solve directly. To this end, it can be reconstructed into a mixed integer linear programming model through strong duality theory and other methods for solution. The conversion process is as follows:

[0132] First, according to the duality theory, the worst-case scenario expectation can be changed into the following formula:

[0133]

[0134] Where σ is the dual variable.

[0135] Then, the distributed robust optimization scheduling model of the port energy system under the support set Ξ can be converted into the first transformation scheduling model:

[0136]

[0137] Where: Ax≤b is the constraint in the pre-planning stage; Zy(x,ω u )≤g(ω u ) is the constraint of the dynamic adjustment stage.

[0138] Then, according to the preset auxiliary variable β m The first transformation scheduling model is converted:

[0139]

[0140] Finally, the above formula is transformed to obtain the mixed integer linear programming model:

[0141]

[0142] Among them, ω u The upper and lower bounds of (ω s ,ω x );

[0143] The mixed integer linear programming model is solved and calculated to obtain the optimal scheduling solution of the port energy system. It is worth noting that the calculation process is well known to those skilled in the art and will not be described in detail here.

[0144] The feasibility of the above method is verified by an example below:

[0145] The energy purchase and sale prices at the port are as follows: Figure 4 The port equipment parameters are shown in Table 1, which shows the parameters of the port energy system equipment. Referring to the lowest market price in recent years, the port product ammonia price is 393.96$ / ton. The port has 1 wind farm and distributed photovoltaic power generation. The forecast error data of renewable energy power generation output pre-planning comes from the public data set of the power grid operator Tennet. The scheduling cycle is 24 hours, and the time interval is 1 hour.

[0146] Table 1

[0147]

[0148]

[0149] The probability distribution of the forecast error of renewable energy power generation output at each forecast time scale obtained by kernel density estimation fitting is as follows: Figure 5 As shown. The renewable energy power generation output range can be obtained by the inverse function of the prediction error probability distribution, and the confidence level is 0.95. The renewable energy power generation output scenario can be obtained by K-means clustering, with 20 scenarios and 1MW sphere radius.

[0150] The comparison results of different optimization methods are shown in Table 2. Table 2 shows the scheduling results of different optimization methods. Deterministic optimization only considers the scheduling in the pre-planning stage, and its scheduling cost in the dynamic adjustment stage is 0. Except for deterministic optimization, the other optimization methods are two-stage scheduling methods.

[0151] Table 2

[0152]

[0153]

[0154] As shown in Table 2, the total dispatch cost of deterministic optimization is the lowest. However, this does not mean that deterministic optimization is better than uncertain optimization. This is because deterministic optimization is based on the forecast information in the pre-planning stage for pre-planning dispatch, without considering the uncertainty risk caused by forecast errors and the dynamic adjustment dispatch cost. In the dynamic adjustment stage, deterministic optimization needs to purchase and sell a large amount of electricity from the municipal power grid to solve the power imbalance caused by forecast errors, resulting in higher actual dispatch costs.

[0155] The cost of pre-planning scheduling and dynamic adjustment scheduling of stochastic optimization is the lowest, mainly because stochastic optimization can improve economic efficiency by pre-planning scheduling based on accurate probability distribution. However, accurate probability distribution will lead to an overly optimistic expected risk attitude in the dynamic adjustment stage. Insufficient energy reserves in the pre-planning stage will reduce the risk resistance of stochastic optimization in the dynamic adjustment stage, and it has the worst robustness.

[0156] The pre-planning scheduling cost and dynamic adjustment scheduling cost of robust optimization are the highest. The main reason is that robust optimization is based on the worst prediction error for pre-planning scheduling. In the pre-planning stage, robust optimization needs to increase energy reserves to improve its risk resistance in the dynamic adjustment stage, and has good robustness. However, the pre-planning scheduling cost of robust optimization is the highest and has the worst economic performance.

[0157] The pre-planning scheduling cost and dynamic adjustment scheduling cost of distributed robust optimization are between random optimization and robust optimization. The main reason is that distributed robust optimization is based on the worst probability distribution of prediction error for pre-planning scheduling. Through the complementary advantages of random optimization and robust optimization, distributed robust optimization can not only improve the conservatism of robust optimization and the risk resistance of random optimization, but also obtain an optimized scheduling solution that takes into account both economy and robustness.

[0158] The cost composition of pre-planning scheduling for different optimization methods is shown in Table 3. Table 3 shows the cost composition of pre-planning scheduling for different optimization methods.

[0159] Table 3

[0160]

[0161]

[0162] As shown in Table 3, compared with deterministic optimization and random optimization, distributed robust optimization and robust optimization have higher pre-planning scheduling costs, which is due to the increase in the purchase of electricity from the municipal power grid by the port energy system. Distributed robust optimization and robust optimization have higher carbon emission costs, because the purchase of electricity from the municipal power grid, which is mainly thermal power, is increased in the pre-planning stage to cope with the expected risks in the dynamic adjustment stage. The increase in the purchase of electricity makes the cost of purchasing gas for distributed robust optimization and robust optimization lower. The power fluctuations of various optimization methods are not much different. The ammonia sales revenue of robust optimization is 243.66$, and the ammonia sales revenue of distributed robust optimization is 294.91$. Compared with robust optimization scheduling, the ammonia sales revenue of distributed robust optimization increased by 21.03%.

[0163] System scheduling results based on distributed robust optimization, such as Figure 6 As shown. Combined Figure 6 (a) with Figure 6 (d) It can be seen that since the cooling efficiency of electric refrigerators is higher than that of absorption refrigerators, the cooling load is mainly supplied by electric refrigerators, and the shortfall is supplemented by absorption refrigerators. During the period of 8:00-19:00, the output of renewable energy is less than the electric load. Since the electricity price is higher during this period, in order to reduce the cost of purchasing electricity from the municipal power grid, the cooling load is mainly supplied by absorption refrigerators. Figure 6 (b) with Figure 6 (d) It can be seen that during the period of 8:00-19:00, the output of renewable energy is less than the electrical load, and the gas turbine is required to meet both the electrical load and the thermal load. The excess heat is stored in the heat storage tank and transferred to the period of 21:00-6:00. During this period, the output of renewable energy generation is high, so the gas turbine maintains minimum power operation to provide backup capacity, and the thermal load is mainly met by the gas boiler. Figure 6 (c) with Figure 6(d) It can be seen that during the 6:00-7:00 period and the 21:00-5:00 period, hydrogen is stored in electrolyzers and hydrogen storage tanks to absorb the output of renewable energy power generation, and the synthetic ammonia equipment also tends to work during this period. During the 9:00-18:00 period, the synthetic ammonia equipment operates at low power to reduce the cost of purchasing electricity from the municipal power grid. During the 21:00-6:00 period, the power sales power did not fluctuate significantly, which was mainly achieved through the power fluctuation smoothing of the electric ammonia equipment. Figure 6 (d) It can be seen that the interaction between the port energy system and the municipal power grid in purchasing and selling electricity is mainly used as a supplementary method when the port energy system cannot support the power load demand and cannot absorb renewable energy generation.

[0164] Distributed robust optimization can achieve a reasonable choice between scheduling economy and robustness by adjusting the Wasserstein sphere radius parameter. The simulation results are as follows: Figure 7 As shown. In addition, distributed robust optimization takes into account the uncertainty of probability distribution and has the advantages of random optimization and robust optimization. Assuming that the forecast error of renewable energy power generation output in each period satisfies the normal distribution, five groups of different mean parameters are selected, and the renewable energy power generation scenarios are generated by Latin hypercube sampling for simulation. The dispatch cost under different mean parameters is analyzed, as shown in Table 4. Table 4 shows the dispatch cost under different mean parameters.

[0165] Table 4

[0166]

[0167] As can be seen from Table 4, deterministic optimization has the lowest scheduling cost and is overly optimistic because it does not take into account the prediction error. At the same time, its scheduling cost remains unchanged and cannot reflect the expected risk based on the historical data of prediction errors.

[0168] Stochastic optimization optimizes scheduling based on probability distribution information. When the actual output of renewable energy is greater than the predicted output (i.e., the mean is greater than 0), the scheduling cost is close to the minimum cost of deterministic optimization, reflecting optimistic expected risks. When the actual output of renewable energy is less than the predicted output (i.e., the mean is less than 0), the scheduling cost increases as the mean decreases, reflecting negative expected risks. However, it does not take into account the uncertainty of probability distribution, so its robustness is poor.

[0169] The scheduling cost of robust optimization is the highest, indicating that it is the most robust. However, it does not utilize probability distribution information, so its economic efficiency is the worst and it shows an overly negative attitude towards expected risks.

[0170] The trend of the distributed robust optimization scheduling cost changing with the mean is the same as that of random optimization, indicating that it has the characteristics of random optimization in reflecting expected risks, and its higher scheduling cost indicates that it has the robustness of robust optimization.

[0171] In order to analyze the versatility of the proposed dispatch model, two groups of 8 scenarios are set for comparison. Scenario 1 uses the original renewable energy forecast output, the renewable energy forecast output of scenario 2 increases by 1000kW on the basis of scenario 1, and the renewable energy forecast output of scenario 3 decreases by 1000kW on the basis of scenario 1. The renewable energy output trend of scenario 4 is opposite to that of scenario 1. The historical forecast error data of renewable energy in scenarios 5 to 8 uses the data from 2018 to 2021. The comparison results are shown in Figure 2. Figure 8 The distributed robust optimization dispatch cost under different scenarios remains between random optimization and robust optimization, indicating that the proposed dispatch model can take into account both dispatch economy and robustness under different scenarios, and verifies its universality under different output levels, output trends and historical forecast error data of renewable energy forecast output in different years.

[0172] Please refer to Fig. 9 The embodiment of the present invention provides a distributed robust optimization scheduling device for a port energy system, the device comprising:

[0173] The first modeling module 900 is used to establish a port energy system coupling model including a power generation system and an energy storage system; wherein the power generation system includes a renewable energy subsystem, a gas energy subsystem and an urban power grid subsystem, and the energy storage system includes a hydrogen production subsystem and an ammonia production subsystem;

[0174] A calculation module 902 is used to calculate an output probability distribution set of the renewable energy subsystem according to the prediction error of the renewable energy subsystem;

[0175] The second modeling module 904 is used to establish a distributed robust optimization scheduling model for the port energy system with stage cost as the objective function and system balance as the constraint condition, and solve the distributed robust optimization scheduling model for the port energy system according to the output probability distribution set to obtain the optimal scheduling plan for the port energy system.

[0176] In an embodiment of the present invention, when the calculation module 902 calculates the output probability distribution set of the renewable energy subsystem based on the prediction error of the renewable energy subsystem, it is specifically used to perform the following operations: calculate the difference between the observed distribution and the sample distribution of the prediction error according to the Wasserstein distance algorithm, and establish a soft set containing all prediction error distributions of the renewable energy output; wherein the sample distribution is determined by a sample set composed of historical prediction error data of the renewable energy output; and calculate the support set of the soft set based on the standardized sample set to determine the output probability distribution set.

[0177] In the embodiment of the present invention, the difference between the observed distribution and the sample distribution of the prediction error is calculated according to the Wasserstein distance algorithm, and a soft set of all prediction error distributions of the renewable energy output is established, including:

[0178] Compute the difference between the observed and sample distributions of forecast errors:

[0179]

[0180] Among them, inf(·) is the infimum function; is the randomness parameter that obeys the sample distribution of the prediction error; ω ti is the randomness parameter that follows the distribution of forecast error observations; D e is the sample distribution; D is the observation distribution; M is the number of elements in the sample set; Π(·) is the joint distribution of the sample distribution and the observation distribution;

[0181] Construct a soft set containing the observation distribution according to the sample distribution

[0182]

[0183] Where: Ξ is the support set; L(Ξ) is the probability distribution of the support set; W(D e ,D) is a sample distribution D e is a Wasserstein sphere with centered ε(M) and radius ε(M).

[0184] In the embodiment of the present invention, the support set of the soft set is calculated according to the sample set after the standardization process, and the output probability distribution set is determined, including:

[0185] Calculate the support set Φ of the sample set after normalization:

[0186]

[0187] Among them, Γ ti is the variance of the sample set; is the mth sample data in the sample set; is θ u The mth element in θ u is the sample of the randomness parameter after standardization; l is the boundaries of;

[0188] According to the calculated optimal value of the boundary l, the support set Ξ of the soft set is determined:

[0189]

[0190] Ξ=(Γ ti) 0.5 Φ+μ ti

[0191] Among them, sup(·) is the supremum function; l max for The upper boundary of p std is θ u The probability distribution of is θ u is a soft set; φ is the confidence level; and the support set Ξ is used as the output probability distribution set of the renewable energy subsystem.

[0192] In the embodiment of the present invention, the second modeling module 904 is specifically used to perform the following operations when establishing a distributed robust optimization scheduling model of the port energy system with the stage cost as the objective function and the system balance as the constraint condition: according to the renewable energy consumption and load supply requirements, determine the first sub-stage cost c of the pre-planning stage without considering the wind abandonment, solar abandonment and load reduction conditions. T x:

[0193]

[0194] Among them, x is the scheduling decision variable in the pre-planning stage; c is the coefficient column vector corresponding to x; is the cost of energy purchase and sale in period t; for the cost of carbon emissions; Penalize costs for grid power fluctuations;

[0195] According to the adjustment consumption of the prediction error, the second sub-stage cost of the dynamic adjustment stage that minimizes the severe scenario under the conditions of wind and solar power abandonment and load reduction is determined

[0196]

[0197] Among them, sup(·) is the supremum function; Q(x,ω u ) is the regulation cost of the renewable energy output; u forecast errors for renewable energy output; To cover the dispatching costs during the dynamic adjustment phase of purchasing and selling energy; Dynamic adjustment of the dispatch costs for carbon emissions; The cost of the dynamic adjustment phase for wind and solar power abandonment and load reduction penalties; E D (·) is the expected function of the severe scenario;

[0198] According to the port energy system coupling model, a first system balance constraint in the pre-planning stage is established to enable the system to maintain a stable operating state; wherein the first system balance constraint includes system equipment constraints, urban power grid operation constraints and system power balance constraints;

[0199] According to the first system balance constraint, a second system balance constraint in a dynamic adjustment phase is established; wherein the second system balance constraint includes wind and solar power abandonment and load reduction constraints, as well as system power balance constraints;

[0200] A distributed robust optimization scheduling model for the port energy system is established according to the first sub-stage cost, the second sub-stage cost, the first system balance constraint and the second system balance constraint.

[0201] In the embodiment of the present invention, the distributed robust optimization scheduling model of the port energy system is established by the following formula:

[0202]

[0203] Q(x,ω u )=min(d T y(x,ω u )),Zy(x,ω u )≤g(ω u )

[0204] Among them, y(x,ω u ) is the scheduling decision variable in the dynamic adjustment stage; d is the coefficient vector of y; Z and g(ω u ) are the coefficient matrix and parameter vector of the constraints in the dynamic adjustment stage respectively; X is the set of scheduling decision variables in the pre-planning stage; A and b are the coefficient matrix and parameter vector of the constraints in the pre-planning stage respectively.

[0205] In an embodiment of the present invention, solving the distributed robust optimization scheduling model of the port energy system to obtain the optimal scheduling solution of the port energy system includes:

[0206] The objective function of the distributed robust optimization scheduling model of the port energy system is transformed into a dual transformation to obtain the first transformation scheduling model:

[0207]

[0208] In the formula, σ is the dual variable;

[0209] According to the preset auxiliary variable β m The first transformation scheduling model is transformed to obtain a mixed integer linear programming model:

[0210]

[0211] The mixed integer linear programming model is solved and calculated to obtain the optimal scheduling solution for the port energy system.

[0212] It should be noted that the distributed robust optimization scheduling device for the port energy system provided in the above embodiment is only illustrated by the division of the above functional modules. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device is divided into different functional modules to complete all or part of the functions described above. In addition, the distributed robust optimization scheduling device for the port energy system provided in the above embodiment and the distributed robust optimization scheduling method embodiment of the port energy system belong to the same concept. The specific implementation process is detailed in the method embodiment and will not be repeated here.

[0213] The embodiment of the present application also provides a computer device, please refer to Fig.10 The computer device includes a processor and a memory, in which at least one instruction, at least one program, a code set or an instruction set is stored, and the at least one instruction, at least one program, a code set or an instruction set is loaded and executed by the processor to implement the distributed robust optimization scheduling method for the port energy system provided by the above-mentioned method embodiments.

[0214] An embodiment of the present application also provides a computer-readable storage medium, on which is stored at least one instruction, at least one program, code set or instruction set, and the at least one instruction, at least one program, code set or instruction set is loaded and executed by a processor to implement the distributed robust optimization scheduling method for the port energy system provided by the above-mentioned method embodiments.

[0215] For the convenience of description, the above system or device is described by dividing it into various modules or units according to its functions. Of course, when implementing the present application, the functions of each unit can be implemented in the same or multiple software and / or hardware.

[0216] It can be known from the description of the above implementation methods that those skilled in the art can clearly understand that the present application can be implemented by means of software plus a necessary general hardware platform. Based on such an understanding, the technical solution of the present application can be essentially or partly contributed to the prior art in the form of a software product, which can be stored in a storage medium such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in the various embodiments of the present application or certain parts of the embodiments.

[0217] Finally, it should be noted that, in this article, relational terms such as first, second, third and fourth are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the statement "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0218] The above is only a preferred implementation of the present application. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present application. These improvements and modifications should also be regarded as the scope of protection of the present application.

Claims

1. A distributed robust optimization scheduling method for a port energy system, characterized in that: The method comprises: Establish a port energy system coupling model including a power generation system and an energy storage system; wherein the power generation system includes a renewable energy subsystem, a gas energy subsystem and an urban power grid subsystem, and the energy storage system includes a hydrogen production subsystem and an ammonia production subsystem; Calculating an output probability distribution set of the renewable energy subsystem according to the prediction error of the renewable energy subsystem; A distributed robust optimization scheduling model for the port energy system is established with stage cost as the objective function and system balance as the constraint condition, and the optimization scheduling model is solved according to the output probability distribution set to obtain the optimal scheduling plan for the port energy system.

2. The method according to claim 1, characterized in that The step of calculating the output probability distribution set of the renewable energy subsystem according to the prediction error of the renewable energy subsystem includes: Calculating the difference between the observed distribution and the sample distribution of the prediction error according to the Wasserstein distance algorithm, and establishing a soft set containing all the prediction error distributions of the renewable energy output; wherein the sample distribution is determined by a sample set consisting of historical prediction error data of the renewable energy output; The support set of the soft set is calculated according to the sample set after the standardization process, and the output probability distribution set is determined.

3. The method according to claim 2, characterized in that The calculation of the difference between the observed distribution and the sample distribution of the prediction error according to the Wasserstein distance algorithm and the establishment of a soft set of all prediction error distributions of the renewable energy output include: Compute the difference between the observed and sample distributions of forecast errors: Among them, inf(·) is the infimum function; is the randomness parameter that obeys the sample distribution of the prediction error; ω ti is the randomness parameter that follows the distribution of forecast error observations; D e is the sample distribution; D is the observation distribution; M is the number of elements in the sample set; Π(·) is the joint distribution of the sample distribution and the observation distribution; Construct a soft set containing the observation distribution according to the sample distribution Where: Ξ is the support set; L(Ξ) is the probability distribution of the support set; W(D e ,D) is a sample distribution D e is a Wasserstein sphere with centered ε(M) and radius ε(M).

4. The method according to claim 3, characterized in that The step of calculating the support set of the soft set according to the sample set after the standardization process and determining the output probability distribution set comprises: Calculate the support set Φ of the sample set after normalization: Among them, Γ ti is the variance of the sample set; is the mth sample data in the sample set; is θ u The mth element in θ u is the sample of the randomness parameter after standardization; l is the boundaries of; According to the calculated optimal value of the boundary l, the support set Ξ of the soft set is determined: Among them, sup(·) is the supremum function; l max for The upper boundary of p std is θ u The probability distribution of is θ u is a soft set; φ is the confidence level; and the support set Ξ is used as the output probability distribution set of the renewable energy subsystem.

5. The method according to claim 2, characterized in that The establishment of a distributed robust optimization scheduling model for the port energy system with stage cost as the objective function and system balance as a constraint condition includes: According to the renewable energy consumption and load supply requirements, determine the first sub-stage cost c of the pre-planning stage without considering wind and solar power abandonment and load reduction. T x: Among them, x is the scheduling decision variable in the pre-planning stage; c is the coefficient column vector corresponding to x; is the cost of energy purchase and sale in period t; for the cost of carbon emissions; Penalize costs for grid power fluctuations; According to the adjustment consumption of the prediction error, the second sub-stage cost of the dynamic adjustment stage that minimizes the severe scenario under the conditions of wind and solar power abandonment and load reduction is determined Among them, sup(·) is the supremum function; Q(x,ω u ) is the regulation cost of the renewable energy output; u forecast errors for renewable energy output; To cover the dispatching costs during the dynamic adjustment phase of purchasing and selling energy; Dynamic adjustment of the dispatch costs for carbon emissions; The cost of the dynamic adjustment phase for wind and solar power abandonment and load reduction penalties; E D (·) is the expected function of the severe scenario; According to the port energy system coupling model, a first system balance constraint in the pre-planning stage is established to enable the system to maintain a stable operating state; wherein the first system balance constraint includes system equipment constraints, urban power grid operation constraints and system power balance constraints; According to the first system balance constraint, a second system balance constraint in a dynamic adjustment phase is established; wherein the second system balance constraint includes wind and solar power abandonment and load reduction constraints, as well as system power balance constraints; A distributed robust optimization scheduling model for the port energy system is established according to the first sub-stage cost, the second sub-stage cost, the first system balance constraint and the second system balance constraint.

6. The method according to claim 5, characterized in that The distributed robust optimization scheduling model of the port energy system is established by the following formula: Q(x,ω u )=min(d T y(x,ω u )),Zy(x,ω u )≤g(ω u ) Among them, y(x,ω u ) is the scheduling decision variable in the dynamic adjustment stage; d is the coefficient vector of y; Z and g(ω u ) are the coefficient matrix and parameter vector of the constraints in the dynamic adjustment stage respectively; X is the set of scheduling decision variables in the pre-planning stage; A and b are the coefficient matrix and parameter vector of the constraints in the pre-planning stage respectively.

7. The method according to claim 6, characterized in that The method of solving the distributed robust optimization scheduling model of the port energy system to obtain the optimal scheduling solution of the port energy system includes: The objective function of the distributed robust optimization scheduling model of the port energy system is transformed into a dual transformation to obtain the first transformation scheduling model: In the formula, σ is the dual variable; According to the preset auxiliary variable β m The first transformation scheduling model is transformed to obtain a mixed integer linear programming model: Among them, ω u The upper and lower bounds of (ω s ,ω x ); The mixed integer linear programming model is solved and calculated to obtain the optimal scheduling solution for the port energy system.

8. A distributed robust optimization dispatching device for a port energy system, characterized in that: The device comprises: The first modeling module is used to establish a port energy system coupling model including a power generation system and an energy storage system; wherein the power generation system includes a renewable energy subsystem, a gas energy subsystem and an urban power grid subsystem, and the energy storage system includes a hydrogen production subsystem and an ammonia production subsystem; A calculation module, configured to calculate an output probability distribution set of the renewable energy subsystem according to a prediction error of the renewable energy subsystem; The second modeling module is used to establish a distributed robust optimization scheduling model for the port energy system with stage cost as the objective function and system balance as the constraint condition, and to solve the distributed robust optimization scheduling model for the port energy system according to the output probability distribution set to obtain the optimal scheduling plan for the port energy system.

9. A computer device, characterized in that: The computer device includes a memory and a processor, the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory to implement the steps of any one of the methods described in claims 1-7.

10. A computer-readable storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method described in any one of claims 1 to 7 are implemented.

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