Non-iterative optimal power flow calculation method for integrated energy system based on projection method

Abstract

The present invention relates to a non-iterative integrated energy system optimal power flow calculation method based on projection method, comprising the following steps: decomposing the concentrated operation model of hydrogen-electricity-heat integrated energy system into hydrogen, electricity and heat subsystems; determining the projection space by the coupling relationship of each subsystem and the demand for privacy protection; finding the initial vertex set of the operation space of the hydrogen, electricity and heat subsystems in the projection space; finding the remaining vertices of the subsystem by translating the boundary on the basis of the initial vertex set of each subsystem; reconstructing the operation space of the hydrogen-electricity-heat integrated energy system in the projection space using the new constraints formed by the found vertices, and the operation space is an equivalent operation space containing all the information of the centralized model; solving the optimization problem in the reconstructed operation space to obtain the optimal solution; reconstructing the hydrogen, electricity and heat sub-problems to obtain the power flow parameters under the optimal solution. The present invention can reconstruct and simplify the mathematical model while retaining key information, and effectively protect privacy information.

Description

Technical Field

[0001] The present invention relates to the field of optimal operation of power systems, and more specifically, to a non-iterative optimal power flow calculation method for integrated energy systems based on the projection method. Background Art

[0002] Hydrogen is one of the important fuels for reducing carbon emissions, with advantages such as high energy density, zero carbon emissions, and zero pollution, and has various energy conversion forms. For example, while a hydrogen fuel cell generates electricity, the waste heat can be recovered for heating. The proportion of hydrogen energy in the energy system is increasing continuously, and it is coupled with both the power and heat systems. The hydrogen-electric-heat integrated energy system has attracted much attention as a new type of energy system.

[0003] The existing main decentralized solution methods for solving the optimal power flow problem of hydrogen-electric-heat integrated energy systems involve alternating iterative solutions, which require too many iterations to converge, hindering their real-time applications. The centralized solution requires all the data of each subsystem and cannot effectively protect the privacy of each subsystem. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a non-iterative optimal power flow calculation method for integrated energy systems based on the projection method, which can hide private variables, solve the optimal power flow under the condition of only disclosing public variables, achieve the purpose of privacy protection, and avoid the hindrance of real-time applications caused by excessive iterations, and has low complexity, high accuracy, and privacy protection.

[0005] The technical solution adopted by the present invention to solve its technical problems is: to construct a non-iterative optimal power flow calculation method for integrated energy systems based on the projection method, including the following steps:

[0006] S1. Decompose the centralized operation model of the hydrogen-electric-heat integrated energy system into hydrogen, electric, and heat subsystems;

[0007] S2. Determine the projection space through the coupling relationship of the hydrogen, electric, and heat subsystems and the requirements of privacy protection;

[0008] S3. Find the initial vertex set of the operation spaces of the hydrogen, electric, and heat subsystems in the projection space;

[0009] S4. Find the remaining vertices of the subsystem by translating the boundary based on the initial vertex set of the hydrogen, electric, and heat subsystems;

[0010] S5. Reconstruct the operation space of the hydrogen-electric-heat integrated energy system in the projection space using the new constraints formed by the found vertices, and the operation space is the equivalent operation space containing all the information of the centralized model;

[0011] S6. Solve the optimization problem in the reconstructed operation space to obtain the optimal solution;

[0012] S7. Reconstruct the hydrogen, electricity, and heat sub - problems to obtain the power flow parameters under the optimal solution.

[0013] According to the above - mentioned solution, in step S1, the mathematical expression of the centralized operation model of the hydrogen - electricity - heat integrated energy system is as follows:

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[0058] Among them, Equation (1) represents the objective function of the optimal power flow of the hydrogen-electric-thermal integrated energy system, and the objective function minimizes the operating cost of the hydrogen-electric-thermal integrated energy system. The operating cost includes the fuel cost of the coal-fired unit the fuel cost of the coal-fired boiler and the hydrogen cost C G , the fuel cost of the coal-fired unit C i,tAs shown in Equation (2), the fuel cost C of the coal-fired boiler q,t As shown in Equation (14), the hydrogen cost C G As shown in Equation (31);

[0059] Equation (3) represents the output power limit of the coal-fired unit, represents the minimum value of the output power of unit i, represents the maximum value of the output power of unit i;

[0060] Equation (4) represents the line capacity constraint of the power system, represents the transmission line capacity;

[0061] Equation (5) represents the node power balance, PW w,t represents the power generation of wind farm w at time t, PH k,t represents the power generation of hydrogen fuel cell k at time t, PB j,t represents the active power demand of load j at time t;

[0062] Equation (6) represents the DC power flow constraint, represents the phase angle of the two ends of transmission line l at time t;

[0063] Equation (7) represents the ramp constraint of the unit, RD i ,RU i represents the ramp up / down limit of unit i;

[0064] Equations (8)-(10) represent the up-spinning reserve constraint of the unit, ru i,t represents the up-spinning reserve capacity of unit i at time t, SRU t represents the up-spinning reserve of the power system;

[0065] Equations (11)-(13) represent the down-spinning reserve constraint of the unit, rd i,t represents the down-spinning reserve capacity of unit i at time t, SRD t represents the down-spinning reserve of the power system;

[0066] Equation (14) represents the fuel cost of the coal-fired boiler, HQ q,t represents the thermal power output of boiler q at time t, e c represents the heat generated per kilogram of coal combustion, ρ H represents the price per kilogram of coal;

[0067] Equation (15) represents the thermal power balance at the heat source node, HH k,t represents the thermal power output of hydrogen fuel cell k at time t, c represents the specific heat capacity of water, m g represents the mass flow rate of water at node g, Denote the supply water temperature and return water temperature of node g at time t;

[0068] Equation (16) represents the limit of the output heat power of the heating boiler, denoting the minimum and maximum values of the output heat power of the heating boiler;

[0069] Equation (17) represents the limit of the supply water temperature at the heat source node, denoting the minimum and maximum values of the supply water temperature at the heat source node;

[0070] Equations (18)-(19) represent the node energy balance at the nodes of the supply water network and return water network of the heating system, denote the supply water temperature and return water temperature at the end of pipeline d at time t, denote the supply mass flow rate and return mass flow rate of pipeline d, denote the supply water temperature and return water temperature of node g at time t;

[0071] Equations (20)-(21) represent that the water temperature at the starting end of the pipeline is equal to the water temperature of the node connected to the starting end of the pipeline;

[0072] Equations (22)-(26) represent the network loss of the heating system, denote the intermediate variables of the supply water temperature and return water temperature at the end of pipeline d at time t, denote the supply water temperature and return water temperature at the starting end of pipeline d at time t, denote the transmission time of water in the supply and return pipelines d, ρ denotes the density of water, A d denote the cross-sectional area of pipeline d, L d denote the length of pipeline d, denote the supply water temperature and return water temperature at the end of pipeline d at time t, denote the ambient temperature at time t, λ d denote the heat transfer coefficient of pipeline d, Δt denotes the time interval;

[0073] Equation (27) represents the heat absorbed by the heat load, HB h,t denote the heat power consumed by the heat load h at time t;

[0074] Equation (28) represents the limit of the return water temperature at the heat load node to ensure normal heating of the heat load, denote the minimum and maximum values of the return water temperature at the heat load;

[0075] Equation (29) describes the building thermal inertia, and the building thermal inertia provides additional flexibility for the operation of the system load, τ h,t denote the temperature of the building heat load h at time t, C h denote the heat capacity of the building heat load h, U hRepresents the thermal conductivity of the building load h;

[0076] Equation (30) represents the temperature constraint inside the building, The minimum and maximum values of the temperature of building h;

[0077] Equation (31) represents the operating cost of the hydrogen system, ρ G Represents the price per standard cubic meter of hydrogen, GB p,t Represents the hydrogen consumed by the hydrogen load p at time t, GH k,t Represents the hydrogen consumed by the hydrogen fuel cell k at time t;

[0078] Equation (32) represents the material balance equation, L f Represents the length of the hydrogen pipeline f, A f Represents the cross-sectional area of the hydrogen pipeline f, Represents the mass flow rates at the beginning and end of the hydrogen pipeline f at time t, Represents the hydrogen pressures at the beginning and end of the hydrogen pipeline f at time t;

[0079] Equation (33) represents the Navier-Stokes equation, representing the conservation of momentum in the hydrogen continuum, λ f Represents the friction coefficient of the hydrogen pipeline f, ω f Represents the flow velocity of hydrogen in the hydrogen pipeline f, d f Represents the diameter of the hydrogen pipeline f;

[0080] Equation (34) represents the upper and lower limit constraints on the hydrogen supplied by the hydrogen source, G o,t Represents the hydrogen output by the hydrogen source o at time t, Represents the minimum and maximum values of the hydrogen output by the hydrogen source o;

[0081] Equation (35) represents the node hydrogen balance;

[0082] Equation (36) defines the initial pressure value at the hydrogen source node, p n,t Represents the hydrogen pressure at node n at time t, p o,0 Represents the hydrogen pressure at the hydrogen source o at steady state;

[0083] Equation (37) represents the constraint on the node hydrogen pressure, Represents the minimum and maximum values of the node hydrogen pressure;

[0084] Equations (38)-(39) represent that the hydrogen pressures at the beginning and end of the pipeline are consistent with the hydrogen pressures at the beginning and end nodes of the pipeline respectively;

[0085] Equations (40)-(41) limit the magnitude of the mass flow rate, Represents the minimum and maximum values of the mass flow rate of the hydrogen pipeline f;

[0086] Equations (42)-(43) represent the electrical conversion and thermal conversion of a hydrogen fuel cell, η p , η h represent the electrical conversion efficiency and thermal conversion efficiency of a hydrogen fuel cell;

[0087] Equation (44) represents the limitation of hydrogen consumption by a hydrogen fuel cell, the minimum and maximum values of hydrogen consumption by a hydrogen fuel cell.

[0088] According to the above solution, in step S1, the operating spaces of the hydrogen, electricity, and heat subsystems are as follows:

[0089] Operating space of the hydrogen subsystem:

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[0103] Operating space of the power subsystem:

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[0119] Operating space of the heating subsystem:

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[0140] According to the above solution, in step S2, the process of determining the projection space based on the coupling relationship and privacy protection requirements of the hydrogen, electricity, and heat subsystems includes the following steps:

[0141] S201. Determine the variable GH with a coupling relationship k,t ;

[0142] S202. According to the requirements of privacy protection and problem-solving, the operating costs y g , y e , y h of the hydrogen, electricity, and heat subsystems are publicly available variables and are necessary for solving the total cost optimization problem;

[0143] S203. From steps S201 and S202, the publicly available variables of the optimal power flow problem can be determined. These publicly available variables determine the projection spaces of each sub-problem. The projection space of the hydrogen system sub-problem is the space composed of the variables GH k,t , y g , which is a (k×t + 1)-dimensional space; the projection space of the power system sub-problem is the space composed of the variables GH k,t , y e , and the projection space of the heat supply system sub-problem is the space composed of the variables GH k,t , y h , all of which are (k×t + 1)-dimensional spaces.

[0144] According to the above solution, in step S3, the process of finding the initial vertex set of the operating spaces of the hydrogen, electricity, and heat subsystems in the projection space includes the following steps:

[0145] S301. Set the initial vertex set Ω init as an empty set;

[0146] S302. Select a variable (such as GH a,b or y) on the projection space as the quantity to be solved;

[0147] S303. Select a suitable initial value for each of the other publicly available variables in the projection space except for the variables mentioned in step S302, and keep it fixed.

[0148] S304. Under the conditions of step S303, solve for the maximum and minimum values of the variables to be solved in step S302, and add the two vertices and (or and ) to the initial vertex set Ω init ;

[0149] S305. Take each of the (k × t + 1) variables in the projection space as the variable to be solved and perform steps S302 - S304 to obtain the final initial vertex set Ω init , and the initial vertex set Ω init contains a total of 2 × (k × t + 1) vertices. Denote the number of vertices in the initial vertex set as N 0 ;

[0150] S306. Translate the coordinate origin to the interior of the convex hull formed by the initial vertex set Ω init :

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[0152] where v i is the i-th vertex in the initial vertex set Ω init .

[0153] According to the above scheme, in step S4, the method of finding other vertices of the subsystem by translating the boundary based on the initial vertex set of each subsystem is to use the outer normal vector of each boundary surface of the convex hull formed by the existing vertex set to find the vertex farthest from this surface outside this surface, that is, it is equivalent to translating this boundary surface outward to select the farthest intersection point of this surface and the operating space of the subsystem.

[0154] According to the above scheme, the process of finding other vertices of the hydrogen, electricity, and heat subsystems by translating the boundary based on the initial vertex sets of the subsystems includes the following steps:

[0155] S401. Set the loop count r = 0, and let the initial value of the vertex set Ω ver = Ω init ;

[0156] S402. r = r + 1;

[0157] S403. Find the convex hull formed by all the vertices in the vertex set Ω ver ;

[0158] S404. Use the following formula to find the outer normal vector of each boundary surface of the convex hull:

[0159] V s,r λ s,r = 1 (94)

[0160] Among them, V s,r is the vertex matrix that constitutes the convex hull boundary surface s in the r-th cycle. This matrix is a matrix of size (k×t + 1)×(k×t + 1), and λ s,r is the outer normal vector to be solved;

[0161] S405. Find the farthest vertex outside each boundary surface, that is, solve the following problem in the operating space:

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[0163] and is defined as the optimal solution of this problem;

[0164] S406. If the following conditions are met, the vertex found is the new vertex:

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[0166] Among them, ε is a relatively small positive number;

[0167] If (96) is satisfied, then is added to the vertex set Ω ver ;

[0168] S407. Repeat steps S402 - S406. When the following conditions are met, end the loop:

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[0170] The larger ε is, the shorter the calculation time, but the lower the accuracy; vice versa; if ε = 0, that is equivalent to then the vertex set Ω ver of the subsystem projection space obtained is completely accurate;

[0171] S408. Obtain the vertex set Ω ver describing the subsystem projection space. For the vertex sets on the hydrogen, electricity, and heat subsystem projection spaces, they are respectively denoted as

[0172] According to the above scheme, in step S5, the method of reconstructing the operating space of the hydrogen - electricity - heat integrated energy system in the projection space using the new constraints formed by the vertices found is: expressing the convex hull formed by the vertex sets on the hydrogen, electricity, and heat subsystem projection spaces in the form of constraints.

[0173] According to the above solution, the process of reconstructing the operation space of the hydrogen-electric-thermal integrated energy system using the new constraints formed by the vertices to be found in the projection space includes the following steps:

[0174] S501. Find the convex hull formed by all vertices in the vertex set Ω ver ;

[0175] S502. Use the following formula to find the outer normal vector of each boundary surface of the convex hull:

[0176] V s λ s = 1 (98)

[0177] where V s is the vertex matrix forming the boundary surface s of the convex hull, and this matrix is a matrix of size (k×t + 1)×(k×t + 1), and λ s is the outer normal vector to be found;

[0178] The outer normal vectors of the boundary surfaces of the different convex hulls formed by the vertex sets of the hydrogen, electric, and thermal subsystems are respectively expressed as

[0179] S503. The operation space of the hydrogen-electric-thermal integrated energy system reconstructed in the projection space is as follows:

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[0183] This operation space is the equivalent operation space containing all the information of the centralized model.

[0184] According to the above solution, in step S6, the optimization problem is:

[0185] min y g +y e +y h (102)

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[0189] Solving this problem can obtain the value of the coupling variable GH k,t under the optimal power flow and the operation costs y g , y e , yh Value

[0190] According to the above solution, in step S7, the method for reconstructing the hydrogen, electricity, and heat sub-problems is to use the coupling variable GH under the optimal power flow obtained in step S6 k,t Value Substitute it into the hydrogen, electricity, and heat sub-problems respectively for solution.

[0191] According to the above solution, substituting the coupling variable GH under the optimal power flow obtained in step S6 k,t Value The process of substituting it into the hydrogen, electricity, and heat sub-problems respectively for solution includes the following steps:

[0192] S701. Reconstruct the hydrogen, electricity, and heat sub-problems;

[0193] Hydrogen system sub-problem:

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[0221] Sub - problem of the heating system:

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[0241] S702. Solve the hydrogen, electricity, and heat sub-problems in S701 respectively to obtain the optimal power flow.

[0242] Implementing the optimal power flow calculation method for the non-iterative integrated energy system based on the projection method of the present invention has the following beneficial effects:

[0243] 1. The optimal power flow calculation method for the non-iterative integrated energy system based on the projection method provided by the present invention can hide the private variables of the hydrogen, electricity, and heat subsystems respectively, and solve the optimal power flow problem under the condition of only opening the public variables, achieving the purpose of privacy protection;

[0244] 2. The optimal power flow calculation method for the non-iterative integrated energy system based on the projection method provided by the present invention has low complexity. This method does not involve iteration, avoiding the slow solution speed caused by excessive iteration and can be applied in real time;

[0245] 3. The optimal power flow calculation method for the non-iterative integrated energy system based on the projection method provided by the present invention has high accuracy. After the operation spaces of each subsystem are projected, the equivalent operation space contains all the information of the centralized model. The reconstruction problem is equivalent to the original problem, with high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0246] The present invention will be further described below in conjunction with the drawings and embodiments. In the drawings:

[0247] Figure 1 is the flowchart of the optimal power flow calculation method for the non-iterative integrated energy system based on the projection method of the present invention;

[0248] Figure 2 is the topology diagram of the 6-6-8 node hydrogen-electricity-heat integrated energy system of the optimal power flow calculation method for the non-iterative integrated energy system based on the projection method of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0249] For a clearer understanding of the technical features, objectives, and effects of the present invention, the specific implementation manners of the present invention will now be described in detail with reference to the drawings.

[0250] Embodiment

[0251] A non-iterative optimal power flow calculation method for integrated energy systems based on the projection method was tested in a hydrogen-electric-heat integrated energy system consisting of a 6-node hydrogen system, a 6-node power system, and an 8-node heating system, and in a hydrogen-electric-heat integrated energy system consisting of a 40-node hydrogen system, a 118-node power system, and a 13-node heating system. The topology diagram of the 6-6-8 node hydrogen-electric-heat integrated energy system is as shown in Figure 2 shown. The 6-6-8 node integrated energy system includes 6 hydrogen nodes, 6 power nodes, 8 heating nodes, 2 hydrogen sources, 2 coal-fired generators, 1 wind farm, 1 heating boiler, and 1 hydrogen fuel cell. The 40-118-13 node integrated energy system includes 40 hydrogen nodes, 118 power nodes, 13 heating nodes, 9 hydrogen sources, 54 coal-fired generators, 2 wind farms, 2 heating boilers, and 1 hydrogen fuel cell. To illustrate the effectiveness of the present invention, the results of directly solving the centralized operation model were compared with the results of the non-iterative optimal power flow calculation method for integrated energy systems based on the projection method:

[0252] First case: directly solve using the centralized operation model;

[0253] Second case: solve using the non-iterative optimal power flow calculation method for integrated energy systems based on the projection method.

[0254] In this integrated energy system, the non-iterative optimal power flow calculation method for integrated energy systems based on the projection method proposed has a process as shown in Figure 1 shown, and specifically includes the following steps:

[0255] S1. Decompose the centralized operation model of the hydrogen-electric-heat integrated energy system into hydrogen, electric, and heat subsystems;

[0256] The mathematical expression of the centralized operation model of the hydrogen-electric-heat integrated energy system is as follows:

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[0301] Among them, Equation (1) represents the objective function of the optimal power flow of the hydrogen-electric-thermal integrated energy system, and the objective function minimizes the operating cost of the hydrogen-electric-thermal integrated energy system. The operating cost includes the fuel cost of the coal-fired unit the fuel cost of the coal-fired boiler and the hydrogen cost C G , the fuel cost of the coal-fired unit C i,t As shown in Equation (2), the fuel cost of the coal-fired boiler C q,t As shown in Equation (14), the hydrogen cost C G As shown in Equation (31).

[0302] Equation (3) represents the output power limit of the coal-fired unit, represents the minimum value of the output power of unit i, represents the maximum value of the output power of unit i.

[0303] Equation (4) represents the line capacity constraint of the power system, represents the transmission line capacity.

[0304] Equation (5) represents the node power balance, PW w,t represents the power generation of wind farm w at time t, PH k,t represents the power generation of hydrogen fuel cell k at time t, PB j,t represents the active power demand of load j at time t.

[0305] Equation (6) represents the DC power flow constraint, represents the phase angle of the two ends of transmission line l at time t.

[0306] Equation (7) represents the ramp constraint of the unit, RD i , RU i represent the ramp-up / ramp-down limits of unit i.

[0307] Equations (8)-(10) represent the up-rotating reserve constraint of the unit, ru i,t represents the up-rotating reserve capacity of unit i at time t, SRU t represents the up-rotating reserve of the power system.

[0308] Equations (11)-(13) represent the down-rotating reserve constraint of the unit, rd i,t represents the down-rotating reserve capacity of unit i at time t, SRD t represents the down-rotating reserve of the power system.

[0309] Equation (14) represents the fuel cost of the coal-fired boiler, HQ q,t represents the thermal power output of boiler q at time t, e c represents the heat generated per kilogram of coal burned, ρ H represents the price per kilogram of coal.

[0310] Equation (15) represents the thermal power balance at the heat source node, HH k,t represents the thermal power output of the hydrogen fuel cell k at time t, c represents the specific heat capacity of water, m g represents the mass flow rate of water at node g, represents the supply water temperature and return water temperature at node g at time t.

[0311] Equation (16) represents the limit of the thermal power output of the heating boiler, represents the minimum and maximum values of the thermal power output of the heating boiler.

[0312] Equation (17) represents the limit of the supply water temperature at the heat source node, represents the minimum and maximum values of the supply water temperature at the heat source node.

[0313] Equations (18)-(19) represent the node energy balance at the supply water network and return water network nodes of the heating system, represents the supply water temperature and return water temperature at the end of pipeline d at time t, represents the supply water mass flow rate and return water mass flow rate of pipeline d, represents the supply water temperature and return water temperature at node g at time t.

[0314] Equations (20)-(21) represent that the water temperature at the starting end of the pipeline is equal to the water temperature of the node connected to the starting end of the pipeline.

[0315] Equations (22)-(26) represent the network loss of the heating system, An intermediate variable representing the supply water temperature and return water temperature at the end of pipeline d at time t, representing the supply water temperature and return water temperature at the beginning of pipeline d at time t, representing the transmission time of water in the supply and return pipelines d, ρ represents the density of water, A d represents the cross-sectional area of pipeline d, L d represents the length of pipeline d, representing the supply water temperature and return water temperature at the end of pipeline d at time t, representing the ambient temperature at time t, λ d represents the heat transfer coefficient of pipeline d, Δt represents the time interval.

[0316] Equation (27) represents the heat absorbed by the heat load, HB h,t representing the heat power consumed by the heat load h at time t.

[0317] Equation (28) represents the return water temperature limit at the heat load node to ensure normal heat supply to the heat load, representing the minimum and maximum values of the return water temperature at the heat load.

[0318] Equation (29) describes the building thermal inertia, and the building thermal inertia provides additional flexibility for the operation of the system load, τ h,t represents the temperature of the building (heat load) h at time t, C h represents the heat capacity of the building (heat load) h, U h represents the thermal conductivity of the building (heat load) h.

[0319] Equation (30) represents the temperature constraint inside the building, the minimum and maximum values of the temperature of building h.

[0320] Equation (31) represents the operating cost of the hydrogen system, ρ G represents the price per standard cubic meter of hydrogen, GB p,t represents the hydrogen consumed by the hydrogen load p at time t, GH k,t represents the hydrogen consumed by the hydrogen fuel cell k at time t.

[0321] Equation (32) represents the material balance equation, L f represents the length of the hydrogen pipeline f, A f represents the cross-sectional area of the hydrogen pipeline f, representing the mass flow rates at the beginning and end of the hydrogen pipeline f at time t, representing the hydrogen pressures at the beginning and end of the hydrogen pipeline f at time t.

[0322] Equation (33) represents the Navier-Stokes equation, which represents the conservation of momentum in the hydrogen continuum, λ f represents the friction coefficient of the hydrogen pipeline f, ω f represents the flow velocity d of hydrogen in the hydrogen pipeline f f represents the diameter of the hydrogen pipeline f.

[0323] Equation (34) represents the upper and lower limit constraints for the hydrogen supply from the hydrogen source, G o,t represents the hydrogen output by the hydrogen source o at time t, represents the minimum and maximum values of the hydrogen output by the hydrogen source o.

[0324] Equation (35) represents the hydrogen balance at the node.

[0325] Equation (36) defines the initial pressure value at the hydrogen source node, p n,t represents the hydrogen pressure at node n at time t, p o,0 represents the hydrogen pressure at the hydrogen source o at steady state.

[0326] Equation (37) represents the constraint on the hydrogen pressure at the node, represents the minimum and maximum values of the hydrogen pressure at the node.

[0327] Equations (38)-(39) indicate that the hydrogen pressures at the beginning and end of the pipeline are consistent with the hydrogen pressures at the beginning and end nodes of the pipeline respectively.

[0328] Equations (40)-(41) limit the magnitude of the mass flow rate, represents the minimum and maximum values of the mass flow rate of the hydrogen pipeline f.

[0329] Equations (42)-(43) represent the electrical conversion and thermal conversion of the hydrogen fuel cell, η p , η h represent the electrical conversion efficiency and thermal conversion efficiency of the hydrogen fuel cell.

[0330] Equation (44) represents the limit on the hydrogen consumption of the hydrogen fuel cell, the minimum and maximum values of the hydrogen consumption of the hydrogen fuel cell.

[0331] The operating spaces of the hydrogen, electricity, and thermal subsystems are as follows:

[0332] Operating space of the hydrogen subsystem:

[0333]

[0334]

[0335]

[0336]

[0337]

[0338]

[0339]

[0340]

[0341]

[0342]

[0343]

[0344]

[0345]

[0346] Operating space of the power subsystem:

[0347]

[0348]

[0349]

[0350]

[0351]

[0352]

[0353]

[0354]

[0355]

[0356]

[0357]

[0358]

[0359]

[0360]

[0361]

[0362] Operating space of the heating subsystem:

[0363]

[0364]

[0365]

[0366]

[0367]

[0368]

[0369]

[0370]

[0371]

[0372]

[0373]

[0374]

[0375]

[0376]

[0377]

[0378]

[0379]

[0380]

[0381]

[0382]

[0383] S2. Determine the projection space based on the coupling relationship between each subsystem and the requirements of privacy protection;

[0384] It includes the following steps:

[0385] S201. Determine the variables GH with coupling relationship k,t .

[0386] S202. According to the requirements of privacy protection and problem-solving, the operating costs y of the hydrogen, electricity, and heat subsystems g , y e , y h are variables that can be made public and are necessary for solving the total cost optimization problem.

[0387] S203. From steps S201 and S202, the publicly available variables of the optimal power flow problem can be determined. These publicly available variables determine the projection spaces of each sub-problem. The projection space of the hydrogen system sub-problem is the space formed by the variables GH k,t , y g , which is a (k × t + 1)-dimensional space; similarly, the projection space of the power system sub-problem is the space formed by the variables GH k,t , y e , and the projection space of the heat supply system sub-problem is the space formed by the variables GH k,t , y h , all of which are (k × t + 1)-dimensional spaces.

[0388] S3. Find the initial vertex set of the operating spaces of the hydrogen, electricity, and heat subsystems in the projection space;

[0389] The process of finding the initial vertex set of the subsystem operating space in the projection space includes the following steps:

[0390] S301. Set the initial vertex set Ω init to be an empty set.

[0391] S302. Select a variable (such as GH a,b or y) on the projection space as the quantity to be solved.

[0392] S303. Select a suitable initial value for each of the other publicly available variables in the projection space except the variable mentioned in step S302, and keep them fixed.

[0393] S304. Under the conditions of step S303, solve for the maximum and minimum values of the variable to be solved in step S302. Add the two vertices and (or and ) into the initial vertex set Ω init .

[0394] S305. Perform steps S302 - S304 with each of the (k × t + 1) variables on the projection space as the quantity to be solved to obtain the final initial vertex set Ω init . The initial vertex set Ω init contains a total of 2 × (k × t + 1) vertices. Denote the number of vertices in the initial vertex set as N 0 .

[0395] S306. Translate the coordinate origin to the inside of the convex hull formed by the initial vertex set Ω init :

[0396]

[0397] where v i is the i-th vertex in the initial vertex set Ω init .

[0398] S4. Based on the initial vertex set of each subsystem, find other vertices of the subsystem by translating the boundary;

[0399] Use the outer normal vector of each boundary surface of the convex hull formed by the existing vertex set to find the vertex farthest from the boundary surface outside the boundary surface, that is, equivalent to translating the boundary surface outward to select the farthest intersection point of this surface and the operating space of the subsystem, including the following steps:

[0400] S401. Set the loop count r = 0, and let the initial value of the vertex set Ω ver = Ω init .

[0401] S402. r = r + 1.

[0402] S403. Find the convex hull formed by all vertices in the vertex set Ω ver .

[0403] S404. Use the following formula to find the outer normal vector of each boundary surface of the convex hull:

[0404] V s,r λ s,r = 1 (94)

[0405] where V s,r is the vertex matrix of the boundary surface s of the convex hull formed in the r-th loop, and this matrix is a matrix of size (k×t + 1)×(k×t + 1), and λ s,r is the outer normal vector to be found.

[0406] S405. Find the vertex farthest from each boundary surface outside, that is, solve the following problem in the operating space:

[0407]

[0408] and is defined as the optimal solution of this problem.

[0409] S406. If the following conditions are met, the vertex found is the new vertex:

[0410]

[0411] where ε is a small positive number.

[0412] If (96) is satisfied, then is added to the vertex set Ω ver .

[0413] S407. Repeat steps S402 - S406. When the following conditions are met, end the loop:

[0414]

[0415] The larger ε is, the shorter the calculation time, but the lower the accuracy; vice versa. If ε = 0, which is equivalent to then the vertex set Ω of the subsystem projection space obtained ver is completely accurate.

[0416] S408. Obtain the vertex set Ω that describes the subsystem projection space ver . Denote the vertex sets on the hydrogen, electricity, and thermal subsystem projection spaces as

[0417] S5. Reconstruct the operation space of the hydrogen - electricity - heat integrated energy system in the projection space using the new constraints formed by the found vertices. This operation space is the equivalent operation space that contains all the information of the centralized model;

[0418] Express the convex hull formed by the vertex sets of the hydrogen, electricity, and thermal subsystems in the form of constraints, including the following steps:

[0419] S501. Find the convex hull formed by all the vertices in the vertex set Ω ver .

[0420] S502. Use the following formula to find the outer normal vector of each boundary surface of the convex hull:

[0421] V s λ s = 1 (98)

[0422] where V s is the vertex matrix that forms the boundary surface s of the convex hull. This matrix is a (k × t + 1) × (k × t + 1) - sized matrix, and λ s is the outer normal vector to be found.

[0423] Denote the outer normal vectors of the boundary surfaces of the different convex hulls formed by the vertex sets of the hydrogen, electricity, and thermal subsystems as

[0424] S503. The operation space of the hydrogen - electricity - heat integrated energy system reconstructed in the projection space is as follows:

[0425]

[0426]

[0427]

[0428] This operating space is the equivalent operating space containing all the information of the centralized model.

[0429] S6. Solve the optimization problem in the reconstructed operating space to obtain the optimal solution.

[0430] The reconstructed optimization problem is:

[0431] min y g +y e +y h (102)

[0432]

[0433]

[0434]

[0435] Solving this problem can obtain the coupling variable GH under the optimal power flow k,t value and the operating costs y of the hydrogen, electricity, and heat subsystems g ,y e ,y h value

[0436] S7. Reconstruct the hydrogen, electricity, and heat sub-problems to obtain the power flow parameters under the optimal solution.

[0437] Substitute the value of the coupling variable GH under the optimal power flow obtained in step S6 k,t value into the hydrogen, electricity, and heat sub-problems and solve them separately, including the following steps:

[0438] S701. Reconstruct the hydrogen, electricity, and heat sub-problems.

[0439] Hydrogen system sub-problem:

[0440] miny g (106)

[0441]

[0442]

[0443]

[0444]

[0445]

[0446]

[0447]

[0448]

[0449]

[0450]

[0451]

[0452] Power system sub - problem:

[0453] min y e (118)

[0454]

[0455]

[0456]

[0457]

[0458]

[0459]

[0460]

[0461]

[0462]

[0463]

[0464]

[0465]

[0466]

[0467] Heating system sub - problem:

[0468] min y h (132)

[0469]

[0470]

[0471]

[0472]

[0473]

[0474]

[0475]

[0476]

[0477]

[0478]

[0479]

[0480]

[0481]

[0482]

[0483]

[0484]

[0485]

[0486]

[0487] S702. Solve the hydrogen, electricity, and heat sub - problems in S701 respectively to obtain the optimal power flow.

[0488] During the operation process of the optimal power flow calculation method for the integrated energy system based on the projection method in the present invention, each subsystem hides its own private variables and only provides publicly available public variables to the system operator. The system operator calculates the optimal power flow according to the equivalent operation space containing only public variables provided by each subsystem, and returns the values of the public variables under the obtained optimal power flow to each subsystem. Each subsystem can use these values to calculate the optimal power flow of its own system. The private variables of each subsystem are not made public during the solution process, achieving the purpose of privacy protection.

[0489] After finding the vertex set of the equivalent operation space of the subsystem, the complexity of the reconstruction problem of each subsystem is greatly reduced, and its solution speed can meet the real - time requirements.

[0490] According to the calculations, in both cases, the power flow parameters solved in the first case are equal to those in the second case (Tables 1 - 8), verifying the effectiveness of the non - iterative optimal power flow calculation method for integrated energy systems based on the projection method in the present invention, and at the same time proving the high accuracy of the present invention. Table 8 shows that the number of variables of the non - iterative optimal power flow calculation method for integrated energy systems based on the projection method in the present invention is much less than that of the centralized solution method, greatly simplifying the complexity of the hydrogen - electricity - heat integrated energy system model. The non - iterative optimal power flow calculation method for integrated energy systems based on the projection method in the present invention has a short calculation time, and its calculation performance is greatly optimized, having a certain prospect of real - time application. According to the above analysis, it can be seen that the present invention has low complexity, high accuracy and real - time applicability, and can achieve the purpose of privacy protection.

[0491] Table 1 Operating costs (10^3$) of the 6 - 6 - 8 - node system under different conditions

[0492]

[0493] Table 2 Power generation of coal - fired generators (MW) of the 6 - 6 - 8 - node system under different conditions

[0494]

[0495] Table 3 Power flow of power transmission lines (MW) of the 6 - 6 - 8 - node system under different conditions

[0496]

[0497]

[0498] Table 4 Building temperature (°C) of the 6 - 6 - 8 - node system under different conditions

[0499]

[0500] Table 5 Hydrogen consumption of hydrogen fuel cells (10^3 SCM) of the 6 - 6 - 8 - node system under different conditions

[0501]

[0502] Table 6 Operating costs (10^3$) of the 40 - 118 - 13 - node system under different conditions

[0503]

[0504] Table 7 Hydrogen consumption of hydrogen fuel cells (10^3 SCM) of the 40 - 118 - 13 - node system under different conditions

[0505]

[0506] Table 8 Number of variables, constraints and calculation time under different conditions of the 40-118-13 node system

[0507]

[0508] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative rather than restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the spirit and scope protected by the claims of the present invention. All of these are within the protection scope of the present invention.

Claims

1. A non-iterative optimal power flow calculation method for an integrated energy system based on projection method, characterized in that: The following steps are involved: S1. Decompose the centralized operation model of the hydrogen-electricity-heat integrated energy system into hydrogen, electricity and heat subsystems; S2, determine the projection space through the coupling relationship between hydrogen, electricity and heat subsystems and the need for privacy protection; S3, find the initial vertex set of the operation space of hydrogen, electricity and heat subsystems in the projection space; The process includes the following steps: S301, set initial vertex set is an empty set; S302, select variables on the projection space or For the quantity to be sought; S303, selecting a suitable initial value for each of the other publicly available variables in the projection space except the variable mentioned in step S302, and fixing them; S304, under the condition of step S303, solve the maximum and minimum values ​​of the variables to be solved in step S302, and convert the two vertices [ and ]or[ and ]Add to the initial vertex set ; S305, Projection Space Each variable is used as the quantity to be determined and steps S302-S304 are performed to obtain the final initial vertex set. , the initial vertex set The Chinese Communist Party vertices, the number of vertices in the initial vertex set is recorded as ; S306: Translate the coordinate origin to the initial vertex set The interior of the convex hull is: (93) in, is the initial vertex set The vertices; S4, searching for the remaining vertices of the hydrogen, electric and thermal subsystems by translating the boundaries based on the initial vertex sets of the hydrogen, electric and thermal subsystems; S5. Reconstructing the operation space of the hydrogen-electricity-heat integrated energy system in the projection space using the new constraints formed by the found vertices, wherein the operation space is an equivalent operation space containing all the information of the centralized model; S6. Solve the optimization problem in the reconstructed operation space and obtain the optimal solution; S7. Reconstruct the hydrogen, electricity and heat sub-problems and obtain the flow parameters under the optimal solution.

2. The non-iterative optimal power flow calculation method for an integrated energy system based on projection method according to claim 1 is characterized in that: In step S1, the mathematical expression of the centralized operation model of the hydrogen-electricity-heat integrated energy system is as follows: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) (39) (40) (41) (42) (43) (44) Wherein, formula (1) represents the objective function of the optimal power flow of the hydrogen-electricity-heat integrated energy system. The objective function minimizes the operating cost of the hydrogen-electricity-heat integrated energy system. The operating cost includes the fuel cost of the coal-fired unit , Coal-fired boiler fuel cost and hydrogen costs , fuel cost of coal-fired units As shown in formula (2), the fuel cost of coal-fired boiler is As shown in formula (14), the cost of hydrogen is As shown in formula (31); Formula (3) represents the output power limit of coal-fired units, Indicates the unit The minimum output power, Indicates the unit Maximum output power; Formula (4) represents the power system line capacity constraint, represents the transmission line capacity; Formula (5) represents the node power balance, Wind power plant exist The power generation at the time, Hydrogen fuel cell exist The power generation at the time, Indicates load exist Active power demand at the time; Formula (6) represents the DC power flow constraint, Represents a transmission line The two end nodes are The phase angle of the moment; Formula (7) represents the ramp constraint of the unit, Indicates the unit Climbing ascent / descent limit; Equations (8)-(10) represent the spinning reserve constraints on the unit, Indicates the unit exist The upper spinning reserve capacity at time, Indicates the spinning reserve on the power system; Equations (11)-(13) represent the unit's lower spinning reserve constraints, Indicates the unit exist The lower spinning reserve capacity at time, It represents the spinning reserve under the power system; Formula (14) represents the fuel cost of a coal-fired boiler, Indicates boiler exist Thermal power output at the moment, It indicates the heat generated by burning each kilogram of coal. Indicates the price per kilogram of coal; Formula (15) represents the thermal power balance at the heat source node, Hydrogen fuel cell exist Thermal power output at the moment, is the specific heat capacity of water, Representation Node The mass flow rate of water, Representation Node exist The supply and return water temperatures at all times; Formula (16) represents the limitation of the thermal power output of the heating boiler. Indicates the minimum and maximum values ​​of the thermal power output of the heating boiler; Formula (17) represents the limit of water supply temperature at the heat source node. Indicates the minimum and maximum values ​​of the water supply temperature at the heat source node; Equations (18)-(19) represent the node energy balance at the nodes of the water supply network and the return network of the heating system. Represents a pipeline End at The supply water temperature and return water temperature at the moment, Represents a pipeline The supply water mass flow rate and return water mass flow rate, Representation Node exist The supply and return water temperatures at all times; Formulas (20)-(21) indicate that the water temperature at the start of the pipeline is equal to the water temperature at the node connected to the start of the pipeline; Equations (22)-(26) represent the network loss of the heating system. Represents a pipeline End at The intermediate variables of the supply water temperature and the return water temperature at each moment, Represents a pipeline Start at The supply water temperature and return water temperature at the moment, Indicates that water is flowing through the supply and return pipes. The transmission time in represents the density of water, Represents a pipeline The cross-sectional area of Represents a pipeline Length, Represents a pipeline End at Supply water temperature and return water temperature at all times, express The ambient temperature at the moment, Represents a pipeline The heat transfer coefficient, Indicates the time interval; Formula (27) represents the heat absorbed by the heat load, Indicates heat load At the moment Thermal power consumed; Formula (28) represents the return water temperature limit at the heat load node to ensure normal heating of the heat load. Indicates the minimum and maximum return water temperature at the heat load; Equation (29) describes the building thermal inertia, which provides additional flexibility for system load operation. Represents the building heat load exist The temperature of the moment, Represents the building heat load The heat capacity, Indicates building load Thermal conductivity; Formula (30) represents the temperature constraint in the building, architecture Minimum and maximum temperature values; Formula (31) represents the operating cost of the hydrogen system, represents the price of hydrogen per standard cubic meter, Indicates hydrogen load exist The hydrogen consumed at any time, Hydrogen fuel cell exist The hydrogen consumed at all times; Formula (32) represents the material balance equation, Indicates hydrogen pipeline Length, Indicates hydrogen pipeline The cross-sectional area of Indicates hydrogen pipeline The first and last paragraphs are The mass flow rate at the moment, Indicates hydrogen pipeline The first and last paragraphs are Hydrogen pressure at the time; Equation (33) represents the Navier-Stokes equation, which expresses the conservation of momentum in the hydrogen continuum, Indicates hydrogen pipeline The friction coefficient, Indicates hydrogen pipeline Hydrogen flow rate Indicates hydrogen pipeline The diameter of Formula (34) represents the upper and lower limit constraints of the hydrogen supply from the hydrogen source, Indicates hydrogen source exist The hydrogen output at all times, Indicates hydrogen source Minimum and maximum values ​​of hydrogen output; Equation (35) represents the node hydrogen balance; Formula (36) defines the initial pressure value at the hydrogen source node, Representation Node exist The hydrogen pressure at the time, Indicates the hydrogen source at steady state The hydrogen pressure at Formula (37) represents the constraint of the node hydrogen pressure, Indicates the minimum and maximum values ​​of the node hydrogen pressure; Formulas (38)-(39) indicate that the hydrogen pressure at the beginning and end of the pipeline is consistent with the hydrogen pressure at the beginning and end nodes of the pipeline respectively; Equations (40)-(41) limit the size of the mass flow rate. Indicates hydrogen pipeline The minimum and maximum values ​​of mass flow rate; Equations (42)-(43) represent the electrical conversion and thermal conversion of hydrogen fuel cells, Indicates the electrical conversion efficiency and thermal conversion efficiency of hydrogen fuel cells; Equation (44) represents the limit of hydrogen consumption of hydrogen fuel cells, The minimum and maximum values ​​of hydrogen consumption by hydrogen fuel cells.

3. The non-iterative optimal power flow calculation method for an integrated energy system based on projection method according to claim 2 is characterized in that: In step S1, the operating space of the hydrogen, electricity and heat subsystems is as follows: Hydrogen subsystem operating space: (45) (46) (47) (48) (49) (50) (51) (52) (53) (54) (55) (56) (57) Power subsystem operating space: (58) (59) (60) (61) (62) (63) (64) (65) (66) (67) (68) (69) (70) (71) (72) Heating subsystem operating space: (73) (74) (75) (76) (77) (78) (79) (80) (81) (82) (83) (84) (85) (86) (87) (88) (89) (90) (91) (92)。 4. The non-iterative optimal power flow calculation method for an integrated energy system based on projection method according to claim 1 is characterized in that: In step S2, the process of determining the projection space based on the coupling relationship between the hydrogen, electricity and heat subsystems and the need for privacy protection includes the following steps: S201. Determine the variables with coupling relationship ; S202. Operating costs of hydrogen, electricity, and heat subsystems based on privacy protection and problem solving requirements The variables are publicly available and necessary for solving the total cost optimization problem; S203: The publicly available variables of the optimal power flow problem can be determined by steps S201 and S202. The publicly available variables determine the projection space of each sub-problem. The projection space of the hydrogen system sub-problem is the variable The space formed by dimensional space; the projection space of the power system subproblem is variable The space formed by the heating system subproblem is the projected space of the variable The space formed is dimensional space.

5. The non-iterative optimal power flow calculation method for an integrated energy system based on projection method according to claim 1 is characterized in that: In step S4, based on the initial vertex set of each subsystem, other vertices of the subsystem are found by translating the boundary. The specific method is to use the outer normal vector of each boundary surface of the convex hull constructed by the existing vertex set to find the vertex farthest from the surface outside the boundary surface, which is equivalent to translating the boundary surface outward to select the farthest intersection of this surface and the operating space of the subsystem.

6. The non-iterative optimal power flow calculation method for an integrated energy system based on projection method according to claim 4 is characterized in that: The process of finding other vertices of the subsystem by translating the boundaries based on the initial vertex set of the hydrogen, electricity and heat subsystems comprises the following steps: S401, set the number of cycles , and let the vertex set initial value ; S402、 ； S403, Finding Vertex Sets The convex hull of all vertices in ; S404, use the following formula to find the external normal vector of each boundary surface of the convex hull: (94) in, For the Convex hull boundary surface is formed in the second cycle The vertex matrix is A matrix of size, is the external normal vector to be found; S405, find the farthest vertex outside each boundary surface, that is, solve the following problem in the running space: (95) and is defined as the optimal solution to the problem; S406. If the following conditions are met, the vertex being searched is a new vertex: (96) in, is a small positive number; If (96) is satisfied, then Add to Vertex Set middle; S407, repeat steps S402-S406, and end the loop when the following conditions are met: (97) The larger the value, the shorter the calculation time, but the lower the accuracy; vice versa; if , which is equivalent to , then the vertex set of the obtained subsystem projection space is It is completely accurate; S408, obtain the vertex set describing the subsystem projection space , the vertex sets on the projection space of the hydrogen, electric, and thermal subsystems are recorded as .

7. The non-iterative optimal power flow calculation method for an integrated energy system based on projection method according to claim 1 is characterized in that: In step S5, the method of reconstructing the operating space of the hydrogen-electricity-heat integrated energy system in the projection space using the new constraints formed by the found vertices is: expressing the convex hull formed by the vertex sets on the projection space of the hydrogen, electricity and heat subsystems as a constraint form.

8. The non-iterative optimal power flow calculation method for an integrated energy system based on projection method according to claim 5 is characterized in that: The process of reconstructing the operation space of the hydrogen-electricity-heat integrated energy system in the projection space using the new constraints formed by the found vertices comprises the following steps: S501, find vertex set The convex hull of all vertices in ; S502, use the following formula to find the external normal vector of each boundary surface of the convex hull: (98) in, To form the convex hull boundary surface The vertex matrix is A matrix of size, is the external normal vector to be found; The normal vectors outside the boundary surfaces of different convex hulls formed by the vertex sets of hydrogen, electricity, and heat subsystems are expressed as ; S503. The operation space of the hydrogen-electricity-heat integrated energy system reconstructed in the projection space is as follows: (99) (100) (101) This operation space is an equivalent operation space that contains all the information of the centralized model.

9. The non-iterative optimal power flow calculation method for an integrated energy system based on projection method according to claim 8 is characterized in that: In step S6, the optimization problem is: (102) (103) (104) (105) Solving this problem, we can obtain the coupling variables under the optimal power flow Value and operating costs of hydrogen, electricity and heat subsystems Value .

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