Robust optimization scheduling method and device for integrated energy system based on controllable capacity

Abstract

The present application belongs to the technical field of energy optimization scheduling, and particularly relates to a robust optimization scheduling method and device for a comprehensive energy system based on adjustable control capacity, which comprises the following steps: establishing a gas supply system pipe storage model; establishing a time-shiftable load control model for a power distribution network, a time-shiftable load control model for a natural gas network, and a demand response load model for the power distribution network; constructing an optimization objective function considering the operation cost of the power distribution network and the operation cost of the natural gas network; establishing a robust optimization model for the comprehensive energy system considering load uncertainty based on the optimization objective function; constructing a double-layer robust optimization algorithm, in which a sub-problem is used to solve the worst operation scenario, and a main problem is used to optimize the operation cost of the comprehensive energy system, so as to obtain an optimized scheduling scheme for the comprehensive energy system. The present application can effectively cope with the complex operation problems of the electric-gas coupled comprehensive energy system through the scheduling strategy, and improve the flexibility and adaptability of the system.

Description

Technical Field

[0001] This invention belongs to the field of energy optimization scheduling technology, specifically relating to a robust optimization scheduling method and apparatus for integrated energy systems based on controllable capabilities. Background Technology

[0002] Integrated Energy Systems (IES), as complex networks involving multiple energy sources, have become a core technological pathway for achieving energy efficiency and low-carbon transformation through the synergistic optimization and complementarity of various energy sources such as electricity, heat, gas, and cooling. In recent years, with the increasing penetration of renewable energy and the diversification of load demand, research on the optimal operation of IES has gradually expanded from deterministic frameworks to uncertainty modeling, and has attempted to integrate demand-side resources to enhance system flexibility. However, existing research still has significant shortcomings: on the one hand, there is a lack of proactive management and synergistic optimization of controllable loads; on the other hand, load uncertainty modeling often focuses on single energy forms or simplified scenarios, making it difficult to characterize the complexity of dynamic demand-side responses under multi-energy coupling.

[0003] For multi-energy coupled systems of electricity, hydrogen, and heat, the paper "Research on Optimal Scheduling of Integrated Energy Microgrid Considering Multiple Uncertainties" improves energy efficiency through a heat recovery model, but its optimization framework is still based on predicted data and does not quantify the impact of load fluctuations on the system's economy and robustness. Similarly, the paper "Low-Carbon Economic Scheduling Method for Hydrogen-Containing Multi-Energy Systems Based on Carbon-Green Certificate Mutual Recognition and Flexible Electricity and Heat Loads" introduces a coupled equipment model, but load demand is mostly assumed to be a rigid parameter, failing to consider the dynamic adjustment potential of demand response strategies such as interruptible loads and transferable loads. Although stochastic optimization and robust optimization methods have been partially applied to IES uncertainty analysis, their modeling objects are still focused on wind and solar power output fluctuations, with insufficient attention paid to the spatiotemporal heterogeneity of user energy consumption behavior and the stochasticity of load response. The paper "Master-Slave Game-Robust Optimal Scheduling of Integrated Energy Systems in Industrial Parks Considering Multi-Scenario Collaborative Carbon Reduction" handles source-side uncertainties through a data-driven sub-brutal robust optimization method, but fails to incorporate flexible demand-side resources into the collaborative optimization framework, making the scheduling scheme difficult to adapt to real-time load fluctuations.

[0004] Regarding the integration of controllable loads, while existing research has made preliminary explorations into the moderating effect of price-based demand response on load curves, it is mostly limited to single energy forms or simple elasticity models. Literature such as "A Virtual Power Plant Master-Slave Game Strategy Based on Time-of-Use Electricity-Carbon Coupled Pricing" and "A Virtual Power Plant Two-Layer Optimization Considering Source-Load Coordinated Response and Dynamic Pricing" optimizes electricity load curves through time-of-use pricing strategies, but does not address the coordinated response mechanisms of heat and gas loads, and the load models ignore differences in user behavior and equipment operating constraints. Furthermore, modeling the dynamic characteristics of typical controllable loads such as electric vehicles and smart homes is still in its early stages. Existing research often employs fixed charging and discharging modes or idealized response assumptions, making it difficult to reflect the interaction between user preferences and equipment physical constraints in real-world scenarios. This lack of modeling can lead to optimization results becoming invalid in actual operation due to load response deviations, limiting the release of the synergistic potential of the entire "source-grid-load-storage" ecosystem.

[0005] In summary, existing solutions have not achieved robust optimal scheduling methods for integrated energy systems that take into account controllability. Therefore, it is necessary to study robust optimal scheduling methods for integrated energy systems that consider controllability. Summary of the Invention

[0006] In view of the shortcomings of the prior art, the purpose of this invention is to provide a robust optimization scheduling method and apparatus for integrated energy systems based on controllable capabilities, so that the scheduling strategy can effectively cope with the complex operation problems of electric-gas coupled integrated energy systems and improve the system's flexibility and adaptability.

[0007] To achieve the above objectives, this invention provides a robust optimization scheduling method for integrated energy systems based on controllable capabilities, comprising the following steps:

[0008] S1. Taking the natural gas supply system and natural gas storage device as the research objects, establish a pipeline storage model of the natural gas supply system, and establish gas pressure constraints, pipeline operation constraints, natural gas gate station gas supply constraints, and gas filling and releasing constraints of the natural gas storage device.

[0009] S2. Taking the controllability of an integrated energy system including distribution networks and natural gas networks as the research object, establish a time-shiftable controllable load model for distribution networks, a time-shiftable controllable load model for natural gas networks, and a demand response load model for distribution networks.

[0010] S3. Taking the operating cost of the integrated energy system as the research objective, construct an optimization objective function that considers the operating costs of the distribution network and the natural gas network;

[0011] S4. Based on the constraints of distribution network operation, energy storage, natural gas gate station adjustment, and the constraints in S1, establish a robust optimization model of the integrated energy system considering load uncertainty based on the optimization objective function in S3.

[0012] S5. Construct a two-layer robust optimization algorithm. The sub-problems solve the worst-case operating scenarios, while the main problem optimizes the operating cost of the integrated energy system. The solution yields the optimized scheduling scheme for the integrated energy system.

[0013] As a preferred embodiment of the present invention, the process of establishing the natural gas supply system pipeline model in S1 is as follows:

[0014] In natural gas supply systems, the pipeline storage state of the natural gas network is described based on the Weymouth equation:

[0015] ;

[0016] In the formula, Let mn be the average natural gas flow rate of the natural gas pipeline during time period t. and Let m and n be the gas pressures at natural gas pipeline nodes m and n respectively, for time period t. It is Weymouth's constant;

[0017] The flow balance of the natural gas network must meet the following requirements:

[0018] ;

[0019] In the formula, Let n be the set of natural gas pipelines connected to node n. This is the set of natural gas storage devices connected to node n; Let n be the set of natural gas gate stations connected to node n. This is the set of natural gas loads connected to node n; Let n be the set of gas turbines connected to node n. and These represent the gas flow rates at the end and beginning of the natural gas pipeline mn during time period t, respectively. and These represent the gas release and gas intake of the natural gas storage device s during time period t, respectively. Let t be the natural gas flow rate at natural gas gate station c during time period t; Let t be the gas flow rate of the natural gas load l connected to node n during time period t; Let t be the gas flow rate of gas turbine g connected to node n during time period t;

[0020] A linear pipeline inventory model is used to describe the dynamic effects of natural gas pipelines, thus establishing a pipeline inventory model for the natural gas supply system. The model is expressed as follows:

[0021] ;

[0022] ;

[0023] ;

[0024] ;

[0025] In the formula, , The pipe inventory of natural gas pipeline mn is respectively for time periods t and t-1; The average pressure of the natural gas pipeline mn; Let mn be the length of the natural gas pipeline.

[0026] As a preferred embodiment of the present invention, in S1, the gas pressure constraint of the natural gas pipeline node is as follows:

[0027] ;

[0028] In the formula, , , These represent the gas pressure and its upper and lower limits at the natural gas pipeline nodes during time period t.

[0029] Pipeline operation constraints are:

[0030] ;

[0031] In the formula, , These represent the upper and lower limits of the natural gas pipeline mn's inventory during time period t;

[0032] Natural gas gate station supply constraints are:

[0033] ;

[0034] In the formula, , These represent the upper and lower limits of the natural gas flow rate at natural gas gate station c during time period t;

[0035] The charging and releasing constraints for natural gas storage devices are:

[0036] ;

[0037] ;

[0038] ;

[0039] ;

[0040] ;

[0041] ;

[0042] In the formula, , These represent the gas storage capacity of the natural gas storage device s during time periods t and t-1, respectively. , These are binary variables, representing the gas filling and gas release states of the gas storage device during time period t, respectively. , These are the filling and releasing efficiencies of the natural gas storage device s, respectively. , These represent the maximum and minimum gas release rates of the gas storage device s during time period t; , These represent the maximum and minimum gas filling amounts of the gas storage device during time period t, respectively.

[0043] As a preferred embodiment of the present invention, in S2, there are time-shiftable loads within the distribution network, and the time-shiftable load model of the distribution network is as follows:

[0044] ;

[0045] ;

[0046] In the formula, This represents the total load that can be shifted within a day. This represents the amount of time-shiftable load connected during time period t. , These represent the upper and lower limits of the load capacity during time period t, respectively; T is the number of time periods, with a value of 24, representing one day.

[0047] There are time-shiftable loads within the natural gas network. The time-shiftable load model for the natural gas network is as follows:

[0048] ;

[0049] ;

[0050] In the formula, The total load of time-transferable gas load within a day; This represents the amount of time-transferable gas load connected during time period t. , These represent the upper and lower limits of the gas load during time period t;

[0051] The demand response load model for the distribution network is as follows:

[0052] ;

[0053] ;

[0054] In the formula, This represents the load reduction level of the z-th load that can be reduced during time period t; This represents the maximum load reduction power during time period t; , , These represent the total amount of energy that can be reduced for the z-th load and its upper and lower limits, respectively.

[0055] As a preferred embodiment of the present invention, in step S3, the optimization objective function considering the operating costs of the power distribution network and the operating costs of the natural gas network is:

[0056] ;

[0057] In the formula, F represents the operating cost of the integrated energy system; The operating cost of the power distribution network; For the operating costs of the natural gas network;

[0058] The calculation method is as follows:

[0059] ;

[0060] In the formula, The cost of purchasing electricity for the power distribution network; Subsidies for time-shifted loads; Subsidies for demand response loads;

[0061] The calculation method is as follows:

[0062] ;

[0063] In the formula, The cost of purchasing gas for the natural gas network; Subsidies for time-shifted loads on natural gas networks.

[0064] As a preferred embodiment of the present invention, in S4, the power distribution network operation constraints are as follows:

[0065] ;

[0066] ;

[0067] ;

[0068] ;

[0069] ;

[0070] ;

[0071] In the formula, The square of the voltage amplitude at node i in the distribution network; , These are the upper and lower limits of the voltage amplitude at distribution network nodes, respectively. The square of the current amplitude flowing through branch ij; This is the upper limit of the square of the current amplitude flowing through branch ij; Let be the active power flowing through branch ij during time period t; This refers to the number of the gas turbine. The number of gas turbines; This is a binary variable indicating whether the gas turbine is installed at node j of the distribution network; For gas turbine The power value; Let be the resistance of branch ij; The active load connected to node j of the distribution network during time period t; Let be the active power flowing through branch ju during time period t; This indicates that distribution network node u is connected to distribution network node j; The numbering of adjustable loads; The number of adjustable loads; This is a binary variable indicating whether the controllable load is connected to the distribution network node j; Adjustable load for time period t The value of charging load; adjustable load includes time-shiftable adjustable load, energy storage load, and demand response load. Let be the reactive power flowing through branch ij during time period t; The reactance of branch ij; For reactive loads connected to distribution network node j during time period t; This indicates that distribution network node h is connected to distribution network node j; Let J be the reactive power flowing through branch Jh during time period t. The square of the voltage amplitude at node j in the distribution network;

[0072] Energy storage constraints are:

[0073] ;

[0074] ;

[0075] ;

[0076] ;

[0077] ;

[0078] In the formula, , These represent the remaining energy stored during time periods t and t-1, respectively. The charging and discharging efficiency of energy storage; , These are binary variables representing the charging and discharging states of energy storage, respectively. , These are the upper and lower limits of the remaining energy storage capacity, respectively. , , These represent the energy storage charging power and its upper and lower limits for time period t. , , These represent the energy storage discharge power and its upper and lower limits for time period t, respectively.

[0079] Natural gas gate station adjustment constraints include natural gas supply flow constraints, supply volume adjustment constraints, supply volume adjustment frequency constraints, and supply flow limit constraints, which are as follows:

[0080] ;

[0081] ;

[0082] ;

[0083] ;

[0084] ;

[0085] ;

[0086] ;

[0087] In the formula, The natural gas flow rate at natural gas gate station c during time period t-1; , These represent the minimum and maximum gas supply adjustment amounts for natural gas gate station C, respectively. , These are binary variables representing the increased gas supply to the natural gas gate station for time periods t and t-1, respectively. , These are binary variables representing the reduction in gas supply at the natural gas gate station during time periods t and t-1, respectively. The maximum number of times the gas supply to the natural gas gate station can be adjusted.

[0088] As a preferred embodiment of the present invention, the process of establishing the robust optimization model of the integrated energy system considering load uncertainty in S4 is as follows:

[0089] During the operation of an integrated energy system, both electrical and gas loads exhibit uncertainty. A box-type uncertainty set is used to define the load uncertainty for distribution network loads:

[0090] ;

[0091] ;

[0092] In the formula, Let t be the load of the distribution network during time period t; The predicted value of the distribution network load for time period t; This refers to the fluctuation deviation of the distribution network load; These are adjustment parameters introduced to address the uncertainty of distribution network load.

[0093] For natural gas network load:

[0094] ;

[0095] ;

[0096] In the formula, Let t be the load of the natural gas network during time period t; The predicted value of the natural gas network load for time period t; This refers to the fluctuation deviation of the natural gas network load; These are adjustment parameters introduced to address the uncertainty of natural gas network load.

[0097] The objective function is transformed into a robust optimization scheduling model, resulting in a robust optimization model for the integrated energy system that considers load uncertainty.

[0098] .

[0099] As a preferred embodiment of the present invention, the process of constructing the two-layer robust optimization algorithm in S5 is as follows:

[0100] After considering the uncertain sets of distribution network load and natural gas network load, the solution of the optimization objective function changes from one stage to two stages. In order to more effectively explain the solution process and solution method, a compact model is designed as follows:

[0101] ;

[0102] ;

[0103] ;

[0104] ;

[0105] ;

[0106] ;

[0107] In the formula, x is the optimization variable in the first stage, namely the time-of-use charging price of each controllable load; the optimization variables in the second stage are v and y, namely the load uncertainty variables and the optimal solution of the distribution network power flow; V is the set of load uncertainty variables; Y is the set of optimal solutions of the distribution network power flow. and To optimize the coefficient matrix of the objective function, the superscript T denotes transpose; d, o, a are constant column vectors; A, H, B, D, E, G This is a sparse matrix of constraints corresponding to different optimization stages;

[0108] The original problem is broken down into a main problem and subproblems. The main problem takes the following form:

[0109] Objective function:

[0110] ;

[0111] In the formula, The solution to the subproblem;

[0112] Constraints:

[0113] ;

[0114] ;

[0115] ;

[0116] ;

[0117] ;

[0118] ;

[0119] ;

[0120] In the formula, k is the index of the iteration number; This represents the maximum number of iterations. Let y be the value at the k-th iteration. Let v be the value at the k-th iteration.

[0121] The specific form of the subproblem is:

[0122] Objective function:

[0123] ;

[0124] In the formula, Let x be a set of solutions for the variable x;

[0125] Constraints:

[0126] ;

[0127] ;

[0128] Given a set of uncertain variables v, the inner-level min problem becomes a second-order cone programming problem. According to strong duality theory, it is transformed into a dual problem in max form, and combined with the outer-level max problem, we obtain the following form:

[0129] Objective function:

[0130] ;

[0131] In the formula, For the dual variable in the subproblem;

[0132] Constraints:

[0133] ;

[0134] ;

[0135] ;

[0136] In the formula, Number the norm constraint coefficient matrix; The number of norm constraints; For the first The coefficient matrix of norm constraints; The dual variable norm is used to constrain the dual variable; For the dual variable, the first The coefficient matrix of norm constraints; , As dual variables; Denotes the L2 norm; b is a constant vector;

[0137] Due to the objective function In This is a bilinear problem, which is linearized using binary expansion and the Big M method. The subproblem is then reconstructed into a mixed-integer second-order cone programming problem.

[0138] ;

[0139] In the formula, M is a constant in the Big M method; For the dual variable corresponding to the part with uncertain variables; This is the upper boundary of the dual variable; This is the lower boundary of the dual variable; This is an auxiliary variable, and it is a binary variable. This is an auxiliary variable, and it is a binary variable. This is an uncertainty adjustment parameter.

[0140] As a preferred embodiment of the present invention, the solution process in S5 is as follows:

[0141] S5.1 Given a set of v values ​​as the initial worst-case scenario, set the lower bound of the running cost as... The upper limit of operating costs is The number of iterations is k=1;

[0142] S5.2, Based on the worst-case scenario Solve the main problem to obtain the optimal solution to the main problem in the k-th iteration. and The result obtained from the main problem The value serves as the new lower bound. ;

[0143] S5.3 Substitute the solution to the main problem into the subproblem to obtain the optimal solution to the subproblem in the k-th iteration. and the worst scenario Update the upper boundary ;

[0144] S5.4, Settings For the preset convergence judgment margin, if If the result is positive, it indicates that the optimization calculation has reached the optimal solution, and the iteration stops; otherwise, add variables and the following constraints:

[0145] ;

[0146] ;

[0147] ;

[0148] ;

[0149] In the formula, Let y be the value at the (k+1)th iteration.

[0150] S5.5 Let k = k + 1, return to S5.2 and continue iterating until the algorithm converges.

[0151] A robust optimization scheduling device for an integrated energy system based on controllability includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The aforementioned method is implemented by executing the computer program through the processor.

[0152] The beneficial effects of this invention are:

[0153] Optimizing scheduling flexibility: This invention establishes a natural gas supply system pipeline storage model, a power grid time-shiftable load model, a gas grid time-shiftable load model, and a power grid demand response load model. It comprehensively considers the operational constraints of the natural gas supply system and gas storage devices, as well as the controllability of the power grid and gas grid. This enables the scheduling strategy to effectively address the complex operational problems of the electricity-gas coupled integrated energy system, thereby improving the system's flexibility and adaptability.

[0154] Reducing operating costs: This invention aims to reduce the operating costs of an integrated energy system by constructing an optimization objective function that considers both distribution network and natural gas network operating costs. By considering load uncertainty, a robust optimization model is established, and a two-layer robust optimization algorithm is used to solve it. This effectively reduces the operating costs of the integrated energy system and improves economic efficiency while ensuring stable system operation.

[0155] Improving system stability: This invention constructs a robust optimization model for the integrated energy system by considering constraints on distribution network operation, natural gas network operation, energy storage capacity, gas storage capacity, charging and discharging constraints, and gas filling and releasing constraints. This model effectively addresses load uncertainty, improves system stability and reliability, and reduces system operational risks caused by load fluctuations.

[0156] Practicality and Innovation: This invention integrates adjustable load resources and employs a robust optimization method to address the dynamic demand-side response problem under multi-energy coupling. Furthermore, simulation verification using real-world case studies demonstrates its effectiveness in reducing active power losses in distribution networks and the operating costs of integrated energy systems, showcasing its high practical value and innovativeness. Attached Figure Description

[0157] Figure 1 This is a flowchart illustrating the principle of this invention;

[0158] Figure 2 This is a topology diagram of the integrated energy system during the verification process of this invention;

[0159] Figure 3 This is a voltage distribution diagram of the power distribution network in scenario 1 during the verification process of this invention;

[0160] Figure 4 This is a voltage distribution diagram of the power distribution network in scenario 2 during the verification process of this invention;

[0161] Figure 5 This is a voltage distribution diagram of the power distribution network in scenario 3 during the verification process of this invention. Detailed Implementation

[0162] The embodiments of the present invention will be further described below with reference to the accompanying drawings:

[0163] like Figure 1 As shown, the robust optimization scheduling method for integrated energy systems based on controllable capabilities includes the following steps:

[0164] S1. Taking the natural gas supply system and natural gas storage device as the research objects, establish a pipeline storage model of the natural gas supply system, and establish gas pressure constraints, pipeline operation constraints, natural gas gate station gas supply constraints, and gas filling and releasing constraints of the natural gas storage device.

[0165] S2. Taking the controllability of an integrated energy system including distribution networks and natural gas networks as the research object, establish a time-shiftable controllable load model for distribution networks, a time-shiftable controllable load model for natural gas networks, and a demand response load model for distribution networks.

[0166] S3. Taking the operating cost of the integrated energy system as the research objective, construct an optimization objective function that considers the operating costs of the distribution network and the natural gas network;

[0167] S4. Based on the constraints of distribution network operation, energy storage, natural gas gate station adjustment, and the constraints in S1, establish a robust optimization model of the integrated energy system considering load uncertainty based on the optimization objective function in S3.

[0168] S5. Construct a two-layer robust optimization algorithm. The sub-problems solve the worst-case operating scenarios, while the main problem optimizes the operating cost of the integrated energy system. The solution yields the optimized scheduling scheme for the integrated energy system.

[0169] In S1, the process of establishing the natural gas supply system pipeline model is as follows:

[0170] In natural gas supply systems, the pipeline storage state of the natural gas network is described based on the Weymouth equation:

[0171] ;

[0172] In the formula, Let mn be the average natural gas flow rate of the natural gas pipeline during time period t. and Let m and n be the gas pressures at natural gas pipeline nodes m and n respectively, for time period t. This is the Weymouth constant, which is related to the physical properties of the pipe, such as temperature, length, diameter, and friction.

[0173] The flow balance of the natural gas network must meet the following requirements:

[0174] ;

[0175] In the formula, Let n be the set of natural gas pipelines connected to node n. This is the set of natural gas storage devices connected to node n; Let n be the set of natural gas gate stations connected to node n. This is the set of natural gas loads connected to node n; Let n be the set of gas turbines connected to node n. and These represent the gas flow rates at the end and beginning of the natural gas pipeline mn during time period t, respectively. and These represent the gas release and gas intake of the natural gas storage device s during time period t, respectively. Let t be the natural gas flow rate at natural gas gate station c during time period t; Let t be the gas flow rate of the natural gas load l connected to node n during time period t; Let t be the gas flow rate of gas turbine g connected to node n during time period t;

[0176] A linear pipeline inventory model is used to describe the dynamic effects of natural gas pipelines, thus establishing a pipeline inventory model for the natural gas supply system. The model is expressed as follows:

[0177] ;

[0178] ;

[0179] ;

[0180] ;

[0181] In the formula, , The pipe inventory of natural gas pipeline mn is respectively for time periods t and t-1; The average pressure of the natural gas pipeline mn; Let mn be the length of the natural gas pipeline.

[0182] The gas pressure constraint of the natural gas pipeline node is:

[0183] ;

[0184] In the formula, , , These represent the gas pressure and its upper and lower limits at the natural gas pipeline nodes during time period t.

[0185] Pipeline operation constraints are:

[0186] ;

[0187] In the formula, , These represent the upper and lower limits of the natural gas pipeline mn's inventory during time period t;

[0188] Natural gas gate station supply constraints are:

[0189] ;

[0190] In the formula, , These represent the upper and lower limits of the natural gas flow rate at natural gas gate station c during time period t;

[0191] The charging and releasing constraints for natural gas storage devices are:

[0192] ;

[0193] ;

[0194] ;

[0195] ;

[0196] ;

[0197] ;

[0198] In the formula, , These represent the gas storage capacity of the natural gas storage device s during time periods t and t-1, respectively. , These are binary variables, representing the gas filling and gas release status of the gas storage device during time period t. A value of 1 indicates filling or releasing gas, and the same applies to the other binary variables. , These are the filling and releasing efficiencies of the natural gas storage device s, respectively. , These represent the maximum and minimum gas release rates of the gas storage device s during time period t; , These represent the maximum and minimum gas filling amounts of the gas storage device during time period t, respectively.

[0199] In S2, there are time-shiftable loads within the distribution network. The time-shiftable load model for the distribution network is as follows:

[0200] ;

[0201] ;

[0202] In the formula, This represents the total load that can be shifted within a day. This represents the amount of time-shiftable load connected during time period t. , These represent the upper and lower limits of the load capacity during time period t, respectively; T is the number of time periods, with a value of 24, representing one day.

[0203] There are time-shiftable loads within the natural gas network. The time-shiftable load model for the natural gas network is as follows:

[0204] ;

[0205] ;

[0206] In the formula, The total load of time-transferable gas load within a day; This represents the amount of time-transferable gas load connected during time period t. , These represent the upper and lower limits of the gas load during time period t;

[0207] The demand response load model for the distribution network is as follows:

[0208] ;

[0209] ;

[0210] In the formula, This represents the load reduction level of the z-th load that can be reduced during time period t; This represents the maximum load reduction power during time period t; , , These represent the total amount of energy that can be reduced for the z-th load and its upper and lower limits, respectively.

[0211] In S3, the optimization objective function considering the operating costs of the distribution network and the natural gas network is:

[0212] ;

[0213] In the formula, F represents the operating cost of the integrated energy system; The operating cost of the power distribution network; For the operating costs of the natural gas network;

[0214] The calculation method is as follows:

[0215] ;

[0216] In the formula, The cost of purchasing electricity for the power distribution network; Subsidies for time-shifted loads; Subsidies for demand response loads;

[0217] The calculation method is as follows:

[0218] ;

[0219] In the formula, The cost of purchasing gas for the natural gas network; Subsidies for time-shifted loads on natural gas networks.

[0220] In S4, the distribution network operation constraints are:

[0221] ;

[0222] ;

[0223] ;

[0224] ;

[0225] ;

[0226] ;

[0227] In the formula, The square of the voltage amplitude at node i in the distribution network; , These are the upper and lower limits of the voltage amplitude at distribution network nodes, respectively. The square of the current amplitude flowing through branch ij; This is the upper limit of the square of the current amplitude flowing through branch ij; Let be the active power flowing through branch ij during time period t; This refers to the number of the gas turbine. The number of gas turbines; This is a binary variable indicating whether the gas turbine is installed at node j of the distribution network; For gas turbine The power value; Let be the resistance of branch ij; The active load connected to node j of the distribution network during time period t; Let be the active power flowing through branch ju during time period t; This indicates that distribution network node u is connected to distribution network node j; The numbering of adjustable loads; The number of adjustable loads; This is a binary variable indicating whether the controllable load is connected to the distribution network node j; Adjustable load for time period t The value of charging load; adjustable load includes time-shiftable adjustable load, energy storage load, and demand response load. Let be the reactive power flowing through branch ij during time period t; The reactance of branch ij; For reactive loads connected to distribution network node j during time period t; This indicates that distribution network node h is connected to distribution network node j; Let J be the reactive power flowing through branch Jh during time period t. The square of the voltage amplitude at node j in the distribution network;

[0228] Energy storage constraints are:

[0229] ;

[0230] ;

[0231] ;

[0232] ;

[0233] ;

[0234] In the formula, , These represent the remaining energy stored during time periods t and t-1, respectively. The charging and discharging efficiency of energy storage; , These are binary variables representing the charging and discharging states of energy storage, respectively. , These are the upper and lower limits of the remaining energy storage capacity, respectively. , , These represent the energy storage charging power and its upper and lower limits for time period t. , , These represent the energy storage discharge power and its upper and lower limits for time period t, respectively.

[0235] Natural gas gate station adjustment constraints include natural gas supply flow constraints, supply volume adjustment constraints, supply volume adjustment frequency constraints, and supply flow limit constraints, which are as follows:

[0236] ;

[0237] ;

[0238] ;

[0239] ;

[0240] ;

[0241] ;

[0242] ;

[0243] In the formula, The natural gas flow rate at natural gas gate station c during time period t-1; , These represent the minimum and maximum gas supply adjustment amounts for natural gas gate station C, respectively. , These are binary variables representing the increased gas supply to the natural gas gate station for time periods t and t-1, respectively. , These are binary variables representing the reduction in gas supply at the natural gas gate station during time periods t and t-1, respectively. The maximum number of times the gas supply to the natural gas gate station can be adjusted.

[0244] The process of establishing a robust optimization model for a comprehensive energy system considering load uncertainty is as follows:

[0245] During the operation of an integrated energy system, both electrical and gas loads exhibit uncertainty. A box-type uncertainty set is used to define the load uncertainty for distribution network loads:

[0246] ;

[0247] ;

[0248] In the formula, Let t be the load of the distribution network during time period t; The predicted value of the distribution network load for time period t; This refers to the fluctuation deviation of the distribution network load; These are adjustment parameters introduced to address the uncertainty of distribution network load. It is the load number of the distribution network;

[0249] For natural gas network load:

[0250] ;

[0251] ;

[0252] In the formula, Let t be the load of the natural gas network during time period t; The predicted value of the natural gas network load for time period t; This refers to the fluctuation deviation of the natural gas network load; These are adjustment parameters introduced to address the uncertainty of natural gas network load.

[0253] The uncertainty parameter represents the number of time periods during which the maximum or minimum value of the fluctuation range described by the distribution network load and the natural gas network load is within the scheduling cycle. It can adjust the conservatism of the optimal solution; the larger the value, the more conservative the optimization scheme.

[0254] The objective function is transformed into a robust optimization scheduling model, resulting in a robust optimization model for the integrated energy system that considers load uncertainty.

[0255] .

[0256] In S5, the process of constructing the two-layer robust optimization algorithm is as follows:

[0257] After considering the uncertain sets of distribution network load and natural gas network load, the solution of the optimization objective function changes from one stage to two stages. In order to more effectively explain the solution process and solution method, a compact model is designed as follows:

[0258] ;

[0259] ;

[0260] ;

[0261] ;

[0262] ;

[0263] ;

[0264] In the formula, x is the optimization variable in the first stage, namely the time-of-use charging price of each controllable load; the optimization variables in the second stage are v and y, namely the load uncertainty variables and the optimal solution of the distribution network power flow; V is the set of load uncertainty variables; Y is the set of optimal solutions of the distribution network power flow. and To optimize the coefficient matrix of the objective function, the superscript T denotes transpose; d, o, a are constant column vectors; A, H, B, D, E, G This is a sparse matrix of constraints corresponding to different optimization stages;

[0265] The original problem is broken down into a main problem and subproblems. The main problem takes the following form:

[0266] Objective function:

[0267] ;

[0268] In the formula, The solution to the subproblem;

[0269] Constraints:

[0270] ;

[0271] ;

[0272] ;

[0273] ;

[0274] ;

[0275] ;

[0276] ;

[0277] In the formula, k is the index of the iteration number; This represents the maximum number of iterations. Let y be the value at the k-th iteration. Let v be the value at the k-th iteration.

[0278] The specific form of the subproblem is:

[0279] Objective function:

[0280] ;

[0281] In the formula, Let x be a set of solutions for the variable x;

[0282] Constraints:

[0283] ;

[0284] ;

[0285] Given a set of uncertain variables v, the inner-level min problem becomes a second-order cone programming problem. According to strong duality theory, it is transformed into a dual problem in max form, and combined with the outer-level max problem, we obtain the following form:

[0286] Objective function:

[0287] ;

[0288] In the formula, For the dual variable in the subproblem;

[0289] Constraints:

[0290] ;

[0291] ;

[0292] ;

[0293] In the formula, Number the norm constraint coefficient matrix; The number of norm constraints; For the first The coefficient matrix of norm constraints; The dual variable norm is used to constrain the dual variable; For the dual variable, the first The coefficient matrix of norm constraints; , As dual variables; Denotes the L2 norm; b is a constant vector;

[0294] Due to the objective function In This is a bilinear problem, which is linearized using binary expansion and the Big M method. The subproblem is then reconstructed into a mixed-integer second-order cone programming problem.

[0295] ;

[0296] In the formula, M is a constant in the Big M method; For the dual variable corresponding to the part with uncertain variables; This is the upper boundary of the dual variable; This is the lower boundary of the dual variable; This is an auxiliary variable, and it is a binary variable. This is an auxiliary variable, and it is a binary variable. This is an uncertainty adjustment parameter.

[0297] The solution process is as follows:

[0298] S5.1 Given a set of v values ​​as the initial worst-case scenario, set the lower bound of the running cost as... The upper limit of operating costs is The number of iterations is k=1;

[0299] S5.2, Based on the worst-case scenario Solve the main problem to obtain the optimal solution to the main problem in the k-th iteration. and ( For the solution of the variable, (the value of the objective function), obtained from the main problem The value serves as the new lower bound. ;

[0300] S5.3 Substitute the solution to the main problem into the subproblem to obtain the optimal solution to the subproblem in the k-th iteration. and the worst scenario (The optimal solution is the k-th iteration, and the optimal solution will yield a worst-case scenario, which will be carried over to the (k+1)-th iteration.) Update the upper bound. ;

[0301] S5.4, Settings For the preset convergence judgment margin, if If the result is positive, it indicates that the optimization calculation has reached the optimal solution, and the iteration stops; otherwise, add variables and the following constraints:

[0302] ;

[0303] ;

[0304] ;

[0305] ;

[0306] In the formula, Let y be the value at the (k+1)th iteration.

[0307] S5.5 Let k = k + 1, return to S5.2 and continue iterating until the algorithm converges.

[0308] The verification process is based on Figure 2 The integrated energy system topology shown is illustrated. A program based on the method described in this embodiment is written using MATLAB for simulation verification, and the solution is obtained using Gurobi. The verification example settings are shown in Table 1, and the simulation comparison scenario settings are shown in Table 2.

[0309] Table 1 Verification Case Settings

[0310]

[0311] Table 2 Simulation comparison scenario settings

[0312]

[0313] Figures 3-5 Table 3 shows the voltage distribution of the distribution network under different scenarios. Table 4 compares the active power loss of the distribution network in each scenario. Table 5 compares the operating costs of the integrated energy system in each scenario.

[0314] Table 3 Comparison of Active Power Losses in Distribution Networks

[0315]

[0316] Table 4 Comparative Analysis of Operating Costs of Integrated Energy Systems

[0317]

[0318] According to Table 3, Table 4 and Figure 3-5 As can be seen, the method proposed in this embodiment achieves the minimum operating costs of the power distribution network and the natural gas network, and the voltage distribution is more stable.

[0319] Example 2: A robust optimization scheduling device for an integrated energy system based on controllability, comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the method in Example 1 is implemented by the processor executing the computer program.

Claims

1. A robust optimization scheduling method for integrated energy system based on controllability, characterized in that It comprises the following steps: S1, taking a natural gas supply system and a natural gas storage device as research objects, establishing a natural gas supply system pipe storage model, and establishing natural gas pipeline node gas pressure constraints, pipeline operation constraints, natural gas gate station gas supply constraints, and natural gas storage device charging and releasing gas constraints; S2, taking the controllable capacity of a comprehensive energy system comprising a power distribution network and a natural gas network as a research object, establishing a power distribution network time-shiftable controllable load model, a natural gas network time-shiftable controllable load model, and a power distribution network demand response load model; S3, taking the operation cost of the comprehensive energy system as a research target, constructing an optimization objective function considering power distribution network operation costs and natural gas network operation costs; S4, based on the power distribution network operation constraints, energy storage constraints, natural gas gate station adjustment constraints, and constraint conditions in S1, establishing a comprehensive energy system robust optimization model considering load uncertainty based on the optimization objective function in S3; S5, constructing a double-layer robust optimization algorithm, the sub-problem realizes the solution of the worst operating scenario, and the main problem realizes the operation cost optimization of the comprehensive energy system, and the optimal scheduling scheme of the comprehensive energy system is obtained by solving.

2. The controllability-based robust optimization scheduling method for integrated energy systems according to claim 1, wherein, In the S1, the process of establishing the natural gas supply system pipe storage model is: In the natural gas supply system, the pipe storage state of the natural gas network is described based on the Weymouth equation: ； wherein is the average flow of natural gas through the natural gas pipeline mn for the time period t; and are the gas pressures at nodes m and n, respectively, of the natural gas pipeline for the time period t; is the Weymouth constant; The flow balance of the natural gas network needs to meet: ； wherein is the set of natural gas pipelines connected to node n; is the set of natural gas storage devices connected to node n; is the set of natural gas gate stations connected to node n; is the set of natural gas loads connected to node n; is the set of gas turbines connected to node n; and are the gas flow rates at the end and the beginning of the natural gas pipeline mn, respectively, at time t; and are the outflow and inflow rates of the natural gas storage device s, respectively, at time t; is the natural gas flow rate of the natural gas gate station c at time t; is the gas flow rate of the natural gas load l connected to node n at time t; is the gas flow rate of the gas turbine g connected to node n at time t; A linear pipe storage model is used to describe the dynamic effect of the natural gas pipeline, and the natural gas supply system pipe storage model is established, and the expression form is as follows: ； ； ； ； wherein , are the pipe inventory of the natural gas pipeline mn for the periods t, t-1, respectively; is the average pressure of the natural gas pipeline mn; is the length of the natural gas pipeline mn.

3. The controllability-based robust optimization scheduling method for integrated energy systems according to claim 2, wherein, In the S1, the natural gas pipeline node gas pressure constraint is: ； In the formula, , , are the upper and lower limits of the gas pressure of the natural gas pipeline node at time t, respectively. The pipeline operation constraint is: ； wherein , are the upper and lower limits of the pipe inventory of the natural gas pipeline mn for the period t, respectively. The natural gas gate station gas supply constraint is: ； wherein , are the upper and lower limits of the natural gas flow at the natural gas gate station c for the time period t, respectively. The charging and releasing gas constraint of the natural gas storage device is: ； ； ； ； ； ； In the formula, , These represent the gas storage capacity of the natural gas storage device s during time periods t and t-1, respectively. , These are binary variables, representing the gas filling and gas release states of the gas storage device during time period t, respectively. , These are the filling and releasing efficiencies of the natural gas storage device s, respectively. , These represent the maximum and minimum gas release rates of the gas storage device s during time period t; , These represent the maximum and minimum gas filling amounts of the gas storage device during time period t, respectively.

4. The controllability-based integrated energy system robust optimization scheduling method according to claim 1, wherein, In the S2, there is a time-shiftable load in the power distribution network, and the power distribution network time-shiftable controllable load model is: ； ； In the formula, is the total amount of load that can be time-shifted within a day; is the amount of access of the time-shiftable load at time period t; , are the upper and lower limits of the access load amount at time period t, respectively; T is the number of time periods, taking the value 24, representing a day; There is a time-shiftable load in the natural gas network, and the natural gas network time-shiftable controllable load model is: ； ； wherein is the total amount of gas load that can be time-shifted within a day; is the amount of gas load that can be time-shifted at time period t; , are the upper and lower limits, respectively, of the amount of gas load that can be time-shifted at time period t. The power distribution network demand response load model is: ； ； In the formula, represents the load curtailment level of the zth curtailable load at the tth time interval; represents the maximum load curtailment power at the tth time interval; , , respectively represent the total amount of curtailed electric energy of the zth curtailable load and its upper and lower limits.

5. The controllability-based integrated energy system robust optimization scheduling method according to claim 3, wherein, In the S3, the optimization objective function considering the power distribution network operation cost and the natural gas network operation cost is: ； In the formula, F is the operation cost of the integrated energy system; is the operation cost of the power distribution network; is the operation cost of the natural gas network; The calculation is as follows: ； In the formula, is the electricity purchase cost of the distribution network; is the subsidy cost of the time-shifted load; is the subsidy cost of the demand response load; The calculation method is as follows: ； wherein is the gas purchase cost for the natural gas network; is the subsidy cost for the time-shifted load of the natural gas network.

6. The controllability-based integrated energy system robust optimization scheduling method according to claim 5, wherein, In the S4, the power distribution network operation constraint is: ； ； ； ； ； ； wherein, is the square of the voltage magnitude of distribution network node i; , are the upper and lower limits of the voltage magnitude of distribution network node, respectively; is the square of the current magnitude flowing through branch ij; is the upper limit of the square of the current magnitude flowing through branch ij; is the active power flowing through branch ij at time period t; is the number of gas turbines; is the number of gas turbines; is a binary variable indicating whether a gas turbine is installed at distribution network node j; is the power value of gas turbine ; is the resistance of branch ij; is the active load connected to distribution network node j at time period t; is the active power flowing through branch ju at time period t; indicates that distribution network node u is connected to distribution network node j; is the number of controllable loads; is the number of controllable loads; is a binary variable indicating whether a controllable load is connected to distribution network node j; is the value of controllable load at time period t, which includes time- shiftable controllable load, energy storage load and demand response load; is the reactive power flowing through branch ij at time period t; is the reactance of branch ij; is the reactive load connected to distribution network node j at time period t; indicates that distribution network node h is connected to distribution network node j; is the reactive power flowing through branch jh at time period t; is the square of the voltage magnitude of distribution network node j; The energy storage constraint is: ； ； ； ； ； In the formula, , respectively are the remaining power of the energy storage in the t, t-1 time period; is the charging and discharging efficiency of the energy storage; , respectively are binary variables representing the charging and discharging state of the energy storage; , respectively are the upper and lower limits of the remaining power of the energy storage; , , respectively are the charging power of the energy storage in the t time period and its upper and lower limits; , , respectively are the discharging power of the energy storage in the t time period and its upper and lower limits; The natural gas gate station adjustment constraint includes the natural gas supply flow constraint, the gas supply adjustment constraint, the gas supply adjustment times constraint, and the gas flow limitation constraint, which are respectively: ； ； ； ； ； ； ； wherein, is the natural gas flow of the natural gas gate station c in the time period t-1; , are the minimum and maximum adjustment of the supply of the natural gas gate station c, respectively; , are binary variables of the increase of the supply of the natural gas gate station in the time periods t and t-1, respectively; , are binary variables of the decrease of the supply of the natural gas gate station in the time periods t and t-1, respectively; is the maximum number of adjustments of the supply of the natural gas gate station.

7. The controllability-based integrated energy system robust optimization scheduling method according to claim 6, characterized in that, In the S4, the process of establishing the comprehensive energy system robust optimization model considering load uncertainty is: During the operation of the comprehensive energy system, both the electric load and the gas load are uncertain, and the uncertainty of the load is defined by using a box-type uncertainty set, for the power distribution network load: ； ； wherein is the load of the distribution grid for the time period t; is the forecast value of the distribution grid load for the time period t; is the fluctuation deviation of the distribution grid load; is the regulation parameter introduced for the distribution grid load uncertainty; For the natural gas network load: ； ； wherein is the load of the natural gas network for the time period t; is the forecast value of the load of the natural gas network for the time period t; is the fluctuation bias of the load of the natural gas network; is a regulation parameter introduced for the uncertainty of the load of the natural gas network; The optimization objective function is converted into a robust optimization scheduling model to obtain the comprehensive energy system robust optimization model considering load uncertainty: 。 8.The controllability-based robust optimization scheduling method of integrated energy systems according to claim 7, wherein, In the S5, the process of constructing the double-layer robust optimization algorithm is: After considering the uncertainty set of the power distribution network load and the natural gas network load, the solution of the optimization objective function changes from one stage to two stages, in order to more effectively explain the solution process and solution method, a compact model is designed as follows: ； ； ； ； ； ； In the formula, x is the optimization variable of the first stage, that is, the time-of-use charging price of each controllable load; the optimization variable of the second stage is v and y, that is, the load uncertainty variable and the optimization solution of the power distribution network power flow; V is the set of load uncertainty variables; Y is the set of optimization solutions of the power distribution network power flow; and is the coefficient matrix of the optimization objective function, and the superscript T represents transposition; d, o, a are constant column vectors; A, H, B, D, E, , G, are sparse matrices of constraint conditions corresponding to different optimization stages; The original problem is divided into a main problem and a sub-problem, and the specific form of the main problem is: Objective function: ； In the formula, is the solution to the subproblem; Constraint condition: ； ； ； ； ； ； ； where k is an index of the iteration number; is the maximum iteration number; is y at the kth iteration; is v at the kth iteration; The specific form of the sub-problem is: Objective function: ； wherein a set of solutions for the variable x; Constraint condition: ； ； In the case of a given set of uncertain variables v, the inner min problem becomes a second-order cone programming problem, which is converted into a max form of a dual problem according to the strong duality theory, and is combined with the outer max problem to obtain the following form: Objective function: ； In the formula, is the dual variable in the subproblem; Constraint condition: ； ； ； wherein is a norm constraint coefficient matrix number; is a number of norm constraints; is a norm constraint coefficient matrix number; is a norm constraint coefficient matrix number; is a dual variable norm constraint dual variable; is a norm constraint coefficient matrix number; is a norm constraint coefficient matrix number; , is a dual variable; denotes the L2 norm; b is a constant vector; Since the objective function is bilinear, the subproblem is reformulated as a mixed integer second order cone programming problem by using binary expansion and big M method: ​ ； where M is a constant in the Big M method; is the dual variable corresponding to the uncertain variable part; is the upper bound of the dual variable; is the lower bound of the dual variable; is a binary variable that is an auxiliary variable; is a binary variable that is an auxiliary variable; is an uncertainty adjustment parameter.

9. The controllability-based integrated energy system robust optimization scheduling method according to claim 8, wherein, In the S5, the solving process is as follows: S5.1, Given a set of v values as initial worst-case scenarios, set the lower bound of the running cost as , the upper bound of the running cost as , and the iteration number as k = 1; S5.2, according to the worst-case scenario Solving the master problem to obtain the optimal solution of the master problem at the kth iteration ;​​​ S5.3, substitute the solution of the main problem into the sub-problem to obtain the optimal solution of the sub-problem at the kth iteration and worst-case scenarios , update the upper bound ; S5.4, Settings For the preset convergence judgment margin, if If the result is positive, it indicates that the optimization calculation has reached the optimal solution, and the iteration stops; otherwise, add variables and the following constraints: ； ； ； ； wherein y is the y at the k+1 iteration; S5.5, let k=k+1, return to S5.2 to continue iteration until the algorithm converges.

10. A robust optimal dispatching device for integrated energy system based on controllability, characterized in that: Computer program product comprising a memory, a processor and a computer program stored on the memory and capable of running on the processor, the computer program being executed by the processor to implement the method of any one of claims 1-9.

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