Electricity-gas energy system day-ahead scheduling method based on natural gas quasi-steady-state model

Abstract

The invention discloses an electricity-gas energy system day-ahead scheduling method based on a natural gas quasi-steady-state model. The method comprises the following steps: step 1, collecting predicted output data of an electric power system, a natural gas system and wind power; 2, building a deterministic model of the electricity-gas integrated energy system; constructing an objective function and constraint conditions of the electricity-gas integrated energy system, and performing piecewise linearization on nonlinear terms existing in the model; 3, a two-stage robust optimization model establishment stage; step 4, Camp is adopted; a CG algorithm solving stage; and through alternate iteration of the main problem and the sub-problems, identifying the worst scene, and adding different constraints into the main problem according to whether the target function of the sub-problems is infinitely classified, so that the upper and lower bounds are continuously close to each other, and finally a target gap is achieved, and a result is obtained.

Description

Technical Field

[0001] This invention relates to the field of energy system modeling and optimization technology, and in particular to a day-ahead scheduling method for an electric-gas energy system based on a quasi-steady-state model of natural gas. Background Technology

[0002] Energy transition is a key issue for global sustainable development. However, the randomness of renewable energy sources such as wind power poses a challenge to the stability of power systems. To address this issue, the Integrated Electricity and Gas System (IEGS) combines the power system with the natural gas system, fully leveraging the low-carbon and high-efficiency characteristics of natural gas and the rapid adjustment advantages of gas turbine units. This system can effectively mitigate supply and demand fluctuations caused by the uncertainty of wind power while reducing carbon emissions.

[0003] The Statistical Review of World Energy 2024 indicates that fossil fuel consumption continued its upward trend in 2023 to meet the world's growing energy demand, and its share of global energy demand remained high, at approximately 80%. Global carbon emissions reached a new high in 2023, and against this backdrop, renewable energy continued its rapid expansion. China's newly added renewable energy power generation exceeded the total of all other regions in the world, accounting for approximately 66% of the newly installed capacity. Increasing the proportion of natural gas in fossil fuel consumption and increasing the installed capacity of renewable energy are inevitable trends.

[0004] Natural gas is cleaner and more efficient than other fossil fuels, making it a crucial transitional energy source during the global energy transition. Compared to traditional coal-fired and oil-fired power plants, gas-fired power plants offer faster response times and more flexible regulation. Furthermore, natural gas is often transported via pipelines, and the "pipeline storage effect" allows for the regulation of the conflict between stable gas supply and unstable demand within a certain range, naturally benefiting its peak-shaving capabilities. With the rapid development of coupled equipment such as gas-fired units (GFUs), a bridge for energy flow and information exchange has been built between the power system and the natural gas system. The resulting integrated electricity-gas energy system breaks down the independent model between systems, playing a significant role in improving energy efficiency and promoting the development and utilization of renewable energy.

[0005] The uncertainties of wind power mainly include the volatility and intermittency of wind speed and the randomness of wind energy. Under the overarching goal of "dual carbon emissions," a large number of new energy power plants, represented by wind power, are connected to the power system in centralized or distributed forms, posing a severe challenge to their dispatch. An integrated electric-gas energy system that considers the uncertainties of wind power can increase the output of gas turbine units to compensate when wind power output cannot meet grid demand, and reduce the output of gas turbine units when wind power is in surplus, achieving bidirectional coupling of the electric-gas system. Robust optimization aims to solve optimization problems with uncertainty or disturbances. It does not require specific probability distribution information of variables, but only needs to collect boundary data of variable fluctuations. The range of variable fluctuations is characterized by a set of intervals in the uncertainty set, and the resulting optimization results can guarantee satisfaction of all uncertain scenarios in the uncertainty set, making it increasingly popular among researchers.

[0006] The economic dispatch problem of an integrated power-gas energy system considering wind power uncertainties is a single-objective, multi-constraint, discrete, and non-convex optimization problem. When constructing a two-stage robust optimization (TSRO) model for the system, linearization is required for the nonlinear terms in the objective function and model constraints. Examples include the unit operating cost within the objective function and the quadratic terms in the Weymouth equation for the natural gas system. The Column-and-Constraint Generation (C&CG) algorithm divides the original problem into a main problem and subproblems. The main problem is solved only for deterministic optimization. By adding relatively severe scenarios and decision variables and constraints to the main problem, the upper and lower bounds of the objective function are continuously improved until the algorithm converges; this idea is also known as "recourse" decision-making. Since C&CG cannot directly handle the min-max-min three-level structure in the model, the Karush-Kuhn-Tucker (KKT) conditions are used to transform the max-min problem in the subproblems into a single-level max problem. Compared to other TSRO solution algorithms, the C&CG algorithm has good global search and convergence capabilities, and can better handle the more complex dynamic characteristics of natural gas systems after the introduction of pipeline storage. This invention designs a two-stage robust optimization solution method for an integrated electric-gas energy system based on a quasi-steady-state model of the natural gas system, aiming to efficiently solve the day-ahead scheduling problem of an integrated electric-gas energy system considering wind power uncertainties. Summary of the Invention

[0007] The purpose of this invention is to provide a day-ahead scheduling method for an electric-gas integrated energy system based on a natural gas quasi-steady-state model. This is a two-stage robust optimization solution method for an electric-gas integrated energy system based on a natural gas system quasi-steady-state model, aiming to efficiently solve the technical problem of day-ahead scheduling of an electric-gas integrated energy system that takes into account the uncertainty of wind power.

[0008] To achieve the above objectives, the technical solution of the present invention is: a day-ahead scheduling method for an electricity-gas energy system based on a quasi-steady-state model of natural gas, specifically including the following steps: Step 1: Data preparation stage; collect power system, natural gas system and wind power forecast output data; Step 2: Build a deterministic model of the integrated electric-gas energy system; construct the objective function and constraints of the integrated electric-gas energy system, and linearize the nonlinear terms in the model piecewise; Step 3: Two-stage robust optimization model establishment stage; Based on the wind power predicted output data input in Step 1, construct the wind power output polyhedral uncertainty set, and then divide the two-stage robust optimization into different stages according to whether the variables / constraints are affected by uncertainty, and simplify the innermost minimization problem by combining KKT conditions and the Big M method. Step 4: Solving stage using C&CG algorithm; through alternating iteration of main problem and subproblems, the worst-case scenario is identified, and different constraints are added to the main problem according to whether the objective function of the subproblem is infinite, so that the upper and lower bounds continuously move closer, and finally the target gap is reached to obtain the result.

[0009] The day-ahead dispatching method for an electricity-gas energy system based on a quasi-steady-state model of natural gas, wherein step 2 considers unit start-up and shutdown costs, power generation costs, gas well production costs, and wind curtailment costs, with the following objective function: (1) In the formula: For indicators in the generator set set; For indicators within the set of natural gas suppliers; A collection of natural gas generator sets; A collection of coal-fired power generating units; A collection of wind turbine generator sets; A set of time periods; ; For natural gas units Non-fuel operating costs; For coal-fired power units Operating costs natural gas supplier Production costs; For wind farm The penalty factor is used to measure the cost of wind power reduction; For generator sets Startup costs; For generator sets Downtime costs; Starting point of the natural gas pipeline and termination node The square difference of air pressure, This is the penalty coefficient for the squared difference in pipeline air pressure; This represents the set of starting nodes for the natural gas pipeline. This is the set of nodes terminating in the natural gas pipeline. , , Collectively referred to as generator units The start and stop variables; where Representative unit In time period Whether it is running; 1 indicates running, 0 indicates otherwise. Representative unit In time period Whether the device is powered on; 1 indicates power on, 0 indicates otherwise. Representative unit In time period Whether to stop the machine; 1 indicates stopping the machine, 0 indicates otherwise. This represents the uncertain variable of active power output from wind power.

[0010] , , Collectively referred to as generator units The start and stop variables; where Representative unit In time period Whether it is running; 1 indicates running, 0 indicates otherwise. Representative unit In time period Whether the device is powered on; 1 indicates power on, 0 indicates otherwise. Representative unit In time period Whether to stop the machine. If the machine is stopped, the value is 1; otherwise, the value is 0. This represents the uncertain variable of active power output from wind power.

[0011] ,use These represent the variables involved in the innermost problem. For generator sets In time period Those who have made contributions For wind turbines In the The predicted active power output for each time period; busbar In time period The phase angle within; For gas turbine units In the Natural gas flow rate consumed in each time period; For the time period Flow into the first The natural gas flow rate of the compressor; For the time period internal outflow The natural gas flow rate of the compressor; For the node Flow to Node Natural gas flow rate; For the node Flow to Node Natural gas flow rate; For time period Internal flow through pipeline Average natural gas flow rate; natural gas supplier In time period The natural gas flow rate provided; For pipelines In time period The storage capacity it possesses; Starting point of the natural gas pipeline During the period The square of the air pressure; Termination node of natural gas pipeline During the period The square of the air pressure; For compressor During the period The square of the inlet node pressure; For compressor During the period The square of the pressure at the export node.

[0012] The day-ahead scheduling method for the power-gas energy system based on a quasi-steady-state model of natural gas, wherein the constraints in step 2 are divided into power system constraints, natural gas system constraints, coupling constraints, and a wind power output uncertainty set. This invention mainly considers 8 sets of power system constraints, 10 sets of natural gas system constraints, 1 set of coupling constraints, and establishes a polyhedral uncertainty set for wind power output, expressed as follows: Power system constraints: (2) (3) (4) (5) (6) (7) (8) (9) In the formula: This is a time index, representing the starting time period of the summation calculated by taking the maximum value on the right side of the equation; For generator sets Minimum boot time; For generator sets Minimum downtime; For the first The generator sets during the time period Those who contribute their efforts; For nodes Load at the location; For connecting nodes and The susceptance of the transmission lines; For generator sets Minimum active power output during operation; For generator sets Maximum active power output during operation; For generator sets Maximum climbing rate; For connecting bus and busbar The maximum transmission capacity of the transmission lines between them; busbar In time period The phase angle within; busbar In time period The phase angle within; It is the set of nodes in a power system; Reserved capacity for upward rotation; Reserved capacity for rotational use; Time period Phase angle of the internal reference node; Natural gas system constraints: (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) Coupling constraints: (20) In the formula: A collection of natural gas wells; A collection of natural gas pipelines; A collection of gas turbine units; A collection of natural gas compression stations; Indicates the connection node and Pipelines; natural gas supplier In time period The natural gas flow rate provided; For the node Flow to Node Natural gas flow rate; For the node Flow to Node Natural gas flow rate; For nodes In time period Demand for natural gas flow; For the first The gas turbine unit during the time period Demand for natural gas flow; For the time period Flow into the first The natural gas flow rate of the compressor; For the time period internal outflow The natural gas flow rate of the compressor; For pipelines In time period The storage capacity it possesses; Indicates the compressor connected to the current node. Input port; Indicates the compressor connected to the current node. The output port; For time period Internal flow through pipeline Average natural gas flow rate; For connecting nodes and The Weymouth constant for the pipe, For nodes Natural gas pressure, For nodes Natural gas pressure, For pipelines In time period Internal storage; For compressor Consumption factor; For compressor During the period Pressure at the entry node; For compressor During the period Export node pressure; For compressor The compression ratio; For compressor During the period The maximum permissible gas flow rate for internal processing; For the time period Inner slave node Flow to Node The upper limit of natural gas flow; For the time period Inner slave node Flow to Node The upper limit of natural gas flow; natural gas supplier The minimum natural gas flow rate provided; natural gas supplier The maximum natural gas flow rate provided; Starting node The lower limit of pressure; Starting node The upper limit of pressure; Termination node The lower limit of pressure; Termination node The upper limit of pressure; For pipelines The lower limit of storage capacity; For pipelines Maximum storage limit; For gas turbine units The efficiency of power-to-natural gas conversion; Uncertain set of wind power output: (twenty one) (twenty two) (twenty three) In the formula: and These respectively characterize the uncertainty set and uncertainty variables of wind power output; and These are the uncertainty factors used to describe the upper and lower ranges of wind power, respectively. and These are the time budget and space budget for the total uncertainty within the scheduling cycle, respectively.

[0013] The day-ahead scheduling method for an electricity-gas energy system based on a quasi-steady-state model of natural gas, wherein C&CG in step 4 is represented as: (twenty four) In the above formula, These are the decision variables for the first stage in a two-stage robust optimization model. These are the decision variables for the second stage; First-stage variables The coefficient matrix, It is a constant vector used to describe the constraints in the first stage; For the first The objective function for the second stage corresponding to each pole. A vector of cost or benefit coefficients. This is the target value for the second stage in the global optimal solution; express A scenario involving quilt problem recognition. Corresponding to the identified severe scenarios, for The coefficient matrix, for coefficient matrix, for coefficient matrix, It is a constant vector used to describe the relationship between two-stage decision variables and uncertain variables; Decision variables for the first stage The feasible domain; For the second stage decision variables The feasible domain; First set of constraints Represents the constraints in the first phase; the second set of constraints Represents the constraints in the second phase; the formula in the second phase constraints within It is the first The poles correspond to the objective function of the second stage, therefore It will definitely be greater than or equal to Because it is a minimization ,therefore And that's exactly what will be obtained. The maximum value in the equation represents an equivalent transformation; at this point... As a cutting plane, it is added to the principal problem; Similarly, the second stage of identification scenarios The corresponding constraints also need to be added to the main problem, that is, the constraints. To be included in the main problem; this ensures that, given the scenario, the decision variables must satisfy the corresponding constraints; and at the same time, new decision variables need to be added to the main problem accordingly. As the algorithm iterates, the decision variables in the main problem... And constraints will continue to increase; The global upper and lower bounds of this algorithm can be calculated using the following formula: (25) in, This is the global upper bound of the algorithm. This is the global lower bound of the algorithm; For the first The first-stage optimal solution to the main problem is obtained in the next iteration; The main problem is in the first The first-stage decision variables obtained in the next iteration cost; For the subproblem in the 1st In this iteration, the decision for the first stage is... The optimal value of the second-stage cost; In the first In each iteration, the estimated optimal cost of the subproblem is obtained by solving the main problem.

[0014] Beneficial Effects: In the context of high-proportion renewable energy integration in new power systems, this invention addresses the problems of poor response to uncertain wind power output and long dynamic model solution times in traditional electric-gas integrated energy systems, as well as the wastage of precision in day-ahead dispatching. It proposes a quasi-steady-state model for natural gas systems that considers pipeline storage effects. By utilizing the compressibility of natural gas, pipelines are used as storage containers, forming an alternative "energy storage facility," and the rapid peak-shaving characteristics of gas turbine units are used to cope with wind power output fluctuations. Therefore, this invention has the ability to address wind power output uncertainty and improve dispatching economy, which is beneficial for efficiently achieving day-ahead optimized dispatching of electric-gas integrated energy systems with high renewable energy integration. Attached Figure Description

[0015] Figure 1 This is a flowchart of the entire process of this invention.

[0016] Figure 2 This is a network structure diagram of an integrated electric-gas energy system according to an embodiment of the present invention.

[0017] Figure 3 This is a schematic diagram of a small-scale system wind power uncertainty set and its actual output without considering pipeline constraints, according to an embodiment of the present invention.

[0018] Figure 4 This is a schematic diagram illustrating the uncertain set of a small-scale wind power system and its actual output, taking into account storage constraints, according to an embodiment of the present invention.

[0019] Figure 5 This is the output diagram of the gas turbine unit according to an embodiment of the present invention, without considering pipe storage constraints.

[0020] Figure 6 This is an output diagram of a gas turbine unit considering pipeline constraints according to an embodiment of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the present invention clearer and more explicit, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0022] To demonstrate the good solution capabilities of the natural gas quasi-steady-state model and the C&CG algorithm, this invention establishes an objective function and constraint model for an integrated electric-gas energy system that takes into account the uncertainties of wind power. Based on the natural gas steady-state model, constraints characterizing the pipeline storage effect are added. Piecewise linearization, KKT conditions, and the Big M method are applied to transform the nonlinear and non-convex two-stage robust optimization problem into a linear problem that is easy to solve with C&CG. The effectiveness of the proposed model is verified using an integrated electric-gas energy system consisting of a 6-node power system and a 7-node natural gas system.

[0023] like Figure 1 As shown, this invention discloses a day-ahead scheduling method for an electricity-gas energy system based on a quasi-steady-state model of natural gas, specifically including the following steps: Step 1: Data preparation stage; collect power system, natural gas system and wind power forecast output data; Step 2: Build a deterministic model of the integrated electric-gas energy system; construct the objective function and constraints of the integrated electric-gas energy system, and linearize the nonlinear terms in the model piecewise; Step 3: Two-stage robust optimization model establishment stage; Based on the wind power predicted output data input in Step 1, construct the wind power output polyhedral uncertainty set, and then divide the two-stage robust optimization into different stages according to whether the variables / constraints are affected by uncertainty, and simplify the innermost minimization problem by combining KKT conditions and the Big M method. Step 4: Solving stage using C&CG algorithm; through alternating iteration of main problem and subproblems, the worst-case scenario is identified, and different constraints are added to the main problem according to whether the objective function of the subproblem is infinite, so that the upper and lower bounds continuously move closer, and finally the target gap is reached to obtain the result.

[0024] Step 2 considers unit start-up and shutdown costs, power generation costs, gas well production costs, and wind curtailment costs. The objective function is as follows: (1) In the formula: For indicators in the generator set set; For indicators within the set of natural gas suppliers; A collection of natural gas generator sets; A collection of coal-fired power generating units; A collection of wind turbine generator sets; A set of time periods; ; For natural gas units Non-fuel operating costs; For coal-fired power units Operating costs natural gas supplier Production costs; For wind farm The penalty factor is used to measure the cost of wind power reduction; For generator sets Startup costs; For generator sets Downtime costs; Starting point of the natural gas pipeline and termination node The square difference of air pressure, This is the penalty coefficient for the squared difference in pipeline air pressure. This represents the set of starting nodes for the natural gas pipeline. This is the set of nodes that terminate the natural gas pipeline.

[0025] , , Collectively referred to as generator units The start and stop variables; where Representative unit In time period Whether it is running; 1 indicates running, 0 indicates otherwise. Representative unit In time period Whether the device is powered on; 1 indicates power on, 0 indicates otherwise. Representative unit In time period Whether to stop the machine; 1 indicates stopping the machine, 0 indicates otherwise. This represents the uncertain variable of active power output from wind power.

[0026] , , Collectively referred to as generator units The start and stop variables; where Representative unit In time period Whether it is running; 1 indicates running, 0 indicates otherwise. Representative unit In time period Whether the device is powered on; 1 indicates power on, 0 indicates otherwise. Representative unit In time period Whether to stop the machine. If the machine is stopped, the value is 1; otherwise, the value is 0. This represents the uncertain variable of active power output from wind power.

[0027] ,use These represent the variables involved in the innermost problem. For generator sets In time period Those who have made contributions For wind turbines In the The predicted active power output for each time period; busbar In time period The phase angle within; For gas turbine units In the Natural gas flow rate consumed in each time period; For the time period Flow into the first The natural gas flow rate of the compressor; For the time period internal outflow The natural gas flow rate of the compressor; For the node Flow to Node Natural gas flow rate; For the node Flow to Node Natural gas flow rate; For time period Internal flow through pipeline Average natural gas flow rate; natural gas supplier In time period The natural gas flow rate provided; For pipelines In time period The storage capacity it possesses; Starting point of the natural gas pipeline During the period The square of the air pressure; Termination node of natural gas pipeline During the period The square of the air pressure; For compressor During the period The square of the inlet node pressure; For compressor During the period The square of the pressure at the export node.

[0028] The optimization scheduling problem of the integrated power-gas energy system considering wind power uncertainty in this invention is a discrete single-objective optimization problem. The accuracy of the natural gas system model has a significant impact on the model's precision and scheduling economy. Compared to the power system, the dynamic process of the natural gas system is slower. In day-ahead scheduling, steady-state gas flow models that do not consider pipeline storage effects are often used. Pipeline storage effect refers to the fact that due to the compressibility of natural gas, a certain amount of natural gas can be stored in pipelines during transportation, thereby regulating the supply and demand balance. In intraday and real-time scheduling problems, dynamic models considering pipeline storage effects can reveal the changes in gas flow state over time, and their flexibility and accuracy are improved compared to steady-state models. However, the partial differential equations introduced by dynamic models are difficult to solve directly and are time-consuming. Therefore, this invention starts from the time scale of day-ahead scheduling, ignores some rapidly changing dynamic effects in dynamic models, retains the pipeline storage effect which is most important for dealing with wind power uncertainty, and proposes a quasi-steady-state model for natural gas. This aims to improve the insufficient response capability of natural gas steady-state models to uncertain wind power output in the process of building day-ahead scheduling models.

[0029] In step 2, the constraints are divided into power system constraints, natural gas system constraints, coupling constraints, and wind power output uncertainty set. This invention mainly considers 8 sets of power system constraints, 10 sets of natural gas system constraints, and 1 set of coupling constraints, and establishes a polyhedral uncertainty set for wind power output, as expressed below: Power system constraints: (2) (3) (4) (5) (6) (7) (8) (9) In the formula: This is a time index, representing the starting time period of the summation calculated by taking the maximum value on the right side of the equation; For generator sets Minimum boot time; For generator sets Minimum downtime; For the first The generator sets during the time period Those who contribute their efforts; For nodes Load at the location; For connecting nodes and The susceptance of the transmission lines; For generator sets Minimum active power output during operation; For generator sets Maximum active power output during operation; For generator sets Maximum climbing rate; For connecting bus and busbar The maximum transmission capacity of the transmission lines between them; busbar In time period The phase angle within; busbar In time period The phase angle within; It is the set of nodes in a power system; Reserved capacity for upward rotation; Reserved capacity for rotational use; Time period Phase angle of the internal reference node; Natural gas system constraints: (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) Coupling constraints: (20) In the formula: A collection of natural gas wells; A collection of natural gas pipelines; A collection of gas turbine units; A collection of natural gas compression stations; Indicates the connection node and Pipelines; natural gas supplier In time period The natural gas flow rate provided; For the node Flow to Node Natural gas flow rate; For the node Flow to Node Natural gas flow rate; For nodes In time period Demand for natural gas flow; For the first The gas turbine unit during the time period Demand for natural gas flow; For the time period Flow into the first The natural gas flow rate of the compressor; For the time period internal outflow The natural gas flow rate of the compressor; For pipelines In time period The storage capacity it possesses; Indicates the compressor connected to the current node. Input port; Indicates the compressor connected to the current node. The output port; For time period Internal flow through pipeline Average natural gas flow rate; For connecting nodes and The Weymouth constant for the pipe, For nodes Natural gas pressure, For nodes Natural gas pressure, For pipelines In time period Internal storage; For compressor Consumption factor; For compressor During the period Pressure at the entry node; For compressor During the period Export node pressure; For compressor The compression ratio; For compressor During the period The maximum permissible gas flow rate for internal processing; For the time period Inner slave node Flow to Node The upper limit of natural gas flow; For the time period Inner slave node Flow to Node The upper limit of natural gas flow; natural gas supplier The minimum natural gas flow rate provided; natural gas supplier The maximum natural gas flow rate provided; Starting node The lower limit of pressure; Starting node The upper limit of pressure; Termination node The lower limit of pressure; Termination node The upper limit of pressure; For pipelines The lower limit of storage capacity; For pipelines Maximum storage limit; For gas turbine units The efficiency of power-to-natural gas conversion; Uncertain set of wind power output: (twenty one) (twenty two) (twenty three) In the formula: and These respectively characterize the uncertainty set and uncertainty variables of wind power output; and These are the uncertainty factors used to describe the upper and lower ranges of wind power, respectively. and These are the time budget and space budget for the total uncertainty within the scheduling cycle, respectively.

[0030] In step 4, C&CG is represented as: (twenty four) In the above formula, These are the decision variables for the first stage in a two-stage robust optimization model. These are the decision variables for the second stage; First-stage variables The coefficient matrix, It is a constant vector used to describe the constraints in the first stage; For the first The objective function for the second stage corresponding to each pole. A vector of cost or benefit coefficients. This is the target value for the second stage in the global optimal solution; express A scenario involving quilt problem recognition. Corresponding to the identified severe scenarios, for The coefficient matrix, for coefficient matrix, for coefficient matrix, It is a constant vector used to describe the relationship between two-stage decision variables and uncertain variables; Decision variables for the first stage The feasible domain; For the second stage decision variables The feasible domain; First set of constraints Represents the constraints in the first phase; the second set of constraints Represents the constraints in the second phase; the formula in the second phase constraints within It is the first The poles correspond to the objective function of the second stage, therefore It will definitely be greater than or equal to Because it is a minimization ,therefore And that's exactly what will be obtained. The maximum value in the equation represents an equivalent transformation; at this point... As a cutting plane, it is added to the principal problem; Similarly, the second stage of identification scenarios The corresponding constraints also need to be added to the main problem, that is, the constraints. To be included in the main problem; this ensures that, given the scenario, the decision variables must satisfy the corresponding constraints; and at the same time, new decision variables need to be added to the main problem accordingly. As the algorithm iterates, the decision variables in the main problem... And constraints will continue to increase; The global upper and lower bounds of this algorithm can be calculated using the following formula: (25) in, This is the global upper bound of the algorithm. This is the global lower bound of the algorithm; For the first The first-stage optimal solution to the main problem is obtained in the next iteration; The main problem is in the first The first-stage decision variables obtained in the next iteration cost; For the subproblem in the 1st In this iteration, the decision for the first stage is... The optimal value of the second-stage cost; In the first In each iteration, the estimated optimal cost of the subproblem is obtained by solving the main problem.

[0031] C&CG algorithm pseudocode: ,

[0032] Example like Figure 2 As shown, this invention uses a comprehensive energy system comprising a 6-node power system and a 7-node natural gas system for simulation. The network structure diagram is shown below. Figure 2 .

[0033] The basic parameters of the system are shown in Table 1 below:

[0034] All experiments in this invention were conducted on a computer equipped with an Intel Core i7-12700H@3.20GHz CPU and 16GB DDR5 4800MHz RAM, using Matlab 2022b and Gurobi 12.0.0. The relevant code parameter settings are as follows: time budget for the uncertain set. Space budget The convergence gap of the C&CG algorithm is set to... The linearization parameter of the Big M method is set to For the piecewise linearization sampling points in the Weymouth equation and the quadratic term in the unit operating cost, respectively, they are set as follows: , Furthermore, this invention also compares the results with those obtained using the natural gas steady-state model. Except for neglecting pipeline inventory, the network topology, code parameters, etc., of the natural gas steady-state model remain consistent with those of the quasi-steady-state model. The following comparisons will focus on economic benefits, number of iterations, and time consumption:

[0035] Analysis of the data in Table 2 shows that adding pipeline storage constraints to the model transforms the natural gas system model from a steady state to a quasi-steady state. In terms of computational efficiency, when using the C&CG algorithm to solve the two-stage robust optimization model, the total number of iterations increases from 3 to 4; the overall program time is improved by 99.16%. This demonstrates that the efficiency of the C&CG algorithm in finding the worst-case scenario ensures that the model can achieve rapid convergence with a small number of iterations; however, due to the changes in the dynamic characteristics of the natural gas system model brought about by the introduction of pipeline storage constraints, the time consumed in each iteration still increases. At this time, the wind power output level is as follows: Figure 3 and 4 As shown in the figure, the light green part represents the uncertainty set of wind power output, that is, the range within which wind power output can fluctuate.

[0036] analyze Figure 3 and 4 It is evident that regardless of whether the model takes into account pipeline inventory, the worst-case scenario is identified when the actual wind power output coincides with the lower bound of the predicted wind power output, and the system then calculates the optimal solution based on this scenario. Further analysis of the output of the two gas turbine units, which are key coupling devices, can be presented as a line graph of output versus scheduling period.

[0037] Figure 3 This is a schematic diagram of wind power output without considering pipe storage. Figure 4 A schematic diagram of wind power output when considering storage. Figure 3 and Figure 4 Essentially, these are the results of running two models separately. From the experimental results, the actual wind power output obtained after solving the problem using our C&CG algorithm, regardless of whether pipeline storage is considered, falls on the lower boundary of the wind power output uncertainty set. Therefore, these two figures actually represent the results of solving two different models. From a model mechanism perspective, the core of this invention lies in considering the "pipeline storage effect" when modeling the "natural gas system." However, regardless of whether the natural gas system model considers the pipeline storage effect, the power system model constructs the exact same wind power uncertainty set for the same set of wind farm data.

[0038] analyze Figure 5 and 6It is evident that without considering pipeline storage, the unit starts and stops more frequently, increasing start-up and shutdown costs while potentially leading to reduced thermal efficiency and higher maintenance costs. In the quasi-steady-state model, because pipeline storage is considered, the gas flow rate stored in the pipeline can vary as needed within certain limits, providing a greater margin for supply and demand regulation of the gas turbine unit. In this case, the model will decide to keep gas turbine unit 2 running for a longer period. This is because it has a smaller conversion factor than gas turbine unit 1, meaning higher gas utilization efficiency, which helps reduce economic dispatch costs.

[0039] In summary, the two-stage robust optimization solution method for the integrated electric-gas energy system based on a quasi-steady-state model of a natural gas system proposed in this paper achieves better economic performance compared to the original system while maintaining relatively controllable solution time. The improved system maintains comparable wind power absorption capacity to the original system and has minimal impact on wind farm operation plans. Furthermore, considering pipeline storage can reduce the frequency of gas turbine start-up and shutdown, which is more beneficial for long-term engineering maintenance.

[0040] In the context of high-proportion renewable energy integration in new power systems, this invention addresses the problems of poor response to uncertain wind power output and long dynamic model solution times in traditional electric-gas integrated energy systems, as well as the wastage of precision in day-ahead dispatching. It proposes a quasi-steady-state model for natural gas systems that considers pipeline storage effects. By leveraging the compressibility of natural gas, pipelines are used as storage containers, forming an alternative "energy storage facility," and the rapid peak-shaving characteristics of gas turbine units are utilized to cope with wind power output fluctuations. Therefore, this invention possesses the ability to address wind power output uncertainty and improve dispatching economy, facilitating efficient day-ahead optimized dispatching of electric-gas integrated energy systems with high renewable energy integration.

[0041] The above are merely preferred embodiments of the present invention, and should not be construed as limiting the scope of the present invention. It should be noted that for those skilled in the art, any modifications or equivalent substitutions to the technical solutions of the present invention without creative effort do not depart from the protection scope of the technical solutions of the present invention.

Claims

1. A day-ahead scheduling method for an electricity-gas energy system based on a quasi-steady-state model of natural gas, characterized in that, Specifically, the following steps are included: Step 1: Data preparation stage; collect power system, natural gas system and wind power forecast output data; Step 2: Build a deterministic model of the integrated electric-gas energy system; construct the objective function and constraints of the integrated electric-gas energy system, and linearize the nonlinear terms in the model piecewise; Step 3: Two-stage robust optimization model establishment stage; Based on the wind power predicted output data input in Step 1, construct the wind power output polyhedral uncertainty set, and then divide the two-stage robust optimization into different stages according to whether the variables / constraints are affected by uncertainty, and simplify the innermost minimization problem by combining KKT conditions and the Big M method. Step 4: Solving stage using C&CG algorithm; through alternating iteration of main problem and subproblems, the worst-case scenario is identified, and different constraints are added to the main problem according to whether the objective function of the subproblem is infinite, so that the upper and lower bounds continuously move closer, and finally the target gap is reached to obtain the result.

2. The day-ahead scheduling method for an electricity-gas energy system based on a quasi-steady-state model of natural gas according to claim 1, characterized in that, Step 2 considers unit start-up and shutdown costs, power generation costs, gas well production costs, and wind curtailment costs. The objective function is as follows: (1) In the formula: For indicators in the generator set set; For indicators within the set of natural gas suppliers; A collection of natural gas generator sets; A collection of coal-fired power generating units; A collection of wind turbine generator sets; A set of time periods; ; For natural gas units Non-fuel operating costs; For coal-fired power units Operating costs natural gas supplier Production costs; For wind farm The penalty factor is used to measure the cost of wind power reduction; For generator sets Startup costs; For generator sets Downtime costs; Starting point of the natural gas pipeline and termination node The square difference of air pressure, This is the penalty coefficient for the squared difference in pipeline air pressure; This represents the set of starting nodes for the natural gas pipeline. This is the set of nodes terminating in the natural gas pipeline. , , Collectively referred to as generator units The start and stop variables; where Representative unit In time period Whether it is running; 1 indicates running, 0 indicates otherwise. Representative unit In time period Whether the device is powered on or off; 1 indicates power on, 0 indicates off. Representative unit In time period Whether to stop the machine; 1 indicates stopping the machine, 0 indicates otherwise. This represents the uncertain variable of active power output from wind power. ,use Represents the variables involved in the innermost problem; For generator sets In time period Those who have made contributions For wind turbines In the The predicted active power output for each time period; busbar In time period The phase angle within; For gas turbine units In the Natural gas flow rate consumed in each time period; For the time period Flow into the first The natural gas flow rate of the compressor; For the time period internal outflow The natural gas flow rate of the compressor; For the node Flow to Node Natural gas flow rate; For the node Flow to Node Natural gas flow rate; For time period Internal flow through pipeline Average natural gas flow rate; natural gas supplier In time period The natural gas flow rate provided; For pipelines In time period The storage capacity it possesses; Starting point of the natural gas pipeline During the period The square of the air pressure; Termination node of natural gas pipeline During the period The square of the air pressure; For compressor During the period The square of the inlet node pressure; For compressor During the period The square of the pressure at the export node.

3. The day-ahead scheduling method for an electricity-gas energy system based on a quasi-steady-state model of natural gas according to claim 2, characterized in that, In step 2, the constraints are divided into power system constraints, natural gas system constraints, coupling constraints, and wind power output uncertainty set. This invention mainly considers 8 sets of power system constraints, 10 sets of natural gas system constraints, and 1 set of coupling constraints, and establishes a polyhedral uncertainty set for wind power output, as expressed below: Power system constraints: （2） （3） （4） （5） （6） （7） （8） （9） In the formula: This is a time index, representing the starting time period of the summation calculated by taking the maximum value on the right side of the equation; For generator sets Minimum boot time; For generator sets Minimum downtime; For the first The generator sets during the time period Those who contribute their efforts; For nodes Load at the location; For connecting nodes and The susceptance of the transmission lines; For generator sets Minimum active power output during operation; For generator sets Maximum active power output during operation; For generator sets Maximum climbing rate; For connecting bus and busbar The maximum transmission capacity of the transmission lines between them; busbar In time period The phase angle within; busbar In time period The phase angle within; It is the set of nodes in a power system; Reserved capacity for upward rotation; Reserved capacity for rotational use; Time period Phase angle of the internal reference node; Natural gas system constraints: （10） （11） （12） （13） （14） （15） （16） （17） （18） （19） Coupling constraints: （20） In the formula: A collection of natural gas wells; A collection of natural gas pipelines; A collection of gas turbine units; A collection of natural gas compression stations; Indicates the connection node and Pipelines; natural gas supplier In time period The natural gas flow rate provided; For the node Flow to Node Natural gas flow rate; For the node Flow to Node Natural gas flow rate; For nodes In time period Demand for natural gas flow; For the first The gas turbine unit during the time period Demand for natural gas flow; For the time period Flow into the first The natural gas flow rate of the compressor; For the time period internal outflow The natural gas flow rate of the compressor; For pipelines In time period The storage capacity it possesses; Indicates the compressor connected to the current node. Input port; Indicates the compressor connected to the current node. The output port; For time period Internal flow through pipeline Average natural gas flow rate; For connecting nodes and The Weymouth constant for the pipe, For nodes Natural gas pressure, For nodes Natural gas pressure, For pipelines In time period Internal storage; For compressor Consumption factor; For compressor During the period Pressure at the entry node; For compressor During the period Export node pressure; For compressor The compression ratio; For compressor During the period The maximum permissible gas flow rate for internal processing; For the time period Inner slave node Flow to Node The upper limit of natural gas flow; For the time period Inner slave node Flow to Node The upper limit of natural gas flow; natural gas supplier The minimum natural gas flow rate provided; natural gas supplier The maximum natural gas flow rate provided; Starting node The lower limit of pressure; Starting node The upper limit of pressure; Termination node The lower limit of pressure; Termination node The upper limit of pressure; For pipelines The lower limit of storage capacity; For pipelines Maximum storage limit; For gas turbine units The efficiency of power-to-natural gas conversion; Uncertain set of wind power output: （21） （22） （23） In the formula: and These respectively characterize the uncertainty set and uncertainty variables of wind power output; and These are the uncertainty factors used to describe the upper and lower ranges of wind power, respectively. and These are the time budget and space budget for the total uncertainty within the scheduling cycle, respectively.

4. The day-ahead scheduling method for an electricity-gas energy system based on a natural gas quasi-steady-state model according to claim 3, characterized in that, The C&CG algorithm in step 4 is represented as follows: （24） In the above formula, These are the decision variables for the first stage in a two-stage robust optimization model. These are the decision variables for the second stage; For the first stage variables The coefficient matrix, It is a constant vector used to describe the constraints in the first stage; For the first The objective function for the second stage corresponding to each pole. A vector of cost or benefit coefficients. This is the target value for the second stage in the global optimal solution; express A scenario involving quilt problem recognition. Corresponding to the identified severe scenarios, for The coefficient matrix, for coefficient matrix, for coefficient matrix, It is a constant vector used to describe the relationship between two-stage decision variables and uncertain variables; Decision variables for the first stage The feasible domain; For the second stage decision variables The feasible domain; First set of constraints Represents the constraints in the first phase; the second set of constraints Represents the constraints in the second phase; the formula in the second phase constraints within It is the first The poles correspond to the objective function of the second stage, therefore It will definitely be greater than or equal to Because it is a minimization ,therefore And that's exactly what will be obtained. The maximum value in the equation represents an equivalent transformation; at this point... As a cutting plane, it is added to the principal problem; Similarly, the second stage of identification scenarios The corresponding constraints also need to be added to the main problem, that is, the constraints. To be included in the main problem; this ensures that, given the scenario, the decision variables must satisfy the corresponding constraints; and at the same time, new decision variables need to be added to the main problem accordingly. As the algorithm iterates, the decision variables in the main problem... And constraints will continue to increase; The global upper and lower bounds of this algorithm can be calculated using the following formula: （25） in, This is the global upper bound of the algorithm. This is the global lower bound of the algorithm; For the first The first-stage optimal solution to the main problem is obtained in the next iteration; The main problem is in the first The first-stage decision variables obtained in the next iteration cost; For the subproblem in the 1st In this iteration, the decision for the first stage is... The optimal value of the second-stage cost; In the first In each iteration, the estimated optimal cost of the subproblem is obtained by solving the main problem.

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