A multi-objective optimal scheduling method for power-gas network considering natural gas pipeline leakage

Abstract

This invention relates to a multi-objective optimization scheduling method for an electric-gas network considering natural gas pipeline leakage, belonging to the technical field of natural gas pipeline leakage objective optimization. The invention includes the following steps: establishing a large-hole leakage rate model for a natural gas pipeline; solving the leakage rate of the large-hole leakage model using the MATLAB Newton-Raphson iteration method; establishing a multi-objective function model for natural gas pipeline leakage with operating cost, environmental protection cost, and load loss as objectives; selecting different multi-objective functions according to the degree of load loss, converting them into single-objective functions through membership functions, and solving the single-objective functions using a genetic particle swarm optimization algorithm. This invention significantly reduces system load loss while controlling costs, improves power supply reliability during system failures, fully utilizes system power, and enhances the load recovery capability of the faulty system.

Description

Technical Field

[0001] This invention relates to a multi-objective optimization scheduling method for an electric-gas network that takes into account natural gas pipeline leakage, and belongs to the technical field of natural gas pipeline leakage target optimization. Background Technology

[0002] With the large-scale grid connection of new energy sources and the rapid development of distributed energy systems, power-to-gas (P2G) interconnection networks have attracted widespread attention from scholars worldwide in order to alleviate environmental pollution and improve energy absorption capacity. On the one hand, the rapid development of gas turbines combined with wind and solar power generation provides a guarantee for mitigating intermittent new energy sources; on the other hand, by integrating P2G technology into integrated energy systems, not only can the absorption of new energy sources be promoted, but load losses can also be reduced during faults. Therefore, research on P2G interconnection networks plays an important role in the future development of integrated energy systems.

[0003] With the rapid development of gas turbines and P2G equipment, the coupling between power systems and natural gas systems is constantly increasing. When a fault occurs in the natural gas network, it can easily transmit its impact to the power network through coupling devices, causing cascading failures and expanding the scope of the fault's impact. Among these, pipeline leakage is a common fault in pipeline networks. Fault models are divided into small-hole models, large-hole models, and pipeline models based on the size of the leak orifice and the speed of the leaking gas flow. Xiang Suping et al.'s natural gas pipeline leakage model is based on the fluid state equation, mass conservation equation, energy equation, and momentum equation, considering the unstable state of the gas in the pipeline and the natural gas flow velocity at the leak point, and establishes a pipeline leakage model. D. Yuhua et al., based on fluid mechanics principles, proposed a large-hole leakage model that is between the small-hole leakage model and the pipeline leakage model. This model is applicable to various leak orifice diameters. Wang Xiaowan et al.'s research on the steady-state leakage calculation model of natural gas pipelines under non-isothermal conditions and Yang Zhao et al.'s steady-state leakage calculation model of non-isothermal long-distance pipelines are based on the large-hole model proposed by D. Yuhua et al., and propose a leakage model that considers the temperature correction coefficient and the friction coefficient. However, this model is only applicable to steady-state calculations.

[0004] The different time scales of the electrical-gas network cause problems such as reduced system inertia and difficulty in optimizing the operation scheduling model. Therefore, while improving energy utilization and building multi-energy complementary systems, it is also important to assess the safe operation of the system, optimize the system scheduling model and solution algorithm during failures, thereby reducing load and economic losses and improving the model solution speed. Chen Yanbo et al. proposed a mathematical model for robust state estimation of an electric-gas integrated energy system based on weighted minimum absolute value, simultaneously considering compressor gas pressure and gas consumption constraints. Based on this model, they constructed a robust estimation model for an electric-gas integrated energy system based on weighted minimum absolute value. Chen Sheng et al.'s review of safety analysis and optimal control research on electric-gas interconnected integrated energy systems studied steady-state and transient power flow models, safety and reliability, and optimal control of electric-gas interconnected integrated energy systems, proposing a multi-period rolling optimal control strategy for fault prevention and correction. Mei Jianchun et al.'s hybrid control method for electric-gas interconnected integrated energy systems considering key fault screening proposed a prevention-correction hybrid control model, screening key faults through alternating solutions of the main problem and sub-problems in an iterative method. Chen Zhaoyu et al.'s research on day-ahead optimal economic dispatch strategy for P2G multi-source energy storage microgrids, based on an energy hub model, established a system for economic dispatch of microgrids containing P2G multi-source energy storage. The following are some of the best microgrid day-ahead optimization scheduling models: Yang Lijun et al. established a fault recovery model based on bi-level optimization theory and used an improved ant colony algorithm and a multi-level recovery model to optimize the upper and lower level models; Li Guoqing et al. established an isolated microgrid economic operation model based on chance-constrained programming by weighting the sub-objective functions using the analytic hierarchy process (AHP); Qu Kaiping et al. established an optimization scheduling model for multi-energy systems based on the knowledge transfer Q-learning algorithm by considering energy supply costs and carbon emission targets, and solved it by converting it into a single-objective function using membership functions; Lu Limin et al. improved the microgrid energy storage optimization configuration based on an improved multi-objective particle swarm algorithm, and Xu Yan et al. improved the photovoltaic grid-connected inverter parameter identification by introducing crossover and mutation operations of the genetic particle swarm algorithm, enhancing the convergence and robustness of the algorithm.

[0005] Currently, there is extensive research on how to operate and schedule the system under objective function constraints after a power-gas network failure, especially the scheduling model research for grid-side failures, which is relatively mature. However, there is less research on scheduling the system operation under natural gas pipeline leakage. The scheduling situation under leakage failure is more complex, and the cost of natural gas leakage is easily ignored, resulting in insufficient estimation of the degree of loss and inaccurate scheduling during actual operation. This type of energy-deficient system failure has a long repair time and high complexity. Therefore, it is of great significance to optimize the system operation scheduling model and solution algorithm under this failure situation to improve the power supply reliability and economy of the system.

[0006] Natural gas, as a clean and high-quality fossil fuel, is primarily transported via pipelines. However, due to its corrosive nature and the influence of extreme weather and gas vibrations, leaks can occur during transportation. Furthermore, with the deep coupling of electricity and gas networks, energy shortage faults caused by natural gas pipeline leaks are transmitted to the power grid through coupling devices, affecting users' production and daily lives and reducing the reliability of the power grid. Therefore, modeling and analyzing the leakage rate of natural gas pipelines is of great significance for ensuring the safe and stable operation of the power grid.

[0007] Different gas flow velocities in pipeline leaks require different leak models, and gas flow velocities are generally classified as sonic or subsonic. Furthermore, based on the changes in gas flow patterns caused by variations in the leak orifice size, pipeline leak models are categorized into three types: small-hole, pipe, and large-hole models. Since small-hole and pipe models have a lower probability of occurrence, and large-hole models are applicable to leaks of various orifice sizes, this invention primarily focuses on large-hole models; other leak models will not be discussed further.

[0008] To address the aforementioned problems, firstly, this invention establishes a large-hole leakage model for natural gas pipelines and solves for its leakage rate using the MATLAB Newton-Raphson iteration method. Secondly, an optimal scheduling model for natural gas pipeline leakage is established with operating costs, environmental protection costs, and load loss as objective functions. Different multi-objective functions are established according to the degree of load loss, which are then converted into single-objective functions using membership functions. Finally, the genetic particle swarm optimization algorithm is used to solve the optimal scheduling model. This invention links the degree of pipeline leakage with the scheduling situation, incorporates the economic losses caused by the leakage into the constraint functions, controls system costs, provides a better assessment of actual losses, and enhances the system's power extraction capability by applying different objective functions according to the degree of load loss. This reduces the amount of load loss, improves the power supply reliability of the system during natural gas pipeline leakage, and accelerates the model solution speed. Summary of the Invention

[0009] This invention provides a multi-objective optimization scheduling method for an electric-gas network that takes into account natural gas pipeline leakage, in order to solve the problems of large load loss, weak load recovery capability of faulted systems, and inaccurate assessment of fault losses when natural gas pipelines have different degrees of leakage.

[0010] The technical solution of this invention is: a multi-objective optimization scheduling method for an electric-gas network considering natural gas pipeline leakage, the specific steps of which are as follows:

[0011] Step 1: Establish a model for the leakage rate of large orifices in natural gas pipelines;

[0012] Step 2: Solve the leakage rate of the natural gas pipeline macro-hole leakage model using the Newton-Raphson iteration method in MATLAB;

[0013] Step 3: Establish a multi-objective function model for natural gas pipeline leakage, with operating costs, environmental protection costs, and load loss as objectives;

[0014] Step 4: Select different multi-objective functions according to the degree of unloading, convert them into single-objective functions through membership functions, and solve the single-objective functions using the genetic particle swarm algorithm.

[0015] As a further aspect of the present invention, the specific steps of Step 1 are as follows:

[0016] Step 1.1: Based on the laws of conservation of energy and momentum, establish the equations for the adiabatic flow of gas in the pipe, where the gas flow in the pipe is adiabatic:

[0017]

[0018] In the formula: k is the adiabatic coefficient of the gas, which is taken as 1.334 for natural gas; T1, T2, P1, and P2 are the temperatures and pressures corresponding to the starting point 1 of the pipeline and the center point 2 inside the leaking pipeline, respectively; M is the molar mass of the gas; R is the gas constant, R = 8.314 Pa·m / (mol·K); G is the mass flow rate per unit area in the pipeline; f is the Fanning friction coefficient, which is 0.0232Re when the Reynolds number Re > 100000. -0.1507 When Re ≤ 100000, f = 0.079Re -0.25 Le is the distance from the leak point to the beginning of the pipeline; D is the inner diameter of the pipeline.

[0019] Step 1.2 Substitute the gas state equation, Poisson equation, and continuity equation into equation (1) to obtain the expression for the gas leakage rate model; where the flow at the release point is isentropic and the flow model is considered as a one-dimensional model. When the gas pressure satisfies equation (2), the expression for the leakage rate model is shown in equation (3):

[0020]

[0021]

[0022] When the air pressure satisfies equation (4), the expression for the leakage rate model is shown in equation (5):

[0023]

[0024]

[0025] In the formula: P a At atmospheric pressure, A or C0 is the cross-sectional area of ​​the leak, and C0 is the empirical flow coefficient.

[0026] As a further aspect of the present invention, the specific steps of Step 2 are as follows:

[0027] Step 2.1: Establish the parameter relationship between the starting point 1 of the pipeline and the center point 2 of the leak outlet pipeline, with the same friction coefficient along the pipeline.

[0028]

[0029] Step 2.2: Establish equations (7)-(8) based on the gas flow continuity equation, and solve for the Mach number Ma2 at the center point 2 inside the leak outlet pipe using equation (7);

[0030]

[0031]

[0032] In the formula: A or A D Ma1 and Ma2 represent the cross-sectional areas of the pipe leak and the pipe, respectively; Ma1 and Ma2 represent the Mach numbers at the starting point 1 of the pipe and the center point 2 of the leak in the pipe, respectively.

[0033] Step 2.3 Substitute equations (6) and (8) into equation (1) to obtain an equation with only Ma1 as the unknown and solve Ma1 using the Newton iteration method. Then solve T2 and P2 using equation (6). Finally, determine the air pressure relationship using equations (2) and (4) and apply the leakage rate formula for different air pressure relationships to solve the leakage amount.

[0034] As a further aspect of the present invention, the specific steps of Step 3 are as follows:

[0035] Step 3.1: A sub-objective function for operation and maintenance costs was established based on the unit operation and maintenance price of each microgrid unit:

[0036]

[0037] In the formula: C grid (t) represents the cost of purchasing electricity from the main power grid; C gas (t) represents the cost of purchasing gas; For the maintenance cost of the battery; C P2G.Y (t) represents the operation and maintenance cost of the P2G (electric-to-gas) equipment; C MT.Y (t) represents the operation and maintenance cost of the gas turbine, T = 24;

[0038] The leakage amount of the natural gas pipeline, obtained from the pipeline leakage rate calculated in Step 2, is included in the operation and maintenance costs.

[0039] C gas(t)=(Q MT (t)+Q load (t)+Q l (t))M gas (27)

[0040] In the formula: Q MT (t) represents the amount of natural gas consumed by the gas turbine; Q load (t) represents the amount of natural gas consumed by the gas load; Q l (t) represents the leakage rate of the natural gas pipeline; M gas The price per cubic meter of natural gas;

[0041] Step 3.2: A sub-objective function for environmental protection costs was established based on the treatment costs of different pollutants from each unit of the microgrid.

[0042]

[0043] In the formula: C GRID.E (t) represents the environmental protection cost of the main network; C P2G.E (t) represents the environmental protection cost of the P2G (Power-to-Gas) equipment; C MT.E (t) represents the environmental protection cost of the gas turbine;

[0044] Step 3.3: Based on the unloading amounts of the system's electrical and gas loads, a sub-objective function for the unloading amount was established:

[0045]

[0046] In the formula: P i (t) represents the load required at time t; P n (t) represents the total power generated by the system at time t;

[0047] According to the law of conservation of energy, the amount of gas flowing into a node is equal to the amount of gas flowing out of the node:

[0048] G(t)-Q l (t)=Q out (t) (30)

[0049] In the formula: G(t) is the pipe flow rate; Q l (t) represents the pipeline leakage; Q out (t) represents the flow rate transmitted to the power grid;

[0050] In equation (12), a large pipeline leakage leads to a large unload Q. out When (t) cannot meet the power generation demand of the grid, P in equation (12) n (t) <P i (t), causing system loss of load.

[0051] As a further aspect of the present invention, the specific steps of Step 4 are as follows:

[0052] Step 4.1: Based on Step 3, the multi-objective function model of equations (9), (11), and (12) can be obtained. This multi-objective function model is applied when the load loss is small. However, when the system load loss is large, the operation and maintenance cost equation (9) and the environmental protection cost equation (11) are temporarily not considered in the multi-objective function. At this time, the multi-objective function is:

[0053]

[0054] Step 4.2: Since the load loss, environmental protection cost, and operation and maintenance cost are three independent objective functions, which are difficult to solve and have a slow optimization speed, the three multi-objective functions are transformed into a single objective function C through the membership function:

[0055] C = f1 + f2 + f3 (32)

[0056] In the formula: f1 is the operating cost; f2 is the environmental protection cost; f3 is the system load loss;

[0057] Step 4.3: Construct the discriminant matrix using the five-part division method in the analytic hierarchy process (AHP), and assign weights to the single objective function in equation (15) to establish the following objective function C1:

[0058] C1+ω1f1+ω2f2+ω3f3 (33)

[0059] Step 4.4: Solve the objective function C1 using the Genetic Particle Swarm Optimization (GAPSO) algorithm. Introduce the mutation factor from the genetic algorithm into the particle swarm optimization algorithm to update the weights and mutation factor during the iteration process.

[0060]

[0061] In the formula: w(i) represents the inertia weight when the iteration number is i; it max represents the maximum number of iterations; ws and we are the initial and final values ​​of the inertia weight; pm(i) represents the value of the mutation factor when the number of iterations is i; mu represents the mutation rate.

[0062] The beneficial effects of this invention are:

[0063] (1) The method proposed in this invention can greatly reduce the system load loss while controlling costs, improve the power supply reliability during system failure, fully tap the system power, and enhance the load recovery capability of the faulty system.

[0064] (2) The difference between normal operation and failure is large, but as the leakage orifice diameter increases, the leakage gradually slows down, and the system loss also tends to slow down. The proposed method is more accurate in assessing failure loss.

[0065] (3) An improved particle swarm algorithm with the introduction of genetic factors is used to solve the objective function. The improved algorithm is superior to the traditional particle swarm algorithm in terms of running speed and optimization ability. In addition, the proposed objective function model has a high optimization speed under the running environment of the improved particle swarm algorithm. Attached Figure Description

[0066] Figure 1 This is a schematic diagram of a natural gas pipeline leak in this invention;

[0067] Figure 2 This is a schematic diagram of the electro-pneumatic network coupling system in this invention;

[0068] Figure 3 This is a schematic diagram of the load forecasting results of the present invention;

[0069] Figure 4 This is a schematic diagram of the scheduling results during normal operation of the present invention;

[0070] Figure 5 This is a schematic diagram of the scheduling result of the conventional objective function of the present invention;

[0071] Figure 6 This is a schematic diagram of the scheduling result of the improved objective function of this invention. Detailed Implementation

[0072] Example 1: As Figures 1-6 As shown, a multi-objective optimization scheduling method for an electric-gas network considering natural gas pipeline leakage is proposed.

[0073] Step 1: Establish a model for the leakage rate of large orifices in natural gas pipelines;

[0074] Step 2: Solve the leakage rate of the natural gas pipeline macro-hole leakage model using the Newton-Raphson iteration method in MATLAB;

[0075] Step 3: Establish a multi-objective function model for natural gas pipeline leakage, with operating costs, environmental protection costs, and load loss as objectives;

[0076] Step 4: Select different multi-objective functions according to the degree of unloading, convert them into single-objective functions through membership functions, and solve the single-objective functions using the genetic particle swarm algorithm.

[0077] As a further aspect of the present invention, the specific steps of Step 1 are as follows:

[0078] Step 1.1: Based on the laws of conservation of energy and momentum, establish the equations for the adiabatic flow of gas in the pipe, where the gas flow in the pipe is adiabatic:

[0079]

[0080] In the formula: k is the adiabatic coefficient of the gas, which is taken as 1.334 for natural gas; T1, T2, P1, and P2 are the temperatures and pressures corresponding to the starting point 1 of the pipeline and the center point 2 inside the leaking pipeline, respectively; where T1 = 288 K, P1 = 0.4 MPa; the molar mass of the gas M = 0.016 kg / mol; the gas constant R = 8.314 Pa·m / (mol·K); and G is the mass flow rate per unit area in the pipeline [kg / m³]. 2 ·s]; Fanning friction coefficient f=0.0035, distance Le from the leak point to the pipeline start point=1000m; pipeline inner diameter D=0.04m;

[0081] Step 1.2 Substitute the gas state equation, Poisson equation, and continuity equation into equation (1) to obtain the expression for the gas leakage rate model; where the flow at the release point is isentropic and the flow model is considered as a one-dimensional model. When the gas pressure satisfies equation (2), the expression for the leakage rate model is shown in equation (3):

[0082]

[0083]

[0084] When the air pressure satisfies equation (4), the expression for the leakage rate model is shown in equation (5):

[0085]

[0086]

[0087] Where: atmospheric pressure P a =0.101 MPa; A or Let C0 be the cross-sectional area of ​​the leak; empirical flow coefficient C0 = 0.61, and natural gas density ρ = 0.71 kg / m³. 3 .

[0088] As a further aspect of the present invention, the specific steps of Step 2 are as follows:

[0089] Step 2.1: Establish the parameter relationship between the starting point 1 of the pipeline and the center point 2 of the leak outlet pipeline, with the same friction coefficient along the pipeline.

[0090]

[0091] Step 2.2: Establish equations (7)-(8) based on the gas flow continuity equation, and solve for the Mach number Ma2 at the center point 2 inside the leak outlet pipe using equation (7);

[0092]

[0093]

[0094] In the formula: A or A D Let A represent the cross-sectional area of ​​the pipe leak and the pipe, respectively. D =0.001256m 2 Ma1 and Ma2 represent the Mach numbers at the starting point 1 of the pipeline and the center point 2 of the leak outlet, respectively.

[0095] Step 2.3: Substitute equations (6) and (8) into equation (1) to obtain an equation with only Ma1 as the unknown. Solve for Ma1 using the Newton-Raphson iteration method. Then, solve for T2 and P2 using equation (6). Finally, determine the pressure relationship using equations (2) and (4), and apply the leakage rate formula for different pressure relationships to solve for the leakage amount. The leakage amounts for different leakage orifice diameters are shown in Table 1.

[0096] Table 1. Leakage rates for different orifice diameters

[0097] Leakage orifice diameter (d) 10mm 20mm 30mm <![CDATA[Leakage rate (m 3 / h)]]> 225.56 352.80 362.80

[0098] As a further aspect of the present invention, the specific steps of Step 3 are as follows:

[0099] Step 3.1: A sub-objective function for operation and maintenance costs was established based on the unit operation and maintenance price of each microgrid unit:

[0100]

[0101] In the formula: C grid (t) represents the cost of purchasing electricity from the main power grid; C gas (t) represents the cost of purchasing gas; For the maintenance cost of the battery; C P2G.Y (t) represents the operation and maintenance cost of the P2G (electric-to-gas) equipment; C MT.Y (t) represents the operation and maintenance cost of the gas turbine, T = 24;

[0102] The leakage amount of the natural gas pipeline, obtained from the pipeline leakage rate calculated in Step 2, is included in the operation and maintenance costs.

[0103] C gas (t)=(Q MT (t)+Q load (t)+Ql (t))M gas (44)

[0104] In the formula: Q MT (t) represents the amount of natural gas consumed by the gas turbine; Q load (t) represents the amount of natural gas consumed by the gas load; Q l (t) represents the leakage rate of the natural gas pipeline; M gas The price per cubic meter of natural gas;

[0105] Step 3.2: A sub-objective function for environmental protection costs was established based on the treatment costs of different pollutants from each unit of the microgrid.

[0106]

[0107] In the formula: C GRID.E (t) represents the environmental protection cost of the main network; C P2G.E (t) represents the environmental protection cost of the P2G (Power-to-Gas) equipment; C MT.E (t) represents the environmental protection cost of the gas turbine; the environmental protection cost of each unit is calculated based on Table 2.

[0108] Table 2 Pollutant Parameters

[0109]

[0110] Step 3.3: Based on the unloading amounts of the system's electrical and gas loads, a sub-objective function for the unloading amount was established:

[0111]

[0112] In the formula: P i (t) represents the load required at time t, with specific data as follows: Figure 3 As shown; P n (t) represents the total power generated by the system at time t;

[0113] According to the law of conservation of energy, the amount of gas flowing into a node is equal to the amount of gas flowing out of the node:

[0114] G(t)-Q l (t)=Q out (t) (47)

[0115] In the formula: G(t) is the pipe flow rate; Q l (t) represents the pipeline leakage; Q out (t) represents the flow rate transmitted to the power grid;

[0116] In equation (12), a large pipeline leakage leads to a large unload Q. out When (t) cannot meet the power generation demand of the grid, P in equation (12)n (t) <P i (t), causing system loss of load.

[0117] As a further aspect of the present invention, the specific steps of Step 4 are as follows:

[0118] Step 4.1: Based on Step 3, the multi-objective function model of equations (9), (11), and (12) can be obtained. This multi-objective function model is applied when the load loss is small. However, when the system load loss is large, the operation and maintenance cost equation (9) and the environmental protection cost equation (11) are temporarily not considered in the multi-objective function. At this time, the multi-objective function is:

[0119]

[0120] Step 4.2: Since the load loss, environmental protection cost, and operation and maintenance cost are three independent objective functions, which are difficult to solve and have a slow optimization speed, the three multi-objective functions are transformed into a single objective function C through the membership function:

[0121] C = f1 + f2 + f3 (49)

[0122] In the formula: f1 is the operating cost; f2 is the environmental protection cost; f3 is the system load loss;

[0123] Step 4.3: The five-part scale method in the analytic hierarchy process is used to construct the discrimination matrix. The single objective function in equation (15) is weighted to obtain three different weights: w1 = 0.106, w2 = 0.261, and w3 = 0.633. To ensure power supply reliability, the load loss is fixed to the sub-objective function with the largest weight coefficient. The optimization results under different weight allocations are shown in Table 3.

[0124] Table 3 Optimization results for different weight assignments of the sub-objective function.

[0125] Weighting <![CDATA[w1f1+w2f2+w3f3]]> <![CDATA[w2f1+w1f2+w3f3]]> <![CDATA[f1+f2+f3]]> Total Economy (RMB) 20623.86 20534.50 20679.18 Loss of load (MW) 0.10 0.14 0.10

[0126] After processing the membership of the indicators in the table above, the membership values ​​corresponding to the three weight assignments are 1.25, 1.25, and 1.27. However, since the second weight assignment method is prone to non-convergence during optimization, this paper adopts the first weight assignment method and establishes the following objective function C1:

[0127] C1=ω1f1+ω2f2+ω3f3 (50)

[0128] Step 4.4: Solve the objective function C1 using the Genetic Particle Swarm Optimization (GAPSO) algorithm. Introduce the mutation factor from the genetic algorithm into the particle swarm optimization algorithm to update the weights and mutation factor during the iteration process.

[0129]

[0130] In the formula: w(i) represents the inertia weight when the iteration number is i; it max Indicates the maximum number of iterations; maximum number of iterations it max =100; initial value of inertia weight ws=1; final value of inertia weight we=0.4; pm(i) represents the value of the mutation factor when the iteration number is i; mutation rate mu=0.1.

[0131] The optimization results of running the proposed method 100 times under different particle swarm optimization algorithms are shown in Table 4:

[0132] Table 4 Comparison of Particle Swarm Optimization Algorithms

[0133]

[0134]

[0135] Table 4 shows that the proposed method, which uses an improved particle swarm optimization algorithm, has a significant advantage in optimization speed compared to the traditional particle swarm optimization algorithm. Furthermore, it can reduce the amount of unloaded data while maintaining similar economic efficiency.

[0136] Table 5 shows the comparison results of 100 runs in GAPSO between the improved multi-objective function where sub-objectives change with the degree of leakage and the traditional multi-objective function where sub-objectives do not change with the degree of leakage.

[0137] Table 5 Comparison of Traditional and Improved Multi-Objective Functions

[0138] objective function Running time (s) Total Economy (RMB) Loss of load (MW) Traditional objective function 40.09 21948.60 0.32 Improve the objective function 33.91 21479.14 0.10

[0139] Table 5 shows that the proposed improved objective function with sub-objectives varying with leakage level and the traditional objective function with sub-objectives not varying with leakage level have higher operating speed in GAPSO and are superior to the traditional objective function in terms of economy and load loss.

[0140] The example provides scheduling results for natural gas pipelines under different leakage levels and objective functions. The normal operation scheduling model is shown below. Figure 4 As shown, the average total cost of the system in this case is 13,621.70 yuan, and the system has no load loss. Figures 5-6 These are the scheduling results during a fault. The output curves of the gas turbines in both graphs are related to the remaining gas supply, gas load, and P2G output. The output units involved in operating costs... Figure 6 The fluctuations are relatively large because economic constraints are not considered during the scheduling process when the load loss is too large. Although P2G only involves environmental protection costs, and these costs account for a small proportion of the total cost, the presence or absence of economic constraints has little impact. However, in order to minimize the load loss, Figure 6The output of P2G in China is still stronger than Figure 5 .from Figure 5-6 As can be seen from the table, the proposed improved objective function scheduling method has a stronger wind power absorption capacity than the traditional objective function scheduling method because wind power generation in this invention has no cost. The proposed scheduling method enhances the output of new energy sources by controlling system costs and reducing load loss. Cost and load loss data can be seen in Table 5. (Comprehensive comparison) Figure 4-6 It can be observed that when no fault occurs, the output fluctuation of each unit is relatively smooth. However, when a fault occurs, in order to meet the constraints of the objective function, the output fluctuation of each unit is large. The scheduling results under normal conditions cannot meet the scheduling requirements under fault conditions, so fault and non-fault scheduling need to be analyzed separately.

[0141] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A multi-objective optimization scheduling method for an electric-gas network considering natural gas pipeline leakage, characterized in that: The specific steps of the method are as follows: Step 1: Establish a model for the leakage rate of large orifices in natural gas pipelines; Step 2: Solve the leakage rate of the natural gas pipeline macro-hole leakage model using the Newton-Raphson iteration method in MATLAB; Step 3: Establish a multi-objective function model for natural gas pipeline leakage, with operating costs, environmental protection costs, and load loss as objectives; Step 4: Select different multi-objective functions according to the degree of load loss, convert them into single-objective functions through membership functions, and solve the single-objective functions using the genetic particle swarm algorithm; The specific steps of Step 1 are as follows: Step 1.1: Based on the laws of conservation of energy and momentum, establish the equations for the adiabatic flow of gas in the pipe, where the gas flow in the pipe is adiabatic: In the formula: k is the adiabatic coefficient of the gas, which is taken as 1.334 for natural gas; T1, T2, P1, and P2 are the temperatures and pressures corresponding to the starting point 1 of the pipeline and the center point 2 inside the leaking pipeline, respectively; M is the molar mass of the gas; R is the gas constant, R = 8.314 Pa·m / (mol·K); G is the mass flow rate per unit area in the pipeline; f is the Fanning friction coefficient, which is 0.0232Re when the Reynolds number Re > 100000. -0.1507 When Re ≤ 100000, f = 0.079Re -0.25 Le is the distance from the leak point to the beginning of the pipeline; D is the inner diameter of the pipeline. Step 1.2 Substitute the gas state equation, Poisson equation, and continuity equation into equation (1) to obtain the expression for the gas leakage rate model; where the flow at the release point is isentropic and the flow model is considered as a one-dimensional model. When the gas pressure satisfies equation (2), the expression for the leakage rate model is shown in equation (3): When the air pressure satisfies equation (4), the expression for the leakage rate model is shown in equation (5): In the formula: P a At atmospheric pressure, A or Where C is the cross-sectional area of ​​the leak, and C0 is the empirical flow coefficient; The specific steps of Step 2 are as follows: Step 2.1: Establish the parameter relationship between the starting point 1 of the pipeline and the center point 2 of the leak outlet pipeline, with the same friction coefficient along the pipeline. Step 2.2: Establish equations (7)-(8) based on the gas flow continuity equation, and solve for the Mach number Ma2 at the center point 2 inside the leak outlet pipe using equation (7); In the formula: A or A D Ma1 and Ma2 represent the cross-sectional areas of the pipe leak and the pipe, respectively; Ma1 and Ma2 represent the Mach numbers at the starting point 1 of the pipe and the center point 2 of the leak in the pipe, respectively. Step 2.3 Substitute equations (6) and (8) into equation (1) to obtain an equation with only Ma1 as the unknown and solve Ma1 using the Newton iteration method. Then solve T2 and P2 using equation (6). Finally, determine the air pressure relationship using equations (2) and (4) and apply the leakage rate formula for different air pressure relationships to solve the leakage amount. The specific steps of Step 3 are as follows: Step 3.1: A sub-objective function for operation and maintenance costs was established based on the unit operation and maintenance price of each microgrid unit: In the formula: C grid (t) represents the cost of purchasing electricity from the main power grid; C gas (t) represents the cost of purchasing gas; For the maintenance cost of the battery; C P2G.Y (t) represents the operation and maintenance cost of the P2G (electric-to-gas) equipment; C MT.Y (t) represents the operation and maintenance cost of the gas turbine, T = 24; The leakage amount of the natural gas pipeline, obtained from the pipeline leakage rate calculated in Step 2, is included in the operation and maintenance costs. C gas (t)=(Q MT (t)+Q load (t)+Q l (t))M gas (10) In the formula: Q MT (t) represents the amount of natural gas consumed by the gas turbine; Q load (t) represents the amount of natural gas consumed by the gas load; Q l (t) represents the leakage rate of the natural gas pipeline; M gas The price per cubic meter of natural gas; Step 3.2: A sub-objective function for environmental protection costs was established based on the treatment costs of different pollutants from each unit of the microgrid. In the formula: C GRID.E (t) represents the environmental protection cost of the main network; C P2G.E (t) represents the environmental protection cost of the P2G (Power-to-Gas) equipment; C MT.E (t) represents the environmental protection cost of the gas turbine; Step 3.3: Based on the unloading amounts of the system's electrical and gas loads, a sub-objective function for the unloading amount was established: In the formula: P i (t) represents the load required at time t; P n (t) represents the total power generated by the system at time t; According to the law of conservation of energy, the amount of gas flowing into a node is equal to the amount of gas flowing out of the node: G(t)-Q l (t)=Q out (t)(13) In the formula: G(t) is the pipe flow rate; Q l (t) represents the pipeline leakage; Q out (t) represents the flow rate transmitted to the power grid; In equation (12), a large pipeline leakage leads to a large unload Q. out When (t) cannot meet the power generation demand of the grid, P in equation (12) n (t) <P i (t), causing system loss of load.

2. The multi-objective optimization scheduling method for an electric-gas network considering natural gas pipeline leakage as described in claim 1, characterized in that: The specific steps of Step 4 are as follows: Step 4.1: Based on Step 3, the multi-objective function model of equations (9), (11), and (12) can be obtained. This multi-objective function model is applied when the load loss is small. However, when the system load loss is large, the operation and maintenance cost equation (9) and the environmental protection cost equation (11) are temporarily not considered in the multi-objective function. At this time, the multi-objective function is: Step 4.2: Since the load loss, environmental protection cost, and operation and maintenance cost are three independent objective functions, which are difficult to solve and have a slow optimization speed, the three multi-objective functions are transformed into a single objective function C through the membership function: C = f1 + f2 + f3 (15) In the formula: f1 is the operating cost; f2 is the environmental protection cost; f3 is the system load loss; Step 4.3: Construct the discriminant matrix using the five-part division method in the analytic hierarchy process (AHP), and assign weights to the single objective function in equation (15) to establish the following objective function C1: C1=ω1f1+ω2f2+ω3f3 (16) Step 4.4: Solve the objective function C1 using the Genetic Particle Swarm Optimization (GAPSO) algorithm. Introduce the mutation factor from the genetic algorithm into the particle swarm optimization algorithm to update the weights and mutation factor during the iteration process. In the formula: w(i) represents the inertia weight when the iteration number is i; it max represents the maximum number of iterations; ws and we are the initial and final values ​​of the inertia weight; pm(i) represents the value of the mutation factor when the number of iterations is i; mu represents the mutation rate.

Images