Gas-electricity combined distribution network distributed robust expansion planning method considering system resilience constraints

Abstract

The present application relates to the technical field of gas-electricity combined system planning and resilience improvement, in particular to a gas-electricity combined distribution network distributed robust expansion planning method considering system resilience constraints; firstly, a gas-electricity combined distribution network expansion planning model is established with the sum of operation cost and planning cost as the objective function; in terms of resilience improvement, the ability of dual-fuel units to change fuel supply load when natural gas is insufficient under disasters is considered, and then the construction of dual-fuel units and tie lines is modeled, and the constraints such as power distribution network reconstruction are considered at the operation level; secondly, the uncertainty of extreme disaster influence is considered by using the KL divergence-based distributed robust optimization method, and a two-stage distributed robust expansion planning model considering the resilience constraints of gas-electricity combined distribution network system under extreme disasters is established. The method can improve the economy of gas-electricity combined distribution network under normal operation, and enhance the resilience ability under extreme disasters.

Description

Technical Field

[0001] The present invention relates to the field of gas-electricity combined system planning and resilience improvement, and in particular to a method for planning robust expansion of a gas-electricity combined distribution network taking into account system resilience constraints. Background Art

[0002] Global climate change has become one of the most daunting challenges facing the world. To address this challenge, optimizing the energy mix for low-carbon development and gradually replacing traditional fossil fuels with clean, renewable energy sources has become an essential path to developing a low-carbon power system. Furthermore, research has shown the importance of integrated energy systems in reducing carbon emissions and improving energy efficiency, leading to increasingly close coupling of power systems with other energy systems such as natural gas and thermal power. Natural gas-fired power generation, with its significant advantages of low carbon, clean energy, and high efficiency, also plays a key role in achieving the "dual carbon" goals. However, as the coupling between gas and electricity deepens, the risk of fault propagation between systems also increases. In one major power outage, an extreme cold wave caused a natural gas system supply shortage, resulting in a large-scale outage. Therefore, traditional power system reliability evaluation metrics have limitations in responding to similar disasters. The concept of resilience, which emphasizes the system's ability to quickly recover from low-probability, high-impact extreme events, has gradually gained attention.

[0003] With the development of smart grids and the widespread use of distributed energy, methods for improving power system resilience are becoming increasingly diverse. Current research focuses on two main categories of resilience enhancement methods: operation-based and planning-based. Optimization methods at the operation level include network reconstruction, emergency resource scheduling, and islanding, while planning methods involve line reinforcement, vegetation management, and investment in backup generators and energy storage equipment. However, existing pre-disaster planning research often overlooks the economic benefits of flexible resources during normal operation, resulting in high investment costs. By expanding planning and incorporating the economic benefits of normal system operation into the objective function, a more balanced investment strategy can be achieved. Furthermore, distributed robust optimization, as an important method for measuring uncertainty, is gradually gaining wider application. Summary of the Invention

[0004] This paper addresses the existing technology by providing a distributed robust expansion planning method for a combined gas-electricity distribution network that takes into account system resilience constraints under extreme disasters. This method considers the investment and construction of various equipment and line upgrades in the gas-electricity combined distribution network planning problem, and considers the role of dual-fuel units and tie lines in improving system resilience. Furthermore, a distributed robust method based on the Kullback-Leibler (KL) divergence is used to model the uncertainty of the impact of extreme disasters, resulting in a two-stage distributed robust planning model. The technical solution is as follows:

[0005] A robust expansion planning method for a gas-electricity combined distribution network considering system resilience constraints includes the following steps:

[0006] Step 1: Considering the coordinated planning of gas turbines, dual-fuel units, power-to-gas equipment, power storage equipment, gas storage equipment, and interconnecting lines, as well as the upgrade of power lines and natural gas pipelines, a gas-power combined distribution network expansion planning model is established with the goal of minimizing the sum of the operating cost and construction cost of the combined gas-power distribution network. This model also considers the safe operation constraints of the gas and distribution networks and the operation constraints of the coupled equipment.

[0007] Step 2: Based on the gas-electricity combined distribution network expansion planning model, the operational constraints of the gas-electricity combined distribution network under the influence of extreme disasters are modeled. The fuel conversion effect of dual-fuel units when natural gas is insufficient under extreme disasters is considered, and the increased flexibility of distribution network reconstruction after the construction of interconnection lines is considered. The minimum load loss of the gas-electricity combined distribution network system during the extreme disaster period is calculated, and then a resilience constraint is established by limiting the upper limit of the allowable load loss. The result is a robust expansion planning model for the gas-electricity combined distribution network that considers the resilience constraint and balances economy and resilience.

[0008] Step 3: Based on the robust expansion planning model for the gas-electricity combined distribution network that balances economy and resilience, and taking into account the uncertainty of the probability of extreme disaster scenarios, a linearized KL divergence is used to describe the distance between the actual distribution of extreme disasters and the empirical distribution, and an extreme disaster uncertainty set is established;

[0009] Step 4: Based on the extreme disaster uncertainty set, a two-stage distributed robust expansion planning model based on KL divergence is established. In the first stage, the basic scenario is used to ensure the economy of system planning. In the second stage, the resilience index under the extreme disaster scenario is used as a constraint to obtain the optimal decision that meets the set resilience constraints.

[0010] Step 5: Use the column and constraint generation algorithm to decouple the two-stage distributed robust extended planning model into the main problem and sub-problems and solve them iteratively.

[0011] The invention has the following advantages and beneficial effects:

[0012] 1) This invention takes into account that the introduction of dual-fuel units and interconnecting lines significantly enhances the system's ability to respond to extreme disasters. By switching to oil-fired power generation during faults, the dual-fuel units reduce the system's dependence on natural gas supply and ensure the continuity of power supply. The construction of interconnecting lines provides greater flexibility for the system, allowing the distribution network to be restructured to form a gas-electricity island when a disaster occurs. The energy within the island can be optimally distributed through optimized scheduling, effectively ensuring the supply of critical electricity or natural gas loads, thereby further improving the overall resilience and reliability of the system.

[0013] 2) This invention combines multiple flexible resources, including dual-fuel units, distribution network interconnectors, distributed units, power-to-gas equipment, and energy storage devices, to achieve dual optimization under both normal operation and extreme disaster conditions. Compared to existing technologies, this invention uses a distributed robust optimization approach to measure the uncertainty of extreme disaster scenarios. This approach is less conservative and more economical than robust optimization methods, reducing investment costs for redundant resources and achieving a balance between cost-effectiveness and resilience during the planning phase, thus possessing high application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 This is a logical diagram of line connectivity when extreme disasters occur.

[0015] Figure 2 Detailed solution flow chart for the present invention.

[0016] Figure 3 This is the gas-electricity combined distribution network system used in the embodiments of the present invention.

[0017] Figure 4 This is the distribution network operation mode in Example 2.

[0018] Figure 5 This is the energy storage and P2G operation curve of Example 3.

[0019] Figure 6 Comparison of load loss penalties under the worst distribution of Examples 1-4.

[0020] Figure 7 The figure shows a comparison of the working status of the dual-fuel unit under the basic scenario and the extreme disaster scenario in the embodiment.

[0021] Figure 8 The figure shows the comparison of P2G power consumption in the basic scenario and the extreme disaster scenario in the embodiment.

[0022] Figure 9 The figure shows the comparison of the transmission power of the tie line (18-33) under the basic scenario and the extreme scenario in the embodiment.

[0023] Figure 10(a) shows the reconstruction results (t=15) of gas-fired power combined island scenario 1 and the intraday load loss situation under extreme disaster scenarios.

[0024] Figure 10(b) shows the reconstruction results (t=15) of gas-fired power combined island scenario 2 and the intra-day load loss situation under extreme disaster scenarios.

[0025] Figure 10(c) shows the reconstruction results (t=15) of gas-fired power combined island scenario 3 and the intra-day load loss situation under extreme disaster scenarios.

[0026] Figure 11 This is a sensitivity analysis of the system cost in the embodiment. DETAILED DESCRIPTION

[0027] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0028] Step 1: Consider the coordinated planning of the construction and investment of gas turbines, dual-fuel units, power-to-gas equipment, power storage equipment, gas storage equipment, and interconnection lines, as well as the upgrade of power supply lines and natural gas pipelines. With the goal of minimizing the sum of the operating cost and construction cost of the gas-electricity combined distribution network, and considering the safe operation constraints of the gas distribution network, the distribution network, and the operation constraints of the coupling equipment, a gas-electricity combined distribution network expansion planning model is established.

[0029] The established gas-electricity combined distribution network expansion planning model is as follows:

[0030] The objective function is the construction cost of gas-electricity combined distribution network C I and operating costs C o The sum is minimized as follows:

[0031] minOF=min(C I +C o ) (1)

[0032] The expansion plan targets investments in gas turbines, dual-fuel units, power-to-gas, replacement of distribution network lines and gas distribution network pipelines, interconnecting lines, and power and gas storage equipment. Each facility has k alternative options, with specific investment and construction costs C I The expression is as follows.

[0033]

[0034] Where: is the average annual unit price of investing in a k-type distributed unit; They represent the cost of investing in power-to-gas equipment, distribution network lines, gas distribution network pipelines, interconnecting lines, gas storage equipment, and electricity storage equipment respectively; is a candidate set of distributed units, including gas turbines and dual-fuel units, L s A collection of alternative investment and construction connecting lines. It is a collection of corresponding power-to-gas equipment, distribution network lines, gas distribution network pipelines, gas storage equipment and electricity storage equipment; is the investment state variable of the distributed generator, which takes 1 to indicate that investment has been made and takes 0 to indicate the original facilities of the system, where the superscript k represents the model of the generator to be selected; They represent the investment and construction status variables of power-to-gas equipment, distribution network lines, gas distribution network pipelines, tie lines, gas storage equipment, and electricity storage equipment respectively.

[0035]

[0036] Where: r is the typical day index, h is the hour index, Indicates the number of days included in a typical day r; Ω GU represents the set of gas generating units connected to the distribution network; L is the set of distribution network lines; Represents the unit fuel price when the dual-fuel unit g is running when it is a diesel generator or a fuel-fired power generation unit; is the fuel quantity of dual-fuel unit g, P g,rh is the output of the g-th distributed unit in the corresponding scheduling period, is the energy cost coefficient, SU g,rh and SD g,rh The amount of fuel consumed for the startup and shutdown of distributed units; is the cost of a single operation of the section switch and tie switch on line (i, j), γ ij,r is the number of switch operations on line (i, j) in a typical day r; is the wind turbine operation and maintenance cost coefficient, is the dispatching output of the wind turbine; The penalty price for unit wind curtailment, is the wind power curtailment; is the gas purchase price at node n in the gas distribution network, Purchasing gas power for the system; is the electricity purchase price of the electricity purchasing node, Purchase active power for the system; is the unit power failure load penalty price of the load node, ΔP j,rh is the power loss power; is the penalty price per unit gas loss load of gas distribution network node n, ΔG n,rh is the lost power.

[0037] Constraints include investment and construction-related constraints, distribution network operation constraints, gas distribution network operation constraints, and coupled equipment operation constraints, as follows:

[0038] (1) Investment and construction constraints

[0039]

[0040] Where: are the construction state variables of the original distribution network lines and gas distribution network pipelines respectively; L is the set of distribution network lines, and PL is the set of gas distribution network pipelines.

[0041] (2) Distribution network operation constraints

[0042] 1) Node power balance constraints

[0043]

[0044] where S(j) is the set of devices connected to distribution network node j, and δ(j) is the set of receiving nodes corresponding to distribution network node j; represents the active power discharged and stored by the energy storage device connected to distribution network node j; P ij,rh is the active power flow on line (i, j); is the active load of distribution network node j, is the power consumption of electric-gas conversion device q; is the reactive power flowing into the power purchase node of the distribution network, is the reactive power generated by wind turbine g, represents the reactive power discharged and stored by the energy storage device connected to distribution network node j; Q ij,rh is the reactive power transmitted on line (i, j); Q g,rh is the reactive power generated by distributed generator g, is the predicted reactive load of distribution network node j, φ j,rh is the proportional coefficient required to satisfy the active and reactive power cut-off at the same distribution network node j.

[0045] 2) Line transmission power constraint and node voltage constraint

[0046]

[0047] where: are the lower and upper limits of the voltage amplitude required by distribution network node j, respectively; is the maximum active power that can be transmitted by the original line and k-type line (i, j); V j,rh is the voltage amplitude of distribution network node j.

[0048] 3) Distribution network reconstruction constraint

[0049]

[0050] where: ij,rh is a binary variable representing the actual connection status of line (i, j), taking 1 to represent connection and 0 to represent line disconnection; ε ij,rh is a binary variable representing whether the switch of line (i, j) is closed at time h of r typical day, taking 1 to represent closure; binary variable β ij represents the virtual connection status of line (i, j), n s is the substation node, and N is the set of distribution network nodes, represents the directed virtual flow on line (i, j) from node ω, λ ij is a binary variable representing the directed connection status of line (i, j).

[0051] Among them, the line connectivity logic diagram when extreme disasters occur is as follows: Figure 1 shown.

[0052] 4) Distribution network flow constraints

[0053]

[0054]

[0055] Where: V j,rh is the voltage amplitude at node j, are the resistance and reactance values ​​of the original line / k-type line (i, j), V0 is the reference value of the voltage amplitude; M is a very large number. is the slack variable. ij,rh is a binary variable indicating whether the switch status of line (i, j) r changes at time h on a typical day. When it is 1, it represents a switch action. ij,r is the number of switching operations of the switch on line (i, j) in typical day r.

[0056] 5) Wind turbine operation constraints

[0057]

[0058] Where: is the predicted output of the unit at time h on typical day r; θ j is the power factor angle of the wind turbine at node j.

[0059] 6) Distributed unit operation constraints

[0060]

[0061] Where: are the up and down climbing rates of the unit, su g and sd g are the fuel consumption of the unit during startup and shutdown, I g,rh is a binary variable representing the start / stop status of the generator at time h. When it is 1, it means it is on. is the set of original units in the system, They are respectively the upper and lower limits of active power output of the original / k type units. The upper and lower limits of reactive output are for the original / k type units.

[0062] 7) Grid transmission power limit

[0063]

[0064] Where: are the maximum / minimum active and reactive transmission powers of node j, respectively.

[0065] 8) Operation constraints of power storage equipment

[0066]

[0067] Where: is the maximum / minimum charging and discharging active power of the k-type energy storage device; is the maximum / minimum charging and discharging reactive power of the k-type energy storage device; is the minimum and maximum capacity of the K-type energy storage device; is the capacity of the storage at time h, The efficiency of discharging and charging energy storage devices.

[0068] (3) Gas distribution network operation constraints:

[0069] 1) Node natural gas balance constraints

[0070]

[0071] Where: S(n) is the set of devices connected to node n in the gas distribution network, δ(n) is the set of receiving nodes corresponding to node n, is the gas discharge and storage power of the gas storage device connected to node n of the gas distribution network, f mn,rh is the flow of the natural gas pipeline (m,n), is the gas production power of the power-to-gas equipment q; is the predicted gas load of node n, G g,rh The gas power consumption of a gas turbine or a dual-fuel unit that uses natural gas to generate electricity.

[0072] 2) Gas distribution network pipeline flow constraints

[0073]

[0074] Where: π m,rh and π n,rh are the air pressures at nodes m and n at this time, is the characteristic coefficient of the original / k type pipeline (m,n).

[0075] 3) Pipeline transmission airflow limitation and node air pressure constraint

[0076]

[0077]

[0078] Where: are the lower and upper limits of the gas pressure allowed at node n in the gas distribution network; are the maximum gas flow rates allowed to be transmitted by the original and K-type natural gas pipelines (m, n), respectively.

[0079] 4) Gas purchase power and gas loss load constraints

[0080]

[0081] Where: are the minimum and maximum gas purchasing powers allowed for node n.

[0082] 5) Gas storage equipment constraints

[0083]

[0084] Where: is the maximum / minimum gas storage and discharge power of the K-type gas storage device; is the minimum and maximum capacity of the K-type gas storage equipment; is the capacity of the gas storage equipment in the time period h, It is the deflation and storage efficiency of gas storage equipment.

[0085] (4) Coupling equipment operation constraints

[0086] 1) Gas turbine operating constraints

[0087] The ramping constraints, start-stop fuel constraints, and active and reactive output constraints of the gas turbine are shown in the unit operation constraints of equations (27)-(30). The gas consumption of the gas turbine is calculated as follows:

[0088]

[0089] Where: G g,rh is the gas consumption power of gas turbine g, is the gas consumption coefficient of the gas turbine; HHV is the high calorific value of natural gas, which is 1.026MBtu / kcf.

[0090] 2) Dual-fuel unit operation constraints

[0091] The ramping constraints and start-stop fuel constraints for dual-fuel units are the same as those in Equations (27) and (28). During operation, a dual-fuel unit can only use either diesel or natural gas for power generation. This state constraint is given in Equation (41). The active power output constraint is given in Equations (42) and (43). The reactive power output constraint is similar to the active power output constraint. The gas consumption constraint for a dual-fuel unit is similar to that for a gas turbine, i.e., (46). There is an upper limit on the number of times a unit can change fuel types in a day, and this constraint is described by Equation (44).

[0092]

[0093]

[0094] Where: Ω DF represents the set of dual-fuel units, It is a binary variable, and when it is 1, it represents gas / oil power generation of dual-fuel unit; Represents the corresponding power of the dual-fuel unit using two fuels; is a binary variable. When it is 1, it means that the unit g switches from fuel oil to gas power generation during the h period. Similarly, It represents the conversion of the unit from gas to oil power generation; The maximum number of fuel changes allowed for unit g in one day.

[0095] 3) Power-to-gas equipment operation constraints

[0096]

[0097] Where: φ is the energy conversion coefficient, which is 3.4MBtu / MW. is the efficiency of the qth P2G device; are the minimum and maximum gas production power of the qth P2G device, A collection of existing devices.

[0098] 4) Other constraints

[0099] To avoid meaningless energy closed loops, the power-to-gas device and the gas turbine or gas-fired dual-fuel power generation unit connected to the same node cannot be turned on at the same time, as shown below.

[0100]

[0101] In the planning model established by the present invention, all constraints except the Weymouth equation are linear constraints. The first-order Taylor series expansion method is now used to linearize the Weymouth equation:

[0102]

[0103]

[0104] Where: The b-th pressure breakpoint, for The b-th pressure breakpoint; and there is are the coefficients in the first-order Taylor series process.

[0105] Step 2: Based on the planning model obtained in step 1, the operating constraints of the gas-electricity combined distribution network under the influence of extreme disasters are modeled, and the fuel conversion of dual-fuel units when natural gas is insufficient under extreme disasters is taken into account. The flexibility of the distribution network reconstruction is increased after the construction of the interconnection line. The minimum load loss of the gas-electricity combined distribution network system during the extreme disaster period is calculated, and then the resilience constraint is constructed by limiting the upper limit of the allowable load loss. The robust expansion planning method of the gas-electricity combined distribution network that considers the resilience constraint and balances economy and resilience is obtained.

[0106] The planning model based on step 1 is used to construct a robust expansion planning model for the gas-electricity combined distribution network that considers resilience constraints and balances economics and resilience. Specifically, the model includes:

[0107] Step 2.1: Consider the constraints of the gas-electricity distribution network after extreme disasters;

[0108] The connectivity of distribution network lines is affected by extreme disastersζ ij,rh 、Line switch closed state ε ij,rh and the construction status of the connecting lines The specific logical relationship determined is as follows Figure 1 Its mathematical expression is shown in the following formula.

[0109]

[0110] Where: ij,rh Is a binary variable representing whether line (i, j) is affected by extreme disasters. When it is 1, it means it is affected. The above formula is nonlinear, and an auxiliary binary variable is introduced. The linearization is performed as follows:

[0111]

[0112] The connectivity status of the pipeline (m,n) in the gas distribution network a mn,rh Only affected by extreme disasters, that is, a mn,rh =1-ζ mn,rh , the gas distribution network flow constraint under the influence of extreme disasters is obtained as follows:

[0113]

[0114] Step 2.2: Construct resilience constraints for the gas-electricity combined distribution network.

[0115] The power loss load and gas loss load penalties are selected as the quantification of the resilience of the gas-electricity combined distribution network, and R is set. 0Denotes the upper limit of the penalty cost for load loss during the fault period, and the resilience constraint is constructed as shown in Equation (63). By setting the resilience constraint, the gas-electricity joint system needs to plan additional flexibility resources to meet this resilience constraint, achieving a trade-off between the economic efficiency of expansion planning and the resilience of the gas-electricity joint distribution network system.

[0116]

[0117] Where: R 0 is the toughness index set, H F Represents the set of time periods during which the system has not yet resumed normal operation after a disaster.

[0118] Step 3: Based on the robust expansion planning model of the gas-electricity combined distribution network that balances economy and resilience obtained in Step 2, taking into account the uncertainty of the probability of extreme disaster scenarios, the linearized KL divergence is used to describe the distance between the actual distribution of extreme disasters and the empirical distribution, and an extreme disaster uncertainty set is established.

[0119] The details are as follows:

[0120] Step 3.1: Generate N extreme disaster scenarios randomly through Monte Carlo simulation, and reduce them through simultaneous back substitution to obtain S representative disaster scenarios and their corresponding empirical distributions.

[0121]

[0122] Step 3.2: Characterize the empirical distribution using the linearized KL divergence and the actual distribution The distance is expressed as And set the threshold d that its distance should not exceed KL , and finally we get the uncertainty set U that describes the probability of extreme disaster scenarios.

[0123]

[0124] Where: ρ s is the probability of scene s in the actual distribution. is the auxiliary variable in the piecewise linearization, and are the left and right endpoints of the interval during piecewise linearization, are the left and right endpoints of each interval, b s,n and α s,n is an auxiliary variable.

[0125] Step 4: Based on Steps 2 and 3, a two-stage distributed robust expansion planning model based on KL divergence is established. In the first stage, the basic scenario is mainly used to ensure the economic efficiency of system planning. In the second stage, the resilience indicators under extreme disaster scenarios are used as constraints to obtain the optimal decision that meets the set resilience constraints.

[0126] Formula (71) represents the objective function and constraints of the basic scenario in the first stage with economy as the goal. The second stage ensures the resilience of system operation under the worst-case scenario. In formula (72), W(x) represents the objectives and resilience indicators for the worst-case scenario of extreme disasters in the second stage.

[0127]

[0128] Where: x represents the investment and construction decision variable, v represents the binary variable other than the investment and construction decision, and y represents the continuous variable; c a 、c b 、c d , b, d, e, h, A, B, C, D, E, F, G, H and I are the corresponding coefficient vectors and matrices in the abstract objective function and constraints. s is the index of the extreme disaster scenario, S is the number of scenarios, ρ s is the probability of scene s, U={ρ s |Kρ s ≤l} represents the fuzzy set of extreme disaster scenarios; z s Represents the amount of power and gas loss in the system in scenario s; represents the unit price of load loss penalty; R is the set maximum allowable load loss index.

[0129] Step 5: Use the column and constraint generation algorithm to decouple the two-stage distributed robust programming model obtained in step 4 into the main problem and subproblems and solve them iteratively. Use the IEEE 33-node distribution network system and the improved Belgian 20-node gas distribution network coupled system for case analysis to verify the ability of the invented model to improve the economy of the normal operation of the gas-electricity combined distribution network and enhance its resilience in extreme disasters.

[0130] The column-and-constraint generation (CCG) algorithm is used to iteratively solve the two-stage model. The master-problem (MP), i.e., the first-stage planning model, is to find the expansion decision that minimizes the sum of the investment and operating costs given the probability distribution of extreme disaster scenarios. The master-problem is expressed in matrix form as follows, where u is the iteration index and N is the number of iterations. I Iteration count value.

[0131]

[0132]

[0133] The sub-problem (SP) is the second-stage model that finds the worst probability distribution of the response to the extreme disaster scenario distribution based on the expansion decision obtained from the main problem. And verify whether this worst-case scenario meets the resilience index requirements of the gas-electricity combined distribution network in the form of a max-min model.

[0134]

[0135] The upper-level variables of the subproblem model do not affect the feasible domain of the lower level, and thus can be decoupled into two independent solution models, where the lower-level subproblem (lower-level SP, LSP) can be expressed as (71), that is, s minimization load problems that can be solved in parallel. After solving the lower-level subproblem, we get Pass it to the upper-level sub-problem (upper-level SP, USP), that is, Equation (72), and get the corresponding main problem decision x * The worst probability distribution

[0136]

[0137] The specific solution process of the model is as follows Figure 2 , the specific steps are as follows:

[0138] 1) Set the iteration count N I =0 and toughness index R.

[0139] 2) Solve the main problem (73)-(75) and obtain the planning decision and pass it to the subproblem.

[0140] 3) Solve the problem of planning decision The LSP (77) at the time of S is used to obtain the minimum load loss of the system under S scenarios. Will Pass it to USP(78) to solve the worst probability distribution

[0141] 4) Verify whether the solution satisfies the toughness constraint, i.e., Equation (79). If the toughness index is satisfied, then output is the optimal planning result, and the solution is completed. If it is not satisfied, update the probability distribution in the main problem to And set N I =N I +1, go back to step 2 and continue to alternately solve the main problem and subproblems.

[0142]

[0143] The model proposed in this paper couples the standard IEEE 33-node distribution network system with the improved Belgian 20-node gas distribution network. Its topology is as follows: Figure 3 As shown in Figure 1, the system includes one diesel generator set, denoted by G1; two distributed wind turbines, denoted by WT; and coupled equipment, including a gas turbine and a power-to-gas unit, denoted by GT and P2G, respectively. To verify the impact of different planning schemes on system operation and resilience, five schemes were set up to calculate the optimal investment and construction strategies for comparative analysis. The specific settings are shown in Table 1.

[0144] The cost and planning results of the five options are shown in Table 2 and Table 3 respectively. In Table 3, the superscript represents the equipment model selected for investment and construction, and the value 0 represents the original equipment. E and P represent the feeder and gas distribution network pipelines respectively. The subscript represents the specific line or pipeline to be upgraded, for example represents the upgrade of the distribution network line (1,2) to model 2; G, D and A represent the gas turbine, dual-fuel unit and power-to-gas equipment respectively. Due to the characteristics of the coupled equipment, the subscripts represent the distribution network node and gas network node to which the equipment is connected, for example represents the model 1 gas turbine that is selected to connect the distribution network node 3 and the gas distribution network node 9; B and T represent the power storage and gas storage equipment, and the subscripts are the corresponding distribution / gas distribution network nodes; S represents the tie line.

[0145] Table 1 Specific settings for schemes 1-5

[0146] plan Lines and pipelines Gas turbines and dual-fuel units Power-to-Gas Electricity and gas storage uncertainty Communication Line 1 √ × × × × × 2 √ √ × × × × 3 √ √ √ √ × × 4 √ √ √ √ √ × 5 √ √ √ √ √ √

[0147] Table 2 Costs of Options 1-5

[0148] plan <![CDATA[投建成本(10 6 Yuan)]]> <![CDATA[运行成本(10 6 Yuan)]]> <![CDATA[总成本(10 6 Yuan)]]> 1 0.760 19.175 19.935 2 0.810 18.029 18.839 3 1.015 12.009 13.024 4 1.310 11.975 13.285 5 1.251 11.959 13.210

[0149] Table 3 Planning results of options 1-5

[0150]

[0151]

[0152] In Option 1, only line and pipeline upgrades are allowed. In the planning results, 4 distribution network lines and 2 gas distribution network pipelines are upgraded, and the lines connecting substations or natural gas suppliers are upgraded to models with larger capacity to meet the load growth. However, after the upgrade, the feeder The power transmitted on the two feeders is still close to its maximum power limit. If the load increases further, the capacity of these two feeders will need to be expanded.

[0153] Scheme 2 adds the site selection and type selection planning of distributed units on the basis of Scheme 1. As can be seen from Table 3, Scheme 2 adds the investment and construction of gas turbines compared with Scheme 1. The number of distribution network line upgrades is reduced to 0, while the number of gas distribution network pipeline upgrades is increased from 2 to 4. As shown in Table 2, the operating cost is reduced by 1.146×10 6 Yuan, the investment and construction cost increased by 0.05×10 6 Yuan, the total cost is reduced by 1.096×10 compared with Plan 1. 6 The output and purchased power curves of distributed units in a typical day in the gas-electricity combined distribution network of Option 2 are as follows: Figure 4 As shown, the net load is the total power load minus the wind power dispatch output and power-to-gas consumption. Figure 4 It was observed that the construction of distributed gas turbines reduced the system's purchased power and alleviated the system's original feeder The pressure to transmit power to downstream nodes does not require feeder upgrades to meet load demands. In Option 2, the gas-fired power distribution network opted not to invest in dual-fuel units due to their higher energy consumption and lower economic performance compared to gas turbines. Furthermore, since all distributed units were gas turbines, this increased pressure on the distribution network to transmit natural gas, leading to an increase in pipeline upgrade decisions compared to Option 1. Distributed units can reduce the power purchased by the distribution network, delaying line upgrades and improving economic efficiency. However, their reliance on fuel supply increases purchasing and transmission pressures on the distribution network.

[0154] Compared with Plan 2, Plan 3 adds the coordinated planning of power-to-gas, power storage and gas storage equipment. As shown in Tables 2 and 3, in this case, one power-to-gas, one power storage and one gas storage are selected, and the decision to upgrade the pipeline is reduced from 4 in Plan 2 to 3: the original pipeline of the system No longer need to upgrade, choose to upgrade to At the same time, the gas distribution network pipeline The model selected for upgrading is the smaller capacity model 1. In Table 2, the investment and construction cost of Scheme 3 is the largest among Schemes 1-3, while the operating cost is reduced by 6.02×10 compared with Scheme 2. 6 The total cost was reduced by 31.95%, a significant decrease, making it the most economical of the top three planning schemes without considering extreme disasters, verifying the economic superiority of coordinated planning of lines and pipelines, distributed units, power-to-gas and energy storage.

[0155] The reduction in operating costs is mainly due to the power-to-gas and power storage equipment The investment and construction of the wind power grid has realized the absorption of excess wind energy in the distribution network, reducing the penalty cost of wind curtailment to 0. In Scheme 2, the gas-electricity combined distribution network system does not have energy storage equipment and does not allow reverse flow. The curtailed wind power is shown in Figure 5 The power-to-gas conversion project of Option 3 is also proposed. The power consumption of the power-to-gas and the daily state of charge (SOC) curves of the power and gas storage are shown in Figure 2. It can be seen that the power consumption of the power-to-gas and the amount of wind curtailment at node 17 in Scheme 2 are the same in each scheduling period, that is, the power-to-gas only converts excess wind energy. This is because the power-to-gas production efficiency is low, only 60%-70%, so the power-to-gas operation mode is not economical. On the other hand, it can be seen from Figure 5 See energy storage equipment This mode of operation, with a storage period of 1:00 AM to 6:00 AM, uses excess wind power and low-cost electricity purchased from substations. While energy storage equipment experiences losses during storage and release, its efficiency far exceeds that of power-to-gas conversion, making it more economical to store low-cost electricity and release it during peak load periods. Figure 5 The SOC curve for China Gas Storage follows a similar pattern, storing gas during periods of low gas prices and releasing it during peak periods. Energy storage improves system economics by shifting peaks and filling valleys. Furthermore, energy storage offers advantages over power-to-gas in absorbing renewable energy.

[0156] Schemes 1-3 do not consider the system resilience requirements when extreme disasters occur. Schemes 4 and 5 consider the resilience index under extreme disasters. In order to observe the additional investment in resilience resources, the resilience index R needs to be less than the expected load loss penalty corresponding to the decision of Scheme 3. The resilience index R is selected as 2.5×10 6 The maximum distance d allowed between the empirical distribution and the actual distribution KL Set to 0.05, the distribution network allows reverse flow after the fault, while the gas distribution network does not. Monte Carlo method is used to generate 5000 extreme disaster scenarios, and three representative extreme disaster scenarios are obtained through synchronous back substitution elimination method. The damage status and initial probability distribution See Table 4.

[0157] Table 4 Introduction to extreme disaster scenarios of the present invention

[0158]

[0159] As can be seen from Table 2, the total cost of Scheme 4 is increased compared to the calculation results of the deterministic model (i.e., Scheme 3). This part of the total cost increase is the result of the combined effect of the increased investment and construction costs and the reduced operating costs. Comparing the planning decisions of Scheme 4 with those of Scheme 3, it is observed that the gas turbine at the distribution network node 30 Dual fuel unit Replacement, also invested in the construction of dual fuel units The power-to-gas type at distribution network node 17 is changed to the more powerful type 1. The investment and construction decisions of options 1-3 are matched with the worst distribution results obtained by option 4. The expected load loss of options 1-4 is calculated and compared. Figure 6 The labels in the figure indicate the minimum load loss penalty for each scenario. After considering the system resilience indicator under extreme disasters, the total cost of Option 4 increases by approximately 2% compared to Option 3. In the worst-case distribution scenario, the load loss penalty for Option 4 is 27.08% lower than that of Option 3. The increase in system cost for Option 4 stems from additional investment in flexible resources such as distributed units, which significantly reduces load loss in extreme disaster scenarios. Figure 6 It can be seen that the expected maximum load loss penalty corresponding to the construction decisions of Schemes 1-3 is greater than the resilience index R, while Scheme 4, which adds the resilience index as a constraint to the planning model, ensures that the resilience of the distribution network system meets the standard in this scenario setting, proving the correctness of the model of the present invention.

[0160] The working modes of the two dual-fuel units in Scheme 4 under the basic scenario and three extreme disaster scenarios are shown in Figure 7 The figure shows the dual-fuel unit built at node 30. There has been a shift from gas-fired power generation in basic scenarios to exclusively fuel oil in extreme disaster scenarios. The ability of dual-fuel units to generate electricity using fuel oil during disasters makes them more reliable than gas turbines, which rely on the transport capacity of the gas distribution network. Dual-fuel units can support critical power loads after extreme disasters.

[0161] Power-to-Gas The output curves for basic scenarios and extreme disaster scenarios are as follows: Figure 8 As shown. It can be seen that the power consumption of power-to-gas is also much greater than that of the case where only wind power is converted and abandoned in the basic scenario. In the example setting of the present invention, since the gas distribution network has fewer means to restore the load and limits the flow direction when it fails, its load loss penalty coefficient is higher than that of the distribution network. At the same time, since the load node 16 of the gas distribution network has the largest load and the highest penalty coefficient, when this node loses connection with the gas supplier, the power-to-gas It can support nodes 15 and 16 and ensure the supply of critical gas loads.

[0162] Option 5 allows investment in tie line S after construction of tie line 18-33 Compared with the construction results of Option 4, the location of the gas storage equipment has changed, and the dual-fuel unit Replace the gas turbine selected in Option 3 with the more economical one Gas turbine In scenarios 1-3, the unit remains shut down after the failure due to lack of gas source. This decision is different from the dual-fuel unit selected in scenario 4. The increased load loss is compensated by the flexibility brought by the interconnection line combined with the distribution network reconstruction. The power transmitted by the interconnection line 18-33 in the basic scenario and the three extreme disaster scenarios in Scheme 5 is as follows: Figure 9 In the basic scenario and scenario 1 with less disaster impact, the contact line S 18-33 The upper switch is disconnected and the transmission power is 0; in extreme disaster scenarios 2 and 3, in order to ensure the supply to the key load node 33 after the disaster, the switch on the tie line is closed to achieve power transmission. 18-33 The power supply mode for the important load node 33 is added, thus achieving the same resilience index requirements as Scheme 4. The calculated cost results can be seen from Table 2. Considering the construction of the interconnection line, the gas turbine For dual fuel units The replacement of the interconnection lines simultaneously reduced both construction and operating costs, bringing the total cost down by 0.565%. This result demonstrates the economic and flexible nature of combining the construction of interconnection lines with network reconstruction.

[0163] The reconstruction and load loss results of the three fault scenarios are Figure 10(a)-Figure 10(c) As shown in the figure, ES and GS represent the electric storage device and gas storage device respectively. After the fault begins, the gas turbine The system remains shut down in all scenarios and is omitted in the figure. The dual-fuel units in the three scenarios after the failure occurs Only fuel-fired power generation is used, so the connection line between the dual-fuel unit and the gas distribution network is ignored. Scenario 1 has fewer faults. The distribution network and the gas distribution network are both connected to the main grid. At this time, the distribution network nodes 12-18 rely on the fuel-fired power generation of the dual-fuel unit to maintain the supply to the key load nodes 13 and 15. In scenario 2, the fault situation is more serious. The tie line S 18-33 The closure of the power grid and the existence of the coupling equipment form a gas-electricity island 1. In the gas-electricity island 1, the limited electric power or natural gas can be optimally allocated to minimize the load loss penalty within the island. As can be seen from Figure 10(b), the supply of key loads to the distribution network is achieved as much as possible. The situation in scenario 3 is similar to scenario 2. As shown in Figure 10(c), one power island and two gas-electricity islands are formed. The power island 1 relies on diesel generators to support the load. There is a coupling device gas turbine in the gas-electricity island 1. The power supply in the isolated island is guaranteed; in the gas-electricity combined isolated island 2, the closed tie line S 18-33The critical load node 33 was connected, restoring power to that node. The planned construction of the interconnection line and the formation of a gas-electricity island increased system flexibility, ensuring continuous power supply to critical electrical and gas loads and enhancing the resilience of the gas-electricity distribution network.

[0164] In the model of this invention, the requirements for the resilience index R are set by the system planning staff according to the needs, and its specific value determines the size of the resilience resources that the system needs to invest in. When constructing the fuzzy set U of disaster uncertainty, the parameter d that limits the maximum distance between the empirical distribution and the actual distribution is KL The value of also plays a decisive role in the worst distribution selected by the distribution robustness model. Based on solution 5, the set toughness index R and the maximum distance d allowed between the empirical distribution and the actual distribution are changed. KL And record the results to get the trend of total system cost and parameter changes as follows Figure 11 As shown in Figure 2, it can be seen that the system cost decreases with the decrease of the resilience index R and the maximum distance d allowed by the empirical distribution and the actual distribution. KL The decrease in the resilience index R means that the upper limit of the minimum load loss allowed during a gas-electricity distribution network disaster is reduced. At this time, the investment in flexible resources such as distributed units should be increased, thereby increasing the total cost. On the other hand, d KL The increase in means that the allowable distance between the worst distribution and the initial distribution increases, which increases the probability corresponding to the worst failure scenario, thereby increasing the difficulty of meeting the resilience constraint. Therefore, such a change trend appears in the sensitivity analysis.

[0165] In light of the recent trend toward multi-energy coupling and the increasing resilience demands posed by the increasing frequency of extreme natural disasters, this paper proposes a robust expansion planning model for a combined gas-electricity distribution network that considers system resilience constraints under extreme disasters. This planning model incorporates various flexible resources that can enhance both economic efficiency during normal operation and system resilience during failures. Case studies provide the following conclusions:

[0166] 1) The economic advantages of coordinated planning of lines and pipelines, distributed units, power-to-gas, and energy storage, as well as their role in accommodating renewable energy, were verified. When considering the uncertainty of faults using a two-stage distributed robustness approach, the total cost increased compared to the deterministic model. Under the resilience constraints of the combined gas-power distribution network disaster scenario, more flexible resources are needed to support critical loads.

[0167] 2) Dual-fuel units, due to their ability to switch fuels during extreme disasters, can use fuel oil for power generation during fault periods, decoupling the combined gas-electricity distribution network and reducing its reliance on the gas distribution network during extreme disasters. Power-to-gas equipment can also effectively ensure the supply of critical natural gas loads in extreme disaster scenarios.

[0168] 3) Comparative analysis has verified that the construction of interconnection lines can improve system flexibility. Reconfiguring the distribution network to form a combined gas-electricity island can help optimize energy distribution within the island and ensure the supply of critical electricity or natural gas loads.

Claims

1. A robust expansion planning method for a combined gas-electricity distribution network taking into account system resilience constraints, characterized in that: The following steps are involved: Step 1: Considering the coordinated planning of gas turbines, dual-fuel units, power-to-gas equipment, power storage equipment, gas storage equipment, and interconnecting lines, as well as the upgrade of power lines and natural gas pipelines, a gas-power combined distribution network expansion planning model is established with the goal of minimizing the sum of the operating cost and construction cost of the combined gas-power distribution network. This model also considers the safe operation constraints of the gas and distribution networks and the operation constraints of the coupled equipment. Step 2: Based on the gas-electricity combined distribution network expansion planning model, the operational constraints of the gas-electricity combined distribution network under the influence of extreme disasters are modeled. The fuel conversion effect of dual-fuel units when natural gas is insufficient under extreme disasters is considered, and the increased flexibility of distribution network reconstruction after the construction of interconnection lines is considered. The minimum load loss of the gas-electricity combined distribution network system during the extreme disaster period is calculated, and then a resilience constraint is established by limiting the upper limit of the allowable load loss. The result is a robust expansion planning model for the gas-electricity combined distribution network that considers the resilience constraint and balances economy and resilience. Step 3: Based on the robust expansion planning model for the gas-electricity combined distribution network that balances economy and resilience, and taking into account the uncertainty of the probability of extreme disaster scenarios, a linearized KL divergence is used to describe the distance between the actual distribution of extreme disasters and the empirical distribution, and an extreme disaster uncertainty set is established; Step 4: Based on the extreme disaster uncertainty set, a two-stage distributed robust expansion planning model based on KL divergence is established. In the first stage, the basic scenario is used to ensure the economy of system planning. In the second stage, the resilience index under the extreme disaster scenario is used as a constraint to obtain the optimal decision that meets the set resilience constraints. Step 5: Use the column and constraint generation algorithm to decouple the two-stage distributed robust extended planning model into the main problem and sub-problems and solve them iteratively.

2. The robust expansion planning method for gas-electricity combined distribution network considering system resilience constraints according to claim 1 is characterized in that: The objective function of the gas-electricity combined distribution network expansion planning model established in step 1 is the gas-electricity combined distribution network construction cost C I and operating costs C o The sum OF is minimized as follows: minOF=min(C I +C o ) (1) Investment and construction cost C I The expression is as follows: Where: is the average annual unit price of investing in a k-type distributed unit; and They represent the cost of investing in power-to-gas equipment, distribution network lines, gas distribution network pipelines, interconnecting lines, gas storage equipment, and electricity storage equipment respectively; is a candidate set of distributed units, including gas turbines and dual-fuel units, L s A collection of alternative investment and construction connecting lines. and It is a collection of corresponding power-to-gas equipment, distribution network lines, gas distribution network pipelines, gas storage equipment and electricity storage equipment; is the investment state variable of the distributed generator. When it is 1, it means that the investment has been made, and when it is 0, it means the original facilities of the system. The superscript k represents the model of the generator to be selected. Similarly, and They represent the investment and construction state variables of K-type power-to-gas equipment, distribution network lines, gas distribution network pipelines, tie lines, gas storage equipment, and electricity storage equipment respectively; Operating cost C o The expression is as follows: Where: r is the typical day index, h is the hour index, Indicates the number of days included in a typical day r; Ω GU represents the set of gas generating units connected to the distribution network; L is the set of distribution network lines; Represents the unit fuel price when the dual-fuel unit g is running when it is a diesel generator or a fuel-fired power generation unit; is the fuel quantity of dual-fuel unit g, P g,rh is the output of the g-th distributed unit in the corresponding scheduling period, is the energy cost coefficient, SU g,rh and SD g,rh The amount of fuel consumed for the startup and shutdown of distributed units; is the cost of a single operation of the section switch and tie switch on line (i, j), γ ij,r is the number of switch operations on line (i, j) in a typical day r; is the wind turbine operation and maintenance cost coefficient, is the dispatching output of the wind turbine; The penalty price for unit wind curtailment, is the wind power curtailment; is the gas purchase price at node n in the gas distribution network, Purchasing gas power for the system; is the electricity purchase price of the electricity purchasing node, Purchase active power for the system; is the unit power failure load penalty price of the load node, ΔP j,rh is the power loss power; is the penalty price per unit gas loss load of gas distribution network node n, ΔG n,rh is the lost power.

3. The robust expansion planning method for gas-electricity combined distribution network considering system resilience constraints according to claim 2 is characterized in that: The constraints of the gas-electricity combined distribution network expansion planning model established in step 1 include investment and construction constraints, distribution network operation constraints, gas distribution network operation constraints, and coupled equipment operation constraints, as follows: (1) Investment and construction constraints Where: and are the state variables of the original distribution network lines and gas distribution network pipelines respectively; PL is the set of gas distribution network pipelines; (2) Distribution network operation constraints 1) Node power balance constraints Where: S(j) is the set of devices connected to the distribution network node j, δ(j) is the set of receiving nodes corresponding to the distribution network node j; and represents the active power released and stored by the storage device connected to the distribution network node j; P ij,rh is the active power flow of line (i, j); is the active load of distribution network node j, is the power consumption of the power-to-gas equipment q; It is the reactive power flowing into the power purchasing node of the distribution network. is the reactive power generated by the wind turbine, and It represents the reactive power released and stored by the storage device connected to the distribution network node j, Q ij,rh is the reactive power transmitted by line (i, j), Q g,rh is the reactive power generated by the distributed generator g, is the predicted reactive load of distribution network node j, φ j,rh is the proportional coefficient that needs to be satisfied for active and reactive power removal at the same distribution network node j; 2) Line transmission power constraints and node voltage constraints Where: and are the lower and upper limits of the voltage amplitude required by the distribution network node j respectively; and is the maximum active power that can be transmitted by the original line and the k-type line (i, j); V j,rh is the voltage amplitude of distribution network node j; 3) Distribution network reconstruction constraints Where: a ij,rh It is a binary variable representing the actual connectivity status of line (i, j). When it is 1, it means it is connected, and when it is 0, it means the line is disconnected. ε ij,rh is a binary variable representing whether the switch of line (i, j) is closed. When it is 1, it means the switch is closed, and when it is 0, it means the switch is open. Binary variable β ij Represents the virtual connection status of line (i, j), n s is the substation node, N is the set of distribution network nodes, represents the virtual traffic on line (i, j) sent to node ω, λ ij is a binary variable representing the directed connectivity status of the link (i, j); 4) Distribution network flow constraints Where: V i,rh is the voltage amplitude at node i, and is the resistance value of the original line and the k-type line (i, j); and is the reactance value of the original line and the k-type line (i, j); V0 is the reference value of the voltage amplitude; M is a very large number; is the slack variable; σ ij,rh is a binary variable indicating whether the switch state of line (i, j) changes at time h on typical day r. When it is 1, it represents a switch action. is the maximum number of switching operations in one day; γ ij,r is the number of switching operations of the switch on line (i, j) in typical day r; 5) Wind turbine operation constraints Where: is the predicted output of the unit at time h on typical day r; θ j is the power factor angle of the wind turbine at node j; 6) Distributed unit operation constraints Where: and are the unit's ramp-up rate and ramp-down rate, respectively, g and sd g The amount of fuel consumed when the unit is started and shut down once; I g,rh is a binary variable representing the start / stop status of the generator at time h. When it is 1, it means it is on. is the set of original units in the system, and They are respectively the upper limits of active power output of the original units and the K-type units; and They are the lower limits of active power output of the original unit and the K-type unit respectively; and The upper limits of reactive power output are for the original units and the K-type units respectively; and The lower limits of reactive power output are for the original units and the K-type units respectively; 7) Grid transmission power limit Where: and are the maximum and minimum active transmission power of node j, respectively; and are the maximum and minimum reactive transmission powers of node j, respectively; 8) Operational constraints of power storage equipment Where: is the maximum charging active power of the k-type energy storage device; is the maximum discharge active power of the k-type energy storage device; is the maximum charging reactive power of the k-type energy storage device; is the maximum discharge reactive power of the k-type energy storage device; and is the minimum and maximum capacity of the K-type energy storage device; is the capacity of the energy storage device at time h, and the efficiency of discharging and charging the energy storage device; (3) Gas distribution network operation constraints: 1) Node natural gas balance constraints Where: S(n) is the set of devices connected to the gas distribution network node n, δ(n) is the set of receiving nodes corresponding to the gas distribution network node n, and is the gas discharge and storage power of the gas storage device connected to the gas distribution network node n, f mn,rh is the flow of the natural gas pipeline (m,n), is the gas production power of the power-to-gas equipment q; is the predicted gas load of node n in the gas distribution network, G g,rh Gas consumption power of gas turbine or dual-fuel unit using natural gas for power generation; 2) Gas distribution network pipeline flow constraints Where: π m,rh and π n,rh are the air pressures at nodes m and n at this time, and is the characteristic coefficient of the original natural gas pipeline and the K-type natural gas pipeline (m, n); 3) Pipeline transmission airflow limitation and node air pressure constraint Where: and are the lower and upper limits of the gas pressure allowed at node n in the gas distribution network; and are the maximum gas flow rates allowed to be transmitted by the original natural gas pipeline and the K-type natural gas pipeline (m, n); 4) Gas purchase power and gas loss load constraints Where: and is the minimum and maximum gas purchase power allowed by the gas distribution network node n; ΔG n,rh is the lost power; 5) Gas storage equipment constraints Where: is the maximum gas storage power of the K-type gas storage equipment; is the maximum deflation power of the K-type gas storage device; and is the minimum and maximum capacity of the K-type gas storage equipment; is the capacity of the gas storage equipment in the time period h, and The deflation and storage efficiency of gas storage equipment; (4) Coupling equipment operation constraints 1) Gas turbine operating constraints The ramping constraints, start-stop fuel constraints, and active and reactive output constraints of the gas turbine are shown in the unit operation constraints of equations (27)-(30). That is, equations (27)-(30), the gas consumption of the gas turbine is calculated as follows: Where: G g,rh is the gas consumption power of the gas turbine g, is the gas consumption coefficient of the gas turbine; HHV is the high calorific value of natural gas; 2) Dual-fuel unit operation constraints The ramping constraint and start-stop fuel constraint of the dual-fuel unit are the same as those in equations (27) and (28). During operation, the dual-fuel unit can only choose one of diesel or natural gas for power generation. This state constraint is shown in equation (41). The active power output constraint is shown in equations (42) and (43). The gas consumption constraint of the dual-fuel unit is shown in equation (46). There is an upper limit on the number of times the unit can change fuel types in a day. This constraint is described by equation (44). Where: Ω DF represents the set of dual-fuel units, It is a binary variable, and when it is 1, it represents gas-fired power generation by a dual-fuel unit; It is a binary variable, and when it is 1, it represents fuel-fired power generation by a dual-fuel unit; and Represents the corresponding power of the dual-fuel unit using two fuels; It is a binary variable. When it is 1, it means that the unit g switches from fuel oil to gas power generation during the h period. It represents that unit g switches from gas-fired to oil-fired power generation during period h; The maximum number of fuel changes allowed for unit g in one day; 3) Power-to-gas equipment operation constraints Where: φ is the energy conversion coefficient, is the efficiency of the qth P2G device; and are the minimum and maximum gas production power of the qth P2G device, A collection of existing equipment; and are the minimum and maximum gas production powers of type k P2G device q respectively; 4) Other constraints Restrictions: The power-to-gas device and the gas turbine or gas-fired dual-fuel generator set connected to the same node cannot be started at the same time, as shown below: The first-order Taylor series expansion method is used to linearize the Weymouth equation: Where: for The b-th pressure breakpoint, for The b-th pressure breakpoint; and there is and are the coefficients in the first-order Taylor series process.

4. The robust expansion planning method for gas-electricity combined distribution network considering system resilience constraints according to claim 3 is characterized in that: In step 2, a robust expansion planning model for the gas-electricity combined distribution network is established that considers resilience constraints and balances economy and resilience. The specific steps are as follows: Step 2.1: Consider the constraints of the gas-electricity distribution network after extreme disasters; The connectivity of distribution network lines is affected by extreme disasters and the line variables ζ ij,rh 、Line switch closed state ε ij,rh and the construction status of the connecting lines The specific logical relationship is as follows: Where: ij,rh is a binary variable representing whether line (i, j) is affected by extreme disasters. When it is 1, it means it is affected; The above formula is nonlinear, so we introduce auxiliary binary variables and The linearization is performed as follows: The connectivity status of the pipeline (m,n) in the gas distribution network a mn,rh Pipeline variables ζ are only affected by extreme disasters mn,rh Decision, that is, a mn,rh =1-ζ mn,rh , the gas distribution network flow constraint under the influence of extreme disasters is obtained as follows: Where: is the slack variable; Step 2.2: Constructing resilience constraints for the gas-electricity distribution network The power loss load and gas loss load penalties are selected as the quantification of the resilience of the gas-electricity combined distribution network, and R is set. 0 The upper limit of the penalty cost for load loss during the fault period is expressed as the resilience indicator. The resilience constraint is constructed as shown in Equation (63). Additional flexibility resources are planned to meet the resilience constraint, achieving a trade-off between the economic efficiency of the expansion plan and the resilience of the gas-electricity combined distribution network system: Where: H F Represents the set of time periods during which the system has not yet resumed normal operation after a disaster.

5. The robust expansion planning method for gas-electricity combined distribution network considering system resilience constraints according to claim 4 is characterized in that: In step 3, the linear KL divergence is used to measure the distance between the actual distribution of extreme disaster scenarios and the initial distribution, and the extreme disaster uncertainty set is established. The specific steps are as follows: Step 3.1: Generate N extreme disaster scenarios randomly through Monte Carlo simulation, and reduce them through simultaneous back substitution to obtain S representative disaster scenarios and their corresponding empirical distributions. Where: is the probability of scenario s occurring in the empirical distribution; Step 3.2: Characterize the empirical distribution using the linearized KL divergence and the actual distribution The distance is expressed as And set the threshold d that its distance should not exceed KL , and finally we get the uncertainty set U that describes the probability of extreme disaster scenarios; Where: ρ s is the probability of scene s in the actual distribution; Δρ s is the length of each interval in the piecewise linearization process; θ s is the auxiliary variable in the piecewise linearization, and θ s =ρ s ln(ρ s ), and are the left and right endpoints of the interval during piecewise linearization, and are the left and right endpoints of each interval, b s,n and α s,n is an auxiliary variable, N pl is the number of segments in the piecewise linearization.

6. The robust expansion planning method for gas-electricity combined distribution network considering system resilience constraints according to claim 5 is characterized in that: In step 4, a two-stage distributed robust programming model is established. The specific model is as follows: Formula (71) represents the objective function and constraints of the basic scenario in the first stage with economy as the goal, and the second stage ensures the resilience of system operation under the worst-case scenario. In formula (72), W(x) represents the objective and resilience index constraints for the worst-case scenario of extreme disasters in the second stage. Where: x represents the investment and construction decision variable, v represents the binary variable other than the investment and construction decision, and y represents the continuous variable; c a 、c b 、c d , b, d, e, h, l, A, B, C, D, E, F, G, H, I and K are the corresponding coefficient vectors and matrices in the abstract objective function and constraints; s is the index of the extreme disaster scenario, S is the number of scenarios, ρ s is the probability of scene s, U={ρ s |Kρ s ≤l} represents the uncertainty set describing the probability of extreme disaster scenarios; z s Represents the amount of power and gas loss of the system in scenario s; v s Represents the binary variables of the system in scenario s except for the investment and construction decision, y s Represents the remaining continuous variables of the system in scenario s; represents the unit price of load loss penalty; R is the set maximum allowable load loss index.

7. The robust expansion planning method for gas-electricity combined distribution network considering system resilience constraints according to claim 6 is characterized in that: The decoupling and iterative solution of the two-stage model in step 5 are specifically as follows: The two-stage model is iteratively solved using the column and constraint generation algorithm. The main problem, i.e., the first-stage planning model, is to solve the expansion decision that minimizes the sum of investment and operation costs when the probability of extreme disaster scenarios is known. The matrix form of the main problem is expressed as follows, where u is the iteration number index and N is the number of iterations. I Count the number of iterations: The sub-problem is that the second-stage planning model obtains the worst probability distribution of the response to the extreme disaster scenario distribution based on the expansion decision obtained in the main problem. And verify whether this worst-case scenario meets the resilience index requirements of the gas-electricity combined distribution network in the form of a max-min model: The sub-problem model is decoupled into two independent solution models, and the lower sub-problem is expressed as Equation (77), which is the minimization of load loss problem solved in parallel. The power loss and gas loss obtained after solving the lower sub-problem is Pass it to the upper sub-problem, that is, formula (78), and get the corresponding main problem decision x * The worst probability distribution The specific steps of iterative solution of the model are as follows: 1) Set the iteration count N I =0 and toughness index R; 2) Solve the main problem through equations (73)-(75) and obtain the planning decision and pass it to the subproblem; 3) Solve the problem by using formula (77) when the planning decision is The lower-level sub-problem when , obtain the minimum load loss of the system under S scenarios Will Pass it to the lower sub-problem, that is, formula (78), and solve N I The worst probability distribution after iterations 4) Verify whether the solution satisfies the following toughness constraint: If the toughness index is met, then output is the optimal planning result, and the solution ends; if it is not satisfied, update the probability distribution in the main problem to N I The worst probability distribution after iterations And set N I =N I +1, return to step 2) and continue to alternately solve the main problem and sub-problems.

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