Electrical integrated energy system toughness planning method considering extreme event tail risk

Abstract

The invention discloses an electrical integrated energy system toughness planning method considering an extreme event tail risk, and relates to the technical field of integrated energy system optimization, and the method comprises the steps: firstly, considering the massive load shedding risk caused by a small-probability extreme event, and constructing a pre-disaster defense-post-disaster emergency response electrical integrated energy system toughness planning frame; secondly, comprehensively considering toughness planning cost, emergency scheduling cost and tail risk loss in a small-probability extreme scene, and establishing an objective function of a planning model; then, for a disaster stage, establishing disaster prevention resource deployment related constraints of the toughness planning model; then, considering operation constraints of the post-disaster power distribution system and the natural gas system, and establishing post-disaster emergency response related constraints; and finally, performing linearization processing on the established planning model, and calling a commercial solver for solving.

Description

Technical Field

[0001] This invention relates to the field of integrated energy system optimization technology, and in particular to a method for resilient planning of integrated electrical energy systems that takes into account the tail risk of extreme events. Background Technology

[0002] Resilience assessment and vulnerability identification of integrated energy systems are fundamental to resilience planning and energy recovery research. However, current research on resilience assessment of multi-energy coupled integrated energy systems still faces many critical issues that urgently need to be addressed. Pre-disaster resilience planning for extreme events can significantly improve the resilience of integrated energy systems, but the strengthening effect of resilience planning measures exhibits diminishing marginal returns, and planning schemes face an inherent contradiction between risk reduction and increased marginal costs. Furthermore, current modeling methods for resilience planning of integrated energy systems primarily focus on the average performance of planning schemes under multiple disaster scenarios, insufficiently considering the extreme risks caused by low-probability events; while robust optimization methods focus on the worst-case scenarios, leading to overly conservative planning schemes. In addition, as the system scale increases and the number of failure scenarios rises, the solution complexity of integrated energy system resilience planning models grows exponentially, posing a significant challenge to efficient model solving. Summary of the Invention

[0003] The technical problem this invention aims to solve is to overcome the shortcomings of existing technologies and provide a resilience planning method for integrated energy systems that considers the tail risks of extreme events. Addressing the low probability, high destructiveness, and strong uncertainty characteristics of extreme disasters, this invention establishes an overall framework for a comprehensive energy system resilience planning method based on the concepts of importance sampling and stratified sampling, taking into account both economic and risk equilibrium. Furthermore, by introducing conditional value risk, a comprehensive energy system resilience planning model that satisfies the economic-risk equilibrium is constructed based on the integrated energy system. Finally, based on an improved Benders boundary algorithm that accelerates the original cut-dual cut process, the original model is decoupled into a main planning problem and an operational subproblem for accelerated iterative solution, providing a theoretical foundation for pre-disaster comprehensive energy system resilience planning and construction in response to extreme events.

[0004] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0005] The proposed method for resilience planning of integrated electrical energy systems, considering tail risks of extreme events, includes:

[0006] Considering the risk of massive load shedding caused by low-probability extreme events, and aiming to solve the balance between increased costs and reduced risks in resilience planning, a framework for resilient planning of integrated electrical energy systems is constructed, which includes pre-disaster defense and post-disaster emergency response.

[0007] Based on the established resilient planning framework for integrated electrical energy systems, and considering the resilient planning costs, emergency dispatch costs, and tail risk losses in extreme scenarios, the objective function of the planning model is further established.

[0008] For disaster phases, with the aim of allocating emergency resources within the budget, establish planning models for disaster prevention resource deployment constraints;

[0009] Considering the operational constraints of the power distribution system and natural gas system after the disaster, and with the aim of minimizing event losses, we establish relevant constraints for the post-disaster emergency response planning model.

[0010] The linearization method based on Taylor expansion and the Big M method are used to linearize the objective function of the planning model, the constraints related to disaster prevention resource deployment, and the constraints related to post-disaster emergency response, and then a commercial solver is called to solve the problem.

[0011] As a further optimization of the electrical integrated energy system resilience planning method considering the tail risk of extreme events described in this invention, the electrical integrated energy system resilience planning framework is as follows:

[0012] Step 1.1: Consider the pre-disaster planning phase model and reinforce power lines and natural gas pipelines;

[0013] Step 1.2: Consider the post-disaster planning stage model. Each graded failure scenario represents the failure state of energy system components under different levels of disaster, and carry out power-gas coordinated emergency dispatch under the graded failure scenarios. Among them, emergency dispatch equipment includes mobile power vehicles and gas turbines.

[0014] The objective functions of the planning models for the pre-disaster and post-disaster phases include investment cost, the expected value of emergency dispatch cost under graded failure scenarios, and tail risk under extreme failure scenarios. The constraints include investment budget constraints, multi-energy flow emergency dispatch constraints, equipment operation constraints, and tail risk constraints under extreme failure scenarios. Tail risk is characterized using the Conditional Value at Risk (CvaR) index.

[0015] Step 1.3: Analyze the sensitivity of the risk control parameters of the planning model.

[0016] As a further optimization of the electrical integrated energy system resilience planning method considering the tail risk of extreme events described in this invention, the objective function of the planning model is as follows:

[0017] min:f Inv +(1-β)f Loss +βCVaR α [f Loss (1)

[0018] Equation (1) is the objective function expression of the planning model, which includes the constraints CvaR of emergency dispatch cost, resilience planning cost, and tail risk in extreme scenarios, β∈[0,1], where β represents the risk aversion parameter, f Inv f represents the investment cost of a comprehensive energy system. Loss CVaR represents the expected value of the emergency dispatch cost of an integrated energy system. α [f Loss [] represents the CVaR value of emergency dispatch costs at confidence level α;

[0019]

[0020] Equation (2) is the investment cost expression for the Integrated Energy System (IES), which includes the reinforcement costs of power lines and natural gas pipelines, where ij represents the serial number of the power line. They represent the sets of power lines and the sets of natural gas pipelines, respectively. This represents the reinforcement cost of the line or pipeline with serial number ij. 0-1 variables representing the reinforcement status of power lines and natural gas pipelines, respectively. A value of 1 indicates that the power line is under reinforcement. A value of 0 indicates that the power line is in an unreinforced state. A value of 1 indicates that the natural gas pipeline is under reinforcement. A value of 0 indicates that the natural gas pipeline is in an unreinforced state;

[0021]

[0022] Equation (3) represents the expected value of the emergency dispatch cost of IES under the graded fault scenario set, where s represents the fault scenario number, t represents the dispatch period number, i and j represent the node numbers, and m represents the mobile power vehicle type number. Represents a set of fault scenarios. Represents the set of scheduling periods. Represent the sets of power nodes and natural gas nodes, respectively. This represents the set of candidate access nodes for the mobile power supply vehicle. C represents the set of mobile power bank vehicle types. Cut C represents the cost reduction per unit load. Rent,m C MEG,m Let γ represent the rental cost and unit operating cost of the m-th type of mobile power vehicle, respectively. g2e Indicates the electro-to-gas conversion coefficient. ρ represents the expected number of earthquakes during the planning period. s Δt represents the probability of a failure scenario occurring, and Δt represents the duration of the scheduling period. μ represents the weighting coefficients for electrical and gas loads, respectively. i,m,s,t This represents the number of mobile power supply vehicles of type m connected to the i-th node. This represents the active power injected into the i-th node by the m-th type of mobile power vehicle. This indicates a reduction in active power by the electrical load. This indicates a reduction in gas flow rate due to gas load.

[0023] As a further optimization of the electrical integrated energy system resilience planning method considering the tail risk of extreme events described in this invention, the disaster prevention resource deployment related constraints of the planning model include:

[0024]

[0025] in, These represent the maximum reinforcement quantities for power lines and natural gas pipelines, respectively. For the reinforcement state 0-1 variables of the power line in fault scenario s, Let s be the 0-1 variables representing the reinforcement status of the natural gas pipeline under the fault scenario with serial number s.

[0026] As a further optimization scheme for the electrical integrated energy system resilience planning method considering the tail risk of extreme events described in this invention, the relevant constraints for post-disaster emergency response include: power distribution system operation constraints modeled using a linearized model, and natural gas system operation constraints modeled using a steady-state gas flow model; wherein...

[0027] The operational constraints of the power distribution system modeled using linearization include: power flow constraints, line capacity constraints, active load shedding and reactive load shedding constraints, radial operation constraints of the pre-disaster power topology, the relationship between the damaged, reinforced, and destroyed states of power lines, upper and lower limit constraints of gas turbine power, upper and lower limit constraints of substation power, upper and lower limit constraints of node voltage, and emergency dispatch constraints of mobile power vehicles after the disaster.

[0028] The constraints for natural gas system operation modeling using steady-state airflow models include: node gas flow balance constraints, Weymouth constraints on natural gas pipelines, numerical relationship constraints between compressor inlet and outlet gas flow, inlet and outlet pressure difference constraints on compressor pipelines, upper and lower limits constraints on gas load reduction, upper and lower limits constraints on gas flow in natural gas pipelines and gate stations, upper and lower limits constraints on node gas pressure, relationships between damaged, reinforced, and destroyed states of natural gas pipelines, and conversion constraints between input gas flow and output active power of gas turbines.

[0029] As a further optimization of the electrical integrated energy system resilience planning method considering the tail risk of extreme events described in this invention, the relevant constraints for post-disaster emergency response include:

[0030] Step 4.1: To reconcile the solution accuracy and complexity of the planning model, the specific details of the power distribution system operation constraints modeled using a linearized model are as follows:

[0031] (1) Power flow constraints:

[0032]

[0033] Among them, formula (6) is the active power balance constraint of the node, k:k→i represents the set of power lines with the i-th node as the end node, and j:i→j represents the set of power lines with the i-th node as the beginning node. and This represents the active power flow of a power line. This indicates the active power output of the substation. This indicates the active power output of the gas turbine. This indicates the active power output of the mobile power supply vehicle. Indicates the active power of the electrical load;

[0034]

[0035] Equation (7) is the balance constraint expression for the reactive power of the nodes. Indicates the reactive power of the electrical load. Let represent the reactive power flow of a power line with the i-th node as its terminal node. Let represent the reactive power flow of a power line with the i-th node as its first and last node. This indicates the reactive power of the substation. This indicates the reactive power of the gas turbine. This indicates the reactive power of the mobile power supply vehicle. To reduce reactive power in electrical loads;

[0036]

[0037] Equation (8) is the line voltage drop constraint expression, R ij X ij Representing the resistance and reactance of the power line, respectively, where K is a sufficiently large positive number, and V... i,s,t and V j,s,t Let ι represent the square of the voltage at node i and node j. ij ι represents a 0-1 variable indicating the pre-disaster operating status of power lines. ij A value of 0 indicates that the device is not in operation. ij A value of 1 indicates that the device is in operation. Indicates the damaged condition of power lines;

[0038] (2) Line capacity constraints:

[0039]

[0040] Equation (9) is the active power flow constraint expression for power lines. This refers to the maximum capacity of the power line;

[0041]

[0042] Equation (10) is the active power flow constraint expression for power lines;

[0043]

[0044] Equation (11) is the expression for the linearization of the branch power flow through two sets of polygon constraints;

[0045] (3) Constraints related to active load shedding and reactive load shedding:

[0046]

[0047] Equation (12) is the correlation constraint expression for active load shedding;

[0048]

[0049] Equation (13) is the correlation constraint expression for reactive load shedding;

[0050] (4) Radial operational constraints of the pre-disaster power topology:

[0051]

[0052] in, For the collection of power loops, Let n be the set of power lines included in loop n;

[0053] (5) Relationship between the damaged, reinforced, and destroyed states of power lines:

[0054]

[0055] in, This indicates that the line has been damaged.

[0056] (6) Power limits of gas turbines:

[0057]

[0058] Equation (17) is the upper and lower limit constraint expression for the active power of the gas turbine. Represents the set of gas turbine nodes. This indicates the maximum output active power of the gas turbine;

[0059]

[0060] Equation (18) represents the upper and lower limit constraint expressions for the ramp power of the gas turbine. This indicates the maximum gradeability of the gas turbine. The active power output of the gas turbine during the t-1 scheduling period;

[0061]

[0062] Equation (19) represents the upper and lower limit constraint expressions for the reactive power of the gas turbine. Indicates the power factor of the gas turbine;

[0063] (7) Upper and lower limits of substation power constraints:

[0064]

[0065] in, Represents the set of substation nodes. These represent the upper limits of the active and reactive power of the substation, respectively.

[0066] (8) Upper and lower limits of node voltage constraints:

[0067]

[0068] Among them, V i,min V i,max These represent the lower and upper limits of the node voltage, respectively.

[0069] (9) Constraints related to the emergency dispatch of mobile power supply vehicles after disasters:

[0070]

[0071] Equation (22) is the constraint expression for the maximum number of mobile power vehicles that can access candidate access points. This represents the maximum number of mobile power vehicles that can be connected to a node.

[0072]

[0073] Equation (23) is the constraint expression for the maximum deployable number of mobile power supply vehicles of type m. The maximum number of mobile power supply vehicles of type m that can be rented;

[0074]

[0075] Equation (24) is the upper and lower limit constraint expression for the output power of the mobile power vehicle. The maximum output active power of the type m mobile power supply vehicle;

[0076]

[0077] Equation (25) represents the upper and lower limit constraint expressions for the power supply capacity of the mobile power vehicle. The maximum capacity of type m mobile power supply vehicle;

[0078]

[0079] Equation (26) is the active power constraint expression for the mobile power vehicle injection on a single candidate node;

[0080]

[0081] Equation (27) indicates the time interval required for the dispatched mobile power vehicle to reach the access candidate node. This refers to the set of dispatch time periods for mobile power supply vehicles.

[0082]

[0083] Equation (28) represents the upper limit constraint expression for the reactive power of the mobile power vehicle. Power factor for mobile power supply vehicles;

[0084] Step 4.2: To simplify the complexity of the planning model, the specific operational constraints of the natural gas system, modeled using a steady-state gas flow model, are as follows:

[0085] (1) Nodal gas flow balance constraints:

[0086]

[0087] Where k':k'→i represents the set of natural gas pipelines with node i as the end node, j':i→j' represents the set of natural gas pipelines with node i as the first end node, and ij' represents the sequence number of the natural gas pipeline. Indicates gas load and gas flow rate. and Indicates the gas flow rate in the natural gas pipeline. Indicates the natural gas gate station flow rate. Indicates the gas flow rate of the gas turbine;

[0088] (2) Weymouth constraint on natural gas pipelines:

[0089]

[0090] in, The Weymouth coefficient represents the natural gas pipeline. This indicates the damage condition of the natural gas pipeline after the disaster. The values ​​of 0 and 1 represent whether the pipeline was damaged or undamaged after the disaster, respectively. i,s,t and π j',s,t These represent the air pressures at the i-th and j'-th nodes, respectively.

[0091] (3) Constraints on the numerical relationship between compressor intake and exhaust volumes:

[0092]

[0093] in, This represents the compressor loss coefficient. These represent the inlet and outlet gas flow rates of the compressor piping, respectively. For compressor piping;

[0094] (4) Pressure difference constraint between the inlet and outlet of the compressor pipeline:

[0095]

[0096] Among them, Γ Com It is the compressor pressurization coefficient. These represent the inlet and outlet air pressures of the compressor piping, respectively.

[0097] (5) Upper and lower limits of gas load reduction:

[0098]

[0099] (6) Upper and lower limits of gas flow rate for natural gas pipelines and gate stations:

[0100]

[0101] in, For natural gas gate station nodes; This represents the maximum gas flow rate of the natural gas pipeline. This represents the maximum gas flow rate at the natural gas gate station.

[0102] (7) Upper and lower limits of nodal pressure:

[0103]

[0104] Where, π i,min and π i,max These are the minimum and maximum values ​​of the nodal pressure, respectively;

[0105] (8) Relationship between the damaged, reinforced, and destroyed states of natural gas pipelines:

[0106]

[0107] in, Indicates the damage status of power lines. Indicates the status of line reinforcement. This indicates that the line has been damaged.

[0108] (9) Conversion constraints between input gas flow rate and output active power of gas turbine:

[0109]

[0110] in, Represents the set of gas turbine nodes in a natural gas system. For the set of gas turbine nodes in the power distribution system; η GT For gas turbine conversion efficiency, n' represents the active power generated by the gas turbine, and n' represents the node number of the natural gas system to which the gas turbine belongs.

[0111] Step 4.3: Introduce the tail risk constraint CvaR under extreme failure scenarios into the planning model. Its expression is:

[0112]

[0113] Among them, CVaR α VaR α An extension of VaR, which represents more than VaR α Partial average loss, VaR α This represents the maximum possible loss value given a confidence level α ∈ [0, 1). Represents the loss function;

[0114] To simplify the tail risk constraint CvaR under nonlinear extreme failure scenarios, an auxiliary variable κ is introduced. s CVaR under graded fault scenarios α The linearization equivalent transformation of the expression is as follows:

[0115]

[0116] As a further optimization scheme for the electrical integrated energy system resilience planning method considering the tail risk of extreme events described in this invention, a linearization method based on Taylor expansion and the Big M method are used to linearize the objective function of the planning model, the constraints related to disaster prevention resource deployment, and the constraints related to post-disaster emergency response, and then a commercial solver is called for solving; as follows:

[0117] Step 5.1: Use a Taylor series-based linearization method to equivalently linearize the Weymouth constraints: Reconstruct the Weymouth constraints into a mixed-integer linear programming problem using Taylor series expansion to achieve linearization. The specific process is as follows:

[0118] (1) Select a feasible reference point x0∈R z As the reference point for Taylor expansion, R z Let z be the set of real numbers;

[0119] (2) For nonlinear inequality constraints g k Calculate the constraint function g if (x)≤0. k (x) takes the value g at the reference point k (x0), and the gradient vector of the constraint function at that point.

[0120] (3) Perform a Taylor expansion of the constraint function at the reference point x0 and substitute it into the original constraint conditions to obtain the linearized constraint: x is the decision variable, and the superscript T is the transpose symbol;

[0121] (4) Rearrange the linearization constraints into standard linear constraint form. in a k,i For x i coefficient, x i Let b be the i-th decision variable. k For constant terms;

[0122] Step 5.2: Use the Big M method to equivalently linearize the bilinear terms formed by the product of continuous variables and 0-1 variables: For expressions that include bilinear terms formed by continuous variables and 0-1 variables, use the Big M method for linearization.

[0123] Step 5.3: Use the YALMIP optimization modeling language interface to integrate the objective function, constraints, and decision variables in the linearized planning model into a complete linear programming problem model. Then, use this interface to call the commercial mathematical programming solver Gurobi, configure the solver parameters, and solve the planning model.

[0124] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0125] (1) This invention fully considers the deep coupling relationship between the power distribution system and the natural gas system, and takes into account the tail risk of low-probability extreme events. It fully considers the balance between economic efficiency and risk, and establishes a resilience planning method for integrated electrical energy systems.

[0126] (2) This invention takes into account the differences between the power distribution system and the natural gas system in the post-disaster stage, and fully considers various costs to establish a planning model that is more in line with the actual needs of the project. At the same time, this invention uses Taylor expansion and the Big M method to linearize the objective function and constraints, and uses an efficient commercial mathematical programming solver to solve the model, thereby improving speed and accuracy. Attached Figure Description

[0127] Figure 1 This is a flowchart of the electrical integrated energy system resilience planning method that considers the tail risk of low-probability extreme events, as described in this invention. Detailed Implementation

[0128] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0129] like Figure 1 The flowchart shown is a process for a resilience planning method for an integrated electrical energy system that considers the tail risk of low-probability extreme events, according to the present invention. The method includes the following steps:

[0130] Step 1: Considering the risk of massive load shedding caused by low-probability extreme events, and aiming to solve the balance between increased costs and reduced risks in resilience planning, construct a comprehensive electrical energy system resilience planning framework encompassing pre-disaster defense and post-disaster emergency response.

[0131] Step 101: Consider the pre-disaster planning phase model and reinforce power lines and natural gas pipelines;

[0132] Step 102: Consider the post-disaster planning stage model. Each graded failure scenario represents the failure state of energy system components under different levels of disaster, and electricity-gas coordinated emergency dispatch is carried out under the graded failure scenarios. Among them, the emergency dispatch equipment considered includes mobile power vehicles and gas turbines. The objective functions of the planning models in the pre-disaster and post-disaster stages include investment cost, expected value of emergency dispatch cost under graded failure scenarios, and tail risk under extreme failure scenarios. The constraints include investment budget constraints, multi-energy flow emergency dispatch constraints, equipment operation constraints, and tail risk constraints under extreme failure scenarios. Tail risk is characterized using the Conditional Value at Risk (CvaR) index.

[0133] Step 103: Analyze the sensitivity of the risk control parameters of the planning model.

[0134] Step 2: Based on the established resilience planning framework for the integrated electrical energy system, considering resilience planning costs, emergency dispatch costs, and tail risk losses in extreme scenarios, further establish the objective function of the planning model:

[0135] min:f Inv +(1-β)f Loss +βCVaR α [f Loss (1)

[0136] Equation (1) is the objective function expression of the planning model, which includes the constraints CvaR of emergency dispatch cost, resilience planning cost, and tail risk under extreme scenarios. The parameter β∈[0,1] represents the risk aversion parameter, f Inv f represents the investment cost of a comprehensive energy system. Loss CVaR represents the expected value of the emergency dispatch cost of an integrated energy system. α [f Loss [] represents the CVaR value of emergency dispatch costs at confidence level α;

[0137]

[0138] Equation (2) is the investment cost expression for the Integrated Energy System (IES), which includes the reinforcement costs of power lines and natural gas pipelines, where ij represents the serial number of the power line. They represent the sets of power lines and the sets of natural gas pipelines, respectively. This represents the reinforcement cost of the line or pipeline with serial number ij. 0-1 variables representing the reinforcement status of power lines and natural gas pipelines, respectively. A value of 1 indicates that the power line is under reinforcement. A value of 0 indicates that the power line is in an unreinforced state. A value of 1 indicates that the natural gas pipeline is under reinforcement. A value of 0 indicates that the natural gas pipeline is in an unreinforced state;

[0139]

[0140] Equation (3) represents the expected value of the emergency dispatch cost of IES under the graded fault scenario set, where the subscript s represents the fault scenario number, t represents the dispatch period number, i and j represent the node number, and m represents the mobile power vehicle type number. Represents a set of fault scenarios. Represents the set of scheduling periods. Represent the sets of power nodes and natural gas nodes, respectively. This represents the set of candidate access nodes for the mobile power supply vehicle. C represents the set of mobile power bank vehicle types. Cut C represents the cost reduction per unit load. Rent,m C MEG,mLet γ represent the rental cost and unit operating cost of the m-th type of mobile power vehicle, respectively. g2e Indicates the electro-to-gas conversion coefficient. ρ represents the expected number of earthquakes during the planning period. s Δt represents the probability of a failure scenario occurring, and Δt represents the duration of the scheduling period. μ represents the weighting coefficients for electrical and gas loads, respectively. i,m,s,t This represents the number of mobile power supply vehicles of type m connected to the i-th node. This represents the active power injected into the i-th node by the m-th type of mobile power vehicle. This indicates a reduction in active power by the electrical load. This indicates a reduction in gas flow rate due to gas load.

[0141] Step 3: For the disaster phase, with the aim of allocating emergency resources within the budget, establish the relevant constraints for disaster prevention resource deployment in the planning model:

[0142]

[0143] In the formula: These represent the maximum number of reinforcements required for power lines and natural gas pipelines, respectively. For the reinforcement state 0-1 variables of the power line in fault scenario s, Let s be the 0-1 variables representing the reinforcement status of the natural gas pipeline under the fault scenario with serial number s.

[0144] Step 4, the constraints related to post-disaster emergency response include: operational constraints of the power distribution system modeled using a linearized model, and operational constraints of the natural gas system modeled using a steady-state gas flow model; among them,

[0145] The operational constraints of the power distribution system modeled using linearization include: power flow constraints, line capacity constraints, active load shedding and reactive load shedding constraints, radial operation constraints of the pre-disaster power topology, the relationship between the damaged, reinforced, and destroyed states of power lines, upper and lower limit constraints of gas turbine power, upper and lower limit constraints of substation power, upper and lower limit constraints of node voltage, and emergency dispatch constraints of mobile power vehicles after the disaster.

[0146] The operational constraints of the natural gas system modeled using a steady-state airflow model include: node gas flow balance constraints, Weymouth constraints on natural gas pipelines, numerical relationship constraints between compressor inlet and outlet gas flows, inlet and outlet pressure difference constraints on compressor pipelines, upper and lower limits constraints on gas load reduction, upper and lower limits constraints on gas flow rates at natural gas pipelines and gate stations, upper and lower limits constraints on node gas pressure, the relationship between damaged, reinforced, and destroyed states of natural gas pipelines, and the conversion constraints between input gas flow and output active power of gas turbines. Step 5 considers the operational constraints of the post-disaster power distribution system and natural gas system, and establishes relevant post-disaster emergency response constraints for the planning model with the aim of minimizing accident losses.

[0147] Step 501, to reconcile the solution accuracy and complexity of the planning model, the specific content of the power distribution system operation constraints modeled using the linearized model is as follows:

[0148] (1) Power flow constraints:

[0149]

[0150] Wherein, Equation (6) is the active power balance constraint of the node, k:k→i represents the set of power lines with the i-th node as the end node, and j:i→j represents the set of power lines with the i-th node as the beginning node. and This represents the active power flow of a power line. This indicates the active power output of the substation. This indicates the active power output of the gas turbine. This indicates the active power output of the mobile power supply vehicle. Indicates the active power of the electrical load;

[0151]

[0152] Equation (7) is the balance constraint expression for the reactive power of the nodes. Indicates the reactive power of the electrical load. Let represent the reactive power flow of a power line with the i-th node as its terminal node. Let represent the reactive power flow of a power line with the i-th node as its first and last node. This indicates the reactive power of the substation. This indicates the reactive power of the gas turbine. This indicates the reactive power of the mobile power supply vehicle. To reduce reactive power in electrical loads;

[0153]

[0154] Equation (8) is the line voltage drop constraint expression, R ijX ij Representing the resistance and reactance of the power line, respectively, where K is a sufficiently large positive number, and V... i,s,t and V j,s,t Let ι represent the square of the voltage at node i and node j. ij ι represents a 0-1 variable indicating the pre-disaster operating status of power lines. ij A value of 0 indicates that the device is not in operation. ij A value of 1 indicates that the device is in operation. Indicates the damaged condition of power lines;

[0155] (2) Line capacity constraints:

[0156]

[0157] Equation (9) is the active power flow constraint expression for power lines. This refers to the maximum capacity of the power line;

[0158]

[0159] Equation (10) is the active power flow constraint expression for power lines;

[0160]

[0161] Equation (11) is the expression for the linearization of the branch power flow through two sets of polygon constraints;

[0162] (3) Constraints related to active load shedding and reactive load shedding:

[0163]

[0164] Equation (12) is the correlation constraint expression for active load shedding, and the variables in the equation have been explained above;

[0165]

[0166] Equation (13) is the correlation constraint expression for reactive load shedding, and the variables in the equation have been explained above;

[0167] (4) Radial operational constraints of the pre-disaster power topology:

[0168]

[0169] in, For the collection of power loops, Let n be the set of power lines contained in loop n;

[0170] (5) Relationship between the damaged, reinforced, and destroyed states of power lines:

[0171]

[0172] in, This indicates that the line has been damaged.

[0173] (6) Power limits of gas turbines:

[0174]

[0175] Equation (17) is the upper and lower limit constraint expression for the active power of the gas turbine. Represents the set of gas turbine nodes. This indicates the maximum output active power of the gas turbine;

[0176]

[0177] Equation (18) represents the upper and lower limit constraint expressions for the ramp power of the gas turbine. This indicates the maximum gradeability of the gas turbine;

[0178]

[0179] Equation (19) represents the upper and lower limit constraint expressions for the reactive power of the gas turbine. Indicates the power factor of the gas turbine;

[0180] (7) Upper and lower limits of substation power constraints:

[0181]

[0182] in, Represents the set of substation nodes. These represent the upper limits of the active and reactive power of the substation, respectively.

[0183] (8) Upper and lower limits of node voltage constraints:

[0184]

[0185] Among them, V i,min V i,max These represent the lower and upper limits of the node voltage, respectively.

[0186] (9) Constraints related to the emergency dispatch of mobile power supply vehicles after disasters:

[0187]

[0188] Equation (22) is the constraint expression for the maximum number of mobile power vehicles that can access candidate access points. This represents the maximum number of mobile power vehicles that can be connected to a node.

[0189]

[0190] Equation (23) is the constraint expression for the maximum deployable number of type m mobile power vehicles. The maximum number of mobile power supply vehicles of type m that can be rented;

[0191]

[0192] Equation (24) is the upper and lower limit constraint expression for the output power of the mobile power vehicle. The maximum output active power of the type m mobile power supply vehicle;

[0193]

[0194] Equation (25) represents the upper and lower limit constraint expressions for the power supply capacity of the mobile power vehicle. The maximum capacity of type m mobile power supply vehicle;

[0195]

[0196] Equation (26) is the active power constraint expression for the mobile power vehicle injection on a single candidate node;

[0197]

[0198] Equation (27) indicates the time interval required for the dispatched mobile power vehicle to reach the access candidate node. This refers to the set of dispatch time periods for mobile power supply vehicles.

[0199]

[0200] Equation (28) represents the upper limit constraint expression for the reactive power of the mobile power vehicle. Power factor for mobile power supply vehicles;

[0201] Step 502: To simplify the complexity of the planning model, the specific operational constraints of the natural gas system, modeled using a steady-state gas flow model, are as follows:

[0202] (1) Nodal gas flow balance constraints:

[0203]

[0204] Where k':k'→i represents the set of natural gas pipelines with node i as the end node, j':i→j' represents the set of natural gas pipelines with node i as the first end node, and ij' represents the sequence number of the natural gas pipeline. Indicates gas load and gas flow rate. and Indicates the gas flow rate in the natural gas pipeline. Indicates the natural gas gate station flow rate. Indicates the gas flow rate of the gas turbine;

[0205] (2) Weymouth constraint on natural gas pipelines:

[0206]

[0207] in, The Weymouth coefficient represents the natural gas pipeline. This indicates the damage condition of the natural gas pipeline after the disaster. The values ​​of 0 and 1 represent whether the pipeline was damaged or undamaged after the disaster, respectively. i,s,t and π j',s,t These represent the air pressures at the i-th and j'-th nodes, respectively.

[0208] (3) Constraints on the numerical relationship between compressor intake and exhaust volumes:

[0209]

[0210] in, This represents the compressor loss coefficient. These represent the inlet and outlet gas flow rates of the compressor piping, respectively. For compressor piping;

[0211] (4) Pressure difference constraint between the inlet and outlet of the compressor pipeline:

[0212]

[0213] Where Γ Com It is the compressor pressurization coefficient. These represent the inlet and outlet air pressures of the compressor piping, respectively.

[0214] (5) Upper and lower limits of gas load reduction:

[0215]

[0216] (6) Upper and lower limits of gas flow rate for natural gas pipelines and gate stations:

[0217]

[0218] in, For natural gas gate station nodes; This represents the maximum gas flow rate of the natural gas pipeline. This represents the maximum gas flow rate at the natural gas gate station.

[0219] (7) Upper and lower limits of nodal pressure:

[0220]

[0221] Where: π i,min and π i,max These are the minimum and maximum values ​​of the nodal pressure, respectively;

[0222] (8) Relationship between the damaged, reinforced, and destroyed states of natural gas pipelines:

[0223]

[0224] in, Indicates the damage status of power lines. Indicates the status of line reinforcement. This indicates that the line has been damaged.

[0225] (9) Conversion constraints between input gas flow rate and output active power of gas turbine:

[0226]

[0227] in, Represents the set of gas turbine nodes in a natural gas system. For the set of gas turbine nodes in the power distribution system; η GT For gas turbine conversion efficiency, n' represents the active power generated by the gas turbine, and n' represents the node number of the natural gas system to which the gas turbine belongs.

[0228] Step 503: Introduce the tail risk constraint CvaR under extreme failure scenarios into the planning model, the expression of which is:

[0229]

[0230] Among them, CVaR α VaR α An extension of VaR, which represents more than VaR α Partial average loss, VaR α This represents the maximum possible loss value given a confidence level α ∈ [0, 1). Represents the loss function;

[0231] To simplify the tail risk constraint CvaR under nonlinear extreme failure scenarios, an auxiliary variable κ is introduced. s CVaR under graded fault scenarios α The linearization equivalent transformation of the expression is as follows:

[0232]

[0233] Step 6: To improve the efficiency of model solving, a linearization method based on Taylor expansion and the Big M method are used to linearize the objective function of the planning model, the constraints related to disaster prevention resource deployment, and the constraints related to post-disaster emergency response. A commercial solver is then called to solve the model.

[0234] Step 601: The Weymouth constraints are equivalently linearized using a Taylor series-based linearization method. This involves reconstructing the Weymouth constraints into a mixed-integer linear programming problem through Taylor series expansion, achieving the linearization goal. The specific process is as follows:

[0235] (1) Select a feasible reference point x0∈R z As the reference point for Taylor expansion, R z Let z be the set of real numbers;

[0236] (2) For nonlinear inequality constraints g k Calculate the constraint function g if (x)≤0. k (x) takes the value g at the reference point k (x0), and the gradient vector of the constraint function at that point.

[0237] (3) Perform a Taylor expansion of the constraint function at the reference point x0 and substitute it into the original constraint conditions to obtain the linearized constraint: x is the decision variable, and the superscript T is the transpose symbol;

[0238] (4) Rearrange the linearization constraints into standard linear constraint form. in a k,i For x i coefficient, x i Let b be the i-th decision variable. k For constant terms;

[0239] Step 602: Use the Big M method to equivalently linearize the bilinear terms formed by the product of continuous variables and 0-1 variables: For expressions containing bilinear terms formed by continuous variables and 0-1 variables, use the Big M method for linearization.

[0240] Step 603: Use the YALMIP optimization modeling language interface to integrate the objective function, constraints, and decision variables in the linearized planning model into a complete linear programming problem model. Then, use this interface to call the efficient commercial mathematical programming solver Gurobi, configure the solver parameters, and solve the model.

[0241] The foregoing description and illustration of the basic principles, features, and advantages of the present invention are presented. The above embodiments are merely illustrative of the technical concept of the present invention; however, the present invention is not limited to the above embodiments. Various changes and modifications based on the present invention fall within the protection scope of the present invention.

Claims

1. A resilience planning method for integrated electrical energy systems considering tail risks of extreme events, characterized in that, include: Considering the risk of massive load shedding caused by low-probability extreme events, and aiming to solve the balance between increased costs and reduced risks in resilience planning, a framework for resilient planning of integrated electrical energy systems is constructed, which includes pre-disaster defense and post-disaster emergency response. Based on the established resilient planning framework for integrated electrical energy systems, and considering the resilient planning costs, emergency dispatch costs, and tail risk losses in extreme scenarios, the objective function of the planning model is further established. For disaster phases, with the aim of allocating emergency resources within the budget, establish planning models for disaster prevention resource deployment constraints; Considering the operational constraints of the power distribution system and natural gas system after the disaster, and with the aim of minimizing event losses, we establish relevant constraints for the post-disaster emergency response planning model. The linearization method based on Taylor expansion and the Big M method are used to linearize the objective function of the planning model, the constraints related to disaster prevention resource deployment, and the constraints related to post-disaster emergency response, and then a commercial solver is called to solve the problem.

2. The method for resilience planning of integrated electrical energy systems considering tail risks of extreme events according to claim 1, characterized in that, The framework for resilience planning of integrated electrical energy systems is as follows: Step 1.1: Consider the pre-disaster planning phase model and reinforce power lines and natural gas pipelines; Step 1.2: Consider the post-disaster planning stage model. Each graded failure scenario represents the failure state of energy system components under different levels of disaster, and carry out power-gas coordinated emergency dispatch under the graded failure scenarios. Among them, emergency dispatch equipment includes mobile power vehicles and gas turbines. The objective functions of the planning models for the pre-disaster and post-disaster phases include investment cost, the expected value of emergency dispatch cost under graded failure scenarios, and tail risk under extreme failure scenarios. The constraints include investment budget constraints, multi-energy flow emergency dispatch constraints, equipment operation constraints, and tail risk constraints under extreme failure scenarios. Tail risk is characterized using the Conditional Value at Risk (CvaR) index. Step 1.3: Analyze the sensitivity of the risk control parameters of the planning model.

3. The method for resilience planning of integrated electrical energy systems considering tail risks of extreme events according to claim 1, characterized in that, The objective function of the planning model is as follows: min:f Inv +(1-β)f Loss +βCVaR α [f Loss ] (1) Equation (1) is the objective function expression of the planning model, which includes the constraints CvaR of emergency dispatch cost, resilience planning cost, and tail risk in extreme scenarios, β∈[0,1], where β represents the risk aversion parameter, f Inv f represents the investment cost of a comprehensive energy system. Loss CVaR represents the expected value of the emergency dispatch cost of an integrated energy system. α [f Loss [] represents the CVaR value of emergency dispatch costs at confidence level α; Equation (2) is the investment cost expression for the Integrated Energy System (IES), which includes the reinforcement costs of power lines and natural gas pipelines, where ij represents the serial number of the power line. They represent the sets of power lines and the sets of natural gas pipelines, respectively. This represents the reinforcement cost of the line or pipeline with serial number ij. 0-1 variables representing the reinforcement status of power lines and natural gas pipelines, respectively. A value of 1 indicates that the power line is under reinforcement. A value of 0 indicates that the power line is in an unreinforced state. A value of 1 indicates that the natural gas pipeline is under reinforcement. A value of 0 indicates that the natural gas pipeline is in an unreinforced state; Wherein, Equation (3) represents the expected value of the emergency dispatch cost of IES under the graded fault scenario set, s represents the fault scenario number, t represents the dispatch period number, i and j represent the node number, m represents the mobile power vehicle type number, S represents the fault scenario set, and T represents the dispatch period set. Represent the sets of power nodes and natural gas nodes, respectively. This represents the set of candidate access nodes for the mobile power supply vehicle. C represents the set of mobile power bank vehicle types. Cut C represents the cost reduction per unit load. Rent,m C MEG,m Let γ represent the rental cost and unit operating cost of the m-th type of mobile power vehicle, respectively. g2e Indicates the electro-to-gas conversion coefficient. ρ represents the expected number of earthquakes during the planning period. s Δt represents the probability of a failure scenario occurring, and Δt represents the duration of the scheduling period. μ represents the weighting coefficients for electrical and gas loads, respectively. i,m,s,t This represents the number of mobile power supply vehicles of type m connected to the i-th node. This represents the active power injected into the i-th node by the m-th type of mobile power vehicle. This indicates a reduction in active power by the electrical load. This indicates a reduction in gas flow rate due to gas load.

4. The method for resilience planning of integrated electrical energy systems considering tail risks of extreme events according to claim 1, characterized in that, Constraints related to disaster prevention resource deployment in the planning model include: in, These represent the maximum reinforcement quantities for power lines and natural gas pipelines, respectively. For the reinforcement state 0-1 variables of the power line in fault scenario s, Let s be the 0-1 variables representing the reinforcement status of the natural gas pipeline under the fault scenario with serial number s.

5. The method for resilience planning of integrated electrical energy systems considering tail risks of extreme events according to claim 1, characterized in that, The constraints related to post-disaster emergency response include: operational constraints of the power distribution system modeled using a linearized model, and operational constraints of the natural gas system modeled using a steady-state gas flow model; among them, The operational constraints of the power distribution system modeled using linearization include: power flow constraints, line capacity constraints, active load shedding and reactive load shedding constraints, radial operation constraints of the pre-disaster power topology, the relationship between the damaged, reinforced, and destroyed states of power lines, upper and lower limit constraints of gas turbine power, upper and lower limit constraints of substation power, upper and lower limit constraints of node voltage, and emergency dispatch constraints of mobile power vehicles after the disaster. The constraints for natural gas system operation modeling using steady-state airflow models include: node gas flow balance constraints, Weymouth constraints on natural gas pipelines, numerical relationship constraints between compressor inlet and outlet gas flow, inlet and outlet pressure difference constraints on compressor pipelines, upper and lower limits constraints on gas load reduction, upper and lower limits constraints on gas flow in natural gas pipelines and gate stations, upper and lower limits constraints on node gas pressure, relationships between damaged, reinforced, and destroyed states of natural gas pipelines, and conversion constraints between input gas flow and output active power of gas turbines.

6. The method for resilience planning of integrated electrical energy systems considering tail risks of extreme events according to claim 1, characterized in that, Post-disaster emergency response constraints include: Step 4.1: To reconcile the solution accuracy and complexity of the planning model, the specific details of the power distribution system operation constraints modeled using a linearized model are as follows: (1) Power flow constraints: Among them, formula (6) is the active power balance constraint of the node, k:k→i represents the set of power lines with the i-th node as the end node, and j:i→j represents the set of power lines with the i-th node as the beginning node. and This represents the active power flow of a power line. This indicates the active power output of the substation. This indicates the active power output of the gas turbine. This indicates the active power output of the mobile power supply vehicle. Indicates the active power of the electrical load; Equation (7) is the balance constraint expression for the reactive power of the nodes. Indicates the reactive power of the electrical load. Let represent the reactive power flow of a power line with the i-th node as its terminal node. Let represent the reactive power flow of a power line with the i-th node as its first and last node. This indicates the reactive power of the substation. This indicates the reactive power of the gas turbine. This indicates the reactive power of the mobile power supply vehicle. To reduce reactive power in electrical loads; Equation (8) is the line voltage drop constraint expression, R ij X ij Representing the resistance and reactance of the power line, respectively, where K is a sufficiently large positive number, and V... i,s,t and V j,s,t Let ι represent the square of the voltage at node i and node j. ij ι represents a 0-1 variable indicating the pre-disaster operating status of power lines. ij A value of 0 indicates that the device is not in operation. ij A value of 1 indicates that the device is in operation. Indicates the damaged condition of power lines; (2) Line capacity constraints: Equation (9) is the active power flow constraint expression for power lines. This refers to the maximum capacity of the power line; Equation (10) is the active power flow constraint expression for power lines; Equation (11) is the expression for the linearization of the branch power flow through two sets of polygon constraints; (3) Constraints related to active load shedding and reactive load shedding: Equation (12) is the correlation constraint expression for active load shedding; Equation (13) is the correlation constraint expression for reactive load shedding; (4) Radial operational constraints of the pre-disaster power topology: in, For the collection of power loops, Let n be the set of power lines included in loop n; (5) Relationship between the damaged, reinforced, and destroyed states of power lines: in, This indicates that the line has been damaged. (6) Power limits of gas turbines: Equation (17) is the upper and lower limit constraint expression for the active power of the gas turbine. Represents the set of gas turbine nodes. This indicates the maximum output active power of the gas turbine; Equation (18) represents the upper and lower limit constraint expressions for the ramp power of the gas turbine. This indicates the maximum gradeability of the gas turbine. The active power output of the gas turbine during the t-1 scheduling period; Equation (19) is the upper and lower limit constraint expression for the reactive power of the gas turbine. Indicates the power factor of the gas turbine; (7) Upper and lower limits of substation power constraints: in, Represents the set of substation nodes. These represent the upper limits of the active and reactive power of the substation, respectively. (8) Upper and lower limits of node voltage constraints: Among them, V i,min V i,max These represent the lower and upper limits of the node voltage, respectively. (9) Constraints related to the emergency dispatch of mobile power supply vehicles after disasters: Equation (22) is the constraint expression for the maximum number of mobile power vehicles that can access candidate access points. This represents the maximum number of mobile power vehicles that can be connected to a node. Equation (23) is the constraint expression for the maximum deployable number of mobile power supply vehicles of type m. The maximum number of mobile power supply vehicles of type m that can be rented; Equation (24) is the upper and lower limit constraint expression for the output power of the mobile power vehicle. The maximum output active power of the type m mobile power supply vehicle; Equation (25) represents the upper and lower limit constraint expressions for the power supply capacity of the mobile power vehicle. The maximum capacity of type m mobile power supply vehicle; Equation (26) is the active power constraint expression for the mobile power vehicle injection on a single candidate node; Equation (27) indicates the time interval required for the dispatched mobile power vehicle to reach the access candidate node. This refers to the set of dispatch time periods for mobile power supply vehicles. Equation (28) represents the upper limit constraint expression for the reactive power of the mobile power vehicle. Power factor for mobile power supply vehicles; Step 4.2: To simplify the complexity of the planning model, the specific operational constraints of the natural gas system, modeled using a steady-state gas flow model, are as follows: (1) Nodal gas flow balance constraints: Where k':k'→i represents the set of natural gas pipelines with node i as the end node, j':i→j' represents the set of natural gas pipelines with node i as the first end node, and ij' represents the sequence number of the natural gas pipeline. Indicates gas load and gas flow rate. and Indicates the gas flow rate in the natural gas pipeline. Indicates the natural gas gate station flow rate. Indicates the gas flow rate of the gas turbine; (2) Weymouth constraint on natural gas pipelines: in, The Weymouth coefficient represents the natural gas pipeline. This indicates the damage condition of the natural gas pipeline after the disaster. The values ​​of 0 and 1 represent whether the pipeline was damaged or undamaged after the disaster, respectively. i,s,t and π j',s,t These represent the air pressures at the i-th and j'-th nodes, respectively. (3) Constraints on the numerical relationship between compressor intake and exhaust volumes: in, This represents the compressor loss coefficient. These represent the inlet and outlet gas flow rates of the compressor piping, respectively. For compressor piping; (4) Pressure difference constraint between the inlet and outlet of the compressor pipeline: Among them, Γ Com It is the compressor pressurization coefficient. These represent the inlet and outlet air pressures of the compressor piping, respectively. (5) Upper and lower limits of gas load reduction: (6) Upper and lower limits of gas flow rate for natural gas pipelines and gate stations: in, For natural gas gate station nodes; This represents the maximum gas flow rate of the natural gas pipeline. This represents the maximum gas flow rate at the natural gas gate station. (7) Upper and lower limits of nodal pressure: Where, π i,min and π i,max These are the minimum and maximum values ​​of the nodal pressure, respectively; (8) Relationship between the damaged, reinforced, and destroyed states of natural gas pipelines: in, Indicates the damage status of power lines. Indicates the status of line reinforcement. This indicates that the line has been damaged. (9) Conversion constraints between input gas flow rate and output active power of gas turbine: in, Represents the set of gas turbine nodes in a natural gas system. For the set of gas turbine nodes in the power distribution system; η GT For gas turbine conversion efficiency, n' represents the active power generated by the gas turbine, and n' represents the node number of the natural gas system to which the gas turbine belongs. Step 4.3: Introduce the tail risk constraint CvaR under extreme failure scenarios into the planning model. Its expression is: Among them, CVaR α VaR α An extension of VaR, which represents more than VaR α Partial average loss, VaR α This represents the maximum possible loss value given a confidence level α ∈ [0, 1). Represents the loss function; To simplify the tail risk constraint CvaR under nonlinear extreme failure scenarios, an auxiliary variable κ is introduced. s CVaR under graded fault scenarios α The linearization equivalent transformation of the expression is as follows:

7. The method for resilience planning of integrated electrical energy systems considering tail risks of extreme events according to claim 1, characterized in that, The linearization method based on Taylor expansion and the Big M method are used to linearize the objective function of the planning model, the constraints related to disaster prevention resource deployment, and the constraints related to post-disaster emergency response, and then a commercial solver is called to solve the problem. as follows: Step 5.1: Use a Taylor series-based linearization method to equivalently linearize the Weymouth constraints: Reconstruct the Weymouth constraints into a mixed-integer linear programming problem using Taylor series expansion to achieve linearization. The specific process is as follows: (1) Select a feasible reference point x0∈R z As the reference point for Taylor expansion, R z Let z be the set of real numbers; (2) For nonlinear inequality constraints g k Calculate the constraint function g if (x)≤0. k (x) takes the value g at the reference point k (x0), and the gradient vector of the constraint function at that point. (3) Perform a Taylor expansion of the constraint function at the reference point x0 and substitute it into the original constraint conditions to obtain the linearized constraint: x is the decision variable, and the superscript T is the transpose symbol; (4) Rearrange the linearization constraints into standard linear constraint form. in a k,i For x i coefficient, x i Let b be the i-th decision variable. k For constant terms; Step 5.2: Use the Big M method to equivalently linearize the bilinear terms formed by the product of continuous variables and 0-1 variables: For expressions that include bilinear terms formed by continuous variables and 0-1 variables, use the Big M method for linearization. Step 5.3: Use the YALMIP optimization modeling language interface to integrate the objective function, constraints, and decision variables in the linearized planning model into a complete linear programming problem model. Then, use this interface to call the commercial mathematical programming solver Gurobi, configure the solver parameters, and solve the planning model.

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