Probabilistic hierarchical fault scene generation method for electrical integrated energy system

Abstract

The invention discloses a probabilistic grading fault scene generation method for an electrical integrated energy system, and relates to the technical field of integrated energy system optimization, and the method comprises the steps: firstly, considering the earthquake intensity uncertainty, discretizing a target earthquake magnitude range into a plurality of equidistant intervals, and calculating the occurrence probabilities of earthquakes of different earthquake magnitudes; secondly, modeling disaster-causing properties of earthquakes with different earthquake magnitudes by adopting a vulnerability curve, and calculating expected values of damaged elements of a power distribution system and a natural gas system; then, randomly generating a fault scene under each classification magnitude by using a Monte Carlo method, carrying out analogue simulation on the cascade fault of the electrical integrated energy system under the random fault scene, and recording the total loss load of the system; and finally, calculating an average load loss amount under each classification magnitude, and selecting a typical fault scene to form a classification fault scene set. According to the method, the tail risk of the small-probability extreme event is quantified, and a scene basis is provided for formulating a toughness improvement strategy of a comprehensive energy system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of integrated energy system optimization, and particularly relates to a probabilistic hierarchical fault scenario generation method for an electrical integrated energy system. BACKGROUND

[0002] The current earthquake resistance evaluation method for the electrical integrated energy system has significant deficiencies, mainly manifested as insufficient consideration of the uncertainty of earthquake disasters. The traditional method usually adopts a deterministic scenario analysis and only evaluates against a single design reference earthquake, which cannot reflect the probability distribution characteristics of earthquake intensity. In the prior art, although the Monte Carlo simulation method can generate random fault scenarios, it lacks hierarchical processing of earthquake magnitudes, resulting in that the generated fault scenarios are inconsistent with the real disaster statistical characteristics. More importantly, the existing method cannot quantify the tail risk of small probability high damage events, and this technical defect leads to the actual damage of the system far exceeding the design expectation. With the expansion of the scale and the deepening of the coupling degree of the electrical integrated energy system, there is an urgent need for a hierarchical fault scenario set generation method combining random fault simulation and average loss of load screening.

[0003] The defects of insufficient consideration of earthquake uncertainty in the prior art are as follows:

[0004] (1) Most of the existing researches on earthquake risk evaluation of the electrical integrated energy system adopt a deterministic analysis method, only consider a single design reference earthquake scenario, and cannot reflect the probability distribution characteristics of earthquake intensity.

[0005] (2) Although the traditional Monte Carlo simulation method can generate random fault scenarios, it lacks hierarchical processing of earthquake magnitudes, resulting in that the generated fault scenarios are inconsistent with the real disaster statistical characteristics.

[0006] (3) The existing technology often ignores the coupling characteristics of the power and natural gas systems when dealing with cascading faults of the electrical integrated energy system. SUMMARY

[0007] The technical problem to be solved by the present application is to overcome the deficiencies of the prior art and provide a probabilistic hierarchical fault scenario generation method for an electrical integrated energy system, which represents the destructive influence of different magnitude earthquake events on the integrated energy system through a probabilistic hierarchical fault scenario set; innovatively combines the discretization processing of earthquake intensity with the generation of system fault scenarios, which can more accurately reflect the differential influence of different magnitude earthquakes on the electrical integrated energy system, and provides a scientific and reliable scenario basis for the development of the resilience improvement strategy of the integrated energy system.

[0008] The present application adopts the following technical solutions to solve the above technical problems:

[0009] According to the probabilistic hierarchical fault scenario generation method for an electrical integrated energy system provided by the present application, the method comprises:

[0010] Step S1, discretizing a target magnitude range [M0, M E ] into N s equidistant intervals, and taking the center value of each equidistant interval as a classified magnitude; wherein M0 and M E represent the lower limit and the upper limit of the target magnitude range, respectively;

[0011] Step S2, for each classified magnitude, determining a peak ground acceleration range, and randomly sampling from the peak ground acceleration range to obtain a peak ground acceleration sample value; and calculating the expected value of the damaged elements in the power distribution system and the natural gas system under the peak ground acceleration sample value;

[0012] The number of failure elements in each scenario is set as the expected value in step S2;

[0013] Under all classified magnitudes, a total of N s ×N MC random failure scenarios are generated;

[0014] In each random failure scenario, the cascading failure of the electrical integrated energy system is simulated, and the load loss amount of each random failure scenario is recorded;

[0015] Step S4, for each classified magnitude, calculating the average load loss amount L MC of the N s random failure scenarios, and calculating the difference between the load loss amount of each random failure scenario and the average load loss amount L s , and selecting the s th scenario with the smallest absolute value of the difference as the typical failure scenario of each classified magnitude, wherein 1≤s≤N s , and the set of classified failure scenarios is denoted as

[0016] As a further optimization scheme of the electrical integrated energy system probabilistic classified failure scenario generation method, in step S3, the failure elements are randomly sampled based on the length attribute of the lines and pipelines, and the repair time of each failure element is randomly generated based on the Weibull distribution.

[0017] As a further optimization scheme of the electrical integrated energy system probabilistic classified failure scenario generation method, the method for calculating ρ s is as follows:

[0018]

[0019] wherein N s represents the number of discrete intervals, and Ms Let l represent the central magnitude value of the s-th interval, l represent the seismic activity parameter, ΔM be the interval width, and M be the value of the central magnitude value. s-1 This represents the central magnitude value of the (s-1)th interval.

[0020] As a further optimization of the probabilistic hierarchical fault scenario generation method for an integrated electrical energy system described in this invention, the expected values ​​of damaged components in the power distribution system and natural gas system in step S2 are calculated as follows:

[0021] Step 2.1: For each earthquake classification, characterize the earthquake's destructiveness and determine the peak ground acceleration range. The general analytical formula is as follows:

[0022]

[0023] Wherein, G represents peak ground acceleration, M represents earthquake magnitude, R represents epicentral distance, A represents land type, ζ represents the uncertainty parameter of seismic wave propagation, a and b represent regression coefficients, k represents geometric attenuation coefficient, R0 represents saturation distance constant, γ represents inelastic attenuation coefficient, A(S) is site amplification factor, c is the basic constant, F1(M) is a function of earthquake magnitude, F2(R) is a function of epicentral distance, and F3(A) is a function of land type; F1(M), F2(R), and F3(A) quantitatively describe the influence of magnitude, epicentral distance, and land type on earthquake catastrophicity, and together construct the functional relationship between earthquake parameters and catastrophicity;

[0024] Step 2.2: The post-earthquake state is characterized by the percentage of damaged power lines in the integrated electrical energy system. The post-earthquake state includes minor damage, moderate damage, severe damage, and complete damage, denoted by symbols. express, The disaster recovery status is categorized as follows: D1 represents minor damage, D2 represents moderate damage, D3 represents severe damage, and D4 represents complete damage. The vulnerability curve for each disaster recovery status is described by the following formula:

[0025]

[0026] Where φ[·] represents the standard normal cumulative distribution function, ω represents the median of peak ground acceleration. d Let P(d|G) represent the log-normal standard deviation, and let P(d|G) be the probability that the integrated electrical energy system IES is in a post-disaster state d given a peak ground acceleration G.

[0027] The expected values ​​of damaged components in a power distribution system under earthquakes of different magnitudes are calculated using the following formula:

[0028] N ED= [P(d >= D n | G) - P(d >= D n+1 | G)]N Dn (8)

[0029] Where, N ED is the expected value of damaged components, D n is the current post-disaster state, D n+1 is the next degree of post-disaster state, N Dn is the total number of lines, P(*) is the probability that the IES damage degree meets a certain level under a given seismic intensity G.

[0030] Under non-seismic level earthquakes, the expected value of damaged components in the natural gas system is also calculated by the connection failure method.

[0031] As a further optimization scheme of the electrical integrated energy system probabilistic hierarchical failure scenario generation method described in the application, the cascading failure of the electrical integrated energy system is simulated under each random failure scenario, as follows:

[0032] Step 3.1, failure scenario generation and the number of generated random failure scenarios formula as follows:

[0033]

[0034] Where, E j is the failure component set of the jth scenario, the repair time set T j ={t e | e E j}, t e ~ Weibull distribution (alpha, beta), t e is the time period, e is the component, alpha is the shape parameter, beta is the scale parameter, is the kth random failure scenario set, N total is the number of generated random failure scenarios;

[0035] Step 3.2, failure component sampling formula as follows:

[0036]

[0037] Where, L e is the length of component e, is the sum of all component length-related quantities in set C, L m is the length of a single component m in set C, P(e E j ) is the probability that component e belongs to failure set E j ;

[0038] Step 3.3, repair time generation according to Weibull distribution formula as follows:

[0039] t e = β(-ln(1-U)) 1 / α , U ~ Uniform(0, 1) (12)

[0040] where U is a random number obeying uniform distribution Uniform(0, 1), U is used for sampling, and Uniform(0, 1) is a uniform distribution function;

[0041] Step 3.4, the objective function is as follows:

[0042]

[0043] where, is a set of scheduling periods, is a set of power nodes, is a set of natural gas nodes, are power and gas load curtailments, respectively, is a weight coefficient, t is a time, and i is a node i;

[0044] Step 3.5, considering the constraints of post-disaster emergency dispatching, the constraints are as follows:

[0045] (1) Distribution system constraint conditions:

[0046] where the active power and reactive power balance constraints of the power node are:

[0047]

[0048] where k: k→i represents a set of power lines with node i as the terminal node, and j: i→j represents a set of power lines with node i as the head node; are the active power and reactive power of the electric load, respectively, and is the active power flow of the power line, is the active power output of the substation, is the active power output of the gas turbine, is the active power output of the mobile power supply vehicle, is the active power input of the electric boiler, and is the reactive power flow of the power line, is the reactive power of the substation, is the reactive power of the gas turbine, is the reactive power of the mobile power supply vehicle, is the active power curtailment of the electric load, is the reactive power curtailment of the electric load;

[0049] The line voltage drop constraint is:

[0050]

[0051] wherein, ι ij is a 0-1 variable of pre-disaster power line operation state, 0 represents non-operation state, and 1 represents operation state; represents the damaged state of post-disaster power line, 0 represents that the line is damaged after the disaster, 1 represents that the line is not damaged after the disaster; R ij is the resistance of the power line, X ij is the reactance of the power line, N is a sufficiently large positive number, V i,s,t and V j,s,t is the square of the node voltage, is a set of power lines, ij is a power line in the set, connecting nodes i, j;

[0052] The active and reactive power flow constraints of the power line are:

[0053]

[0054]

[0055] wherein, is the maximum capacity of the power line;

[0056] The correlation constraint between active load shedding and reactive load shedding is:

[0057]

[0058]

[0059] wherein, represents the active power reduced by the electric load, represents the reactive power reduced by the electric load;

[0060] The radial operation constraint of the pre-disaster power topology is considered:

[0061]

[0062] wherein, is a set of power loops, is a set of power lines contained in loop n, represents the number of nodes of the power distribution system;

[0063] The logical relationship between the damaged state of the power line and the line reinforcement state and the line destruction state is:

[0064]

[0065] wherein, is the line reinforcement state, is the line damage state;

[0066] Considering the upper and lower limit constraints of the active power, climbing power and reactive power of the gas turbine:

[0067]

[0068] wherein, is the gas turbine node set, is the maximum active power output of the gas turbine, is the maximum climbing power of the gas turbine, is the power factor of the gas turbine, is the active power output of the gas turbine at the last time, and Δt is the time step;

[0069] Considering the upper and lower limit constraints of the active power and reactive power of the substation:

[0070]

[0071] wherein, is the substation node set, is the upper limit value of the active power of the substation, is the upper limit value of the reactive power of the substation;

[0072] Considering the upper and lower limit constraints of the node voltage:

[0073]

[0074] wherein, V i,min is the lower limit value of the node voltage, and V i,max is the upper limit value of the node voltage;

[0075] (2) Natural gas system operation constraints:

[0076] wherein, considering the node gas flow balance constraint:

[0077]

[0078] wherein, k':k'→i' represents a set of natural gas pipelines with node i' as the terminal node, and j':i'→j' represents a set of natural gas pipelines with node i' as the head node, is the gas load gas flow, and is the natural gas pipeline gas flow, is the natural gas gate station gas flow, is the gas turbine gas flow, Qg is the gas flow rate of the gas pipeline;

[0079] The Weymouth gas flow equation constraint of the gas pipeline is considered:

[0080]

[0081] wherein, is the Weymouth gas flow equation coefficient of the gas pipeline, is the damaged state of the post-disaster gas pipeline, is 0, indicating that the pipeline is damaged after the disaster, is 1, indicating that the pipeline is not damaged after the disaster, and is the node gas pressure;

[0082] The numerical relationship constraint between the inlet and outlet gas flow rates of the compressor is considered:

[0083]

[0084] wherein, is the compressor pipeline set, is the compressor loss coefficient, is the inlet gas flow rate of the compressor pipeline, is the outlet gas flow rate of the compressor pipeline;

[0085] The inlet and outlet pressure difference constraint of the compressor pipeline is:

[0086]

[0087] wherein, Γ Com is the compressor pressure coefficient, is the inlet gas pressure of the compressor pipeline, is the outlet gas pressure of the compressor pipeline;

[0088] The upper and lower limit constraints of the gas load reduction amount are:

[0089]

[0090] wherein, is the natural gas basic load demand of node i' at time t;

[0091] The upper and lower limit constraints of the gas flow rate of the gas pipeline are:

[0092]

[0093] wherein, is the maximum gas flow rate of the gas pipeline;

[0094] The upper and lower limit constraints of the gas flow rate of the gas gate station are:

[0095]

[0096] wherein, is a set of natural gas gate station nodes, is a maximum gas flow of the natural gas gate station;

[0097] The upper and lower limit constraints of the node gas pressure are:

[0098]

[0099] wherein, is a minimum value of the node gas pressure, is a maximum value of the node gas pressure;

[0100] The logical relationship between the damaged state of the natural gas pipeline and the pipeline reinforcement state and the pipeline destruction state is:

[0101]

[0102] wherein, represents the damaged state of the natural gas pipeline, represents the pipeline reinforcement state, represents the pipeline destruction state;

[0103] The conversion constraint of the input gas flow and the output active power of the gas turbine is:

[0104]

[0105] wherein, is a set of gas turbine group nodes of the natural gas system, is a set of gas turbine group nodes of the power distribution system, respectively, GT is a conversion efficiency of the gas turbine, g2e is a natural gas energy conversion coefficient, is an output active power of the gas turbine,

[0106] As a further optimization scheme of the electrical integrated energy system probabilistic hierarchical fault scenario generation method described in the present application, the determination of the typical fault scenario in step S4 is as follows:

[0107] Step 4.1, at each classification magnitude, calculate the average loss of load L MC of N s random fault scenarios, the formula is as follows:

[0108]

[0109] Step 4.2, calculate the loss of load L s,m of each random fault scenario and the average loss of load Ls The difference d between the two values s,m , the formula is as follows:

[0110]

[0111] Step 4.3, selecting the scene with the minimum absolute value of the difference d s,m As a typical failure scene of the classified magnitude, the scene is:

[0112]

[0113] Step 4.4, repeating steps 4.1-4.3 until all N s Typical failure scenes corresponding to each classified magnitude are obtained to form a set of hierarchical failure scenes

[0114] As a further optimization scheme of the method for generating a probabilistic hierarchical failure scene of an electrical integrated energy system according to the present application, in step 2.2, the post-disaster state includes light damage, moderate damage, severe damage and complete damage, wherein,

[0115] When the percentage of damaged power lines to the total power lines is in the interval [0, 25%], it is light damage, when the percentage of damaged power lines to the total power lines is in the interval [25%, 50%], it is moderate damage, when the percentage of damaged power lines to the total power lines is in the interval [50%, 75%], it is severe damage, and when the percentage of damaged power lines to the total power lines is in the interval [75%, 100%], it is complete damage.

[0116] Compared with the prior art, the above technical scheme has the following technical effects:

[0117] (1) The present application realizes the systematic evaluation of the uncertainty of earthquake disaster by innovative magnitude interval discretization processing and probability grading mechanism, which can more comprehensively reflect the destructive effect of earthquakes of different magnitudes on the system. Especially by constructing a set of hierarchical failure scenes with statistical representation, the problem of quantifying small probability high damage events in the prior art is effectively solved, which provides more scientific technical support for system seismic design.

[0118] (2) The present application innovatively combines magnitude probability distribution analysis with system vulnerability assessment, and through multi-state damage model and component damage expectation value calculation, the damage assessment of key infrastructure is more scientific and accurate. Practical application shows that the prediction accuracy of load loss of moderate intensity earthquakes is significantly improved compared with traditional methods.

[0119] ​(3) The present application realizes accurate simulation of system cascade failure by establishing a complete multi-energy flow coordination simulation framework. Especially in the post-disaster emergency dispatch scheme design, the resource allocation strategy based on typical scenarios can greatly shorten the system recovery time, and significantly improve the anti-seismic resilience of the integrated energy system. BRIEF DESCRIPTION OF DRAWINGS

[0120] Figure 1 is a flow chart of the method for generating a probabilistic hierarchical failure scenario of an electrical integrated energy system considering the uncertainty of earthquake disasters according to the present application. DETAILED DESCRIPTION

[0121] The embodiments of the present application will be described in detail below, examples of which are shown in the accompanying drawings. The embodiments described below by referring to the accompanying drawings are exemplary and are only used to explain the present application, and cannot be interpreted to represent a limitation on the present application.

[0122] As shown in Figure 1 , a flow chart of the method for generating a probabilistic hierarchical failure scenario of an electrical integrated energy system considering the uncertainty of earthquake disasters according to the present application is shown, which includes the following steps:

[0123] Step 1, discretize the target magnitude range [M0, M E ] into N s equal intervals, and calculate the center value of each equal interval to represent the classified magnitude. Calculate the occurrence probability of each equal interval. s .

[0124] The general analytical expression of magnitude interval discretization and the occurrence probability of each equal interval is as follows:

[0125]

[0126] where M0 and M E represent the lower limit and upper limit of the target magnitude range, N s represents the number of discrete intervals, M s represents the center magnitude value of the s-th interval, l represents the seismic activity parameter, ΔM is the interval width, and M s-1 represents the center magnitude value of the s-1-th interval.

[0127] Step 2, for each classified magnitude, determine the possible peak ground acceleration range and randomly sample from it. Calculate the expected value of the damaged elements in the power distribution system and the natural gas system under the peak ground acceleration sampling value.

[0128] Step 2.1, for each classified magnitude, characterize the earthquake disaster and determine the peak ground acceleration range, the general analytical expression of which is as follows:

[0129]

[0130] wherein G represents peak ground acceleration, M represents earthquake magnitude, R represents epicentral distance, A represents land type, ζ represents an uncertainty parameter of seismic wave propagation, a, b represent regression coefficients, k represents a geometric attenuation coefficient, R0 represents a saturation distance constant, γ represents a non-elastic attenuation coefficient, A(S) is a site amplification factor, c is a base constant, F1(M) is a function related to earthquake magnitude, F2(R) is a function related to epicentral distance, F3(A) is a function related to land type; F1(M), F2(R), F3(A) respectively quantitatively describe the influence of magnitude, epicentral distance, land type on earthquake disaster, and jointly build a functional relationship between earthquake parameters and disaster.

[0131] Step 2.2, the post-disaster state caused by the earthquake is represented by the percentage of damaged power lines in the electrical integrated energy system, and the post-disaster state includes four kinds of light damage, moderate damage, severe damage and complete damage, which are represented by symbols , , the percentage of damaged power lines in the total power lines is in the interval [0, 25%], which is light damage, represented by D1, the percentage of damaged power lines in the total power lines is in the interval [25%, 50%], which is moderate damage, represented by D2, the percentage of damaged power lines in the total power lines is in the interval [50%, 75%], which is severe damage, represented by D3, and the percentage of damaged power lines in the total power lines is in the interval [75%, 100%], which is complete damage, represented by D4; the vulnerability curve corresponding to each post-disaster state is described by the following formula:

[0132]

[0133] wherein φ[·] represents a standard normal cumulative distribution function, represents the median of peak ground acceleration, ω d represents the logarithmic normal standard deviation, P(d|G) is the probability of the electrical integrated energy system IES being in the post-disaster state d under the condition of a given peak ground acceleration G. Further, the expected value of damaged elements in the distribution system under different magnitude earthquakes is calculated by the following formula:

[0134] N ED = [P(d≥D n |G) - P(d≥D n+1 |G)]N Dn (8)

[0135] wherein N ED is the expected value of damaged elements, D n is the current post-disaster state, D n+1 is the next degree of post-disaster state, P(*) is the probability that the IES damage degree meets a certain level when the given seismic intensity G is satisfied;

[0136] The expected value of damaged elements in the natural gas system under non-shock intensity earthquakes is also calculated by the above connection failure method.

[0137] Step 3, using the Monte Carlo method, randomly generate N MC failure scenarios at each classified earthquake magnitude. In each scenario, the number of failure elements is set to the expected value in step 2, and the failure elements are randomly sampled based on the length attributes of lines and pipelines, and the repair time of each failure element is randomly generated based on the Weibull distribution. A total of N s ×N MC random failure scenarios are generated at all classified earthquake magnitudes; in each random failure scenario, the cascading failure of the electrical integrated energy system is simulated, and the total amount of system load loss is recorded;

[0138] Step 3.1, failure scenario generation and the number of generated random failure scenarios formula as follows:

[0139]

[0140] where E j is the jth scenario failure element set, T j ={t e ∣e∈E j} is the repair time set, t e ~ Weibull distribution (α,β), t e is the time period, e is the element, α is the shape parameter, β is the scale parameter, is the kth random failure scenario set, N total is the number of generated random failure scenarios;

[0141] Step 3.2, failure element sampling formula as follows:

[0142]

[0143] where L e is the length of element e, is the sum of all element length-related quantities in set C, L m is the length of a single element m in set C, P(e∈E j ) is the probability that element e belongs to the failure set E j ;

[0144] Step 3.3, repair time generated according to Weibull distribution formula as follows:

[0145]

[0146] where U is a random number obeying uniform distribution Uniform(0, 1) for sampling, and Uniform(0, 1) is a uniform distribution function.

[0147] Step 3.4, the objective function is as follows:

[0148]

[0149] where, is a set of scheduling periods, is a set of electric nodes, is a set of natural gas nodes, is an electric and gas load curtailment, is a weight coefficient, and i is a node i;

[0150] Step 3.5, considering the post-disaster emergency scheduling constraints are as follows:

[0151] (1) Power distribution system constraint condition:

[0152] where the active power and reactive power balance constraints of the electric nodes are:

[0153]

[0154]

[0155] where k:k→i represents a set of electric lines with node i as the terminal node, and j:i→j represents a set of electric lines with node i as the head node; are the active power and reactive power of the electric load, respectively, and is the active power flow of the electric line, is the active power output of the transformer substation, is the active power output of the gas turbine, is the active power output of the mobile power supply vehicle, is the active power input of the electric boiler, and is the reactive power flow of the electric line, is the reactive power of the transformer substation, is the reactive power of the gas turbine, is the reactive power of the mobile power supply vehicle, is the active power curtailment of the electric load, is the reactive power curtailment of the electric load, and t is the time;

[0156] The line voltage drop constraint is:

[0157]

[0158] wherein, ι ij is a 0-1 variable of pre-disaster power line operation state, 0 represents non-operation state, 1 represents operation state respectively, represents the damaged state of post-disaster power line, 0 represents that the line is damaged after the disaster, 1 represents that the line is not damaged after the disaster. ij is the resistance of the power line, X ij is the reactance of the power line, N is a large positive number, V i,s,t and V j,s,t is the square of the node voltage, is a set of power lines, ij is a specific power line (connecting nodes i, j) in the set;

[0159] The active and reactive power flow constraints of the power line are:

[0160]

[0161]

[0162] wherein, is the maximum capacity of the power line, is the damaged state of the power line;

[0163] The correlation constraint between active load shedding and reactive load shedding is:

[0164]

[0165] wherein, represents the active power of the power load reduction, represents the reactive power of the power load reduction, is the active power of the power load, is the reactive power of the power load;

[0166] The radial operation constraint of the pre-disaster power topology is considered:

[0167]

[0168] wherein, is a set of power loops, is a set of power lines contained in loop n, represents the number of nodes of the power distribution system.

[0169] The logical relationship between the damaged state of the power line and the line reinforcement state and the line destruction state is:

[0170]

[0171] wherein, is the damaged state of the power line, is the line reinforcement state, is the line destruction state.

[0172] Considering the upper and lower limit constraints of the active power, climbing power and reactive power of the gas turbine:

[0173]

[0174] wherein, is the set of gas turbine nodes, is the maximum active power output of the gas turbine, is the maximum climbing power of the gas turbine, is the power factor of the gas turbine, is the active power output of the gas turbine at the last time; is the reactive power of the gas turbine, is the active power output of the gas turbine, and Δt is the time step;

[0175] Considering the upper and lower limit constraints of the active power and reactive power of the substation:

[0176]

[0177] wherein, is the set of substation nodes, is the upper limit value of the active power of the substation, is the upper limit value of the reactive power of the substation;

[0178] Considering the upper and lower limit constraints of the node voltage:

[0179]

[0180] wherein, V i,min is the lower limit value of the node voltage, and V i,max is the upper limit value of the node voltage;

[0181] (2) Natural gas system operation constraints:

[0182] wherein, considering the node gas flow balance constraint:

[0183]

[0184] wherein, k':k'→i' represents the set of natural gas pipelines with node i' as the terminal node, and j':i'→j' represents the set of natural gas pipelines with node i' as the head node, is the gas load gas flow, and is the natural gas pipeline gas flow, for the gas flow rate of the natural gas gate station, for the gas flow rate of the gas turbine, for the gas load reduction gas flow rate;

[0185] considering the Weymouth gas flow equation constraint of the natural gas pipeline:

[0186]

[0187] wherein, is the Weymouth gas flow equation coefficient of the natural gas pipeline, is the post-disaster damaged state of the natural gas pipeline, is 0 indicating that the pipeline is damaged after the disaster, is 1 indicating that the pipeline is not damaged after the disaster, and is the node gas pressure;

[0188] considering the numerical relationship constraint between the inlet and outlet gas flow rates of the compressor:

[0189]

[0190] wherein, is the compressor pipeline set, is the compressor loss coefficient, is the inlet gas flow rate of the compressor pipeline, is the outlet gas flow rate of the compressor pipeline;

[0191] the inlet and outlet pressure difference constraint of the compressor pipeline is:

[0192]

[0193] wherein, Γ Com is the compressor pressure coefficient, is the inlet gas pressure of the compressor pipeline, is the outlet gas pressure of the compressor pipeline;

[0194] the upper and lower limit constraints of the gas load reduction amount are:

[0195]

[0196] wherein, is the natural gas basic load demand of node i', time t;

[0197] the upper and lower limit constraints of the gas flow rate of the natural gas pipeline are:

[0198]

[0199] wherein, is the maximum gas flow rate of the natural gas pipeline;

[0200] The upper and lower limits of gas flow at natural gas gate stations are as follows:

[0201]

[0202] in, For the set of natural gas gate station nodes, This represents the maximum gas flow rate at the natural gas gate station.

[0203] The upper and lower limits of the nodal pressure are:

[0204]

[0205] in, This represents the minimum value of the nodal pressure. This represents the maximum value of the nodal pressure.

[0206] The logical relationship between the damaged state of a natural gas pipeline and its reinforced state and state of damage is as follows:

[0207]

[0208] in, This indicates the damage status of the natural gas pipeline. Indicates the reinforcement status of the pipeline. This indicates that the pipeline has been damaged.

[0209] The conversion constraint between the input gas flow rate and the output active power of a gas turbine is:

[0210]

[0211] in, For the gas turbine unit node set of the natural gas system, These are the sets of gas turbine nodes in the power distribution system, η GT For gas turbine conversion efficiency, γ g2e The energy conversion coefficient of natural gas. n' represents the active power output of the gas turbine, and n' represents the node to which the gas turbine unit is connected.

[0212] Step 4: For each classification magnitude, calculate N. MC The average load loss L in a random fault scenario s And calculate the load loss and average load loss L for each random failure scenario. s Choose the scenario with the smallest absolute value of the difference between them. As a typical fault scenario for this type of earthquake magnitude, the graded fault scenario set is denoted as follows:

[0213] Step 4.1, for each classification magnitude Ms , calculate the average loss of load L MC of N s random failure scenarios

[0214]

[0215] Step 4.2, calculate the loss of load L s,m of each random failure scenario, and the difference between L s and the average loss of load L

[0216] d s,m = L s,m - L s (41)

[0217] Step 4.3, select the scenario with the smallest absolute value of d s,m as the typical failure scenario of the classified magnitude:

[0218]

[0219] Step 4.4, repeat steps 4.1-4.3 until all N s typical failure scenarios corresponding to each classified magnitude are obtained, forming a set of classified failure scenarios

[0220] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto, any changes or replacements within the technical range disclosed by the present application can be easily thought of by those skilled in the art, and should be covered within the protection scope of the present application.​

Claims

1. A method for generating probabilistic hierarchical fault scenarios in an integrated electrical energy system, characterized in that, include: Step S1: Define the target magnitude range [M0, M...] E Discretized into N s There are equidistant intervals, and the center value of each interval represents the classified magnitude; among them, M0 and M E These represent the lower and upper limits of the target magnitude range, respectively; Step S2: For each classification magnitude, determine the peak ground acceleration range and randomly sample from it to obtain peak ground acceleration sample values; under the peak ground acceleration sample values, calculate the expected values ​​of damaged components in the power distribution system and natural gas system; Step S3: Using the Monte Carlo method, randomly generate N for each classification magnitude. MC A random fault scenario; wherein the number of faulty components in each scenario is set to the expected value in step S2; A total of N earthquakes were generated across all magnitude classifications. s ×N MC A random failure scenario; In each random fault scenario, the cascading faults of the integrated electrical energy system are simulated, and the load loss in each random fault scenario is recorded. Step S4: For each classification magnitude, calculate N. MC The average load loss L in a random fault scenario s And calculate the load loss and average load loss L for each random failure scenario. s Choose the s-th scenario with the smallest absolute value of the difference between them. As a typical fault scenario for each magnitude classification, where 1≤s≤N s The set of graded fault scenarios is denoted as 2. The method for generating probabilistic hierarchical fault scenarios in an integrated electrical energy system according to claim 1, characterized in that, Step S3 also includes: randomly sampling faulty components based on the length attributes of lines and pipes, and randomly generating the repair time for each faulty component based on the Weibull distribution.

3. The method for generating probabilistic hierarchical fault scenarios in an integrated electrical energy system according to claim 1, characterized in that, Calculate ρ s The method is as follows: Where, N s M represents the number of discrete intervals. s Let l represent the central magnitude value of the s-th interval, l represent the seismic activity parameter, ΔM be the interval width, and M be the value of the central magnitude value. s-1 This represents the central magnitude value of the (s-1)th interval.

4. The method for generating probabilistic hierarchical fault scenarios in an integrated electrical energy system according to claim 1, characterized in that, The expected values ​​of the damaged components in the power distribution system and natural gas system in step S2 are calculated as follows: Step 2.1: For each earthquake classification, characterize the earthquake's destructiveness and determine the peak ground acceleration range. The general analytical formula is as follows: F1(M)=a·M+b·(M-M0) 2 (4) F2(R)=-k·ln(R+R0)-γ·R (5) F3(S)=ln(A(S)) (6) Where G represents peak ground acceleration, M represents earthquake magnitude, R represents epicenter distance, and A represents land type. The parameters represent the uncertainty of seismic wave propagation, a and b are regression coefficients, k is the geometric attenuation coefficient, R0 is the saturation distance constant, γ is the inelastic attenuation coefficient, A(S) is the site amplification factor, c is the basic constant, F1(M) is a function of earthquake magnitude, F2(R) is a function of epicentral distance, and F3(A) is a function of land type. F1(M), F2(R), and F3(A) quantitatively describe the influence of magnitude, epicentral distance, and land type on earthquake catastrophicity, and together construct the functional relationship between earthquake parameters and catastrophicity. Step 2.2: The post-earthquake state is characterized by the percentage of damaged power lines in the integrated electrical energy system. The post-earthquake state includes minor damage, moderate damage, severe damage, and complete damage, denoted by symbols. express, The disaster recovery status is categorized as follows: D1 represents minor damage, D2 represents moderate damage, D3 represents severe damage, and D4 represents complete damage. The vulnerability curve for each disaster recovery status is described by the following formula: Where φ[·] represents the standard normal cumulative distribution function, ω represents the median of peak ground acceleration. d Let P(d|G) represent the log-normal standard deviation, and let P(d|G) be the probability that the integrated electrical energy system IES is in a post-disaster state d given a peak ground acceleration G. The expected values ​​of damaged components in a power distribution system under earthquakes of different magnitudes are calculated using the following formula: Where, N ED D represents the expected value of the damaged component. n Given the current post-disaster situation, D n+1 For the next level of post-disaster status, Let P(*) be the total number of lines, and let P(*) be the probability that the damage level of IES meets a certain level condition when given an earthquake intensity G. Under normal earthquake conditions, the expected value of damaged components in the natural gas system is also calculated using the connection failure method.

5. The method for generating probabilistic hierarchical fault scenarios in an integrated electrical energy system according to claim 1, characterized in that, In each random fault scenario, the cascading faults of the integrated electrical energy system are simulated, as follows: Step 3.1, the formulas for fault scenario generation and the number of generated random fault scenarios are as follows: N total =N s ×N MC (10) Among them, E j Let T be the set of faulty components and the set of repair times for the j-th scenario. j ={t e |e∈E j }, t e ~Weibull distribution (α,β), t e Where e is the duration of the time period, α is the element, β is the shape parameter, and β is the scale parameter. Let N be the set of the k-th random fault scenarios. total The number of random fault scenarios generated; Step 3.2, the formula for sampling faulty components is as follows: Among them, L e Let e ​​be the length of element e. L is the sum of all length-related quantities of all elements in set C. m Let m be the length of a single element m in set C, and P(e∈E) be the length of the element m. j ) indicates that component e belongs to the fault set E. j The probability of; Step 3.3: The repair time is generated according to the Weibull distribution formula as follows: t e =β(-ln(1-U)) 1 / α ,U~Uniform(0,1) (12) Where U is a random number following a uniform distribution Uniform(0,1), U is used for sampling, and Uniform(0,1) is the uniform distribution function; Step 3.4, the objective function is as follows: in, For the set of scheduling periods, For a set of power nodes, For a set of natural gas nodes, These are the reductions in electricity and gas loads, respectively. Here, t represents the weight coefficient, t represents time, and i represents node i. Step 3.5, Consider the following post-disaster emergency dispatch constraints: (1) Constraints of the power distribution system: The active and reactive power balance constraints at the power nodes are as follows: Where k:k→i represents the set of power lines with node i as the end node, and j:i→j represents the set of power lines with node i as the beginning node; These are the active power and reactive power of the electrical load, respectively. and For the active power flow of the power line, To output active power to the substation To output active power for the gas turbine, To output active power to the mobile power supply vehicle, Input active power to the electric boiler. and For the reactive power flow of power lines, For the reactive power of the substation, This refers to the reactive power of the gas turbine. The reactive power of the mobile power supply vehicle. To reduce active power for electrical loads, To reduce reactive power in electrical loads; The line voltage drop constraint is: Among them, ι ij The variable represents the pre-disaster operating status of power lines, with 0 indicating that the lines are not in operation and 1 indicating that they are in operation. This indicates the state of damage to power lines after the disaster. A value of 0 indicates that the line was damaged in the disaster. A value of 1 indicates that the line was not damaged after the disaster; R ij X is the resistance of the power line. ij V is the reactance of the power line, where N is a sufficiently large positive number. i,s,t and V j,s,t The square of the node voltage. Let be a set of power lines, and ij be a power line in the set, and the connecting nodes i and j. The active and reactive power flow constraints of power lines are: in, This represents the maximum capacity of the power line. The correlation constraint between active load shedding and reactive load shedding is: in, This indicates a reduction in active power by the electrical load. This indicates that the electrical load is reducing reactive power. Considering the radial operating constraints of the pre-disaster power topology: in, For the collection of power loops, Let n be the set of power lines contained in the loop. Indicates the number of nodes in the power distribution system; The logical relationship between the damaged state of power lines, the reinforced state of power lines, and the damaged state of power lines is as follows: in, The line is in a reinforced state. The line is in a damaged state; Considering the upper and lower limits of the active power, ramp power, and reactive power of the gas turbine: in, For the gas turbine node set, This represents the maximum output active power of the gas turbine. This represents the maximum gradeability of the gas turbine. For gas turbine power factor, Δt represents the active power output of the gas turbine at the previous moment, and Δt is the time step. Considering the upper and lower limits of active and reactive power in the substation: in, For the set of substation nodes, This represents the upper limit of the active power of the substation. This represents the upper limit of reactive power in a substation. Consider the upper and lower limits of node voltage constraints: Among them, V i,min V represents the lower limit of the node voltage. i,max This represents the upper limit of the node voltage. (2) Natural gas system operation constraints: Among them, the node gas flow balance constraint is considered: Where k':k'→i' represents the set of natural gas pipelines with node i' as the terminal node, and j':i'→j' represents the set of natural gas pipelines with node i' as the head node. For gas load and gas flow rate, and This refers to the gas flow rate in the natural gas pipeline. This refers to the gas flow rate at the natural gas gate station. This refers to the gas flow rate of the gas turbine. Reduce gas flow rate to reduce gas load; Consider the Witmouth gas flow equation constraints for natural gas pipelines: in, These are the coefficients of the Witmouth gas flow equation for natural gas pipelines. This shows the state of damage to the natural gas pipeline after the disaster. A value of 0 indicates that the pipeline was damaged in the disaster. A value of 1 indicates that the pipeline was undamaged after the disaster, π i',s,t and π j',s,t The node pressure; Considering the numerical constraints between the compressor's intake and exhaust volumes: in, For compressor piping collection, This is the compressor loss coefficient. This represents the inlet gas flow rate of the compressor pipeline. This represents the outlet gas flow rate of the compressor pipeline; The pressure difference constraint between the inlet and outlet of the compressor pipeline is: Among them, Γ Com This is the compressor pressurization coefficient. This refers to the inlet gas pressure of the compressor pipeline. This refers to the outlet gas pressure of the compressor pipeline; The upper and lower limits of the gas load reduction are: in, Let i' be the base load demand for natural gas at time t. The upper and lower limits of natural gas pipeline flow rate are constrained as follows: in, This represents the maximum gas flow rate of the natural gas pipeline. The upper and lower limits of gas flow at natural gas gate stations are as follows: in, For the set of natural gas gate station nodes, This represents the maximum gas flow rate at the natural gas gate station. The upper and lower limits of the nodal pressure are: Where, π i',min π represents the minimum nodal pressure. i',max This represents the maximum value of the nodal pressure. The logical relationship between the damaged state of a natural gas pipeline and its reinforced state and state of damage is as follows: in, This indicates the damage status of the natural gas pipeline. Indicates the reinforcement status of the pipeline. This indicates that the pipeline has been damaged. The conversion constraint between the input gas flow rate and the output active power of a gas turbine is: in, For the gas turbine unit node set of the natural gas system, These are the sets of gas turbine nodes in the power distribution system, η GT For gas turbine conversion efficiency, γ g2e The energy conversion coefficient of natural gas. n' represents the active power output of the gas turbine, and n' represents the node to which the gas turbine unit is connected.

6. The method for generating probabilistic hierarchical fault scenarios in an integrated electrical energy system according to claim 4, characterized in that, The typical fault scenarios are determined in step S4 as follows: Step 4.1: For each magnitude category, calculate N. MC The average load loss L in a random fault scenario s The formula is as follows: Step 4.2: Calculate the load loss L for each random failure scenario. s,m With average load loss L s The difference d between s,m The formula is as follows: d s,m L s,m -L s (41) Step 4.3: Select the difference d s,m The scenario with the smallest absolute value Typical fault scenarios for this type of earthquake magnitude: Step 4.4: Repeat steps 4.1-4.3 until all N are obtained. s Each category of earthquake magnitude corresponds to a typical fault scenario, forming a graded fault scenario set.

7. The method for generating probabilistic hierarchical fault scenarios in an integrated electrical energy system according to claim 4, characterized in that, In step 2.2, the post-disaster status includes minor damage, moderate damage, severe damage, and complete damage. When the percentage of damaged power lines in the total power lines is in the range of [0, 25%], it is considered minor damage; when the percentage is in the range of [25%, 50%], it is considered moderate damage; when the percentage is in the range of [50%, 75%], it is considered severe damage; and when the percentage is in the range of [75%, 100%], it is considered complete damage.

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