A method and system for improving the cold wave resilience of a comprehensive energy system considering endogenous and exogenous uncertainties

Abstract

The application discloses a cold wave resilience improvement method and system of a comprehensive energy system considering endogenous and exogenous uncertainties, and the method comprises the following steps: constructing a multi-component disaster model of the comprehensive energy system under an extreme cold wave to obtain system operation parameters under disaster influence; respectively establishing an exogenous uncertainty model and an endogenous uncertainty model; constructing a two-stage mixed integer stochastic programming model; the first stage is a pre-disaster reinforcement decision stage; the second stage is a disaster dispatching stage; the two-stage mixed integer stochastic programming model is solved by using an SAA algorithm to obtain an optimal reinforcement scheme and an optimal dispatching strategy; pre-disaster reinforcement is performed according to the optimal reinforcement scheme, and multi-energy coordinated dispatching of the comprehensive energy system is performed during the extreme cold wave according to the optimal dispatching strategy. Through the collaborative optimization of the pre-disaster reinforcement scheme of the power distribution network line and the heating pipeline and the disaster multi-energy coordinated dispatching strategy, the collaborative optimization of the system resilience and the economy under the limited investment is realized.

Description

Technical Field

[0001] This invention belongs to the field of power grids and relates to integrated energy system planning and operation technology. Specifically, it relates to a method and system for improving the cold wave resilience of integrated energy systems that takes into account endogenous and exogenous uncertainties. Background Technology

[0002] With the advancement of the global "carbon peaking and carbon neutrality" strategy, the penetration rate of renewable energy in power distribution networks continues to rise, exacerbating the operational uncertainty of power distribution systems and making the demand for system flexibility increasingly urgent. At the same time, high-impact, low-probability extreme weather events occur frequently, posing a serious threat to the safe and reliable operation of power distribution systems. Among these, extreme cold waves, accompanied by low temperatures, freezing rain, icing, and strong winds, can easily cause destructive impacts on integrated energy systems.

[0003] Integrated power and heating systems are typical integrated energy systems, consisting of a power distribution network and a district heating system interconnected through coupled equipment such as combined heat and power (CHP) units and electric boilers. During extreme cold waves, low temperatures and strong winds cause wind turbine blades to ice over and solar panels to be covered in snow, resulting in a significant decrease in renewable energy output. Simultaneously, a surge in heating demand leads to a substantial increase in both electrical and thermal loads. Furthermore, power distribution lines and heating pipelines face risks of icing-induced weight gain and low-temperature embrittlement. These combined effects of multiple factors can trigger cascading failures across the network, seriously threatening the energy supply security of the integrated energy system.

[0004] Most existing studies focus only on single networks of power or heating systems, failing to fully characterize the multi-component collaborative damage mechanisms of extreme cold waves on electricity-heat coupled networks, and lacking refined modeling of the disaster impact across the entire source-grid-load-storage chain. Furthermore, existing resilience planning methods typically treat line reinforcement decisions as deterministic protection (i.e., components will not fail after reinforcement) or only consider exogenous uncertainties (such as renewable energy and load fluctuations), neglecting the endogenous impact of reinforcement decisions on component failure probabilities. In reality, reinforcement measures only reduce the probability of conditional failure of components, rather than completely eliminating the risk of failure; this coupling relationship between decision-making and uncertainty has a significant impact on planning results. Simultaneously, existing methods face challenges such as high computational complexity and non-convex models when simultaneously handling endogenous and exogenous uncertainties, lacking scalable and efficient solution algorithms, making them difficult to apply to the resilience planning problem of large-scale integrated energy systems. Summary of the Invention

[0005] Purpose of the invention: To address the shortcomings of existing technologies in the resilience planning of integrated energy systems under extreme cold waves, this invention provides a method and system for enhancing the cold wave resilience of integrated energy systems by considering both endogenous and exogenous uncertainties. By collaboratively optimizing the pre-disaster reinforcement schemes of distribution network lines and heating pipelines, as well as the multi-energy coordinated dispatch strategy during disasters, the invention achieves synergistic optimization of system resilience and economy under limited investment.

[0006] Technical Solution: To achieve the above objectives, this invention provides a method for enhancing the cold wave resilience of a comprehensive energy system considering both endogenous and exogenous uncertainties, comprising the following steps:

[0007] S1: Construct a multi-component disaster model of the integrated energy system under extreme cold wave, and modify the model for the source-side renewable energy output, grid-side line and pipeline failure probability, load-side electric and heat load demand, and storage-side energy storage efficiency to obtain the system operating parameters under the influence of disaster.

[0008] S2: Based on system operating parameters, exogenous uncertainty model and endogenous uncertainty model are established respectively; exogenous uncertainty model is used to characterize the random fluctuation characteristics of the decline in renewable energy output and the surge in electricity and heat load demand under extreme cold waves; endogenous uncertainty model is used to characterize the coupled influence characteristics of disaster prevention and reinforcement decisions on the failure probability of distribution network lines and heating pipelines.

[0009] S3: Based on exogenous uncertainty models and endogenous uncertainty models, a two-stage mixed integer stochastic programming model is constructed. The first stage of the two-stage mixed integer stochastic programming model is the disaster prevention and reinforcement decision-making stage, and the decision variables include the insulation layer reinforcement scheme of the distribution network line and the insulation layer reinforcement scheme of the heating pipeline. The second stage of the two-stage mixed integer stochastic programming model is the disaster dispatching stage, and the decision variables include the unit output, energy storage charging and discharging, load reduction and network operation strategy under various scenarios.

[0010] S4: The SAA algorithm is used to solve the two-stage mixed integer stochastic programming model to obtain the optimal reinforcement scheme and the optimal scheduling strategy;

[0011] S5: Conduct pre-disaster reinforcement of power distribution lines and heating pipelines according to the optimal reinforcement scheme, and conduct multi-energy coordinated scheduling of the integrated energy system during extreme cold waves according to the optimal scheduling strategy.

[0012] Furthermore, the construction of the multi-component disaster model in step S1 includes:

[0013] Source-side model: The influence of wind turbine blade icing on power output is corrected based on the Makkonen icing model, and the photovoltaic power output is corrected based on the temperature-snow coupling effect;

[0014] Grid-side models: A fault probability model for distribution network lines is established based on ice thickness and wind speed; a fault probability model for heating pipelines is established based on minimum temperature difference and exposure time.

[0015] Load-side model: A temperature-corrected model of the electrical-thermal load is established based on the temperature sensitivity coefficient;

[0016] Storage-side model: A temperature-corrected model for energy storage charging and discharging efficiency is established based on the temperature decay coefficient.

[0017] Furthermore, the establishment of the exogenous uncertainty model in step S2 includes:

[0018] A1: The combined uncertainty of wind turbine output, photovoltaic output, electricity demand and heat demand is characterized by the sub-Bruker joint chance constraint method. The sub-Bruker joint chance constraint method constructs fuzzy sets based on the mean and covariance information of the uncertain variables, without assuming precise probability distributions.

[0019] A2: The joint opportunity constraint is decomposed into individual opportunity constraints using the Bonferroni inequality, and the individual opportunity constraints are transformed into solvable second-order cone constraints based on the conditional value-at-risk security approximation.

[0020] Furthermore, in step A2, the method of decomposing the joint opportunity constraint into individual opportunity constraints using the Bonferroni inequality is as follows:

[0021] The upper limit of the joint constraint violation probability is evenly distributed to each individual constraint to obtain the upper limit of the individual constraint violation probability corresponding to each uncertainty source;

[0022] Based on the moment uncertainty set and the conditional risk value security approximation, each individual opportunity constraint is transformed into a second-order cone programming constraint, resulting in the safe output boundary or safe load boundary for each uncertainty source.

[0023] Furthermore, the establishment of the endogenous uncertainty model in step S2 includes:

[0024] B1: Establish a failure probability model for power distribution lines and heating pipelines based on vulnerability curves; vulnerability curves characterize the functional relationship between component failure probability and extreme cold wave intensity;

[0025] B2: The vulnerability curve is shifted downwards based on the disaster prevention and reinforcement decision to obtain the conditional failure probability after reinforcement; the magnitude of the downward shift represents the degree to which the reinforcement measures reduce the component failure probability.

[0026] B3: Generate component failure scenarios based on Monte Carlo sampling, and determine the actual operating status of components in each scenario based on the hardened conditional failure probability.

[0027] Furthermore, the process of establishing a fault probability model for distribution network lines and heating pipelines based on fragility curves in step B1 includes:

[0028] For distribution network lines, the probability of ice accumulation fault is calculated based on the relationship between real-time ice thickness and maximum tolerable ice thickness, and the probability of strong wind fault is calculated based on the relationship between real-time wind speed and design wind speed. The combined probability of ice accumulation fault and strong wind fault is obtained by weighted combination.

[0029] For heating pipelines, a functional relationship between failure probability and minimum temperature difference, low temperature exposure time, pipeline service life and corrosion layer damage density is established based on a logistic regression model.

[0030] Furthermore, in step S3, the objective function of the two-stage mixed integer stochastic programming model is to minimize the total expected cost, which includes reinforcement investment cost, load reduction penalty cost, and system operating cost.

[0031] The cost of reinforcement investment includes the installation cost of insulation layers for power distribution lines and heating pipelines;

[0032] Load shedding penalty costs include electricity load shedding penalty costs and heat load shedding penalty costs;

[0033] System operating costs include upstream power grid purchase costs, combined heat and power (CHP) unit power generation costs, wind turbine power generation costs, photovoltaic power generation costs, energy storage discharge costs, and heat pump heating costs.

[0034] Furthermore, the constraints of the two-stage mixed-integer stochastic programming model in step S3 include:

[0035] Distribution network distflow constraints include node power balance constraints, branch voltage drop constraints, and branch power constraints;

[0036] Linearization constraints for heating networks include auxiliary heat variable constraints, heat loss constraints, and nodal heat power balance constraints;

[0037] Energy storage operation constraints include dynamic balance constraints of state of charge, charging and discharging power constraints, and daily operation cycle constraints;

[0038] Operating constraints for combined heat and power (CHP) units include feasible operating domain constraints and extreme point combination constraints;

[0039] Load reduction constraints include load reduction not exceeding load demand constraints and constant power factor constraints;

[0040] Component operational state constraints include fault relaxation constraints and hardened mutual exclusion constraints based on the Big M method.

[0041] Furthermore, the process of solving the two-stage mixed integer stochastic programming model using the SAA algorithm in step S4 includes:

[0042] C1: Generate multiple sets of fault scenario sample sets, each set containing N scenarios;

[0043] C2: Solve independently for each sample set to obtain M candidate reinforcement schemes;

[0044] C3: Evaluate the M candidate reinforcement schemes using a large-scale evaluation scenario set, and select the candidate scheme with the lowest average cost as the optimal reinforcement scheme;

[0045] C4: Calculate the confidence interval of the optimal solution, quantifying the gap between the quality and optimality of the solution.

[0046] This invention also provides a comprehensive energy system cold wave resilience enhancement system considering endogenous and exogenous uncertainties, comprising:

[0047] The disaster modeling module is used to construct a multi-component disaster model of the integrated energy system under extreme cold waves. It modifies and models the renewable energy output on the source side, the failure probability of the grid-side lines and pipelines, the electricity and heat load demand on the load side, and the energy storage efficiency on the storage side to obtain the system operating parameters under the impact of disasters.

[0048] The uncertainty modeling module is used to establish exogenous uncertainty models and endogenous uncertainty models based on system operating parameters. The exogenous uncertainty model is used to characterize the stochastic fluctuation characteristics of the decline in renewable energy output and the surge in electricity and heat load demand under extreme cold waves. The endogenous uncertainty model is used to characterize the coupled impact characteristics of disaster prevention and reinforcement decisions on the failure probability of distribution network lines and heating pipelines.

[0049] The stochastic programming module is used to construct a two-stage mixed-integer stochastic programming model based on the exogenous uncertainty model and the endogenous uncertainty model. The first stage of the two-stage mixed-integer stochastic programming model is the disaster prevention and reinforcement decision-making stage, and the second stage is the disaster scheduling stage.

[0050] The solution module is used to solve the two-stage mixed integer stochastic programming model using the SAA algorithm to obtain the optimal reinforcement scheme and the optimal scheduling strategy;

[0051] The scheduling execution module is used to perform pre-disaster reinforcement of power distribution lines and heating pipelines according to the optimal reinforcement plan, and to perform multi-energy coordinated scheduling of the integrated energy system during extreme cold waves according to the optimal scheduling strategy.

[0052] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0053] 1. This invention constructs a multi-component disaster model of an integrated energy system under extreme cold waves, which depicts the multidimensional impact of extreme cold waves on system operation from the entire process of source-grid-load-storage. It overcomes the limitations of existing technologies that only focus on a single network or a single disaster factor, and improves the precision and comprehensiveness of disaster modeling.

[0054] 2. By establishing an exogenous uncertainty model, the combined uncertainty of declining renewable energy output and surging electricity and heat load demand is simultaneously characterized by the use of the split-bar joint opportunity constraint method. This avoids the problem of underestimating the joint risk caused by independently handling each uncertainty source, and improves the reliability of the planning scheme.

[0055] 3. By establishing an endogenous uncertainty model, the coupled impact of disaster prevention and reinforcement decisions on component failure probability is quantified based on the vulnerability curve. This overcomes the simplistic assumption of treating reinforcement decisions as deterministic protection in existing technologies, making the planning results more in line with engineering reality and avoiding the problems of over-investment or insufficient protection.

[0056] 4. By constructing a two-stage mixed integer stochastic programming model, the disaster prevention and reinforcement decision and the disaster scheduling strategy are optimized in a coordinated manner, achieving Pareto optimality of system resilience and economy under limited investment, and avoiding suboptimal solutions caused by staged optimization.

[0057] 5. By adopting the SAA algorithm, continuous expectations are transformed into sample means, and the uncertainty of decision dependence is decoupled into deterministic parameter selection, which greatly reduces the complexity of problem solving, realizes efficient solution of large-scale integrated energy system resilience planning problem, and ensures the scalability and computational efficiency of the algorithm.

[0058] 6. This invention simultaneously addresses four aspects: accurate disaster modeling, collaborative handling of endogenous and exogenous uncertainties, two-stage collaborative optimization, and efficient solution algorithms. It significantly enhances the resilience, anti-disturbance capability, and continuous energy supply capability of integrated energy systems under extreme cold wave weather, providing practical decision support for extreme weather defense planning of energy infrastructure. Attached Figure Description

[0059] Figure 1 This is a flowchart of the method of the present invention;

[0060] Figure 2 This is a flowchart illustrating the solution process of the SAA algorithm in this invention.

[0061] Figure 3 The cost results are shown in the diagram for comparison with the numerical examples. Detailed Implementation

[0062] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0063] Example 1:

[0064] like Figure 1As shown, this embodiment provides a method for improving the cold wave resilience of a comprehensive energy system considering both endogenous and exogenous uncertainties, including the following steps:

[0065] S1: Construct a multi-component disaster model of the integrated energy system under extreme cold wave, and modify the model for the source-side renewable energy output, grid-side line and pipeline failure probability, load-side electric and heat load demand, and storage-side energy storage efficiency to obtain the system operating parameters under the influence of disaster.

[0066] The construction of a multi-component disaster model includes:

[0067] Source-side model: The influence of wind turbine blade icing on power output is corrected based on the Makkonen icing model, and the photovoltaic power output is corrected based on the temperature-snow coupling effect;

[0068] Grid-side models: A fault probability model for distribution network lines is established based on ice thickness and wind speed; a fault probability model for heating pipelines is established based on minimum temperature difference and exposure time.

[0069] Load-side model: A temperature-corrected model of the electrical-thermal load is established based on the temperature sensitivity coefficient;

[0070] Storage-side model: A temperature-corrected model for energy storage charging and discharging efficiency is established based on the temperature decay coefficient.

[0071] S2: Based on the system operating parameters, an exogenous uncertainty model (Formula 1-10) and an endogenous uncertainty model (Formula 11-12) are established respectively. The exogenous uncertainty model is used to characterize the stochastic fluctuation characteristics of the decline in renewable energy output and the surge in electricity and heat load demand under extreme cold waves. The endogenous uncertainty model is used to characterize the coupled influence characteristics of disaster prevention and reinforcement decisions on the failure probability of distribution network lines and heating pipelines.

[0072] The establishment of an exogenous uncertainty model includes:

[0073] A1: The combined uncertainty of wind turbine output, photovoltaic output, electricity demand and heat demand is characterized by the sub-Bruker joint chance constraint method. The sub-Bruker joint chance constraint method constructs fuzzy sets based on the mean and covariance information of the uncertain variables, without assuming precise probability distributions.

[0074] A2: The joint opportunity constraint is decomposed into individual opportunity constraints using the Bonferroni inequality, and the individual opportunity constraints are transformed into solvable second-order cone constraints based on the conditional value-at-risk security approximation.

[0075] The method of decomposing joint chance constraints into individual chance constraints using the Bonferroni inequality is as follows:

[0076] The upper limit of the joint constraint violation probability is evenly distributed to each individual constraint to obtain the upper limit of the individual constraint violation probability corresponding to each uncertainty source;

[0077] Based on the moment uncertainty set and the conditional risk value security approximation, each individual opportunity constraint is transformed into a second-order cone programming constraint, resulting in the safe output boundary or safe load boundary for each uncertainty source.

[0078] The establishment of an endogenous uncertainty model includes:

[0079] B1: Establish a failure probability model for power distribution lines and heating pipelines based on vulnerability curves; vulnerability curves characterize the functional relationship between component failure probability and extreme cold wave intensity;

[0080] For distribution network lines, the probability of ice accumulation fault is calculated based on the relationship between real-time ice thickness and maximum tolerable ice thickness, and the probability of strong wind fault is calculated based on the relationship between real-time wind speed and design wind speed. The combined probability of ice accumulation fault and strong wind fault is obtained by weighted combination.

[0081] For heating pipelines, a functional relationship between failure probability and minimum temperature difference, low temperature exposure time, pipeline service life and corrosion layer damage density is established based on a logistic regression model.

[0082] B2: The vulnerability curve is shifted downwards based on the disaster prevention and reinforcement decision to obtain the conditional failure probability after reinforcement; the magnitude of the downward shift represents the degree to which the reinforcement measures reduce the component failure probability.

[0083] B3: Generate component failure scenarios based on Monte Carlo sampling, and determine the actual operating status of components in each scenario based on the hardened conditional failure probability.

[0084] S3: Based on exogenous uncertainty models and endogenous uncertainty models, a two-stage mixed integer stochastic programming model is constructed. The first stage of the two-stage mixed integer stochastic programming model is the disaster prevention and reinforcement decision-making stage, and the decision variables include the insulation layer reinforcement scheme of the distribution network line and the insulation layer reinforcement scheme of the heating pipeline. The second stage of the two-stage mixed integer stochastic programming model is the disaster dispatching stage, and the decision variables include the unit output, energy storage charging and discharging, load reduction and network operation strategy under various scenarios.

[0085] The objective function of the two-stage mixed integer stochastic programming model is to minimize the total expected cost, which includes reinforcement investment cost, load reduction penalty cost, and system operating cost.

[0086] The cost of reinforcement investment includes the installation cost of insulation layers for power distribution lines and heating pipelines;

[0087] Load shedding penalty costs include electricity load shedding penalty costs and heat load shedding penalty costs;

[0088] System operating costs include upstream power grid purchase costs, combined heat and power (CHP) unit power generation costs, wind turbine power generation costs, photovoltaic power generation costs, energy storage discharge costs, and heat pump heating costs.

[0089] The constraints of the two-stage mixed-integer stochastic programming model include:

[0090] Distribution network distflow constraints include node power balance constraints, branch voltage drop constraints, and branch power constraints (Equations 24-25, 27-28).

[0091] Linearization constraints for heating networks include auxiliary heat variable constraints, heat loss constraints, and nodal heat power balance constraints (Equations 47-63).

[0092] Energy storage operation constraints include dynamic balance constraints of state of charge, charging and discharging power constraints, and daily operation cycle constraints (Equations 32-34).

[0093] Heat pump operating constraints include the deterioration of the electro-thermal conversion relationship and the coefficient of performance (Equations 35-36).

[0094] Operating constraints for combined heat and power units include feasible operating domain constraints and extreme point combination constraints (Equations 30-31).

[0095] Component operating state constraints, including fault relaxation constraints based on the Big M method (Equations 26, 29, 37-46).

[0096] S4: The SAA algorithm is used to solve the two-stage mixed integer stochastic programming model to obtain the optimal reinforcement scheme and the optimal scheduling strategy;

[0097] The process of solving a two-stage mixed integer stochastic programming model using the SAA algorithm includes:

[0098] C1: Generate multiple sets of fault scenario sample sets, each set containing N scenarios;

[0099] C2: Solve independently for each sample set to obtain M candidate reinforcement schemes;

[0100] C3: Evaluate the M candidate reinforcement schemes using a large-scale evaluation scenario set, and select the candidate scheme with the lowest average cost as the optimal reinforcement scheme;

[0101] C4: Calculate the confidence interval of the optimal solution, quantifying the gap between the quality and optimality of the solution.

[0102] S5: Conduct pre-disaster reinforcement of power distribution lines and heating pipelines according to the optimal reinforcement scheme, and conduct multi-energy coordinated scheduling of the integrated energy system during extreme cold waves according to the optimal scheduling strategy.

[0103] Example 2:

[0104] This embodiment elaborates and applies the method of Embodiment 1 to provide a method for enhancing the cold wave resilience of a comprehensive energy system that considers both endogenous and exogenous uncertainties, including the following steps:

[0105] 1) Conduct disaster impact assessments on the source side, grid side, load side, and storage side of the integrated energy system under cold waves to obtain the source side renewable energy output correction, grid side line and pipeline failure probability, load side correction electric and heat load, and storage side correction charging and discharging efficiency.

[0106] 1.1) Perform source-side assessment using the source-side model

[0107] During cold waves, icing on wind turbine blades and strong winds jointly affect power output. The Makkonen icing model is used to calculate ice accumulation; the ice accumulation rate is related to the liquid water content in the air, wind speed, and icing coefficient. Taking into account both the increased load caused by blade icing and changes in wind speed, the wind turbine output is adjusted as follows:

[0108]

[0109]

[0110]

[0111] in, This is the corrected baseline value for the active power output of the wind turbine. For rated output, For wind speed, This is the icing coefficient. Liquid water content, This is the proportionality coefficient. This refers to the intensity of precipitation.

[0112] Photovoltaic unit output is affected by both low temperatures and snow accumulation: low temperatures increase photoelectric conversion efficiency, but snow accumulation reduces effective irradiance. Correction of photovoltaic output:

[0113]

[0114] in, This is the corrected photovoltaic power output baseline value. For rated output, For temperature coefficient, The standard test temperature is 25℃. For ambient temperature, This refers to the snow cover rate.

[0115] 1.2) Perform network-side evaluation using a network-side model.

[0116] Power line faults are mainly caused by icing. The probability of an icing-related fault is:

[0117]

[0118] in, This represents the probability of a line failure due to icing. For correction factor, , This is the power outage rate coefficient (empirical values ​​can be taken as 0.7031 and 18). To the maximum ice thickness that the line can withstand, This refers to the real-time ice thickness. The real-time ice thickness is determined by the initial ice thickness, the ice accumulation rate, and the ice melting rate.

[0119]

[0120] in, For the initial ice thickness, For the rate of ice accumulation, This represents the ice melting rate.

[0121] The failure probability of thermal pipelines is determined using a logistic regression model, based on factors such as the difference between the minimum temperature and the design temperature, the duration of low temperature, the pipeline's service life, and the density of corrosion layer damage.

[0122]

[0123] in, Let be the pipeline failure probability, and a1, b1, b2, b3, and b4 be regression coefficients obtained through maximum likelihood estimation based on historical maintenance data. This is the difference between the minimum temperature and the design temperature. This refers to the number of hours the temperature remained below freezing. For the service life of the pipeline, This represents the density of damage to the anti-corrosion layer.

[0124] 1.3) Perform load-side assessment using a load-side model

[0125] The cold wave caused a significant increase in electrical heating load, which was divided into temperature-sensitive and non-sensitive components:

[0126]

[0127] in, For the corrected electrical load, As the reference electrical load, For temperature sensitivity coefficient, , These are the proportional coefficients for insensitive and sensitive loads, respectively.

[0128] 1.4) Performing reservoir-side assessment using a reservoir-side model

[0129] Low temperatures reduce the charge-discharge efficiency of electrochemical energy storage; a temperature-dependent efficiency decay model is employed.

[0130]

[0131] in, The corrected charge / discharge efficiency. The rated efficiency is at 25℃. This is the temperature sensitivity coefficient.

[0132] 2) Based on the failure probability of network-side lines and pipelines, generate the original failure scenario; and for candidate reinforcement decisions, generate the reinforced failure scenario according to the reduction of failure probability by the reinforcement measures, so as to characterize the endogenous uncertainty brought about by the reinforcement decision.

[0133] 2.1) Generate the original fault scenario

[0134] For each power line and heating pipe, a uniformly distributed random number (0-1) is generated at each time step. If this random number is less than or equal to the fault probability at that time, the component is determined to have failed; otherwise, it operates normally. The original fault scenario includes the time-varying operating states of all components. This embodiment uses a power line as an example:

[0135]

[0136] in, This represents the original operating state of the line at any given time (1 for normal, 0 for fault). It is a random number. For power distribution line collection, To study the time node set, For the study of scene sets.

[0137] 2.2) Generation of hardened failure scenarios considering endogenous uncertainties

[0138] Reinforcement measures cannot completely eliminate faults, but rather reduce the probability of faults by a certain percentage. Let the reduction in the probability of faults after reinforcement be... (For power lines) and (For heating pipelines). Taking the power distribution network as an example, the failure probability after reinforcement is:

[0139]

[0140] The hardened operating state is still obtained by comparing random numbers with the hardened failure probability. However, since the hardening decision itself is an optimization variable, the failure probability and state depend on the decision, constituting an inherent uncertainty in decision dependence. To handle this relationship in optimization, this embodiment adopts a scenario-based approach: for each set of candidate hardening decisions, a corresponding hardened failure scenario is generated, coupling the decision with the scenario. Specifically, for any hardening decision variable, its actual operating state is uniformly expressed by the following formula:

[0141]

[0142] in, This represents the original fault state before reinforcement. This is the fault state after reinforcement. This is the decision variable for reinforcement. This formula ensures that the original state is taken when the pipeline is not reinforced, and the reinforced state is taken when it is reinforced. The same treatment method is used for thermal pipelines.

[0143] 3) Based on the source-side renewable energy output correction, the load-side correction of electric and thermal load, the storage-side correction of charging and discharging efficiency, as well as the original fault scenario and the fault scenario after reinforcement, a resilience enhancement planning model is constructed. The optimization objective is to minimize the sum of investment cost, load loss cost and operating cost. The sample average approximation algorithm is used to solve the resilience enhancement planning model to obtain the optimal reinforcement scheme and disaster dispatch scheme.

[0144] 3.1) Handling exogenous uncertainties

[0145] In addition to the endogenous uncertainties arising from the reinforcement decision-making process, the predicted values ​​of wind power, photovoltaic power output, and electric heating load fluctuate during the cold wave, constituting exogenous uncertainties. This embodiment employs a split-Brow bar combined chance constraint to model these fluctuations, ensuring that the planning scheme meets the safety constraints with a high probability.

[0146] For renewable energy power generation, Joint opportunity constraints on wind turbine and photovoltaic power output for the probability of default:

[0147]

[0148] in Represents a probability function. The Bonferroni inequality will... The constraints are evenly distributed across each constraint. While this leads to higher confidence requirements for each individual constraint and makes the overall model more conservative, it significantly reduces the complexity of solving the model. Take a wind turbine as an example:

[0149]

[0150] in This represents the probability of wind turbine default. The parameters required for the joint opportunity constraint are: , , ,and .in, and These are the perturbation coefficients of the uncertain moment set. It is the CvaR / SOCP safety factor. It is the inverse CDF (quantile function) of the standard normal distribution. This is the prediction standard deviation coefficient of the wind turbine. Next, a fuzzy set is constructed to obtain the upper and lower bounds of the torque uncertainty set:

[0151]

[0152]

[0153]

[0154] in, and These are the lower and upper bounds of the predicted wind turbine output, respectively. Finally, the CvaR safety approximation is used and written as a directly solvable SOCP constraint:

[0155]

[0156] in, This takes into account the upper limit of wind turbine output, which is subject to fluctuations and randomness. The same applies to photovoltaic power.

[0157] Load also needs to consider its inherent predictability volatility. Unlike the former, renewable energy generation generally declines with the arrival of cold waves, while load shows the opposite trend. Therefore, the equivalent safety boundary of the one-dimensional CvaR / SOCP load in the linear case is expressed as:

[0158]

[0159] The same applies to heat load.

[0160] 3.2) Constructing a resilience-enhancing planning model

[0161] This embodiment employs a two-stage mixed integer stochastic programming model. The first stage involves deciding on reinforcement plans before the cold wave arrives, and the second stage involves disaster relief scheduling under various scenarios after the cold wave occurs.

[0162] (1) Objective function

[0163] The objective is to minimize total cost, including investment cost, loss-of-load cost, and operating cost:

[0164]

[0165]

[0166]

[0167]

[0168] in, For investment costs, For loss of load cost, Operating costs. To increase the cost of reinforcing power lines, Cost of reinforcing heating pipelines. and These are the lengths of the power distribution lines and the heating pipes, respectively. It is the number of test scenarios. and These are electrical loads. and thermal load unit cost , , , , and These are, respectively, the power transmitted from the upstream power grid, the active power output of the combined heat and power unit, the power output of the wind turbine, the power output of the photovoltaic system, the energy storage discharge power, and the heat output of the heat pump. , , , , as well as These are their unit costs. and These are the distribution network node set and the heating network node set, respectively.

[0169] (2) Constraints

[0170] I. Constraints of Power Distribution Network:

[0171] Distflow constraints:

[0172]

[0173] In the formula, Represented by node The set of child nodes of the parent node's path. Represented by node The set of parent nodes for the lines of the child nodes. and These refer to the active power and reactive power transmitted through the line, respectively. For the current in the line, and These are the resistance and reactance of the line, respectively. and These represent the active power and reactive power injected into the node, respectively, and are specifically expressed by the following formula:

[0174]

[0175] In the formula, The charging power for energy storage, The electrical power consumed by the heat pump , , , and These are the reactive power transmitted from the upper-level power grid, the reactive power output of wind turbines, the reactive power output of photovoltaic power, reactive power loss, and reactive power load demand.

[0176] Because fault conditions of power lines are taken into account, the constraint on branch voltage drop needs to be relaxed using the Big M method:

[0177]

[0178] In the formula, For node voltage, It is a sufficiently large positive number.

[0179] The branch power is controlled by the following exact nonlinear equation derived from Ohm's law:

[0180]

[0181] Due to the nonlinearity of the above equation, it needs to be relaxed into the following second-order cone form:

[0182]

[0183] Power factor constraint:

[0184]

[0185] In the formula, and These are the power factors for wind turbines and photovoltaics, respectively.

[0186] Output constraints of combined heat and power units:

[0187] The operating point of a combined heat and power (CHP) plant must be within a feasible range, and its output electrical and thermal power are determined by the limiting output point. and The output values ​​are linearly combined, and the calculation formula is as follows:

[0188]

[0189] Combination coefficients of extreme point output values satisfy:

[0190]

[0191] Energy storage charging and discharging model:

[0192]

[0193]

[0194]

[0195] In the formula, It is the amount of electricity stored in energy storage. This is the initial amount of energy stored. (Formula) The initial state of charge of the energy storage was determined, and the equation was... Considering charging and discharging losses, a dynamic balance relationship between energy storage capacity and power in adjacent time periods is established, as shown in the equation. To constrain the daily operating cycle of energy storage, it is required that energy storage maintain energy balance at the beginning and end of the scheduling cycle.

[0196] The electro-thermal conversion model of a heat pump:

[0197] In the power balance of a distribution network, heat pumps are modeled as electrical loads that consume active power, while in a heating network, heat pumps operate as heat sources that provide heat energy. The electro-thermal conversion relationship is expressed as follows:

[0198]

[0199] Due to the sharp drop in ambient temperature caused by the cold wave, the coefficient of performance of heat pumps... Significant deterioration:

[0200]

[0201] In the formula, This represents the initial coefficient of performance (COP) of the heat pump. The percentage decrease.

[0202] Grid upper and lower limit constraints:

[0203]

[0204]

[0205]

[0206]

[0207]

[0208]

[0209]

[0210]

[0211]

[0212]

[0213] Mode In This indicates the working status of the energy storage; 1 indicates charging, and 0 indicates discharging.

[0214] II. Heating Network Constraints:

[0215] The heat network elements in this invention include heat sources (combined heat and power units and heat pumps), load nodes, supply water pipes, and return water pipes, with water as the heat transfer medium. Heat energy is transferred from the heat source to the load nodes through the supply water pipes, and then returned through the return water pipes.

[0216] Basic heating network modeling:

[0217] a) Mass flow conservation constraint:

[0218]

[0219] Mode Indicates the mass flow rate of the water supply pipeline and the mass flow rate of the return water pipe They are equal. In the formula... It is a collection of heating pipes.

[0220] b) Mass flow rate upper and lower limit constraints:

[0221]

[0222] In the formula and These are the lower and upper limits of the pipeline's mass flow rate, respectively. This indicates a pipeline malfunction, similar to that in power distribution lines.

[0223] c) Node mass flow balance constraints:

[0224]

[0225] In the formula It is the set of child nodes of the pipe with node n as its parent node. Let n be the set of parent nodes of a pipeline with node n as a child node. This formula indicates that the mass flow rate flowing into a node is equal to the mass flow rate flowing out of the node.

[0226] d) Nodal mixing temperature constraints:

[0227] The first law of thermodynamics states that the total heat power entering a node is equal to the total heat power leaving the node, and the node temperature is determined by the mixing law, as shown in the following equation:

[0228]

[0229] In the formula Indicates the pipe temperature. This indicates the node temperature.

[0230] The temperature at the starting point of the pipeline is equal to the temperature at the node where it is located.

[0231]

[0232] e) Pipeline temperature upper and lower limits constraints:

[0233]

[0234] f) Pipeline unload constraint:

[0235] The following formula calculates the pipe outlet temperature based on a heat conduction model, describing the temperature decay of hot water during pipe transportation and reflecting the temperature drop effect caused by heat dissipation along the pipe:

[0236]

[0237] In the formula Indicates the temperature of the underground environment. It is the thermal conductivity of the pipe. The cross-sectional area of ​​the pipe. The density of water, This is the specific heat capacity of water.

[0238] g) Node thermal power balance constraints:

[0239]

[0240] In the formula Indicates the thermal power injected into the node. For the heat output of the combined heat and power unit. It can be calculated using the following formula:

[0241]

[0242] Similarly, thermal power demand This can be expressed as the energy difference between the end of the water supply pipe and the beginning of the return pipe:

[0243]

[0244] Heating network reconstruction:

[0245] When both mass flow rate and temperature are variables, the formula - , , , The constraints are nonlinear. Therefore, thermal network reconstruction is essential, as it can significantly reduce model complexity and improve computational efficiency. The first step in thermal network reconstruction is to construct auxiliary heat variables:

[0246]

[0247] Auxiliary heat variables Unifying the supply and return pipelines into a single pipeline represents a unified heat power at the end or beginning of the heat pipe. Therefore, the formula... Japanese style Available Japanese style replace:

[0248]

[0249]

[0250] The heating network reconfigured through the above simplification process is a linear model, independent of mass flow rate and water temperature.

[0251] The following formula represents the upper and lower limits of the auxiliary heat variable:

[0252]

[0253] In the reconstructed heating network, the heat loss in the pipes is expressed as:

[0254]

[0255] This formula can be replaced by the following formula. In the formula middle, Since it is close to 0, the expression can be rewritten as:

[0256]

[0257] Since the heat loss along the heat pipe is much smaller than the actual heat demand at the nodes, its minimum allowable value can be used instead of the formula. The inlet temperature variable in the equation can be used without significantly reducing accuracy. Ultimately, it can be rewritten as:

[0258]

[0259] 3.3) Solve using the SAA algorithm

[0260] Because the above model contains many discrete scenarios (including fault scenarios and renewable energy / load fluctuation scenarios), direct solution is difficult. This embodiment uses the SAA algorithm to solve the model, such as... Figure 2 As shown, its core steps are:

[0261] 3.3.1) Generating a Sample Set: Based on the scenario generation method mentioned in step 2, generate M batches of fault scenarios for both the original and hardened fault scenarios, with N scenarios in each batch, as test scenarios. Then generate N more fault scenarios using the same method. E One scenario was used as the evaluation scenario.

[0262] 3.3.2) Batch Solving for Candidate Solutions: The test scenario generated in the previous step is solved in batches. The expected cost is approximated by the sample mean, resulting in M ​​candidate reinforcement solutions. The objective function for this step is:

[0263]

[0264] In the formula, Let N be the average cost of the m-th batch of N scenarios. and To strengthen decision variables and their unit costs, Decision variables and model variables The functional relationship, The coefficient matrix, It is a constant matrix.

[0265] 3.3.3) Evaluate candidate solutions: Substitute each candidate solution into the evaluation scenario and calculate its actual average total cost. Select the solution with the lowest average cost as the optimal solution. The average cost of the m-th candidate solution is expressed as:

[0266]

[0267] 3.3.4) Quality Assessment: Calculate the lower bound estimate and upper bound estimate and their confidence intervals, and quantify the approximate accuracy:

[0268]

[0269]

[0270]

[0271]

[0272] in, and These are the lower bound estimate and the upper bound estimate, respectively. and These are their variances. If we take α' as the confidence level, then the confidence interval is:

[0273]

[0274] Among them, t α’ / 2,M-1 denoted by z, the quantile of the t-distribution, particularly the upper α' / 2 quantile of the t-distribution with M−1 degrees of freedom, is used to estimate the mean in small sample cases where the population standard deviation is unknown. α’ / 2 The quantile represents the standard normal distribution, specifically the upper α' / 2 percentile of the standard normal distribution, and is applicable to situations with large samples or when the population standard deviation is known.

[0275] 4) Reinforce the power lines and heating pipelines of the integrated energy system according to the optimal reinforcement plan, and control the generator sets, cogeneration units, heat pumps and energy storage equipment to provide power and heat in coordination according to the disaster dispatch plan.

[0276] Before the actual cold wave arrives, insulation layers are added to designated power lines and heating pipelines according to the optimal reinforcement scheme obtained from the solution. During the cold wave, the output of each generator unit (including thermal power, wind power, photovoltaic, energy storage, combined heat and power, heat pumps, etc.) is adjusted in real time according to the disaster dispatch plan for each scenario, and power and heat coordinated dispatch is carried out to minimize the load loss while ensuring the safe operation of the system.

[0277] Compared with the prior art, the present invention has the following advantages:

[0278] This invention overcomes the shortcomings of existing technologies that only focus on a single energy network or simplify the impact of disasters by performing refined disaster modeling on all aspects of the integrated energy system, including the source, grid, load, and storage, under cold waves. It can comprehensively capture the multi-dimensional damage mechanisms of cold waves on the electro-thermal coupled system, providing accurate basic data for resilience enhancement decisions.

[0279] This invention introduces a model to reduce the probability of failure by strengthening decisions, treating strengthening measures as reducing the probability of failure rather than completely eliminating it, thus retaining the residual failure probability and realistically reflecting the inherent uncertainties in engineering practice. By combining exogenous renewable energy output fluctuations and load forecasting deviations with the joint opportunity constraint of the Bruker bar, it simultaneously addresses both decision-dependent and decision-independent uncertainties, avoiding overly optimistic or conservative planning schemes and improving the adaptability and reliability of strengthening schemes in real cold wave scenarios.

[0280] This invention employs a two-stage mixed integer stochastic programming framework, aiming to minimize the sum of investment cost, load shedding cost, and operating cost, thus balancing economy and resilience. It utilizes a sample average approximation algorithm for efficient solution, and through batch sampling, candidate scheme evaluation, and confidence interval calculation, significantly reduces computational complexity while ensuring solution quality, making it suitable for planning problems in large-scale integrated energy systems. Simultaneously, it employs Distflow power flow constraints and auxiliary heat flow linearization constraints to ensure the accurate solvability of operational constraints in the power and thermal networks, improving the feasibility and rationality of scheduling schemes.

[0281] This invention works synergistically from two aspects: pre-disaster reinforcement and proactive defense, and multi-energy coordinated scheduling during disasters. It effectively blocks the propagation of chain failures caused by cold waves, and achieves synergistic optimization of the economy and resilience of the integrated energy system with limited investment. It significantly improves the continuous power and heat supply capacity and anti-disturbance capability of the integrated energy system under cold waves.

[0282] Example 3:

[0283] This embodiment provides a comprehensive energy system cold wave resilience enhancement system that considers both endogenous and exogenous uncertainties, including:

[0284] The disaster modeling module is used to construct a multi-component disaster model of the integrated energy system under extreme cold waves. It modifies and models the renewable energy output on the source side, the failure probability of the grid-side lines and pipelines, the electricity and heat load demand on the load side, and the energy storage efficiency on the storage side to obtain the system operating parameters under the impact of disasters.

[0285] The uncertainty modeling module is used to establish exogenous uncertainty models and endogenous uncertainty models based on system operating parameters. The exogenous uncertainty model is used to characterize the stochastic fluctuation characteristics of the decline in renewable energy output and the surge in electricity and heat load demand under extreme cold waves. The endogenous uncertainty model is used to characterize the coupled impact characteristics of disaster prevention and reinforcement decisions on the failure probability of distribution network lines and heating pipelines.

[0286] The stochastic programming module is used to construct a two-stage mixed-integer stochastic programming model based on the exogenous uncertainty model and the endogenous uncertainty model. The first stage of the two-stage mixed-integer stochastic programming model is the disaster prevention and reinforcement decision-making stage, and the second stage is the disaster scheduling stage.

[0287] The solution module is used to solve the two-stage mixed integer stochastic programming model using the SAA algorithm to obtain the optimal reinforcement scheme and the optimal scheduling strategy;

[0288] The scheduling execution module is used to perform pre-disaster reinforcement of power distribution lines and heating pipelines according to the optimal reinforcement plan, and to perform multi-energy coordinated scheduling of the integrated energy system during extreme cold waves according to the optimal scheduling strategy.

[0289] Example 4:

[0290] To verify the effectiveness and impact of this invention, this embodiment uses a comprehensive electrothermal coupling system consisting of 33 IEEE nodes and 18 heating network nodes as an example, and sets up the following 5 sets of comparative calculation examples:

[0291] Example 1 only hardens the distribution network and does not consider dual uncertainties. Examples 2-5 all perform dual hardening on the integrated electric heating system. Example 2 only considers endogenous uncertainties, Example 3 only considers exogenous uncertainties, and Examples 4 and 5 both consider dual uncertainties. Example 5 is a robustness test, i.e., only performing preliminary solutions under the most severe cold wave scenario. All the above comparative examples only reflect the different test scenarios in the preliminary solution part of the SAA algorithm, while the evaluation part considers dual uncertainties.

[0292] The result of the total system cost is as follows Figure 3 As shown, the results indicate that Example 4, by considering both uncertainties and implementing dual reinforcement, has the lowest average cost in practical engineering applications, demonstrating the significant improvement in the resilience and economy of integrated energy systems achieved by this invention. Example 5, on the other hand, demonstrates the superior robustness of the resilience enhancement framework of this invention, exhibiting a certain degree of effectiveness even in extremely harsh engineering environments.

Claims

1. A method for enhancing the cold wave resilience of a comprehensive energy system considering both endogenous and exogenous uncertainties, characterized in that, Includes the following steps: S1: Construct a multi-component disaster model of the integrated energy system under extreme cold wave, and modify the model for the source-side renewable energy output, grid-side line and pipeline failure probability, load-side electric and heat load demand, and storage-side energy storage efficiency to obtain the system operating parameters under the influence of disaster. S2: Based on system operating parameters, exogenous uncertainty model and endogenous uncertainty model are established respectively; exogenous uncertainty model is used to characterize the random fluctuation characteristics of the decline in renewable energy output and the surge in electricity and heat load demand under extreme cold waves; endogenous uncertainty model is used to characterize the coupled influence characteristics of disaster prevention and reinforcement decisions on the failure probability of distribution network lines and heating pipelines. S3: Based on exogenous uncertainty models and endogenous uncertainty models, a two-stage mixed integer stochastic programming model is constructed. The first stage of the two-stage mixed integer stochastic programming model is the disaster prevention and reinforcement decision-making stage, and the decision variables include the insulation layer reinforcement scheme of the distribution network line and the insulation layer reinforcement scheme of the heating pipeline. The second stage of the two-stage mixed integer stochastic programming model is the disaster dispatching stage, and the decision variables include the unit output, energy storage charging and discharging, load reduction and network operation strategy under various scenarios. S4: The SAA algorithm is used to solve the two-stage mixed integer stochastic programming model to obtain the optimal reinforcement scheme and the optimal scheduling strategy; S5: Conduct pre-disaster reinforcement of power distribution lines and heating pipelines according to the optimal reinforcement scheme, and conduct multi-energy coordinated scheduling of the integrated energy system during extreme cold waves according to the optimal scheduling strategy.

2. The method for enhancing the cold wave resilience of a comprehensive energy system considering endogenous and exogenous uncertainties according to claim 1, characterized in that, The construction of the multi-component disaster model in step S1 includes: Source-side model: The influence of wind turbine blade icing on power output is corrected based on the Makkonen icing model, and the photovoltaic power output is corrected based on the temperature-snow coupling effect; Grid-side models: A fault probability model for distribution network lines is established based on ice thickness and wind speed; a fault probability model for heating pipelines is established based on minimum temperature difference and exposure time. Load-side model: A temperature-corrected model of the electrical-thermal load is established based on the temperature sensitivity coefficient; Storage-side model: A temperature-corrected model for energy storage charging and discharging efficiency is established based on the temperature decay coefficient.

3. The method for enhancing the cold wave resilience of a comprehensive energy system considering endogenous and exogenous uncertainties according to claim 2, characterized in that, The establishment of the exogenous uncertainty model in step S2 includes: A1: The combined uncertainty of wind turbine output, photovoltaic output, electricity demand and heat demand is characterized by the sub-Bruker joint chance constraint method. The sub-Bruker joint chance constraint method constructs fuzzy sets based on the mean and covariance information of the uncertain variables, without assuming precise probability distributions. A2: The joint opportunity constraint is decomposed into individual opportunity constraints using the Bonferroni inequality, and the individual opportunity constraints are transformed into solvable second-order cone constraints based on the conditional value-at-risk security approximation.

4. The method for enhancing the cold wave resilience of a comprehensive energy system considering endogenous and exogenous uncertainties according to claim 3, characterized in that, In step A2, the method for decomposing the joint opportunity constraint into individual opportunity constraints using the Bonferroni inequality is as follows: The upper limit of the joint constraint violation probability is evenly distributed to each individual constraint to obtain the upper limit of the individual constraint violation probability corresponding to each uncertainty source; Based on the moment uncertainty set and the conditional risk value security approximation, each individual opportunity constraint is transformed into a second-order cone programming constraint, resulting in the safe output boundary or safe load boundary for each uncertainty source.

5. The method for enhancing the cold wave resilience of a comprehensive energy system considering endogenous and exogenous uncertainties according to claim 4, characterized in that, The establishment of the endogenous uncertainty model in step S2 includes: B1: Establish a failure probability model for power distribution lines and heating pipelines based on vulnerability curves; vulnerability curves characterize the functional relationship between component failure probability and extreme cold wave intensity; B2: The vulnerability curve is shifted downwards based on the disaster prevention and reinforcement decision to obtain the conditional failure probability after reinforcement; the magnitude of the downward shift represents the degree to which the reinforcement measures reduce the component failure probability. B3: Generate component failure scenarios based on Monte Carlo sampling, and determine the actual operating status of components in each scenario based on the hardened conditional failure probability.

6. The method for enhancing the cold wave resilience of a comprehensive energy system considering endogenous and exogenous uncertainties according to claim 5, characterized in that, The process of establishing the failure probability model of the power distribution network lines and heating pipelines based on the fragility curve in step B1 includes: For distribution network lines, the probability of ice accumulation fault is calculated based on the relationship between real-time ice thickness and maximum tolerable ice thickness, and the probability of strong wind fault is calculated based on the relationship between real-time wind speed and design wind speed. The combined probability of ice accumulation fault and strong wind fault is obtained by weighted combination. For heating pipelines, a functional relationship between failure probability and minimum temperature difference, low temperature exposure time, pipeline service life and corrosion layer damage density is established based on a logistic regression model.

7. A method for enhancing the cold wave resilience of a comprehensive energy system considering endogenous and exogenous uncertainties according to claim 1, characterized in that, The objective function of the two-stage mixed integer stochastic programming model in step S3 is to minimize the total expected cost, which includes reinforcement investment cost, load reduction penalty cost and system operation cost. The cost of reinforcement investment includes the installation cost of insulation layers for power distribution lines and heating pipelines; Load shedding penalty costs include electricity load shedding penalty costs and heat load shedding penalty costs; System operating costs include upstream power grid purchase costs, combined heat and power (CHP) unit power generation costs, wind turbine power generation costs, photovoltaic power generation costs, energy storage discharge costs, and heat pump heating costs.

8. A method for enhancing the cold wave resilience of a comprehensive energy system considering endogenous and exogenous uncertainties according to claim 7, characterized in that, The constraints of the two-stage mixed integer stochastic programming model in step S3 include: Distribution network distflow constraints include node power balance constraints, branch voltage drop constraints, and branch power constraints; Linearization constraints for heating networks include auxiliary heat variable constraints, heat loss constraints, and nodal heat power balance constraints; Energy storage operation constraints include dynamic balance constraints of state of charge, charging and discharging power constraints, and daily operation cycle constraints; Operating constraints for combined heat and power (CHP) units include feasible operating domain constraints and extreme point combination constraints; Load reduction constraints include load reduction not exceeding load demand constraints and constant power factor constraints; Component operational state constraints include fault relaxation constraints and hardened mutual exclusion constraints based on the Big M method.

9. A method for enhancing the cold wave resilience of a comprehensive energy system considering endogenous and exogenous uncertainties according to claim 8, characterized in that, The process of solving the two-stage mixed integer stochastic programming model using the SAA algorithm in step S4 includes: C1: Generate multiple sets of fault scenario sample sets, each set containing N scenarios; C2: Solve independently for each sample set to obtain M candidate reinforcement schemes; C3: Evaluate the M candidate reinforcement schemes using a large-scale evaluation scenario set, and select the candidate scheme with the lowest average cost as the optimal reinforcement scheme; C4: Calculate the confidence interval of the optimal solution, quantifying the gap between the quality and optimality of the solution.

10. A comprehensive energy system cold wave resilience enhancement system considering endogenous and exogenous uncertainties, characterized in that, The system for implementing the method according to any one of claims 1 to 9 comprises: The disaster modeling module is used to construct a multi-component disaster model of the integrated energy system under extreme cold waves. It modifies and models the renewable energy output on the source side, the failure probability of the grid-side lines and pipelines, the electricity and heat load demand on the load side, and the energy storage efficiency on the storage side to obtain the system operating parameters under the impact of disasters. The uncertainty modeling module is used to establish exogenous uncertainty models and endogenous uncertainty models based on system operating parameters. The exogenous uncertainty model is used to characterize the stochastic fluctuation characteristics of the decline in renewable energy output and the surge in electricity and heat load demand under extreme cold waves. The endogenous uncertainty model is used to characterize the coupled impact characteristics of disaster prevention and reinforcement decisions on the failure probability of distribution network lines and heating pipelines. The stochastic programming module is used to construct a two-stage mixed-integer stochastic programming model based on the exogenous uncertainty model and the endogenous uncertainty model. The first stage of the two-stage mixed-integer stochastic programming model is the disaster prevention and reinforcement decision-making stage, and the second stage is the disaster scheduling stage. The solution module is used to solve the two-stage mixed integer stochastic programming model using the SAA algorithm to obtain the optimal reinforcement scheme and the optimal scheduling strategy; The scheduling execution module is used to perform pre-disaster reinforcement of power distribution lines and heating pipelines according to the optimal reinforcement plan, and to perform multi-energy coordinated scheduling of the integrated energy system during extreme cold waves according to the optimal scheduling strategy.

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