Electric heating system distribution robust load recovery method and system considering secondary strike

Abstract

The invention discloses an electric heating system distribution robust load recovery method and system considering secondary strike, and belongs to the technical field of comprehensive energy system load recovery. The method comprises the following steps: firstly, constructing a virtual energy storage model based on thermal inertia characteristics of a regional heat supply network, and embedding the virtual energy storage model into an electric heating system two-stage plan-implementation load recovery preliminary model; then, a fuzzy set is constructed based on fault data to describe secondary strike uncertain event distribution, a support set is constructed to capture the fault position and time of a vulnerable branch, and an infinite dimension optimization problem of the model is converted into a finite dimension problem through an infinite dimension dual technology; and finally, after non-convex constraints in the to-be-solved model are converted into linear constraints, an improved column and constraint generation algorithm is adopted to iteratively solve the two-stage plan-implementation load recovery model, and an optimal load recovery scheme is obtained. The method can effectively improve the robustness of the system to cope with post-disaster secondary strike, improve the emergency resource utilization rate, and guarantee the reliable recovery of the system after the disaster.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of comprehensive energy system load recovery, and particularly relates to a method and system for distributed robust load recovery of an electric-thermal system considering secondary strikes. BACKGROUND

[0002] With the advancement of global energy transformation, electric-thermal comprehensive energy systems have become one of the key paths to achieve the zero-carbon target, and their operation safety and disaster resistance are increasingly valued. In recent years, extreme natural disasters such as hurricanes, floods, and ice disasters have caused large-scale power outages in power grids, exposing the vulnerability of traditional power systems under extreme events, and there is an urgent need to develop efficient load recovery strategies to ensure critical load power supply and reduce economic losses.

[0003] However, the existing electric-thermal comprehensive energy system load recovery technology has the following key defects: first, existing strategies focus on system recovery after the initial impact of extreme events, ignoring subsequent possible secondary random strikes (such as secondary floods, line re-faults, etc.), which makes the original recovery scheme invalid and difficult to continuously guarantee the power supply reliability of critical loads. Second, regional heating networks have virtual energy storage characteristics due to thermal inertia, but existing technologies either do not model this characteristic or only equivalent it to centralized energy storage, without considering the actual physical constraints of the pipeline, and unable to improve energy flexibility during the load recovery process and reduce heat load shedding through virtual energy storage. Third, in terms of optimization methods, traditional load recovery relies on stochastic programming or robust optimization. Stochastic programming requires accurate probability distribution, but fault distribution is difficult to obtain under extreme events, and overfitting may occur, leading to invalidity of the scheme under deviated samples. Robust optimization method only considers the worst-case scenario boundary, which is too conservative, resulting in a sharp increase in recovery cost and low resource utilization. Finally, existing recovery strategies usually independently use microgrid reconstruction, mobile emergency generator configuration or standby scheduling, lack of multi-strategy coordination mechanism, and difficult to fully utilize the overall efficiency of emergency resources, limiting the improvement of critical load recovery rate.

[0004] In summary, the existing electric-thermal comprehensive energy system load recovery method is difficult to handle the uncertainty of secondary strikes, effectively utilize the virtual energy storage potential of regional heating networks, and balance robustness and economy during the optimization process when dealing with extreme events. Therefore, there is an urgent need to develop a new load recovery method that can comprehensively address the above challenges. SUMMARY

[0005] The purpose of the present application is to solve the problems in the prior art and provide a method and system for distributed robust load recovery of an electric-thermal system considering secondary strikes.

[0006] The specific technical solutions adopted by the present application are as follows:

[0007] In a first aspect, the present invention provides a method for restoring the load of a split-blower rod in an electrothermal system considering secondary impacts, the specific steps of which are as follows:

[0008] S1: Based on the thermal inertia characteristics of the district heating network, a virtual energy storage model is constructed; a two-stage planning-implementation preliminary load recovery model of the electric heating system embedded with the virtual energy storage model is constructed, which consists of a planning stage and an implementation stage coupled together;

[0009] S2: Based on historical fault data, construct a support set to capture the location and time of faults in vulnerable branches, and construct a fuzzy set to describe the distribution of uncertain secondary impact events in the planning phase; use the Lagrange duality technique to reconstruct the infinite-dimensional optimization problem in the two-stage planning-implementation load recovery preliminary model constructed in step S1 into a finite-dimensional optimization problem, and obtain the two-stage planning-implementation load recovery model;

[0010] S3: The convexity relaxation technique is used to transform the non-convex constraints in the two-stage planning-implementation load recovery model into linear constraints;

[0011] S4: An improved column and constraint generation algorithm is used to iteratively solve the reconstructed two-stage plan-implementation load recovery model to obtain the optimal load recovery scheme considering post-disaster secondary impacts.

[0012] As a preferred embodiment, the construction of the virtual energy storage model for the district heating network in step S1 is as follows:

[0013] S11: Introduce the concept of fluid micro-elements and calculate the outlet temperature of the pipe using a weighted average method; the outlet temperature of the pipe is equal to the sum of the product of the temperature distribution coefficient C1 and the outlet temperature of the Kth fluid micro-element in the pipe at the current moment, and the product of the temperature distribution coefficient C2 and the outlet temperature of the (K+1)th fluid micro-element at the current moment; where the temperature distribution coefficients C1 and C2 are determined by the mass flow rate of the fluid micro-element and its flow time in the pipe;

[0014] S12: Establish the time coupling relationship between the pipe inlet temperature and the outlet temperature, as follows:

[0015] ;

[0016] In the formula: This represents the outlet temperature of pipe p in the water supply and return networks at the current moment. and C3 and C4 represent the inlet temperatures of pipe p in the supply and return water networks at two different historical moments, respectively; C3 and C4 represent the corresponding heat loss coefficients. t A Indicates the current ambient temperature; and Let C3 and C4 represent the pipe and time sets, respectively; where the heat loss coefficients C3 and C4 are related to the pipe length, friction coefficient, specific heat capacity of the fluid, and mass flow rate of the fluid.

[0017] Preferably, in step S1, the planning phase involves formulating a recovery plan under the premise of satisfying the various physical and logical constraints of this phase. The recovery plan takes minimizing the total cost of this phase as the objective function, while also considering the worst-case scenario caused by the uncertainty of the secondary attack, and incorporating the expected losses caused by the implementation phase into the decision objectives of the planning phase.

[0018] The implementation phase is based on the recovery plan formulated in the planning phase, combined with the specific scenario of the actual secondary attack. By adjusting the operational variables in this phase, the objective function is to minimize the load reduction while meeting all operational safety constraints.

[0019] As a preferred embodiment, step S2 is as follows:

[0020] The support set limits the number of branches that fail simultaneously at any given time to a preset upper limit, and also limits the total cumulative power outage time of all faulty branches to a preset total time threshold.

[0021] The fuzzy set is a set of distributions defined around an empirical distribution formed from historical data; the boundary of the set of distributions is defined by the Wasserstein metric distance and is controlled by the radius of the fuzzy set.

[0022] The fuzzy set Specifically as follows:

[0023] ;

[0024] Fuzzy set radius ;

[0025] In the formula: Let C represent the confidence level, and C represent the fuzzy set radius distance coefficient, which is determined by a [missing information - likely a variable or parameter]. The optimization problem, presented as the optimization variable, is as follows:

[0026] ;

[0027] In the formula: This represents the optimization variable used to calculate the radius distance coefficient of the fuzzy set. Represents the historical values ​​of random variables in the selected scenario s. The average value; p s This represents the probability of the corresponding scenario occurring.

[0028] Furthermore, the infinite-dimensional duality technique described in step S2 is as follows:

[0029] S21: Identify the infinite-dimensional optimization problem in the planning phase of the two-stage planning-implementation load recovery preliminary model, expand the pursuit function of the problem, and introduce the corresponding dual variable for each constraint;

[0030] S22: Based on Lagrange duality theory, the dual variables are substituted to obtain the dual form of the expanded tracing function, which transforms the problem of maximizing the probability distribution into an equivalent problem of minimizing the dual variables, thus obtaining a solvable finite-dimensional optimization problem.

[0031] S23: Substitute the reconstructed finite-dimensional optimization problem into the two-stage planning-implementation load recovery preliminary model to obtain the two-stage planning-implementation load recovery model.

[0032] As a preferred embodiment, in the two-stage plan-implementation load restoration model, the planning stage takes minimizing the total cost of the stage as the objective function and establishes an optimization model that includes three major constraint systems: mobile emergency power allocation, defensive microgrid reconfiguration, and unit standby capacity setting.

[0033] The implementation phase aims to minimize operating costs by establishing an optimization model that includes three major constraint systems: equipment operation, power distribution network flow, and district heating network flow, in order to achieve real-time voltage and power support.

[0034] Furthermore, the defensive microgrid reconfiguration constraint system includes operational constraints and microgrid radial topology constraints;

[0035] The operational constraints are used to limit the disconnection of branches between each bus and branch microgrid and between microgrids.

[0036] The radial topology constraint of the microgrid is used to ensure that the internal structure of the microgrid is a tree-like, acyclic network and a connected network. Specifically, it includes: constraining the internal structure of the microgrid to be a tree-like, acyclic network by ensuring that the difference between the number of buses and the number of branches is equal to the number of buses at the root node; and constraining the internal structure of the microgrid to be a connected network by constructing a virtual commodity flow model, injecting virtual flows at the root node bus, generating corresponding sinks in the remaining non-root node buses, and limiting the virtual flows to be transmitted only in closed branches within the microgrid.

[0037] As a preferred embodiment, the convexity relaxation technique described in step S3 is as follows:

[0038] S31: For defensive microgrid reconfiguration during the planning phase, introduce binary auxiliary variables. and And define the logical state: when the condition When established, define If equal to 1, otherwise defined Equals 0; when the condition When established, define If equal to 1, otherwise defined Equal to 0; introduce a sufficiently small coefficient and a sufficiently large coefficient Two sets of linear constraints are established to achieve the above-mentioned mandatory relationship:

[0039] ;

[0040] In the formula: Represents the root node busbar The case where it is assigned to microgrid m; Indicates the root node bus The flow of goods generated at the location;

[0041] S32: To address the dual impact of the branch state on the planning phase—both the defensive microgrid reconstruction results and the worst-case secondary attack event—on the implementation phase, a coordination variable is constructed to represent the coordination relationship between the two. The specific constraints are as follows: Ensure the coordination variables The value of is simultaneously less than or equal to the value of the random variable for the second-strike event under the worst-case distribution and the result of the defensive microgrid reconstruction during the planning phase; and ensures that the coordination variable The value of must be greater than or equal to the value of the random variable of the second-strike event under the worst distribution and the result of the defensive microgrid reconstruction in the planning phase.

[0042] As a preferred embodiment, the solution process described in step S4 is as follows:

[0043] S41: The reconstructed two-stage planning-implementation load recovery model is split into a main problem optimized for minimization and sub-problems optimized for maximization; a convergence tolerance is set. Initialize the lower bound LB to The upper UB is And initialize the iteration count c=1;

[0044] S42: Solve the main problem to obtain the optimal decision scheme in the planning phase, including mobile emergency power allocation, defensive microgrid reconfiguration scheme, and backup capacity configuration; during the iteration process, the main problem continuously accumulates optimality cutting planes from feedback from subproblems, so that its decision scheme gradually enhances its adaptability to uncertainty; after the solution is completed, the lower bound LB is updated using the objective value of the main problem.

[0045] S43: Substitute the optimal solution obtained from the main problem, and solve the corresponding subproblems for each uncertain secondary attack scenario; after summarizing the evaluation results under each scenario, update the upper bound UB using the sum of the optimal values ​​of the subproblems and the optimal values ​​of the main problem in this iteration;

[0046] S44: Calculate the relative difference based on the updated lower bound LB and upper bound UB, and compare it with the convergence tolerance. Compare and determine whether convergence has occurred;

[0047] S45: If the convergence condition is met, output the current optimal solution; otherwise, add the new constraints and cutting plane generated by the subproblem to the main problem, update the iteration count c→c+1, and repeat steps S42~S44 until convergence, to obtain the optimal load recovery scheme considering post-disaster secondary impact.

[0048] In a second aspect, the present invention provides a load recovery system for a split-blower rod of an electrothermal system that takes into account secondary impacts, the system being used to implement the load recovery method for a split-blower rod of an electrothermal system that takes into account secondary impacts as described in any of the first aspects.

[0049] Compared with the prior art, the present invention has the following advantages:

[0050] (1) This invention proposes a novel load recovery strategy for integrated electric and thermal energy systems. This strategy constructs a multi-level recovery and defense system through integrated and collaborative defensive microgrid reconfiguration, emergency mobile power supply allocation and unit standby capacity formulation. It effectively ensures the continuous power supply capability of critical loads during load recovery and significantly enhances the survivability and power supply reliability of the system in response to subsequent random secondary impact events.

[0051] (2) The present invention innovatively models the thermal inertia of the district heating system as virtual energy storage and integrates it as an emergency resource into the implementation process of the load recovery strategy. This can enhance the flexibility reserve before the second impact, thereby reducing the heat load reduction in the district heating system after the thermal integrated energy system is affected.

[0052] (3) This invention integrates fuzzy set and support set phases in a robust optimization method to accurately describe the uncertainty of secondary impact events in an integrated electrothermal energy system. This model considers potential probability distributions, including the worst-case scenario, through fuzzy sets and rationally defines uncertainty boundaries using support sets. This avoids the dependence of traditional stochastic programming on precise probabilities while overcoming the overly conservative nature of classical robust optimization.

[0053] (4) This invention utilizes the logical constraint convexity relaxation technique to transform the non-convex constraints in the reconstructed two-stage plan-implementation load recovery model into linear constraints, and decomposes the problem into a main problem of load recovery strategy formulation and a sub-problem describing the worst-case distribution. An improved column and constraint generation algorithm is proposed to iteratively solve the above main problem and sub-problems. This ensures the executability and computational efficiency of the optimized strategy obtained in actual engineering. Attached Figure Description

[0054] Figure 1The overall flowchart of the method for restoring the load of the split-blower rod in an electric heating system provided by the present invention is shown below.

[0055] Figure 2 This is a schematic diagram of the improved column and constraint generation algorithm of the present invention. Detailed Implementation

[0056] The present invention will be further described and illustrated below with reference to the accompanying drawings and specific embodiments. The technical features of each embodiment of the present invention can be combined accordingly, provided that there is no mutual conflict.

[0057] Figure 1 The following is an overall flowchart of the load recovery method provided by the present invention, and the specific operation of each step is as follows.

[0058] Step 1: Considering the thermal inertia characteristics of the district heating network, a virtual energy storage model is proposed and used as an emergency resource. A two-stage planning-implementation load restoration preliminary model for the electric heating system is constructed, as follows:

[0059] (1) Introduce the concept of fluid infinitesimal element and calculate the outlet temperature of the pipe using the weighted average method:

[0060] ;

[0061] ;

[0062] ;

[0063] In the formula: This represents the outlet temperature of pipe p in the water supply and return networks at the current moment. and q represents the pipeline and time set, respectively; subscripts p and t represent the indices of the pipeline and scheduling time in the district heating network, respectively; superscripts s and r indicate the supply and return water networks in the district heating network, respectively; superscripts K and K+1 represent the fluid element indices in the pipeline of the district heating network, respectively; K and q K+1 These represent the mass flow rates of the outflowing fluid element within the corresponding time interval; the superscripts in and out represent the pipe inlet and outlet, respectively. The time interval for the division; Let be the time it takes for a fluid element to flow from the inlet through pipe p to the outlet; and C1 and C2 represent the outlet temperatures of the Kth fluid element and the (K+1)th fluid element in pipe p in the water supply network and return network, respectively, at the current moment; C1 and C2 represent the temperature distribution coefficients of the Kth fluid element and the (K+1)th fluid element, respectively.

[0064] The time-coupled constraint between the inlet and outlet temperatures of the pipe is expressed as:

[0065]

[0066] and These represent the pipes p in the water supply network and return network, respectively. and Inlet temperature at any given time; T t A This represents the current ambient temperature; C3 and C4 represent the corresponding heat loss coefficients, a K and a K+1 These represent their corresponding auxiliary parameters; L p , λ p Let p represent the length of pipe and the coefficient of friction, respectively; c P This indicates the specific heat capacity of the fluid.

[0067] (2) Construct a two-stage planning-implementation load recovery preliminary model for the electric heating system, wherein the first stage is the planning stage and the second stage is the implementation stage;

[0068] The first stage is to meet the requirements. Minimize the total cost of this stage under constraints. Furthermore, it considers the losses that the implementation phase might face under the worst-case probability distribution; given the decisions of the first phase and the second-strike scenario, the second phase adjusts the operational variables of this phase to ensure that... Minimize the load reduction under constraints;

[0069] Specifically as follows:

[0070]

[0071] In the formula: st represents the constraint condition that follows; x and Let A and F represent the continuous and discrete decision variables of the first stage problem, respectively; let F and F represent the coefficient matrices of the continuous and discrete decision variables of the first stage, respectively; let c be the coefficient matrix of the objective function of the first stage; and let b be the coefficients of the right-hand side of the discrete decision variables. A fuzzy set constructed based on fault data; P represents the distribution variable, E p This represents the expectation operator for this distribution; It is a random variable; Let y be the value function of the second-stage problem; y is the decision variable for the second stage. d represents the coordination variable for the second stage; d represents the coefficient matrix of the objective function for the second stage; E, G, and M represent the continuous variable x and the discrete decision variable x for the first stage problem in the second stage problem, respectively. and coordinating variables The coefficient matrix, This represents the coefficient of the right-hand side of the constraint in the second-stage problem.

[0072] Step 2: Based on historical fault data, construct a support set to capture the location and time of faults in vulnerable branches, construct a fuzzy set to describe the distribution of uncertain secondary impact events, and reconstruct the two-stage planning-implementation load recovery preliminary model constructed in Step 1 into a finite-dimensional mixed integer programming problem using the infinite-dimensional duality technique.

[0073] (1) The range of random variables is constructed using support sets to represent the fault state of branches at different time periods, while limiting the number of branches that fail simultaneously at time t to no more than The expression for the support set is shown below:

[0074] ;

[0075] In the formula: Represents the set of branches. Indicates a branch road. This indicates the total disconnection time for all faulty branches in the support cluster. This indicates the maximum number of branches that can fail simultaneously at the current moment. For random variables, and They represent the branches at the current time. The fault situation at that moment and the fault situation after that moment.

[0076] (2) A fuzzy set is established based on the Wasserstein metric distance definition. This distance quantifies the minimum expected distance between the distribution of the random variable and the historical data in the joint distribution.

[0077] ;

[0078] ;

[0079] ;

[0080] In the formula: Represents the true distribution. Represents the empirical distribution. This represents a joint probability distribution that follows both the true distribution and the empirical distribution. Indicates conditional distribution; inf represents the infm operator. and Represent the random variable and its historical values, respectively. This represents the Dirac measure of the s-th sample; Represents the support set, N represents the complete distribution on this support set; sp represents the total number of selected scenes. s This represents the probability of the corresponding scenario occurring.

[0081] Based on the above, the joint probability distribution Substituting the Wasserstein metric distance expression, the formula can be rewritten as:

[0082] ;

[0083] Fuzzy set The distance metric is established based on the revised Wasserstein metric definition, as follows:

[0084] ;

[0085] in The radius of the fuzzy set is shown below.

[0086] ;

[0087] In the formula: Let C represent the confidence level, and C represent the fuzzy set radius distance coefficient, which is determined by a [missing information - likely a variable or parameter]. The optimization problem, presented as the optimization variable, is as follows:

[0088] ;

[0089] In the formula: This represents the optimization variable used to calculate the radius distance coefficient of the fuzzy set. This represents the average historical value of the random variable under the selected scenario s.

[0090] (3) Based on the above definitions of fuzzy sets and support sets, the two-stage planning-implementation load recovery preliminary model proposed in step one can be substituted. However, the integral operation introduced at the same time will lead to the tracing function in the first stage. This problem, represented as an infinite-dimensional optimization problem, is difficult to solve directly. Therefore, it is reconstructed into a finite-dimensional optimization problem using the infinite-dimensional duality technique.

[0091] First, substitute the fuzzy set from step (2) and expand the tracing function from the first stage:

[0092] ;

[0093] In the formula: and These are the dual variables of the corresponding constraints. The dual form of the above formula is obtained based on the Lagrange function:

[0094] ;

[0095] This unifies the optimization direction in the first stage, and also allows us to determine the optimal solution under the worst-case distribution for the s-th scenario based on the optimality condition. It can be represented as:

[0096] ;

[0097] Integrating the above formula into the preliminary two-stage planning-implementation load recovery model proposed in step one, we reconstruct the two-stage planning-implementation load recovery model, as shown in the following expression:

[0098] ;

[0099] Since the optimization direction in the first stage is to obtain the minimum value, it can be guaranteed that when the optimal solution is obtained, the optimization variables are minimized. The optimal solution was obtained.

[0100] Step 3: Optimize the first phase of the two-stage plan – implementing the preliminary load restoration model. The first phase aims to minimize the cost of the load restoration plan, and includes three major constraints: mobile emergency power allocation, defensive microgrid reconfiguration, and unit reserve capacity. The specific objective function is as follows:

[0101] ;

[0102] In the formula: denoted as a set of combined heat and power (CHP) units, where c represents a CHP unit. denoted as a set of mobile emergency power supplies, where g represents a mobile emergency power supply; Let t represent a time set; This represents a collection of electric boilers, where h represents an electric boiler and b represents a combined heat and power unit and an emergency mobile power source.

[0103] , and These represent the start-up, shutdown, and standby costs of the combined heat and power (CHP) unit and the emergency mobile power supply, respectively. , and These indicate the current operating status, start-up status, and shutdown status of the mobile emergency power supply and the combined heat and power unit, respectively. , and These represent the unit standby costs of combined heat and power units, electric boilers, and mobile emergency power supplies, respectively. and These represent the upper and lower reserves of the active power output of the cogeneration unit at the current moment; and These represent the upper and lower reserves of the mobile emergency power supply's active power output at the current moment; and These represent the upper and lower reserve boundaries of the active power consumed by the electric boiler at the current moment.

[0104] The three constraint systems are as follows:

[0105] (1) Constraints on the distribution of mobile emergency power supply

[0106] During the distribution of mobile emergency power supplies, each mobile emergency power supply can only be allocated to a single busbar, and the total number of allocated mobile emergency power supplies cannot exceed the limit. The corresponding constraints are as follows:

[0107] ;

[0108] In the formula: Let i represent the set of buses; This indicates the situation where the mobile emergency power supply is distributed to bus i. This indicates the total number of mobile emergency power supplies.

[0109] (2) Defensive microgrid reconfiguration constraints

[0110] Defensive microgrid reconfiguration decomposes the original network into multiple microgrids by separating or closing the interconnecting switches in the network, while maintaining radial topology constraints within each microgrid. The relationship between buses and branches and their subordinate microgrids can be represented by the defensive microgrid reconfiguration operation constraints, while the radial topology requirements of the microgrid can be represented by the quantitative relationship between buses, branches, and root node buses, as well as single-item flow connectivity constraints.

[0111] 1) Defensive microgrid reconfiguration operation constraints, used to represent the microgrid to which each bus and branch belongs, and the branch disconnection relationships between microgrids. Furthermore, each microgrid requires a bus as the root node bus to maintain consistency with the subsequent radial topology requirements. Specific constraints are as follows:

[0112] ;

[0113] In the formula: Let m represent a set of micronets; , and Indicates busbar busbar With the root node bus The case where it is assigned to microgrid m; Indicates a branch The case where it is assigned to microgrid m; Indicates a branch The switch status on;

[0114] 2) The radial topology of a microgrid requires, on the one hand, that the internal structure of the microgrid be a tree-like, loop-free network, and on the other hand, that it be a connected network. The tree-like, loop-free network structure is represented by the quantitative relationship between the number of buses, branches, and the root node bus. Specifically, it is a mathematical relationship where the difference between the number of buses and the number of branches is equal to the number of buses at the root node, as shown below: ;

[0115] The requirement for a connected network is maintained through a single-item flow constraint, represented as generating a virtual item flow at the root node bus, creating corresponding sinks in all other non-root node buses, and transmitting item flows on branches connected to the root node bus. The single-item flow constraint is represented as:

[0116] ;

[0117] In the formula: and These represent the busbars at the root node, respectively. The flow of goods generated at bus i; and These represent virtual goods flows in different branches, where the subscript ji indicates the branch between bus j and bus i, and the subscript ik' indicates the branch between bus i and bus k'. This indicates that branch ij belongs to the micronetwork. A branch can be represented by either the l index or the ij index. Branch ij represents the branch between bus i and bus j, and so on.

[0118] (3) Unit standby capacity constraints

[0119] 1) The minimum start-up and shutdown time constraints for mobile emergency power supplies and combined heat and power units are as follows:

[0120]

[0121] in: and These represent the minimum start-up and shutdown times for mobile emergency power supplies and combined heat and power units, respectively. , and These represent the current operating status, start-up status, and shutdown status of the mobile emergency power supply and the combined heat and power unit, respectively. and These represent the operating status of the mobile emergency power supply and the combined heat and power unit at the previous and next moments, respectively.

[0122] 2) The standby capacity constraints for combined heat and power (CHP) units are as follows:

[0123] ;

[0124] In the formula: and These represent the uphill power limit and downhill power limit of the combined heat and power unit, respectively. and These represent the minimum and maximum active power output of the combined heat and power unit, respectively. This indicates the current operating status of the combined heat and power unit; This indicates the operating status of the combined heat and power unit at the previous moment; and These represent the upper and lower reserves of the active power output of the cogeneration unit at the current moment; and These represent the upper and lower reserves of the active power output of the combined heat and power unit at the previous moment.

[0125] 3) The standby capacity constraints for mobile emergency power supplies are as follows:

[0126] ;

[0127] In the formula: and These represent the uphill and downhill power output limits of the mobile emergency power supply, respectively. and These represent the minimum and maximum active power output of the mobile emergency power supply, respectively. and These represent the upper and lower reserves of the mobile emergency power supply's active power output at the current moment; and These represent the upper and lower backup boundaries of the mobile emergency power supply's active power output at the previous moment.

[0128] 4) The standby capacity constraints for electric boilers are as follows:

[0129] ;

[0130] In the formula: and These represent the uphill power limit and downhill power limit for the active power consumption of an electric boiler, respectively. and These represent electric boilers. The minimum and maximum active power consumption; and These represent the upper and lower reserve boundaries of the active power consumed by the electric boiler at the current moment, respectively. and These represent the upper and lower reserve boundaries of the active power consumed by the electric boiler at the previous moment, respectively.

[0131] Step 4: Optimize the two-stage plan – implement the second stage of the preliminary load restoration model. The second stage uses minimizing operating costs as the objective function and establishes a three-pronged constraint system including equipment operation, power distribution network flow, and district heating network flow to achieve immediate voltage and power support.

[0132] The operating costs of the second phase consist of unplanned load reduction losses, wind curtailment losses, and unit regulation costs. The specific objective function is as follows:

[0133] ;

[0134] In the formula: and These are the unit penalty costs for power load and heat load, respectively; This represents the penalty cost per unit of wind curtailment power. , and These are the unit operating costs of combined heat and power units, emergency mobile power supplies, and electric boilers, respectively. and These represent the wind power absorption capacity and the predicted power, respectively. This indicates the gas power consumed by the combined heat and power unit. Indicates the active power output of the emergency portable power supply. This indicates the active power consumed by the electric boiler; Represents a node in a power distribution network The electrical power loss at the current moment; Represents the load nodes in the district heating network The power loss due to heat at the current moment; This represents the set of load nodes in a district heating network; Represents the set of load nodes in a power distribution network; This represents a collection of wind turbine units.

[0135] The three constraint systems are as follows:

[0136] (1) Equipment operation constraints

[0137] According to the load restoration plan formulated in the first phase, during the implementation of the second phase, the units can reallocate power according to the planned reserve capacity. The wind turbines can adjust the absorption capacity according to the actual wind power output. The equipment operation constraint boundaries in the second phase are as follows:

[0138] ;

[0139] In the formula: This indicates the active power output of the combined heat and power (CHP) unit. This indicates the active power output of the emergency power supply; This indicates the active power consumed by the electric boiler at the current moment.

[0140] The operating constraints for combined heat and power units and electric boilers are as follows:

[0141] ;

[0142] In the formula: This indicates the thermal power output of the combined heat and power unit; This indicates the gas power consumed by the combined heat and power unit; This indicates the current heat output consumed by the electric boiler. and These represent the efficiency and heat-to-power ratio of a combined heat and power unit, respectively. This indicates the efficiency of an electric boiler.

[0143] (2) Power flow in the distribution network

[0144] The first phase of defensive microgrid reconfiguration ensures a radial topology. The second phase of operation can then leverage the Distflow model to decouple active and reactive power flows, with the following specific constraints:

[0145] ;

[0146] In the formula: This indicates the reactive power output of the combined heat and power unit at the current moment; This indicates the reactive power output of the emergency power supply at the current moment; and These represent the active power and reactive power flowing through the branch at the current moment during the operation of the distribution network; and These represent the starting busbars of branch ij respectively. and end busbar The voltage amplitude at the current moment; and These represent the maximum active power flow and reactive power flow that the branch is allowed to carry, respectively. This represents the slack variable that indicates the voltage drop on that branch. and These represent the resistance and reactance of the branch, respectively; V represents the reference value of the bus voltage. and They represent the busbars respectively. The minimum and maximum amplitudes.

[0147] (3) District heating system power flow

[0148] The district heating system operates in a constant-flow variable-temperature control mode, achieving power distribution within the system by maintaining a constant mass flow rate while changing the temperature of the working fluid in the heating network. Specific constraints are as follows:

[0149] ;

[0150] In the formula: , and These represent the sets of heat source nodes, load nodes, and intermediate nodes in a district heating network, respectively. Represents a node The heat load power at the current moment; and These represent the supply water temperature and return water temperature of the heat source node at the current moment, respectively. and These represent the supply water temperature and return water temperature of the load node at the current moment, respectively. This indicates the mixed temperature at the current moment at the intermediate node of the water supply network and the return water network; and These represent the pipes in the water supply network and the return network, respectively. The inlet temperature and outlet temperature at the current moment; Represents a node The quality flow rate at the current moment; Indicates the pipes in the water supply network and return network. The mass flow rate at the current moment; c P This indicates the specific heat capacity of the fluid.

[0151] Step 5: Solve the two-stage plan-implementation load recovery model reconstructed in Step 2. The specific steps are as follows:

[0152] (1) Convexation treatment

[0153] In the two-phase planning-implementation load recovery model, the defensive microgrid reconfiguration in the first phase requires determining the location of the root node bus and then using this to determine the microgrid partitioning, which is difficult to solve directly. Therefore, a logical constraint convex relaxation technique is proposed. A binary auxiliary variable is introduced. and And define the logical state: when the condition When established, define If equal to 1, otherwise defined Equals 0; when the condition When established, define If equal to 1, otherwise defined Equals 0. Introduce a sufficiently small coefficient. and a sufficiently large coefficient Two sets of linear constraints are established to achieve the above-mentioned mandatory relationship:

[0154] ;

[0155] In the second phase, the branch state is simultaneously affected by both the defensive microgrid reconstruction results from the first phase and the worst-case secondary attack event. The coordination relationship between the two is determined by variables. The specific constraints are as follows:

[0156] ;

[0157] In the formula: This indicates the results of the defensive microgrid reconstruction in the first phase; A random variable representing a second-strike event under the worst-case distribution; This represents the coordinating variable between the two.

[0158] In the two-stage plan-implementation load recovery model reconstructed in step two, the first-stage continuous decision variables... The commodity flow generated at the root node bus in step three Single commodity flow on branch roads Combined heat and power units have active power output on standby. Standby power output of cogeneration units Portable emergency power supply with active power output and backup power. Mobile emergency power supply with active power output as backup Electric boilers consume active power for standby. Electric boilers standby power consumption Together they form;

[0159] First stage discrete decision variables The mobile emergency power supply is distributed in step three. When the busbar is allocated to the microgrid When branch lines are assigned to microgrids Switch status on branch lines Operating status of mobile emergency power supplies and combined heat and power units Power-on status Shutdown status Together they form a whole.

[0160] (2) Two-stage plan-implementation load recovery model after decomposition and reconstruction

[0161] Based on the reconstructed two-stage plan-implementation load recovery model obtained in step two, which is a two-stage, three-level optimization problem of min-max-min, it is therefore broken down into main and sub-problems for an iterative solution approach, as follows: Figure 2 As shown.

[0162] First, regarding The problem represented can be reconstructed using duality theory as follows:

[0163] ;

[0164] In the formula: To constrain The dual variable.

[0165] Therefore, the above problem can be transformed into a main problem with minimization as the optimization direction at the upper level, and sub-problems with maximization as the optimization direction at the lower level. Since the second-stage optimization problem contains norm terms... This invention introduces an auxiliary variable. and The norm operation is moved to the first stage to ensure that the second stage is a linear optimization problem. The transformed main problem is represented as follows:

[0166] ;

[0167] The subproblem can be represented as:

[0168] ;

[0169] (3) Iterative solution of the principal-subproblem

[0170] 1) Initialization: Set convergence tolerance , will the lower realm Set as Upper Realm Set as and initialize the number of iterations. .

[0171] 2) Solve the main problem after the above decomposition:

[0172] ;

[0173] In the formula: Indicates the first In the nth iteration Random variables in a scenario The optimal value is obtained by solving the subproblems; The optimal solution to the subproblem; This represents the cutting plane added to the main problem after the first iteration; and This represents the constraints added to the main problem after the first iteration.

[0174] Record the optimal solution , , , and the objective function value, and the lower bound. Update the objective function value of the main problem.

[0175] 3) For each scenario and its corresponding The optimal solution obtained by substituting into the principal problem , , Then, solve the subproblems resulting from the above decomposition:

[0176] ;

[0177] Where: bilinear term It is represented as the product of a binary variable and a continuous variable, and is strictly transformed into multiple linear constraints using McCormick envelope relaxation. The defensive microgrid reconstruction result in the first stage of step (1) above. The optimal solution.

[0178] Record the optimal solution , and the The optimal objective value of the subproblem in each scenario is and the upper bound of the records in the previous iteration process. and Update the minimum value in the range.

[0179] 4) If satisfied If the result is positive, save the current result and terminate the iteration process; otherwise, update the current result. and number of iterations Return to step 2) and add a new cutting plane and constraints to the main problem, then solve again until convergence.

[0180] Example

[0181] On the IEEE 33-node and Bali 32-node systems, this invention and three other load restoration schemes were compared and analyzed to demonstrate the effectiveness of the proposed solution in load restoration. The schemes are as follows:

[0182] Option 1: Deterministic model, where the reserve commitment is maintained at approximately 5% of the total load capacity.

[0183] Option 2: Stochastic optimization model. This model uses stochastic optimization methods to determine the corresponding load recovery and uses secondary strike events constructed from historical data for verification to obtain a more suitable scheduling scheme.

[0184] Option 3: The traditional two-stage robust optimization model, which uses an uncertainty set to characterize the secondary attack event, with the uncertainty set parameter Γ taking the maximum value in historical data.

[0185] Table 1 compares the load recovery performance of the method of the present invention with that of three other schemes.

[0186] Table 1 Comparison of load recovery results from different schemes

[0187]

[0188] In terms of load shedding penalty costs, the performance order from best to worst is: this scheme > scheme 2 > scheme 3 > scheme 1. Scheme 1's deterministic model purely formulates load shedding strategies from an economic perspective, aiming to minimize the cost of formulating such strategies. However, because the allocation of mobile emergency power, the deployment of unit backups, and the defensive microgrid reconfiguration ignore the uncertainty of second-strike attacks, this scheme incurs the highest unexpected load shedding penalty, rendering the load shedding strategy ineffective in this scenario.

[0189] Considering the uncertainty of secondary impact events, the total cost of Schemes 2 and 3 is significantly lower than that of Scheme 1. However, the performance of the stochastic optimization model (Scheme 2) is superior to that of the traditional two-stage robust optimization model (Scheme 3). The two-stage robust optimization model only focuses on the worst-case scenario, but the probability of these extreme cases occurring is very low. Therefore, the load shedding strategy formulated by the traditional two-stage robust optimization model cannot protect critical loads in many non-worst-case scenarios, resulting in higher load shedding penalty costs.

[0190] Scheme 2 employs a stochastic optimization model, which considers various secondary strike scenarios and can adapt to various branch power outage scenarios, thus achieving better out-of-sample performance on most test data. However, the stochastic optimization model may lead to overfitting; that is, if the actual secondary strike events deviate significantly from most of the considered scenarios, the formulated load restoration strategy will fail.

[0191] In contrast, the sub-Brussels robust optimization model (in this scheme) uses the Wasserstein radius parameter γ to find the worst-case distribution within a fuzzy set centered on an empirical distribution, which encompasses the true probability distribution of secondary strike events. This approach allows for the simultaneous consideration of worst-case and various non-worst-case scenarios in load restoration strategy formulation. By adjusting the control coefficients Γ of the support set, the sub-Brussels robust optimization model limits the worst-case branch outages that may occur in each scenario, thus balancing economic efficiency (lower cost of load restoration strategy formulation) and robustness (lower load shedding losses). Compared to stochastic optimization models and traditional two-stage robust optimization models, the total cost of the sub-Brussels robust optimization model is reduced by 10.29% and 12.85%, respectively.

[0192] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A method for restoring the load of a split-blower rod in an electrothermal system considering secondary impact, characterized in that, The specific steps are as follows: S1: Based on the thermal inertia characteristics of the district heating network, a virtual energy storage model is constructed; a two-stage planning-implementation preliminary load recovery model of the electric heating system embedded with the virtual energy storage model is constructed, which consists of a planning stage and an implementation stage coupled together; S2: Based on historical fault data, construct a support set to capture the location and time of faults in vulnerable branches, and construct a fuzzy set to describe the distribution of uncertain secondary impact events in the planning phase; use the Lagrange duality technique to reconstruct the infinite-dimensional optimization problem in the two-stage planning-implementation load recovery preliminary model constructed in step S1 into a finite-dimensional optimization problem, and obtain the two-stage planning-implementation load recovery model; S3: The convexity relaxation technique is used to transform the non-convex constraints in the two-stage planning-implementation load recovery model into linear constraints; S4: An improved column and constraint generation algorithm is used to iteratively solve the reconstructed two-stage plan-implementation load recovery model to obtain the optimal load recovery scheme considering post-disaster secondary impacts.

2. The method for restoring the load of a split-blower rod in an electrothermal system considering secondary impacts according to claim 1, characterized in that, The construction of the virtual energy storage model for the district heating network in step S1 is as follows: S11: Introduce the concept of fluid infinitesimal elements and calculate the outlet temperature of the pipe using a weighted average method; the outlet temperature of the pipe is equal to the sum of the product of the temperature distribution coefficient C1 and the outlet temperature of the Kth fluid infinitesimal element in the pipe at the current moment, and the product of the temperature distribution coefficient C2 and the outlet temperature of the (K+1)th fluid infinitesimal element at the current moment; where The temperature distribution coefficients C1 and C2 are determined by the mass flow rate of the fluid element and its flow time in the pipe; S12: Establish the time coupling relationship between the pipe inlet temperature and the outlet temperature, as follows: ； In the formula: This represents the outlet temperature of pipe p in the water supply and return networks at the current moment. and C3 and C4 represent the inlet temperatures of pipe p in the supply and return water networks at two different historical moments, respectively; C3 and C4 represent the corresponding heat loss coefficients. t A Indicates the current ambient temperature; and Let C3 and C4 represent the pipe and time sets, respectively; where the heat loss coefficients C3 and C4 are related to the pipe length, friction coefficient, specific heat capacity of the fluid, and mass flow rate of the fluid.

3. The method for restoring the load of a split-blower rod in an electrothermal system considering secondary impacts according to claim 1, characterized in that, In step S1, the planning phase involves formulating a recovery plan while satisfying the various physical and logical constraints of this phase. The recovery plan aims to minimize the total cost of this phase, while also considering the worst-case scenario caused by the uncertainty of a second strike, and incorporating the expected losses caused by the implementation phase into the decision objectives of the planning phase. The implementation phase is based on the recovery plan formulated in the planning phase, combined with the specific scenario of the actual secondary attack. By adjusting the operational variables in this phase, the objective function is to minimize the load reduction while meeting all operational safety constraints.

4. The method for restoring the load of a split-blower rod in an electrothermal system considering secondary impacts according to claim 1, characterized in that, Specifically as follows: The support set limits the number of branches that fail simultaneously at any given time to a preset upper limit, and also limits the total cumulative power outage time of all faulty branches to a preset total time threshold. The fuzzy set is a set of distributions defined around an empirical distribution formed from historical data; the boundary of the set of distributions is defined by the Wasserstein metric distance and is controlled by the radius of the fuzzy set. The fuzzy set Specifically as follows: ； Fuzzy set radius ; In the formula: Let C represent the confidence level, and C represent the fuzzy set radius distance coefficient, which is determined by a [missing information - likely a variable or parameter]. The optimization problem, presented as the optimization variable, is as follows: ； In the formula: This represents the optimization variable used to calculate the radius distance coefficient of the fuzzy set. Represents the historical values ​​of random variables in the selected scenario s. The average value; p s This represents the probability of the corresponding scenario occurring.

5. The method for restoring the load of a split-blower rod in an electrothermal system considering secondary impact, as described in claim 4, is characterized in that... The infinite-dimensional duality technique described in step S2 is as follows: S21: Identify the infinite-dimensional optimization problem in the planning phase of the two-stage planning-implementation load recovery preliminary model, expand the pursuit function of the problem, and introduce the corresponding dual variable for each constraint; S22: Based on Lagrange duality theory, the dual variables are substituted to obtain the dual form of the expanded tracing function, which transforms the problem of maximizing the probability distribution into an equivalent problem of minimizing the dual variables, thus obtaining a solvable finite-dimensional optimization problem. S23: Substitute the reconstructed finite-dimensional optimization problem into the two-stage planning-implementation load recovery preliminary model to obtain the two-stage planning-implementation load recovery model.

6. The method for restoring the load of a split-blower rod in an electrothermal system considering secondary impacts according to claim 1, characterized in that, In the two-stage plan-implementation load restoration model, the planning stage aims to minimize the total cost of the stage and establishes an optimization model that includes three major constraint systems: mobile emergency power allocation, defensive microgrid reconfiguration, and unit standby capacity setting. The implementation phase aims to minimize operating costs by establishing an optimization model that includes three major constraint systems: equipment operation, power distribution network flow, and district heating network flow, in order to achieve real-time voltage and power support.

7. The method for restoring the load of a split-blower rod in an electrothermal system considering secondary impacts according to claim 6, characterized in that, The defensive microgrid reconfiguration constraint system includes operational constraints and microgrid radial topology constraints; The operational constraints are used to limit the disconnection of branches between each bus and branch microgrid and between microgrids. The radial topology constraint of the microgrid is used to ensure that the internal structure of the microgrid is a tree-like, acyclic network and a connected network. Specifically, it includes: constraining the internal structure of the microgrid to be a tree-like, acyclic network by ensuring that the difference between the number of buses and the number of branches is equal to the number of buses at the root node; and constraining the internal structure of the microgrid to be a connected network by constructing a virtual commodity flow model, injecting virtual flows at the root node bus, generating corresponding sinks in the remaining non-root node buses, and limiting the virtual flows to be transmitted only in closed branches within the microgrid.

8. The method for restoring the load of a split-blower rod in an electrothermal system considering secondary impacts according to claim 1, characterized in that, The convexity relaxation technique described in step S3 is as follows: S31: For defensive microgrid reconfiguration during the planning phase, introduce binary auxiliary variables. and And define the logical state: when the condition When established, define If equal to 1, otherwise defined Equals 0; when the condition When established, define If equal to 1, otherwise defined Equal to 0; introduce a sufficiently small coefficient and a sufficiently large coefficient Two sets of linear constraints are established to achieve the above-mentioned mandatory relationship: ； In the formula: Represents the root node busbar The case where it is assigned to microgrid m; Indicates the root node bus The flow of goods generated at the location; S32: To address the dual impact of the branch state on the planning phase—both the defensive microgrid reconstruction results and the worst-case secondary attack event—on the implementation phase, a coordination variable is constructed to represent the coordination relationship between the two. The specific constraints are as follows: Ensure the coordination variables The value of is simultaneously less than or equal to the value of the random variable for the second-strike event under the worst-case distribution and the result of the defensive microgrid reconstruction during the planning phase; and ensures that the coordination variable The value of must be greater than or equal to the value of the random variable of the second-strike event under the worst distribution and the result of the defensive microgrid reconstruction in the planning phase.

9. The method for restoring the load of a split-blower rod in an electrothermal system considering secondary impacts according to claim 1, characterized in that, The solution process described in step S4 is as follows: S41: The reconstructed two-stage planning-implementation load recovery model is split into a main problem optimized for minimization and sub-problems optimized for maximization; a convergence tolerance is set. Initialize the lower bound LB to The upper UB is And initialize the iteration count c=1; S42: Solve the main problem to obtain the optimal decision scheme in the planning phase, including mobile emergency power allocation, defensive microgrid reconfiguration scheme, and backup capacity configuration; during the iteration process, the main problem continuously accumulates optimality cutting planes from feedback from subproblems, so that its decision scheme gradually enhances its adaptability to uncertainty; after the solution is completed, the lower bound LB is updated using the objective value of the main problem. S43: Substitute the optimal solution obtained from the main problem, and solve the corresponding subproblems for each uncertain secondary attack scenario; after summarizing the evaluation results under each scenario, update the upper bound UB using the sum of the optimal values ​​of the subproblems and the optimal values ​​of the main problem in this iteration; S44: Calculate the relative difference based on the updated lower bound LB and upper bound UB, and compare it with the convergence tolerance. Compare and determine whether convergence has occurred; S45: If the convergence condition is met, output the current optimal solution; Otherwise, add the new constraints and cutting planes generated by the subproblems to the main problem, update the iteration count c→c+1, and repeat steps S42~S44 until convergence, to obtain the optimal load recovery scheme considering post-disaster secondary impact.

10. A split-bar load recovery system for an electrothermal system considering secondary impact, characterized in that, This method is used to implement the sub-bulb load recovery method for an electrothermal system considering secondary impacts as described in any one of claims 1 to 9.

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