Unified optimization method for physical toughness and operation configuration of power system

Abstract

The invention discloses a unified optimization method for physical toughness and operation configuration of an electric power system. The method comprises the following steps: establishing a double-layer computing architecture comprising an upper-layer power grid physical system model and a lower-layer energy community model; generating a random scene set and a robust uncertainty set; executing a numerical optimization process under a two-stage random-robust hybrid optimization framework: in the process, determining a physical topology reinforcement parameter in a long-term planning stage, determining a physical repair scheduling parameter in a short-term operation stage, and carrying out mathematical coupling on the two stages through technical constraints; and carrying out convergence solution on the unified optimization process. According to the method, a power grid operator can consider the physical toughness constraint and economic cost of coupling short-term emergency repair scheduling under the attack of the worst case when carrying out planning decision-making of long-term physical topology reinforcement, so that an engineering decision-making scheme with the highest physical security level and the optimal economic benefit is output.

Description

Technical Field

[0001] This invention belongs to the field of power distribution network planning and calculation operation technology, specifically relating to a unified optimization method for the physical resilience and operational configuration of power systems. Background Technology

[0002] In modern power systems, physical disturbances caused by extreme weather events or malicious cyberattacks pose a severe technical challenge to the safe and stable operation of the system. To enhance the physical resilience of power systems (i.e., the system's ability to resist, adapt to, and recover from disturbances), existing technical solutions mainly focus on two independent areas: one is long-term physical planning through hardening physical facilities or deploying emergency resources; the other is short-term emergency dispatching of maintenance resources or grid operation status after a disturbance occurs.

[0003] However, existing technologies suffer from three fundamental technical flaws in addressing these issues, preventing them from providing a solution that combines physical security with computational efficiency: 1. Lack of Technological Coupling in "Cross-Cycle" Decision-Making: Existing technologies treat long-term planning and short-term operations as two computationally separate sub-problems. Long-term physical planning (e.g., deciding which lines to harden) is typically based on static or simplified operational assumptions; while short-term emergency scheduling (e.g., deciding how to repair or reconfigure the network) can only be performed within a given, fixed physical topology. This technological fragmentation results in a lack of a unified, cross-cycle mathematical optimization framework between the two. Existing technologies cannot, during the long-term planning phase, proactively and quantitatively assess the specific technological constraints and impacts of planning decisions (e.g., a specific set of physical topology hardening parameters) on future short-term emergency operations (e.g., a set of physical repair scheduling parameters).

[0004] 2. The Mathematical Modeling Gap for Mixed Uncertainties: Power systems simultaneously face two entirely different types of uncertainty: (a) stochastic uncertainty caused by fluctuations in renewable energy output or conventional loads, which is typically modeled based on its probability distribution; and (b) strategic uncertainty caused by malicious cyberattacks or physical sabotage, which is typically modeled based on worst-case robust set theory. Existing technologies typically only handle one type (e.g., purely stochastic optimization or purely robust optimization), lacking a unified mathematical optimization engine capable of handling both types of mixed uncertainties simultaneously in a single computational process.

[0005] 3. The Paradox of Distributed Computing Architectures: With the integration of numerous distributed energy sources (such as photovoltaics and energy storage) and energy communities, the system exhibits typical upper-lower-layer (i.e., grid operator-energy community) computational characteristics. However, this leads to a computational paradox: on the one hand, solving the aforementioned complex model involving cross-period and mixed uncertainties requires efficient but highly centralized optimization algorithms; on the other hand, the autonomy, privacy, and computational scale of energy communities naturally necessitate a distributed computing architecture. Although existing distributed algorithms have been applied to single, simplified short-term operational problems such as day-ahead scheduling, no existing technology can be applied to solve the aforementioned extremely complex, unified, cross-period, mixed-uncertainty two-layer optimization problem.

[0006] In summary, current technology suffers from severe technological gaps and deficiencies in three areas: decision-making cycle, mathematical model, and computational architecture. Therefore, there is an urgent need in this field for a novel technological solution to overcome these shortcomings. Summary of the Invention

[0007] The purpose of this invention is to address the shortcomings of the aforementioned background technology by providing a unified optimization method for the physical resilience and operational configuration of power systems. This method intelligently couples and collaboratively solves the long-term physical topology hardening of the upper-level power grid and the short-term emergency operation scheduling of the lower-level energy community in a mixed risk field that simultaneously includes random uncertainties (such as renewable energy fluctuations) and strategic uncertainties (such as cyberattacks). This achieves synergistic optimization and high unification of physical security resilience and economic operation benefits at the system level. That is, while significantly improving the stable operation capability of the power system under complex disturbances, it also ensures that the economic cost-effectiveness of long-term physical hardening and short-term emergency scheduling is optimal by solving their respective minimization objective functions.

[0008] The technical solution adopted in this invention is: a unified optimization method for the physical resilience and operational configuration of power systems, which is executed by one or more processors of a computing system, and includes: (a) In the computing system, a two-layer computing architecture is established, the architecture including an upper-layer power grid physical system model and a lower-layer energy community model; (b) The computing system generates a set of random scenarios representing random uncertainty, the set being generated based on a probability measure; and a set of robust uncertainty representing adversarial attack scenarios, the set being generated based on robust set theory. (c) The computing system performs a unified, cross-cycle numerical optimization process, the process comprising: During the long-term planning phase, based on the aforementioned set of random scenarios: a set of physical topology hardening parameters are determined by the upper-level power grid physical system model; and a set of distributed energy physical configuration parameters are determined by the lower-level energy community model. During the short-term operation phase, based on the robust uncertainty set: the physical repair scheduling parameters are determined by the upper-level power grid physical system model; and the internal energy exchange scheduling dataset is determined by the lower-level energy community model. (d) The long-term planning phase and the short-term operation phase are coupled by technical constraints, wherein the physical repair scheduling parameters determined by the upper-level power grid physical system model in the short-term operation phase are mathematically constrained by the physical topology hardening parameters determined by the upper-level power grid physical system model in the long-term planning phase. (e) The unified, cross-period numerical optimization process is solved by using a distributed numerical optimization algorithm to iteratively exchange the original and dual variables between the upper-level power grid physical system model and the lower-level energy community model.

[0009] In the above technical solution, the robust uncertainty set models the adversarial attack scenario as a set of network topology states constrained by a maximum attack count budget.

[0010] In the above technical solution, the distributed numerical optimization algorithm is the alternating direction multiplier method.

[0011] In the above technical solution, the upper-level power grid physical system model and the lower-level energy community model are connected through coupling variables. The coupling variables are used as benefit terms in the objective function of the upper-level power grid physical system model and as cost terms or penalty terms in the objective function of the lower-level energy community model.

[0012] In the above technical solution, the step (c) in which the parameters are determined by the upper-level power grid physical system model is performed based on minimizing the objective function of the upper-level power grid physical system model. The objective function is a combination of its total cost item and total revenue item, wherein: the total cost item includes at least capital expenditure cost item, energy dissipation cost item, emergency investment cost item and dynamic scheduling cost item; and the total revenue item includes at least infrastructure usage fee revenue item and network service fee revenue item.

[0013] In the above technical solution, the lower-level energy community model includes: The upper-level community coordination subject model determines the internal exchange price based on the objective function of minimizing the total community expenditure. The total community expenditure includes the external electricity purchase cost and the grid connection usage fee paid to the upper-level power grid physical system model. The lower-level autonomous entity model collaboratively determines its distributed energy physical configuration parameters and proactive load reduction parameters based on the internal exchange price and the objective function of minimizing individual net costs.

[0014] In the above technical solution, when the upper-level power grid physical system model performs the numerical optimization process in the long-term planning stage, it further includes: enforcing the radial network topology through virtual power flow constraints; and transforming the non-convex power flow constraints into convex constraints using second-order cone relaxation.

[0015] In the above technical solution, when the upper-level power grid physical system model determines the physical repair scheduling parameters during the short-term operation phase, it further includes: optimizing the scheduling of mobile reconfiguration units under the constraint of the number of maintenance personnel.

[0016] In the above technical solution, the distributed energy physical configuration parameters determined by the lower-level energy community model include the physical capacity parameters of the fixed energy storage device, and the physical operation of the fixed energy storage device is further constrained by one or more constraints during the short-term operation phase. The constraints include: daily state of charge balance constraints, logic constraints to prevent simultaneous charging and discharging, or physical limits on charging and discharging power.

[0017] This invention provides a unified optimization system for the physical resilience and operational configuration of power systems, the system comprising: processor; A memory storing instructions that, when executed by the processor, configure the system to perform the method described in the above technical solution.

[0018] The beneficial effects of this invention are as follows: This invention provides a specific, end-to-end computational method and system that can solve extremely complex minimization optimization problems, providing a technically superior, more reliable, and engineering-executable optimal solution. Existing technologies, due to their fragmentation and siloed nature, can either only solve a simplified, non-optimal subset of these problems, or their solutions are physically infeasible. This invention, through its complete computational architecture, and the physical topology hardening parameters and physical repair scheduling parameters it outputs, simultaneously achieves stronger physical resilience, higher computational efficiency, and better system economy in terms of technical effects; that is, the solution to its minimization objective function is numerically lower.

[0019] Furthermore, this invention provides a provable, engineering-grade physical security guarantee in terms of technical effectiveness by mathematically defining the abstract risk of "malicious attack" as a "topology vulnerability assessment model constrained by the maximum attack budget." The physical topology hardening parameters output by this invention are mathematically guaranteed to withstand any (i.e., worst-case) attack combination within the attack budget. This replaces the guesswork in traditional probabilistic models with a quantifiable, deterministic security lower bound, making the final physical system more robust and reliable.

[0020] Furthermore, this invention employs the alternating direction multiplier method, simultaneously achieving computational feasibility and data privacy protection. Facing the global problem that cannot be solved centrally, this algorithm technically decomposes it into multiple smaller, solvable subproblems that can be processed in parallel. At the algorithmic level, it avoids the need for the lower-level energy community model to submit its internal cost functions and other private data to the upper-level power grid physical system model, thus resolving the distributed solution paradox in existing technologies.

[0021] Furthermore, this invention connects the upper and lower level models through a coupling variable, creating an efficient and non-intrusive information transmission channel. This variable technically serves as a price signal. The upper-level power grid physical system model does not need to know the internal details of the lower-level energy community model; it can efficiently transmit its own physical constraints (such as network congestion) to the lower level simply by passing this single, quantified parameter, thereby guiding the entire system to find a convergent and unified optimal solution mathematically.

[0022] Furthermore, this invention explicitly defines the objective function of the upper-level power grid physical system model as a minimized net cost combination that includes total cost and total benefit terms. The technical effect is to prevent over-design and waste of physical resources in engineering. By forcing the mathematical model to simultaneously consider benefit terms, the physical topology hardening parameters it outputs represent an engineering solution with the lowest net cost and highest economic benefits, while technically achieving the same physical resilience target.

[0023] Furthermore, this invention establishes the lower-level energy community model as an internal two-layer architecture and introduces proactive load shedding decisions, which greatly improves the fidelity of the computational model and unlocks the physical resilience of the demand side. This internal two-layer architecture more accurately simulates the real physical-economic structure of the energy community, making the global optimization calculation results closer to physical reality and more reliable. Simultaneously, adding proactive load shedding decisions provides the system with a second source of physical resilience, enabling the system to absorb disturbances at a lower overall cost.

[0024] Furthermore, this invention mandates that long-term planning must satisfy a radial network topology and employs second-order cone relaxation, ensuring the physical feasibility and computational possibility of the calculation results. The radial constraint prevents the optimization model from outputting a physically impossible (e.g., ring-shaped) distribution network topology. Second-order cone relaxation is a key, non-obvious mathematical enabling technique that technically transforms this computationally unsolvable non-convex power flow constraint problem into a convex problem that can be solved efficiently, thus making the computation of the entire long-term planning possible.

[0025] Furthermore, this invention explicitly limits the short-term emergency response of the upper-level power grid physical system model to simultaneously consider the limitations on the number of mobile reconfiguration units and maintenance personnel. Its technical effect is to greatly improve the engineering feasibility of the emergency plan. The physical repair scheduling parameters it outputs are no longer an idealized mathematical solution, but a truly engineering-executable, high-fidelity operational plan that has already considered core physical response methods and is constrained by key physical bottlenecks.

[0026] Furthermore, this invention provides the necessary set of engineering constraints for stationary energy storage in lower-level energy community models, ensuring the physical security of the calculation results and the non-destructive nature of the equipment. Technically, it prevents the optimization model from outputting a physically destructive control command (e.g., commanding simultaneous charging and discharging of the energy storage) in pursuit of a minimization objective, ensuring that the output parameters are safe, non-destructive, and compliant with hardware engineering specifications. Attached Figure Description

[0027] Figure 1 This is a flowchart of a method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the model structure in this embodiment. Detailed Implementation

[0028] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments to facilitate a clear understanding of the present invention, but these descriptions do not constitute a limitation on the present invention.

[0029] like Figure 1 As shown, this invention provides a unified optimization method for the physical resilience and operational configuration of power systems. This method is executed by one or more processors of a computing system and includes: (a) In the computing system, a two-layer computing architecture is established, the architecture including an upper-layer power grid physical system model and a lower-layer energy community model; (b) The computing system generates a set of random scenarios representing random uncertainty and a set of robust uncertainty representing adversarial attack scenarios. (c) The computational system performs a numerical optimization process, including: During the long-term planning phase, based on the aforementioned set of random scenarios: the physical topology hardening parameters are determined by the upper-level power grid physical system model; and the distributed energy physical configuration parameters are determined by the lower-level energy community model. During the short-term operation phase, based on the robust uncertainty set: the physical repair scheduling parameters are determined by the upper-level power grid physical system model; and the internal energy exchange scheduling dataset is determined by the lower-level energy community model. (d) The long-term planning phase and the short-term operation phase are coupled by technical constraints, wherein the physical repair scheduling parameters determined by the upper-level power grid physical system model in the short-term operation phase are mathematically constrained by the physical topology hardening parameters determined by the upper-level power grid physical system model in the long-term planning phase. (e) A distributed numerical optimization algorithm is used to converge the numerical optimization process by iteratively exchanging the original and dual variables between the upper-level power grid physical system model and the lower-level energy community model.

[0030] Example 1 This embodiment aims to illustrate the core technology of the present invention in detail, rather than limiting its scope of protection. The non-obviousness of the computational method and system provided by the present invention lies in the fact that it does not provide an abstract business rule, but rather a concrete, end-to-end computational process. This process, for the first time, solves three major technical problems existing in the prior art: the lack of cross-cycle decision coupling, the gap in mixed uncertainty modeling, and the distributed solution paradox.

[0031] For detailed implementation steps of this method, please refer to [link / reference]. Figure 1 The calculation flowchart shown, and Figure 2 The two-stage optimization framework shown in the diagram includes the following steps: Step 1: Construct a two-layer computing architecture: This method first performs the steps defined in step (a) above in a computing system (e.g., a server or computing cluster containing one or more processors and memory), i.e., establishing a two-tier computing architecture. This architecture is the technical foundation for the distributed collaboration of this invention. Mathematically, this architecture is defined as: Upper-level grid physical system model (GO model): This model represents the decision of the grid operator (GO), whose technical objectives are driven by a two-stage stochastic-robust objective function defined by Equation (1) below.

[0032] Lower-level energy community model (EC model): This model represents the decision-making of the energy community (EC).

[0033] In a preferred embodiment, the lower-level energy community model itself is also a technically highly sophisticated internal two-tier architecture (see [link]). Figure 2 The P2P transaction layer in the middle includes: Upper-level community coordination subject model: Its technical objective is defined by formula (39) below, namely, minimizing the total community expenditure. As shown in formulas (40) and (41) below, this total expenditure is technically defined as the sum of external purchase and sale costs and internet access usage fees; The lower-level autonomous entity model: its technical objective is defined by formula (44) below, namely, minimizing the individual net cost. As shown in formulas (45) to (48) below, this net cost is technically defined as a combination of investment cost, equipment operation and maintenance cost and internal purchase or replacement cost.

[0034] Existing technologies generally separate physical systems from market activities, leading to one-sided analytical models. The explicit, multi-layered computational architecture constructed in this step provides, for the first time, a high-fidelity, non-abstract mathematical framework for the physical-economic interaction between the GO model and the EC model (including their complex coordinator-autonomous system structures), thus laying the necessary technical foundation for subsequent, non-obvious coupled solutions.

[0035] Step 2: Generate a set of mixed uncertainties: After the architecture is established, this method performs the aforementioned step (b), which generates a set of mixed uncertainties in the computing system.

[0036] Existing technologies, when modeling, typically require a choice between random uncertainty (such as renewable energy fluctuations) and policy uncertainty (such as malicious attacks). This invention generates two completely different types of risks simultaneously: Random scenario set: generated based on probability measure, used to simulate long-term wind and solar power output uncertainty. This scenario set is the technical input for minimizing the expectation calculation operator in formulas (1), (39) and (44) below.

[0037] Robust uncertainty set: generated based on robust set theory, used to simulate malicious network attacks. This set is technically modeled precisely as a topological vulnerability model constrained by a maximum attack budget, as shown in Equation (21) below.

[0038] This step provides the subsequent optimization engine with a hybrid risk input that is mathematically more complete and engineering-wise closer to physical reality. The resulting computation is mathematically guaranteed to withstand both random fluctuations (through expectation minimization) and worst-case malicious attacks (through robust optimization), thus providing a provable, engineering-grade physical security guarantee that cannot be provided by existing technologies.

[0039] Step 3: Perform unified, cross-cycle numerical optimization: This is the core technology of the present invention, corresponding to step (c) above. The computational system performs a unified numerical optimization process based on the hybrid risk field generated in step 2. This process is technically decomposed into two independent stages that are forcibly coupled through technical constraints (see...). Figure 2 The two-stage stochastic-robust hybrid optimization framework corresponds to the aforementioned step (d): Step 3.1 Long-term planning phase (stochastic optimization, corresponding to...) Figure 2 (Left side): At this stage, the system calculates optimal parameters for long-term decision-making based on a set of random scenarios. The GO model determines a set of physical topology hardening parameters, namely the 0-1 variables defined in Equation (8) below. This decision is based on minimizing the net cost objective function shown in Equation (1) below. This objective function is technically a combination of its total cost term as defined in Equations (2), (3), (5), and (6) below and its total revenue term as defined in Equations (4) and (7) below.

[0040] To ensure the physical feasibility of the calculation results, the optimization process is subject to the virtual power flow constraints defined by the formulas (9)-(11) below. The beneficial effect is to ensure that the output topology is radial, preventing the model from outputting a distribution network topology that is physically impossible to build (e.g., a ring).

[0041] To ensure computational feasibility, the optimization process employs the second-order cone relaxation technique defined in Equation (19) below. It technically transforms a computationally unsolvable non-convex power flow constraint problem, as described in Equation (14) below, into a convex problem that can be solved efficiently.

[0042] In a preferred embodiment, to ensure basic physical feasibility, the GO model is further subject to the following restrictions: reinforcement quantity as shown in Equation (8) below, power balance constraints as shown in Equations (12)-(13) below, power, voltage and current constraints as shown in Equations (15)-(18) below, and non-negative rate constraints as shown in Equation (20) below.

[0043] The lower-level EC model collaboratively determines the goal of minimizing individual net cost based on formula (44) below, which is defined by formulas (45)-(48) below: 1) Distributed energy physical configuration parameters, such as the 0-1 configuration variables of FESS, WTG, and PVG as shown in formulas (46) and (50) below; The active load reduction parameters, as shown in formulas (60)-(61) below, unlock the physical resilience of the demand side, enabling the system to absorb disturbances at a lower overall cost.

[0044] To ensure the physical security of the calculation results and the non-destructive nature of the equipment, the optimization process is subject to strict physical constraints on the stationary energy storage device (FESS) as defined in Equations (52) to (59) below, such as the daily state of charge balance shown in Equation (52) below, the prevention of simultaneous charging and discharging shown in Equation (55) below, and the limit on the number of charging and discharging cycles shown in Equations (58, 59) below.

[0045] In a preferred embodiment, the autonomous entity model is further subject to energy balance constraints as shown in Equation (49) below, P2P transaction reciprocity constraints as shown in Equations (50)-(51) below, and renewable energy output ceiling constraints as shown in Equations (62)-(65) below.

[0046] 3.2 Short-term operation phase (robust optimization, corresponding to) Figure 2 (Right side) At this stage, the system calculates the optimal parameters for short-term decision-making based on a robust uncertainty set: A set of physical repair scheduling parameters is determined by the upper-level GO model.

[0047] To greatly improve the engineering feasibility of the emergency response plan, this optimization process is not an idealized mathematical solution, but is technically constrained by two core physical bottlenecks: the scheduling of mobile reconfigurable units and the limitation on the number of maintenance personnel. The scheduling of mobile reconfigurable units is defined in formula (25) below; the limitation on the number of maintenance personnel is defined in formula (26) below.

[0048] In a preferred embodiment, the GO model is further constrained at this stage by the repair logic as shown in formulas (23)-(24) below, and by the network operation constraints in the robust scenario as shown in formulas (27)-(38) below.

[0049] The internal energy exchange scheduling dataset (i.e., P2P market clearing) is determined by the lower-level EC model based on the minimization of total community expenditure target in formula (39) below.

[0050] In a preferred embodiment, the coordinating agent model is further constrained by regional energy balance as shown in Equation (42) below and external transaction reciprocal constraints as shown in Equation (43) below.

[0051] 3.3 Cross-stage technology coupling, corresponding to step (d) above: The two stages described above are not separate as in the prior art. The technical constraints of this invention, defined by the aforementioned step (d) (see...) Figure 2 The central coupling arrow in the diagram forces them to couple.

[0052] This coupling is mathematically achieved by formula (22) as described below.

[0053] This formula technically and mathematically binds the output of the long-term planning phase (i.e., physical topology hardening parameters) with the input of the short-term operation phase (i.e., physical repair scheduling parameters). This fundamentally solves the technical problem of the lack of cross-cycle decision coupling in existing technologies. Its technical effect is that the long-term planning decisions produced by this method automatically anticipate and are immune to short-term worst-case attacks.

[0054] Step 4: Perform distributed solution using the ADMM framework: The unified optimization problem defined in step 3, such as formulas (1), (39), and (44) and all their constraints, is a computationally intensive problem that cannot be solved centrally by a single calculator. Therefore, this invention implements step 4, corresponding to the aforementioned step (e), which is to use the Alternating Direction Multiplier Method (ADMM) to perform distributed collaborative computation on the model.

[0055] The following are the core technical means of this invention to solve the distributed solution paradox in the prior art.

[0056] Decomposition (corresponding) Figure 1 Upper-level optimization, lower-level optimization): The ADMM algorithm technically decomposes this huge global problem into two (or more) subproblems that can be solved in parallel: the upper-level GO model (main problem) and the lower-level EC model (subproblems).

[0057] Iteration (corresponding) Figure 1 (Whether the iteration converges): As described in step (e) above, the algorithm gradually converges to the optimal solution by iteratively exchanging the original and dual variables between the upper and lower model layers.

[0058] Information Channel: The key to this invention is that the dual variable is technically implemented as a coupled variable, namely the network access fee or price signal defined in formula (4) or (41) below.

[0059] This architecture achieves both computational feasibility and data privacy protection. The upper-layer GO and the lower-layer EC do not need to exchange their internal, private, and complex cost functions or physical topology data; they only need to iteratively exchange the single, non-intrusive parameter of price (i.e., the dual variable) to mathematically guarantee the entire complex, two-layer, cross-cycle system (such as...) Figure 2 As shown, the solution converges to a unified, globally optimal solution.

[0060] Ultimately, as Figure 1 As shown, after the iteration converges, the system outputs the configuration location and capacity of each distributed resource, namely the physical topology hardening parameters, distributed energy physical configuration parameters and physical repair scheduling parameters described in step (c) above, which are more superior, more reliable and executable in engineering.

[0061] The principle of this embodiment will be further explained below with reference to the formula. For simplicity, the following standardized naming convention, using the first letter instead of the English abbreviation, is adopted: Fixed Energy Storage System (FESS): Wind Turbine Generator (WTG): Photovoltaic Generator (PVG): As the upper-level coordinator, GO constructs an NK topology vulnerability model and a reconstruction unit scheduling model that consider network attack vectors. Essentially, it is a two-stage stochastic-robust hybrid optimization system, which can be formally expressed as: Objective function of the GO layer: ; in, This represents the capital expenditure matrix for the GO grid topology reinforcement phase. This represents the energy dissipation cost of an energy transmission network under steady-state operating conditions. This reflects the total revenue from infrastructure usage fees collected by the grid access service from all users; Quantify the urgent investment costs for repairing fault propagation paths during the resistance enhancement phase; The dynamic scheduling cost matrix represents the mobile reconfiguration unit; The instantaneous revenue stream of network service fees corresponding to the emergency operation mode; and Let E represent the sets of uncertainties in renewable energy output in the long-term planning domain and the short-term operation domain, respectively. E represents the expectation.

[0062] ; ; ; ; ; ; in, The discount rate; For the planning period; For the collection of lines to be strengthened; For the line Increased cost per unit length; Its length; To indicate the line The reinforcement status is a 0-1 variable, with values ​​of 1 and 0 corresponding to whether reinforcement has been carried out, respectively. This represents the electricity price that GO purchases from the wholesale market at time t; for time The square of the branch current in the given scenario; The impedance of the branch; index Indicates the connection node and nodes A specific branch of the power grid; a collection This represents the set of all time steps within the optimization time domain (e.g., 24 hours in a day). In the formula... It is a time index within the set. (Set) This represents the set of all nodes in the power grid. The formula... and They are all node indices in this set; Indicates producer-consumer and The efficiency of P2P transactions between them; Indicate its and The network access fee for transactions between them; Indicates a branch The cost of repairing the fixed dispatch unit; Indicates in the scene Has the branch line been attacked and malfunctioned? Indicates a fault; branch road The labor cost per unit time for maintenance personnel; Indicates a branch Repair time required; Indicates that it is in Whether the time has been repaired is indicated by a value of 1 if repaired, otherwise 0.

[0063] Constraints of the stochastic optimization part of GO during the network topology reinforcement phase: ; ; ; ; ; ; ; ; ; ; ; ; ; All of these variables occur during long-term wind and solar power output uncertainties. In this scenario. Indicates the limit value for the amount of reinforcement; express Current Line Whether a refactoring occurs is disconnected; 0 indicates a disconnection, otherwise 1 indicates a disconnection. This represents the total number of nodes in the distribution network; Represents a set of physical networks; Represents a virtual set; This represents a continuous auxiliary variable, indicating its position within the network. Current Line A flowing virtual trend; Represents a node The output branch set; Indicates the input set; Represents a sufficiently large positive number; This indicates a limit on the number of maintenance personnel; and In the scene respectively Down The active and reactive power of the generators at the current moment; and They represent the scenes respectively. Down From the node Outflow, inflow to node The active and reactive power; and They represent the scenes respectively. Down From the node Outflow, inflow to node The active and reactive power; and Branch roads Resistance and reactance; and They represent the scenes respectively. Down Time Branch First-segment voltage and last-segment voltage; and These represent the configurations on the nodes. The upper limits of active and reactive power of traditional generators; and They represent The upper and lower limits of the voltage at the location; This indicates the upper limit of the current.

[0064] and In the scene respectively Down Flowing through the side road The active power and reactive power.

[0065] Indicates in the scene Down Flowing through the side road The square of the current amplitude. Representative in the scene Down Time Node The voltage amplitude. These two variables are introduced to transform the non-convex power flow constraint into a convex constraint that can be solved efficiently through "second-order cone relaxation". It represents the Euclidean norm (or L2 norm) of a vector. On behalf of grid operators (GOs) targeting prosumers With producers and consumers The unit "network access fee" (or network usage rate) charged for P2P (Peer-to-Peer) energy transactions between them. This indicates that for all prosumers who engage in transactions... .

[0066] Formula (8) represents the limit on the number of reinforcements in the first stage; Formula (9) ensures that the network is radial; Formula (10) ensures that each The virtual power flow balance; Formula (11) uses the Big M method to limit the virtual power flow; Formulas (12) and (13) respectively represent the balance of the virtual power flow at the nodes. The balance of active and reactive power; Formula (14) represents the voltage drop; Formulas (15) and (16) respectively represent the power limit of the traditional generator; Formula (17) represents the voltage amplitude limit; Formula (18) represents the current limit; Formula (19) represents the second-order cone relaxation; Formula (20) ensures that the grid operator's grid access fee must be non-negative, which is a basic economic constraint.

[0067] Constraints of the robust optimization part of GO in handling emergency operation mode: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; All of these variables occur during the short-term uncertainty of wind and solar power output. In this scenario. Indicates the maximum number of cyberattacks; This indicates a limit on the number of maintenance personnel. It is a key binary uncertainty variable, representing the worst-case attack scenario. Downline Whether it survives (1 for survival, 0 for being attacked); Formula (21) is based on the attack budget. This limits the total number of lines an attacker can compromise. Once a line is attacked, the repair decision is determined by binary variables. Indicates whether at time A team was dispatched to begin repairing the lines. Formulas (23) and (24) stipulate that each attacked line must be repaired once and only once, and the repair work begins immediately after the attack occurs (i.e., (Time). The entire repair process is resource-constrained, as shown in Equation (26), at any given time. The total number of maintenance tasks performed simultaneously cannot exceed the number of available maintenance teams. Ultimately, these physical events and decisions directly affect the operating state of the power grid, which is determined by binary variables. (Indicates the line) At any moment Whether the switch is closed or open is determined; the key coupling constraint formulas (22) and (25) link long-term planning with short-term operations: Formula (22) stipulates that an unreinforced ( And was attacked () The time required for the repair of the line. The internal connection must be kept disconnected. Formula (25) ensures that only after the repair work is completed (i.e., from the start of the repair) is the repair work completed. go through After a certain period of time, the switch on the line is closed. It is only possible to become 1).

[0068] Formulas (27)-(38) are similar to formulas (9)-(20) in the stochastic optimization part of long-term planning, except that the scenario has changed.

[0069] The energy symbiotic system comprises a dual decision-making layer consisting of an autonomous entity and a community coordinating entity. Its collaborative optimization architecture can be formally expressed as: Upper-level community coordinating body Objective function: ; ; ; All variables exhibit uncertainty in both the long-term and short-term weather conditions. This occurs in the following scenario. Represents a specific scenario of uncertainty. and time Internal electricity trading prices within the energy community's peer-to-peer (P2P) market. Specifically, it refers to the internal transaction price of electricity within the community members' market. To another member The unit price of electricity that needs to be paid when purchasing electricity. This price is determined by the "community coordinating entity" in the lower-level model, which is used to clear internal electricity transactions. Representing the subject Other Power purchased externally at any given time; Indicates external buying and selling costs; This indicates the cost of internet access. express Other The network access fee for transactions between them.

[0070] Upper-level community coordinating body Constraints: ; ; Among them, set This represents the set of all energy communities in the system. (The formula contains...) and Each element in the set represents a specific energy community. Representing the energy community A collection of other communities that can conduct P2P external transactions. In most cases, this can be understood as a set. Chinese community All other communities besides oneself. (Collection) It belongs to a specific energy community The set of all internal prosumers. Constraint (42) represents the total energy balance within the region; It is the optimal solution to the lower-level problem, which depends on the internal price set by the upper level; (43) indicates the reciprocal nature of external transactions.

[0071] Lower-level autonomous entities Objective function: ; ; ; ; ; in, Indicates autonomous consumer Investment costs; , and They represent producers and consumers respectively. The cost of investing in stationary energy storage devices, wind turbine generators, and photovoltaic generators; , and They represent the scenes respectively. Lower-level consumers The operation and maintenance costs of investing in stationary energy storage devices, wind turbine generators, and photovoltaic generators; Indicates autonomous consumer In the scene Reduce equipment maintenance costs; Indicates producer-consumer In the scene time Internal purchase costs below; Indicates in the scene time Lower-level consumers With the community Replacement costs; Indicates in the scene Time period Internal Producers and Consumers Towards The price at which electricity is purchased; Indicates in the scene Time period Its electricity sales capacity; Indicates in the scene time The price at which lower-level producers and consumers trade with each other is set by higher-level managers as the buying and selling price for the energy pool they manage; Producers and consumers With its regional energy pool In the scene The moment The power of the transactions performed.

[0072] Taking stationary energy storage device FESS as an example: ; ; in, Indicates producer-consumer The configured energy storage is factored into the daily investment cost; Representing the subject Daily operating costs; Configure energy storage variables for the first stage, i.e., 0-1 variables ( Not configured at the time (Time configuration); The capacity factor is the ratio of the actual power generation of a power generation device to its theoretical maximum power generation within a certain period of time. It is used to evaluate the utilization rate of the system. It is the annual operating hours of energy storage, which is the total number of operating hours throughout the year; The term refers to the entire lifecycle, or float life, measured in years; where r is the annual interest rate. For nodes The actual capacity configured; Cost per unit capacity This represents the unit operating cost coefficient.

[0073] lower-level producers and consumers Constraints: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; in, In the scene time Producers and consumers Sold to another consumer The power; In the scene time Producers and consumers The total power that needs to be transmitted outward must either be sold to other producers and consumers or to community energy pools. In the scene time Producers and consumers and their community The power of the energy pool trading. If positive, it indicates... Selling electricity to the energy pool; if negative, it means... Purchase electricity from an energy pool. and They represent producers and consumers respectively. Whether it is a binary variable involving both photovoltaic and wind turbine configurations; express Producers and consumers at all times The change in the state of charge and discharge of the energy storage device in adjacent time periods, if the state changes (e.g., charging → discharging), then Otherwise, it is 0; and They represent the scenes respectively. time Producers and consumers Real-time energy flux of the configured energy storage device during discharge; and They represent the scenes respectively. time Producers and consumers The actual power of the configured fan; and They represent the scenes respectively. time Producers and consumers The actual power output of the configured photovoltaic system; and They represent the scenes respectively. time Producers and consumers The actual power output when the load is cut off; and Scenes time Producers and consumers The charging power of the configured energy storage device; Representing a scene time Producers and consumers The amount of energy stored in the configured energy storage device; and Representing the scene respectively Producers and consumers The energy storage capacity of the system at times 0 and 23; Representing a scene time Producers and consumers The maximum energy storage capacity of the configured energy storage device; Representing a scene time Producers and consumers The maximum charging and discharging power of the configured energy storage device; and These represent the system's charging and discharging efficiencies, respectively. Indicates a time interval; Indicates the number of charge / discharge cycles; and Representing the scene respectively time Producers and consumers The maximum power of the configured fan; and Representing the scene respectively time Producers and consumers The maximum output of the configured photovoltaic power. This is not a physical quantity, but a binary state indicator variable (with a value of 0 or 1). When energy storage devices are at time This value is 1 when charging, and 0 otherwise. When energy storage devices are at time During discharge, this value is 1; otherwise, it is 0. Therefore, This ensures that at most one of these two state indicator variables can be 1, thus achieving mutual exclusion of the three states of charging, discharging, and idle.

[0074] Formula (51) represents the power balance constraint of prosumers; Formula (52) represents the reciprocity constraint of power exchange in P2P transactions; Formula (53) defines the net P2P transaction power of prosumers; Formula (54) represents the energy state balance (daily cycle consistency) of the energy storage system at the beginning and end of the scheduling cycle; Formula (55) describes the relationship between the energy state changes of the energy storage system at adjacent times; Formula (56) represents the upper and lower limit constraints of the energy storage capacity of the energy storage system; Formula (57) represents the logical constraint that charging and discharging cannot be carried out simultaneously at any time; Formulas (58) and (59) represent the upper limit limits of the charging power and discharging power of the energy storage system, respectively; Formula (60) defines the auxiliary variable for the switching (cycle) of the energy storage charging and discharging state; Formula (61) represents the limit on the maximum number of charging and discharging cycles of the energy storage device; Formulas (62) and (63) represent the limits on the active and reactive power of the load that can be cut off, respectively; formulas (64) and (65) represent the limits on the active and reactive power output of the wind turbine, respectively; formulas (66) and (67) represent the limits on the actual active and reactive power output of the photovoltaic system, respectively.

[0075] Example 2 This invention provides a unified optimization system for the physical resilience and operational configuration of power systems, the system comprising: processor; A memory storing instructions that, when executed by the processor, configure the system to perform the method described in Embodiment 1.

[0076] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A unified optimization method for the physical resilience and operational configuration of power systems, the method being executed by one or more processors of a computing system, characterized in that, The method includes: (a) In the computing system, a two-layer computing architecture is established, the architecture including an upper-layer power grid physical system model and a lower-layer energy community model; (b) The computing system generates a set of random scenarios representing random uncertainty and a set of robust uncertainty representing adversarial attack scenarios; (c) The computational system performs a numerical optimization process, including: During the long-term planning phase, based on the aforementioned set of random scenarios: the physical topology hardening parameters are determined by the upper-level power grid physical system model; and the distributed energy physical configuration parameters are determined by the lower-level energy community model. During the short-term operation phase, based on the robust uncertainty set: the physical repair scheduling parameters are determined by the upper-level power grid physical system model; and the internal energy exchange scheduling dataset is determined by the lower-level energy community model. (d) The long-term planning phase and the short-term operation phase are coupled by technical constraints, wherein the physical repair scheduling parameters determined by the upper-level power grid physical system model in the short-term operation phase are mathematically constrained by the physical topology hardening parameters determined by the upper-level power grid physical system model in the long-term planning phase. (e) A distributed numerical optimization algorithm is used to converge the numerical optimization process by iteratively exchanging the original and dual variables between the upper-level power grid physical system model and the lower-level energy community model.

2. The method according to claim 1, characterized in that, The robust uncertainty set models the adversarial attack scenario as a set of network topology states constrained by a maximum attack count budget.

3. The method according to claim 1, characterized in that, The distributed numerical optimization algorithm is the alternating direction multiplier method.

4. The method according to claim 1, characterized in that, The upper-level power grid physical system model and the lower-level energy community model are connected by coupling variables. The coupling variables are used as benefit terms in the objective function of the upper-level power grid physical system model and as cost or penalty terms in the objective function of the lower-level energy community model.

5. The method according to claim 1, characterized in that, The step of determining parameters by the upper-level power grid physical system model is performed based on minimizing the objective function of the upper-level power grid physical system model, and the objective function is a combination of its total cost items and total revenue items, wherein: the total cost items include at least capital expenditure cost items, energy dissipation cost items, emergency investment cost items, and dynamic scheduling cost items; and the total revenue items include at least infrastructure usage fee revenue items and network service fee revenue items.

6. The method according to claim 1, characterized in that, The lower-level energy community model includes: The upper-level community coordination subject model determines the internal exchange price based on the objective function of minimizing the total community expenditure. The total community expenditure includes the external electricity purchase cost and the grid connection usage fee paid to the upper-level power grid physical system model. The lower-level autonomous entity model collaboratively determines its distributed energy physical configuration parameters and proactive load reduction parameters based on the internal exchange price and the objective function of minimizing individual net costs.

7. The method according to claim 1, characterized in that, When the upper-level power grid physical system model performs the numerical optimization process during the long-term planning phase, it further includes: enforcing a radial network topology through virtual power flow constraints; and transforming non-convex power flow constraints into convex constraints using second-order cone relaxation.

8. The method according to claim 1, characterized in that, When the upper-level power grid physical system model determines the physical repair scheduling parameters during the short-term operation phase, it further includes optimizing the scheduling of mobile reconfiguration units under the constraint of the number of maintenance personnel.

9. The method according to claim 1, characterized in that, The distributed energy physical configuration parameters determined by the lower-level energy community model include the physical capacity parameters of the stationary energy storage device, and the physical operation of the stationary energy storage device is further constrained by one or more constraints during the short-term operation phase. These constraints include: daily state of charge balance constraints, logic constraints to prevent simultaneous charging and discharging, or physical limits on charging and discharging power.

10. A unified optimization system for the physical resilience and operational configuration of power systems, the system comprising: processor; A memory having instructions stored thereon, characterized in that, when the instructions are executed by the processor, the system is configured to perform the method according to any one of claims 1-9.

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