A method and system for estimating dynamic security limit value of power distribution network under extreme weather based on deep balanced network and resilience scheduling

Abstract

The application discloses a kind of based on depth balanced network's extreme weather under power distribution network dynamic security limit value estimation and resilience scheduling method and system, method includes: constructing balanced perception condition vector, and amplification dynamic security limit value sample;Enhanced sample is input into depth balanced network, and according to balance hidden state, obtains bus voltage dynamic security upper and lower limit and line flow dynamic security upper limit;Dynamic security limit value is embedded in power distribution network two-stage robust resilience scheduling model, obtains extreme weather under power distribution network resilience scheduling scheme;Decision focus learning strategy is introduced to evaluate resilience scheduling scheme and update dynamic security limit value, form dynamic security limit value estimation and resilience scheduling collaborative optimization closed loop.The application can alleviate the problem of unstable security boundary estimation under extreme weather small sample condition, improve dynamic security limit value estimation accuracy and robust scheduling feasibility, reduce power distribution network load loss and operating cost under extreme weather, improve power distribution network resilience operation ability.

Description

Technical Field

[0001] This invention belongs to the field of power grids and relates to distribution network resilient dispatch, power system artificial intelligence estimation and robust optimization operation technology. Specifically, it relates to a method and system for dynamic safety limit estimation and resilient dispatch of distribution networks under extreme weather conditions based on deep equilibrium networks. It is applicable to dynamic safety boundary estimation and adaptive resilient operation of distribution networks under extreme weather conditions such as icing, strong winds, low temperatures and freezing rain. Background Technology

[0002] With the increasing integration of distributed photovoltaic, wind power, energy storage systems, and flexible loads into distribution networks, the operational status of distribution networks is exhibiting greater randomness and dynamism. Under extreme weather conditions, icing, low temperatures, strong winds, and freezing rain can alter line carrying capacity, equipment safety margins, and load demand characteristics, making it difficult for traditional dispatch models based on fixed safety limits to accurately reflect real-time changes in line power flow limits and bus voltage boundaries.

[0003] Existing distribution network resilience optimization scheduling methods typically treat the safety limits of line power flow constraints and bus voltage constraints as given constants, or estimate the safety limits based on explicit time-series estimation models. These methods have two main drawbacks: First, extreme weather samples occur infrequently, and samples of high-risk operating conditions such as severe icing, high wind speeds, and high loads are scarce. Explicit estimation models tend to learn operating patterns under normal weather conditions, making it difficult to accurately characterize the abrupt changes in safety limits during extreme periods. Second, safety limit estimation and scheduling optimization are often disconnected, and the impact of estimation errors on scheduling costs, load losses, and safety feasibility is difficult to feed back into the estimation model training process.

[0004] Deep equilibrium networks can represent the long-term evolution of dynamic systems as implicit fixed-point relationships without explicit expansion of deep time-series networks, making them suitable for characterizing the coupled equilibrium relationships between weather disturbances, load states, dispatch feedback, and electrical equipment safety limits. However, directly applying deep equilibrium networks to estimate safety limits in extreme weather conditions is still affected by insufficient extreme sample coverage, unstable equilibrium convergence, and the absence of dispatch targets in training. Therefore, a method is needed that can simultaneously consider extreme weather sample augmentation, dynamic safety limit estimation, robust resilient scheduling, and closed-loop update of dispatch feedback. Summary of the Invention

[0005] Purpose of the Invention: To address the problems of unstable dynamic safety boundary estimation, conservative or distorted fixed safety limit scheduling, and disconnect between estimation and scheduling models under extreme weather conditions with small sample sizes, this invention proposes a method and system for dynamic safety limit estimation and resilient scheduling of distribution networks under extreme weather conditions based on a deep equilibrium network. Through the collaborative design of equilibrium sensing sample enhancement, deep equilibrium network safety limit estimation, two-stage robust resilient scheduling, and closed-loop scheduling feedback update, this invention can alleviate the problem of unstable safety boundary estimation under extreme weather conditions with small sample sizes, improve the accuracy of dynamic safety limit estimation and the feasibility of robust scheduling, reduce distribution network load loss and operating costs under extreme weather conditions, and enhance the resilient operation capability of the distribution network.

[0006] Technical Solution: To achieve the above-mentioned objectives, this invention provides a method for estimating dynamic safety limits and resilient scheduling of distribution networks under extreme weather conditions based on deep equilibrium networks, comprising the following steps:

[0007] Step 1: Based on historical data of distribution network operation data, resource equipment data, and meteorological data, construct the equilibrium sensing condition vector, and perform data augmentation on the safety limit value samples based on Wasserstein generative adversarial network to obtain the augmented sample set;

[0008] Step 2: Input the amplified sample set obtained in Step 1 into the deep equilibrium network, establish the implicit equilibrium relationship between the dynamic safety limit value and meteorological conditions, load status, and dispatching decisions, and output the dynamic safety upper and lower limits of the bus voltage and the dynamic safety upper limit of the line power flow based on the implicit equilibrium state.

[0009] Step 3: Embed the dynamic safety limit value obtained in Step 2 into the two-stage robust and resilient dispatch model of the distribution network. The first stage of the two-stage robust and resilient dispatch model determines the initial dispatch scheme, and the second stage performs corrective dispatch after given weather and load uncertainty disturbances. Based on the column constraint generation algorithm, a distribution network resilient dispatch scheme under extreme weather conditions that satisfies the upper and lower limits of dynamic safety of bus voltage and the upper limit of dynamic safety of line power flow is obtained.

[0010] Step 4: Introduce a decision-focused learning strategy to evaluate the resilient scheduling scheme obtained in Step 3 and update the dynamic safety limit value, forming a closed loop of collaborative optimization between dynamic safety limit value estimation and resilient scheduling.

[0011] Furthermore, the distribution network operation data in step 1 includes the voltage of each bus, active power flow, reactive power flow, line load rate and load demand; the resource and equipment data includes the capacity, upper and lower power limits, ramp rate, energy storage status of charge and charge and discharge efficiency of distributed photovoltaic, distributed wind power, energy storage system and main grid power purchase interface; and the meteorological data includes ambient temperature, relative humidity, wind speed, freezing rain rate and icing thickness.

[0012] Furthermore, in step 1, the relevant decision variables determined include:

[0013] For each scheduling period t and node k, the active power output of the distributed generation unit ;

[0014] For each scheduling period t, the power purchased by the distribution network from the upstream main grid is... ;

[0015] For each scheduling period t, the energy storage charging power Energy storage and discharge power ;

[0016] For each scheduling period t and load node k, the load loss is... ;

[0017] For each uncertain scenario Second phase of adjusting scheduling variables .

[0018] Furthermore, in step 1, the equalization sensing condition vector Represented as ,in Let t be the meteorological variable. Let t be the load variable for time period t. For scheduling decisions during time period t; sample the actual equilibrium safety limit values. With condition vector As input to the discriminator, the condition vector and random noise As input to the generator, samples of generated equilibrium safety limit values ​​are obtained. Sample augmentation is achieved by minimizing the Wasserstein distance between the true equilibrium distribution and the generated equilibrium distribution.

[0019] Furthermore, the balanced safety limit value samples generated in step 1 are used to supplement the sample space boundary region under severe icing, low temperature, high wind speed and high load conditions, so as to expand the coverage of the fixed point convergence training samples of the deep equalization network.

[0020] Furthermore, the input features of the deep equalization network in step 2 Balanced hidden state satisfy ,in For a nonlinear equilibrium mapping with parameter θ; the equilibrium residuals As a nonlinear equation, it is solved using the Broyden iteration. The equilibrium hidden state is obtained. Then through output mapping Obtain dynamic safety limit values .

[0021] Furthermore, the nonlinear equilibrium mapping Implemented by a gated implicit balancing operator, specifically expressed as follows:

[0022] (1)

[0023] (2)

[0024] (3)

[0025] (4)

[0026] (5)

[0027] In the formula, To update the door; To reset the door; Use the Sigmoid activation function; , and This is the hidden state weight matrix; This is the current hidden state; This represents a candidate equilibrium state. , and The input weight matrix; , and To adjust the bias term of the update gate output; This represents the Hadamard product.

[0028] Furthermore, the objective function of the two-stage robust scheduling model in step 3 is as follows:

[0029] (6)

[0030] (7)

[0031] (8)

[0032] (9)

[0033] (10)

[0034] (11)

[0035] (12)

[0036] In the formula, ; This represents the initial scheduling cost for the first phase; This represents the cost of the second-stage correction under the most unfavorable uncertainty scenario. Indicating an uncertain scenario Corrective decisions made accordingly; The dynamic safety limits estimated by the DEQ model include the upper and lower limits of dynamic voltage safety and the upper limit of dynamic line power flow. Robust risk weights; The uncertainty set consists of weather and load estimation errors; Total operating cost; Indicates the cost of distributed generation; This indicates the cost of purchasing electricity from the main grid; Indicates the operating cost of energy storage; Indicates the cost of load loss; , This indicates the unit cost of distributed generation, time-varying electricity price, etc. , This represents the active power of distributed generation, the power purchased by the main grid, and... The duration of the ice storm is indicated by t, where t represents the period of the ice storm. Indicates the busbar in the distribution network; This indicates the type of distributed generation, where 1 represents distributed photovoltaic generation and 2 represents distributed wind power generation. This represents the energy storage degradation cost coefficient; This represents the load loss penalty coefficient; and These represent the current charging power and discharging power, respectively. This indicates the amount of lost load.

[0037] Furthermore, the constraints of the two-stage robust and resilient scheduling model in step 3 include:

[0038] Distributed generation output upper and lower limits constraints, ramping constraints, and start-stop constraints;

[0039] Energy storage state of charge recursive constraints, upper and lower limits of state of charge constraints, charging power constraints, and discharging power constraints;

[0040] Main grid power purchase capacity limit constraint;

[0041] Active power balance constraints and reactive power balance constraints;

[0042] The dynamic constraints on bus voltage and line power flow are determined by the dynamic safety limit values ​​obtained in step 2.

[0043] Non-negativity constraints on load loss and constraints on safe system operation.

[0044] Furthermore, weather and load uncertainties are described using a budgetary uncertainty set, which defines the upper and lower bounds of estimation errors for various meteorological variables and nodal loads, and is further defined by uncertain budget parameters. By controlling the total deviation of all estimation errors, the conservatism of the robust scheduling scheme can be adjusted.

[0045] Furthermore, the training objectives of the deep balanced network in step 4 include estimation loss, balance consistency loss, and decision loss, as follows:

[0046] (13)

[0047] (14)

[0048] (15)

[0049] (16)

[0050] In the formula, The overall objective loss function; To estimate the loss; To balance network losses; Losses due to decision-making; This represents a scheduling scheme based on estimated dynamic safety limits; This represents the actual dynamic safety limit value.

[0051] The estimation loss is used to measure the deviation between the estimated dynamic safety limit value and the actual safety limit value. The equilibrium consistency loss is used to measure the residual between the equilibrium hidden state and the nonlinear equilibrium mapping output. The decision loss is used to measure the operating cost and load loss level of the robust scheduling scheme based on the estimated safety limit value.

[0052] Furthermore, in step 3, the two-stage robust and resilient scheduling model is solved using a column constraint generation algorithm. After initializing a finite set of uncertain scenarios, the main problem and the worst-case subproblem are solved alternately. When the worst-case subproblem generates a new scenario that violates the robust constraints or a scenario with a higher correction cost, the scenario is added to the scenario set and the main problem is solved again until the difference between the upper and lower bounds is less than the preset convergence threshold.

[0053] This invention also provides a dynamic safety limit estimation and resilience dispatching system for distribution networks under extreme weather conditions based on a deep equilibrium network, comprising:

[0054] The distribution network data analysis and sample enhancement module is used to construct equilibrium sensing condition vectors based on historical data of distribution network operation data, resource equipment data and meteorological data, and enhance the scarce equilibrium safety limit value samples under extreme weather conditions based on Wasserstein generative adversarial network to obtain an expanded sample set.

[0055] The dynamic safety limit estimation module is used to input the extended sample set obtained by the distribution network data analysis and sample enhancement module into the deep equilibrium network, establish the implicit equilibrium relationship between the dynamic safety limit and meteorological conditions, load status, and dispatch decisions, solve the implicit equilibrium state through Broyden fixed point iteration, and output the dynamic safety upper and lower limits of bus voltage and the dynamic safety upper limit of line power flow based on the implicit equilibrium state.

[0056] The robust and resilient scheduling decision module is used to embed the dynamic safety limit value obtained by the dynamic safety limit value estimation module into the two-stage robust and resilient scheduling model. The first stage determines the initial scheduling scheme, and the second stage performs corrective scheduling after given weather and load uncertain disturbances, and solves for a resilient scheduling scheme that satisfies dynamic voltage constraints, dynamic line power flow constraints and equipment operation constraints.

[0057] The closed-loop feedback update module is used to feed back the resilient scheduling scheme obtained by the robust resilient scheduling decision module to the distribution network operation status update and deep equilibrium network training process. It performs rolling updates on the input characteristics, equilibrium hidden state and dynamic safety limit value in subsequent periods, forming a closed loop of dynamic safety limit value estimation and resilient scheduling co-evolution.

[0058] Beneficial effects: Compared with the prior art, the present invention has the following technical effects:

[0059] 1. This invention models the evolution of power safety limits under extreme weather conditions as an implicit equilibrium process jointly determined by meteorological disturbances, load conditions, and dispatch feedback. Compared with fixed safety limits or explicit sequence estimation methods, it can more accurately characterize the time-varying features of bus voltage boundaries and line power flow boundaries.

[0060] 2. This invention utilizes Wasserstein generative adversarial networks to expand the sample coverage of high-risk operating conditions such as severe icing, low temperature, high wind speed, and high load, thereby alleviating the instability of fixed point convergence in deep equilibrium networks caused by the scarcity of extreme weather samples and improving the generalization ability of dynamic safety limit estimation.

[0061] 3. This invention embeds the estimated dynamic safety limit value into a two-stage robust and resilient scheduling model, and drives model updates through scheduling feedback and decision loss, so that the safety limit value estimation no longer only serves the purpose of estimation accuracy, but directly serves to reduce operating costs, reduce load loss and improve robust feasibility. Attached Figure Description

[0062] Figure 1 This is the overall flowchart of the method of the present invention. Detailed Implementation

[0063] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0064] Example 1:

[0065] This embodiment provides a method for estimating the dynamic safety limit value and resilient scheduling of distribution networks under extreme weather conditions based on a deep equilibrium network, referring to... Figure 1 It includes the following steps:

[0066] Step 1: Input historical data of distribution network operation, resource equipment, and meteorological data; construct a balance sensing condition vector; and enhance the scarce balance safety limit value samples under extreme weather conditions using a Wasserstein generative adversarial network to obtain an expanded sample set, as detailed below:

[0067] Distribution network operation data includes bus voltage, active power flow, reactive power flow, line load rate, and node load demand; resource and equipment data includes the capacity, upper and lower power limits, ramp rate, energy storage status of charge, and charge and discharge efficiency of distributed photovoltaic, distributed wind power, energy storage systems, and main grid power purchase interfaces; meteorological data includes ambient temperature, relative humidity, wind speed, freezing rain rate, and icing thickness.

[0068] Assume the distribution network consists of multiple nodes and routes Busbar Set Route Collection Distributed generation collection and energy storage collection Composition. For each scheduling period t, the dynamic safety limit vector is defined as:

[0069] (17)

[0070] In the formula, Represents the vector of dynamic safety limit values ​​for time period t; and These represent the lower and upper limits of the dynamic safety limit for bus voltage, respectively. This indicates the upper limit of dynamic safety for power flow on the line.

[0071] Training samples for dynamic safety limits under extreme weather conditions are scarce, especially under the combined effects of severe icing, low temperatures, high wind speeds, and high loads, where real samples are often located at the boundaries of the sample space. To improve the coverage of high-risk operating conditions by deep equalization networks, this invention constructs an equalization sensing condition vector:

[0072] (18)

[0073] In the formula, Represents the equilibrium sensing condition vector for time period t; For meteorological conditions, Ambient temperature; Relative humidity; Wind speed; For freezing rain rate; This refers to the thickness of the ice layer. Indicates load conditions; This indicates the scheduling decision.

[0074] Unlike generating regular running samples, the WGAN proposed in this invention aims to learn conditional equilibrium distributions:

[0075] (19)

[0076] In the formula, To balance the safety limits.

[0077] The generator outputs an equilibrium state trajectory, which is used to enrich the coverage of equilibrium manifolds under extreme and rare weather conditions:

[0078] (20)

[0079] Generators accept condition variables and random noise The conditional Wasserstein adversarial objective function is defined as follows:

[0080] (twenty one)

[0081] In the formula, G is the equilibrium trajectory generator; D is the discriminator; Measuring a true balanced sample; Measure the generation of balanced samples.

[0082] By minimizing the Wasserstein distance, the true equilibrium distribution is approximated to the generated distribution:

[0083] (twenty two)

[0084] In the formula, To generate a balanced distribution; This achieves a true balanced distribution. Through the above optimizations, the generated samples form a supplementary coverage in extreme weather boundary regions, which is used to expand the training sample set for subsequent deep equalization networks.

[0085] Step 2: Train a deep equalization network based on the expanded sample set obtained in Step 1. Solve the equilibrium hidden state through Broyden fixed-point iteration and output the dynamic safety upper and lower limits of bus voltage and the dynamic safety upper limit of line power flow, as detailed below:

[0086] The input feature vector is defined as:

[0087] (twenty three)

[0088] In the formula, For meteorological variables; For load variables; The scheduling decisions from the previous time period; This represents the dynamic electrical equipment safety limit value for the previous time period.

[0089] For each time interval t, the equilibrium hidden state satisfies:

[0090] (twenty four)

[0091] In the formula, To balance the hidden states; Represents input features; The parameters are from Defined nonlinear equilibrium mapping.

[0092] To enhance the ability to express the coupling relationship between meteorological disturbances, operational status, and dispatch feedback, this embodiment employs a gated implicit balancing operator. :

[0093] (25)

[0094] (26)

[0095] (27)

[0096] (28)

[0097] (29)

[0098] In the formula, To update the door; To reset the door; Use the Sigmoid activation function; , and This is the hidden state weight matrix; This is the current hidden state; This represents a candidate equilibrium state. , and The input weight matrix; , and To adjust the bias term of the update gate output; This represents the Hadamard product.

[0099] To avoid the long-term error accumulation and computational burden caused by explicitly expanding deep sequence networks, the equilibrium residual is defined as:

[0100] (30)

[0101] Solving the DEQ equilibrium state is equivalent to solving the following nonlinear equation:

[0102] (31)

[0103] This invention employs the Broyden method to perform fixed-point iterative solution of the DEQ equilibrium residual equation corresponding to equation (31). The conventional Newton method requires explicit calculation and updating of the Jacobian matrix in each iteration, resulting in a heavy computational burden in high-dimensional hidden states and multi-stage scheduling feedback training. Therefore, the Broyden method solves the equilibrium hidden state by recursively maintaining the Jacobian approximation matrix, reducing computational overhead while ensuring iterative convergence, making it more suitable for embedding into subsequent decision-focused training processes. Its iterative process is as follows:

[0104] (32)

[0105] (33)

[0106] (34)

[0107] In the formula, Indicates the first The Jacobian approximation matrix under the next iteration; This represents the change in hidden state between two consecutive iterations.

[0108] The iteration termination condition is:

[0109] (35)

[0110] In the formula, To balance the convergence threshold. After convergence is achieved, the dynamic safety limit is obtained by output mapping:

[0111] (36)

[0112] In the formula, This is the output mapping function.

[0113] Step 3: Under the influence of extreme weather, distribution network dispatching needs to simultaneously consider operating costs, power supply reliability, and dynamic security constraints. This invention models the resilient dispatching problem of the distribution network as a two-stage robust optimization problem, as follows:

[0114] Under extreme weather conditions, the operation of power distribution networks is simultaneously affected by weather, load, and dynamic safety limits. This invention models the resilient scheduling problem as a two-stage robust optimization problem: the first stage determines the initial scheduling scheme, and the second stage performs corrective scheduling after a given uncertain disturbance to ensure that the system still meets voltage, line power flow, and equipment operation constraints under the most unfavorable weather and load scenarios.

[0115] After considering weather and load uncertainties, the robust scheduling model can be written as:

[0116] (37)

[0117] (38)

[0118] (39)

[0119] (40)

[0120] (41)

[0121] (42)

[0122] (43)

[0123] In the formula, ; This represents the initial scheduling cost for the first phase; This represents the cost of the second-stage correction under the most unfavorable uncertainty scenario. Indicating an uncertain scenario Corrective decisions made accordingly; The dynamic safety limits estimated by the DEQ model include the upper and lower limits of dynamic voltage safety and the upper limit of dynamic line power flow. Robust risk weights; The uncertainty set consists of weather and load estimation errors; Total operating cost; Indicates the cost of distributed generation; This indicates the cost of purchasing electricity from the main grid; Indicates the operating cost of energy storage; Indicates the cost of load loss; , This indicates the unit cost of distributed generation, time-varying electricity price, etc. , This represents the active power of distributed generation, the power purchased by the main grid, and... The duration of the ice storm is indicated by t, where t represents the period of the ice storm. Indicates the busbar in the distribution network; This indicates the type of distributed generation, where 1 represents distributed photovoltaic generation and 2 represents distributed wind power generation. This represents the energy storage degradation cost coefficient; This represents the load loss penalty coefficient; and These represent the current charging power and discharging power, respectively. This indicates the amount of lost load.

[0124] To control the conservatism of robust optimization, this embodiment uses a budgetary uncertainty set to describe the uncertainties of weather and load:

[0125] (44)

[0126] In the formula, Indicates the first Estimation error of meteorological variables, Represents a node The load estimation error; and These are the upper bounds of the error; This represents the normalized uncertain budget consumption; For an uncertain budget.

[0127] The key constraints of the two-stage robust and resilient dispatch model include distributed generation constraints, energy storage constraints, grid power purchase constraints, network power flow balance constraints, dynamic voltage constraints, and dynamic line power flow constraints. Among them, the dynamic voltage constraints and dynamic line power flow constraints are determined by the safety limit values ​​obtained in step 2.

[0128] Distributed generation constraints:

[0129] (45)

[0130] (46)

[0131] (47)

[0132] In the formula, Indicates the rate of ascent; and These represent the continuous operation and shutdown times of the micro-turbine generator, respectively. This indicates the start / stop status of distributed generation, with 1 indicating start and 0 indicating stop.

[0133] Energy storage constraints:

[0134] (48)

[0135] (49)

[0136] (50)

[0137] (51)

[0138] In the formula, Indicates the current energy storage status; This indicates the energy storage status at the previous moment; and These represent charging efficiency and discharging efficiency, respectively. and These represent the minimum permissible state of charge and the maximum permissible state of charge of energy storage, respectively. and These represent the maximum allowable charging power and the maximum allowable discharging power of the energy storage, respectively.

[0139] Main grid power purchase constraints:

[0140] (52)

[0141] In the formula, This is the maximum permissible power purchase capacity for the tie line.

[0142] Power flow constraints:

[0143] (53)

[0144] In the formula, This indicates the actual active power.

[0145] Bus voltage constraint:

[0146] (54)

[0147] In the formula, This represents the actual bus voltage.

[0148] Network power flow equations include active power balance and reactive power balance:

[0149] (55)

[0150] (56)

[0151] In the formula, Indicates the busbar in the distribution network; and Indicates the line conductance and inductance; This indicates the phase angle.

[0152] The two-stage robust scheduling model is solved using a column constraint generation algorithm. First, a finite set of scenarios is initialized. In the r-th iteration, based on the set of identified scenes Solving the main problem yields the first-stage scheduling decision. and target lower bound Then fix Solve the worst-case subproblem to obtain the scenario that maximizes the correction cost or results in the tightest robust constraints. and update the target upper bound. ;like If the condition is met, the algorithm terminates; otherwise, it will terminate. join in And continue to iterate.

[0153] Step 4: To avoid the safety limit estimation model and the scheduling model becoming isolated from each other, this invention feeds back the resilient scheduling results to the distribution network operation status update and deep equilibrium network training process, as follows:

[0154] First, we introduce a decision-focused learning strategy, which directly optimizes the DEQ model based on robust scheduling performance. Then, the decision-oriented loss is defined as... The overall training objective is:

[0155] (57)

[0156] (58)

[0157] (59)

[0158] (60)

[0159] In the formula, The overall objective loss function; To estimate the loss; To balance network losses; Losses due to decision-making; This represents a scheduling scheme based on estimated dynamic safety limits; This represents the actual dynamic safety limit value.

[0160] The evolution process of the system's operating state is as follows:

[0161] (61)

[0162] In the formula, This represents the system state update mapping driven by scheduling behavior.

[0163] Secondly, the updated running status will be fed back to the DEQ model:

[0164] (62)

[0165] Optimization during training Finally obtained :

[0166] (63)

[0167] After training, the optimal parameters are used to obtain the dynamic safety limit value:

[0168] (64)

[0169] Further solution for the optimal scheduling strategy:

[0170] (65)

[0171] Through the above training objectives, the dynamic safety limit estimation model not only pursues estimation accuracy, but also feeds back scheduling costs, load losses and safety feasibility to the model parameter update process, forming a closed-loop collaborative mechanism of estimation, scheduling and feedback.

[0172] As can be seen from the above, at the technical level, the method of this invention unifies the modeling of meteorological disturbances, load status, historical dispatch information, and electrical equipment safety limits into an implicit equilibrium relationship. It utilizes Wasserstein to generate adversarial networks to extend scarce equilibrium safety limit samples under extreme weather conditions, and estimates the dynamic safety upper and lower limits of bus voltage and the dynamic safety upper limit of line power flow through deep equilibrium networks and Broyden fixed-point iterations, improving the stability and accuracy of dynamic safety boundary estimation under small sample conditions in extreme weather. At the operational level, the dynamic safety limits are embedded into a two-stage robust and resilient dispatch model, enabling the distribution network to still meet dynamic voltage constraints, dynamic line power flow constraints, and equipment operation constraints under the most unfavorable weather and load disturbances, thus improving the robust feasibility of dispatch schemes under extreme weather conditions. At the economic level, by collaboratively optimizing distributed power output, energy storage charging and discharging, main grid power purchase, and load loss, the system operating cost and correction dispatch cost are reduced, improving the utilization efficiency of flexible resources in the distribution network. In terms of resilience enhancement, by feeding the scheduling results back to the distribution network operation status update and deep equilibrium network training process, the estimation of safety limit values ​​no longer merely serves the purpose of estimation accuracy, but directly serves to reduce load losses, mitigate operational risks, and improve power supply continuity. Through closed-loop coordination of estimation, scheduling, and status updates, this method enables the distribution network to exhibit stronger adaptability, safety, and resilience in complex and extreme weather environments such as icing, strong winds, low temperatures, and freezing rain, providing technical support for adaptive and safe dispatching of new distribution networks.

[0173] Example 2:

[0174] Based on the scheme of Embodiment 1, this embodiment provides a dynamic safety limit estimation and resilience dispatching system for distribution networks under extreme weather conditions based on a deep equilibrium network, including:

[0175] The distribution network data analysis and sample enhancement module is used to construct equilibrium sensing condition vectors based on historical data of distribution network operation data, resource and equipment data, and meteorological data. It enhances the scarce equilibrium safety limit value samples under extreme weather conditions using Wasserstein generative adversarial network to obtain an expanded sample set. The distribution network operation data includes the voltage of each bus, active power flow, reactive power flow, line load rate, and load demand. The resource and equipment data includes the capacity, upper and lower power limits, ramp rate, state of charge and charge / discharge efficiency of distributed photovoltaic, distributed wind power, energy storage systems, and main grid power purchase interfaces. The meteorological data includes ambient temperature, relative humidity, wind speed, freezing rain rate, and icing thickness.

[0176] The dynamic safety limit estimation module is used to input the extended sample set obtained by the distribution network data analysis and sample enhancement module into the deep equilibrium network, establish the implicit equilibrium relationship between the dynamic safety limit and meteorological conditions, load status, and dispatch decisions, solve the implicit equilibrium state through Broyden fixed point iteration, and output the dynamic safety upper and lower limits of bus voltage and the dynamic safety upper limit of line power flow based on the implicit equilibrium state.

[0177] The robust and resilient dispatch decision module is used to establish a two-stage robust and resilient dispatch model based on the dynamic safety upper and lower limits of bus voltage and the dynamic safety upper limit of line power flow obtained by the dynamic safety limit estimation module. The first stage determines the initial dispatch scheme, and the second stage performs corrective dispatch after given weather and load uncertainties. The solution obtains a resilient dispatch scheme that satisfies dynamic voltage constraints, dynamic line power flow constraints, and equipment operation constraints. The resilient dispatch scheme includes distributed generation output, energy storage charging and discharging power, main grid power purchase power, and load loss.

[0178] The closed-loop feedback update module is used to feed back the resilient scheduling scheme obtained by the robust resilient scheduling decision module to the distribution network operation status update and deep equilibrium network training process. It performs rolling updates on the input characteristics, equilibrium hidden state and dynamic safety limit value in subsequent periods, and updates the deep equilibrium network parameters based on the estimated loss, equilibrium consistency loss and decision loss, forming a closed loop of dynamic safety limit value estimation and resilient scheduling co-evolution.

[0179] It should be understood that the dynamic safety limit estimation and resilience scheduling system for distribution networks under extreme weather conditions based on deep equilibrium networks in this embodiment can realize all the technical solutions in Embodiment 1. The functions of each functional module can be specifically implemented according to the methods in the above method embodiments. The specific implementation process can be referred to the relevant descriptions in the above embodiments, which will not be repeated here.

Claims

1. A method for estimating dynamic safety limits and resilient scheduling of distribution networks under extreme weather conditions based on deep equilibrium networks, characterized in that, The method includes the following steps: Step 1: Based on historical data of distribution network operation data, resource equipment data, and meteorological data, construct the equilibrium sensing condition vector, and perform data augmentation on the safety limit value samples based on Wasserstein generative adversarial network to obtain the augmented sample set; Step 2: Input the amplified sample set obtained in Step 1 into the deep equilibrium network, establish the implicit equilibrium relationship between the dynamic safety limit value and meteorological conditions, load status, and dispatching decisions, and output the dynamic safety upper and lower limits of the bus voltage and the dynamic safety upper limit of the line power flow based on the implicit equilibrium state. Step 3: Embed the dynamic safety limit value obtained in Step 2 into the two-stage robust and resilient dispatch model of the distribution network. The first stage of the two-stage robust and resilient dispatch model determines the initial dispatch scheme, and the second stage performs corrective dispatch after given weather and load uncertainty disturbances. Based on the column constraint generation algorithm, a distribution network resilient dispatch scheme under extreme weather conditions that satisfies the upper and lower limits of dynamic safety of bus voltage and the upper limit of dynamic safety of line power flow is obtained. Step 4: Introduce a decision-focused learning strategy to evaluate the resilient scheduling scheme obtained in Step 3 and update the dynamic safety limit value, forming a closed loop of collaborative optimization between dynamic safety limit value estimation and resilient scheduling.

2. The method for estimating dynamic safety limits and resilient scheduling of distribution networks under extreme weather conditions based on deep equilibrium networks according to claim 1, characterized in that, The distribution network operation data in step 1 includes the voltage of each bus, active power flow, reactive power flow, line load rate and load demand; the resource and equipment data includes the capacity, upper and lower power limits, ramp rate, energy storage status of charge and charge and discharge efficiency of distributed photovoltaic, distributed wind power, energy storage system and main grid power purchase interface; the meteorological data includes ambient temperature, relative humidity, wind speed, freezing rain rate and icing thickness.

3. The method for estimating dynamic safety limits and resilient scheduling of distribution networks under extreme weather conditions based on deep equilibrium networks according to claim 1, characterized in that, In step 1, the equalization sensing condition vector Represented as ,in Let t be the meteorological variable. Let t be the load variable for time period t. For scheduling decisions during time period t; sample the actual equilibrium safety limit values. With condition vector As input to the discriminator, the condition vector and random noise As input to the generator, samples of generated equilibrium safety limit values ​​are obtained. Sample augmentation is achieved by minimizing the Wasserstein distance between the true equilibrium distribution and the generated equilibrium distribution.

4. The method for estimating dynamic safety limits and resilient scheduling of distribution networks under extreme weather conditions based on deep equilibrium networks according to claim 1, characterized in that, The input features of the deep equalization network in step 2 Balanced hidden state satisfy ,in For a nonlinear equilibrium mapping with parameter θ; Balance residuals As a nonlinear equation, it is solved using the Broyden iteration. The equilibrium hidden state is obtained. Then through output mapping Obtain dynamic safety limit values .

5. A method for estimating dynamic safety limits and resilient scheduling of distribution networks under extreme weather conditions based on deep equilibrium networks, as described in claim 4, is characterized in that... The nonlinear equilibrium mapping Implemented by a gated implicit balancing operator, specifically expressed as follows: （1）； （2）； （3）； （4）； （5）； In the formula, To update the door; To reset the door; Use the Sigmoid activation function; , and The hidden state weight matrix; This is the current hidden state; This represents a candidate equilibrium state. , and The input weight matrix; , and To adjust the bias term of the update gate output; This represents the Hadamard product.

6. The method for estimating dynamic safety limits and resilient scheduling of distribution networks under extreme weather conditions based on deep equilibrium networks according to claim 1, characterized in that, The objective function of the two-stage robust scheduling model in step 3 is as follows: （6）； （7）； （8）； （9）； （10）； （11）； （12）； In the formula, ; This represents the initial scheduling cost for the first phase; This represents the cost of the second-stage correction under the most unfavorable uncertainty scenario. Indicating an uncertain scenario Corrective decisions made accordingly; The dynamic safety limits estimated by the DEQ model include the upper and lower limits of dynamic voltage safety and the upper limit of dynamic line power flow. Robust risk weights; The uncertainty set consists of weather and load estimation errors; Total operating cost; Indicates the cost of distributed generation; This indicates the cost of purchasing electricity from the main grid; Indicates the operating cost of energy storage; Indicates the cost of load loss; , This indicates the unit cost of distributed generation, time-varying electricity price, etc. , This represents the active power of distributed generation, the power purchased by the main grid, and... The duration of the ice storm is indicated by t, where t represents the period of the ice storm. Indicates a busbar in a power distribution network; This indicates the type of distributed generation, where 1 represents distributed photovoltaic generation and 2 represents distributed wind power generation. This represents the energy storage degradation cost coefficient; This represents the load loss penalty coefficient; and These represent the current charging power and discharging power, respectively. This indicates the amount of lost load.

7. A method for estimating dynamic safety limits and resilient scheduling of distribution networks under extreme weather conditions based on deep equilibrium networks, as described in claim 6, is characterized in that... The constraints of the two-stage robust and resilient scheduling model in step 3 include: Distributed generation output upper and lower limits constraints, ramping constraints, and start-stop constraints; Energy storage state of charge recursive constraints, upper and lower limits of state of charge constraints, charging power constraints, and discharging power constraints; Main grid power purchase capacity limit constraint; Active power balance constraints and reactive power balance constraints; The dynamic constraints on bus voltage and line power flow are determined by the dynamic safety limit values ​​obtained in step 2. Non-negativity constraints on load loss and constraints on safe system operation.

8. A method for estimating dynamic safety limits and resilient scheduling of distribution networks under extreme weather conditions based on deep equilibrium networks, as described in claim 6, is characterized in that... Weather and load uncertainties are described using a budgetary uncertainty set, which defines the upper and lower bounds of the estimation errors for various meteorological variables and nodal loads, and is further defined by uncertain budget parameters. By controlling the total deviation of all estimation errors, the conservatism of the robust scheduling scheme can be adjusted.

9. A method for estimating dynamic safety limits and resilient scheduling of distribution networks under extreme weather conditions based on deep equilibrium networks, as described in claim 1, is characterized in that... In step 3, the two-stage robust and resilient scheduling model is solved using a column constraint generation algorithm. After initializing a finite set of uncertain scenarios, the main problem and the worst-case subproblem are solved alternately. When the worst-case subproblem generates a new scenario that violates the robust constraints or a scenario with a higher correction cost, the scenario is added to the scenario set and the main problem is solved again until the difference between the upper and lower bounds is less than the preset convergence threshold.

10. A dynamic safety limit estimation and resilient dispatching system for distribution networks under extreme weather conditions based on a deep equilibrium network, characterized in that, The system for implementing the method according to any one of claims 1 to 9 comprises: The distribution network data analysis and sample enhancement module is used to construct equilibrium sensing condition vectors based on historical data of distribution network operation data, resource equipment data and meteorological data, and enhance the scarce equilibrium safety limit value samples under extreme weather conditions based on Wasserstein generative adversarial network to obtain an expanded sample set. The dynamic safety limit estimation module is used to input the extended sample set obtained by the distribution network data analysis and sample enhancement module into the deep equilibrium network, establish the implicit equilibrium relationship between the dynamic safety limit and meteorological conditions, load status, and dispatch decisions, solve the implicit equilibrium state through Broyden fixed point iteration, and output the dynamic safety upper and lower limits of bus voltage and the dynamic safety upper limit of line power flow based on the implicit equilibrium state. The robust and resilient scheduling decision module is used to embed the dynamic safety limit value obtained by the dynamic safety limit value estimation module into the two-stage robust and resilient scheduling model. The first stage determines the initial scheduling scheme, and the second stage performs corrective scheduling after given weather and load uncertain disturbances, and solves for a resilient scheduling scheme that satisfies dynamic voltage constraints, dynamic line power flow constraints and equipment operation constraints. The closed-loop feedback update module is used to feed back the resilient scheduling scheme obtained by the robust resilient scheduling decision module to the distribution network operation status update and deep equilibrium network training process. It performs rolling updates on the input characteristics, equilibrium hidden state and dynamic safety limit value in subsequent periods, forming a closed loop of dynamic safety limit value estimation and resilient scheduling co-evolution.

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