Power system heterogeneous flexible resource aggregation method and device based on limit charging and discharging curve, and computer readable storage medium
By constructing a refined adjustment capability model for multiple types of flexible resources and a mathematical model of the limit charge-discharge curve, and combining it with the Lagrange mean value theorem, the problems of low computational efficiency and low accuracy of distributed flexible resource scheduling are solved, and efficient and reliable power system scheduling is achieved.
Patent Information
- Application Number
- CN202511486858.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-17
- Publication Date
- 2025-11-14
- Estimated Expiration
- 2045-10-17
AI Technical Summary
Existing single-unit modeling methods are insufficient to meet the scheduling needs of large-scale clusters, especially given the large number of distributed flexible resources, heterogeneous parameters, and complex dynamic characteristics, resulting in low scheduling computation efficiency and low accuracy.
A refined regulation capability model for multiple types of flexible resources is constructed, a mathematical modeling method for the extreme charge-discharge curve is proposed, and a conservative internal approximation is achieved by combining the Lagrange mean value theorem. A unified model is constructed through virtual energy storage, and an equivalent energy storage aggregation model is built to optimize resource scheduling.
It improves the efficiency and accuracy of scheduling calculations, simplifies computational complexity, enables efficient and reliable scheduling of heterogeneous resources, and reduces the demand for computing resources.
Smart Images

Figure CN120955649A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power system dispatching and operation, specifically to a method, apparatus, and computer-readable storage medium for the aggregation of heterogeneous flexible resources in a power system based on limit charge-discharge curves. Background Technology
[0002] Against the backdrop of an accelerated global energy structure transition towards low-carbon development, the integration of a high proportion of renewable energy into the grid has become an inevitable trend in power system development. However, the large-scale integration of fluctuating power sources such as wind and solar power has significantly exacerbated the uncertainty on both the supply and demand sides of electricity. Traditional centralized regulation resources (such as thermal power and pumped storage) are gradually becoming unable to meet the needs of new power systems in terms of response speed, regulation accuracy, and environmental impact. In this context, distributed flexible resources—including distributed energy storage systems, electric vehicles, temperature-controlled loads, and demand-side adjustable loads—have become key elements supporting the safe and stable operation of power systems due to their wide geographical distribution, flexible regulation response, and environmental friendliness. However, distributed resources are characterized by their large quantity, heterogeneous parameters, and complex dynamic characteristics, making it difficult for existing individual modeling methods to meet the scheduling needs of large-scale clusters. Summary of the Invention
[0003] The purpose of this invention is to provide a method, device, and computer-readable storage medium for heterogeneous flexible resource aggregation in power systems based on extreme charge / discharge curves. It constructs a refined regulation capability model for multiple types of flexible resources (battery energy storage systems, electric vehicles, and temperature-controlled loads). For battery energy storage systems, it proposes an energy storage power allocation strategy based on dynamic weighting coefficients; for electric vehicles, it establishes a Monte Carlo-particle swarm optimization model; for temperature-controlled loads, it establishes a high-order RC equivalent model and proposes a unified modeling method for virtual energy storage forms for various resources. It proposes a mathematical modeling method for extreme charge / discharge curves (ECC / EDC), achieving a conservative internal approximation of ECC / EDC based on the Lagrange mean value theorem; and it proposes an equivalent energy storage aggregation model considering extreme charge / discharge conditions, theoretically covering extreme operating conditions such as sudden power shortages and resource heterogeneity through the construction of the gentlest ECC / EDC curve, thereby solving the problems mentioned in the background art.
[0004] To achieve the above objectives, the present invention provides the following technical solution: A method for aggregating heterogeneous flexible resources in a power system based on limiting charge-discharge curves includes the following steps: (1) Construct a refined regulation capability model for multiple types of flexible resources such as battery energy storage systems, electric vehicles, and temperature-controlled loads, and propose a unified modeling method for virtual energy storage for each type of resource; (2) A mathematical modeling method for the limiting charge-discharge ECC / EDC curve is proposed, and a conservative internal approximation of the ECC / EDC is achieved based on the Lagrange mean value theorem; (3) An equivalent energy storage aggregation model considering extreme charge and discharge conditions is proposed, and the theory is constructed to cover extreme working conditions by using the gentlest ECC / EDC curve.
[0005] As a preferred embodiment of the present invention, the method for constructing a refined regulation capability model of the battery energy storage system in step (1) is as follows: The initial energy storage is ;in, It is the initial state of charge. This is the maximum energy limit. The integral model for the dynamic energy storage capacity changing over time is: ;in, This refers to the charging and discharging power. The total stored energy can be calculated using the following expression: .
[0006] Among these, the charging and discharging power and energy must meet the constraints. The relationship between total charge and discharge power is expressed as follows: ,in For maximum discharge power, Maximum charging power, This is the lower limit of energy.
[0007] As a preferred embodiment of the present invention, the method for constructing the refined adjustment capability model of the electric vehicle in step (1) is as follows: Charging behavior modeling: The formula for charging duration is shown below. Wherein, It refers to the charging duration. It is the initial state of charge. It refers to battery capacity. It's the charging power. It refers to charging efficiency; The formula for the probability of selecting a charging mode is shown below. Where, It is in charging mode. This is the charging start time.
[0008] As a preferred embodiment of the present invention, the method for constructing the refined regulation capability model of the temperature-controlled load in step (1) is as follows: For temperature-controlled loads, a high-order RC equivalent model is established; A uniform temperature offset ratio (TOR) is defined to ensure that all buildings involved in regulation contribute load adjustment at the same level of thermal comfort compromise. The uniform definition of the TOR is as follows. It is the total load adjustment target. It is the building sensitivity coefficient. This is the maximum permissible temperature offset.
[0009] As a preferred embodiment of the present invention, the unified modeling method for virtual energy storage in step (1) is as follows: Considering the flexible adjustment characteristics of various resources such as battery energy storage systems, electric vehicles, and temperature-controlled loads, three-dimensional equivalent parameters are defined for virtual energy storage: power dimension, energy dimension, and time dimension. Among them, , and These represent the instantaneous upper limit of adjustable power of aggregated resources, the equivalent schedulable energy capacity, and the continuous adjustment time window, respectively. It refers to the adjustable power of a single resource. It is the time when resources are saturated.
[0010] As a preferred embodiment of the present invention, the mathematical modeling method for the extreme charge / discharge ECC / EDC curve in step (2) is specifically as follows: For a single flexible resource, the mathematical expression for its limiting charge / discharge ECC / EDC curve is derived based on the power-energy-time relationship as follows: in, It is the upper limit of energy. It is the initial state of charge. That is the maximum charging power. It is the maximum discharge power of the energy storage system. It is the absolute value of the maximum discharge power. This is the extreme charging time curve. This is the limiting discharge time curve. It is a time interval.
[0011] The extreme charge / discharge ECC / EDC curves can intuitively reflect the power and energy constraints of energy storage, providing a simplified characterization for aggregation modeling; For a cluster containing N flexible resources, its overall characteristic curve is generated by superimposing the limit charge / discharge ECC / EDC curves of each unit. The slope of the overall characteristic curve of charging power aggregation and discharging power aggregation satisfies the following relationship with the energy limit.
[0012] in, It is the maximum charging power of aggregated resources. It is the maximum discharge power of the aggregated resource. It is the slope of the k-th segment of the overall ECC. It is the slope of the k-th segment of the overall EDC. M It is the number of segments; As a preferred embodiment of the present invention, the method for achieving a conservative internal approximation of ECC / EDC based on the Lagrange mean value theorem in step (2) is as follows: First, change the ECC / EDC curve from t=0 to t= Divide into two segments and determine the midpoint using Lagrange's Mean Value Theorem. This midpoint divides the ECC / EDC curve into two segments with different slopes. Then, the mean value theorem is repeatedly applied to each sub-curve to further subdivide it to a predetermined number of segments, ultimately yielding an equivalent ECC / EDC curve composed of multiple linear broken lines. ; in, It is energy The derivative with respect to time at this moment, yes The energy of moments It is the energy at the initial moment.
[0013] As a preferred embodiment of the present invention, the following steps are included: First, based on the initial SoC optimization allocation strategy, the gentlest ECC / EDC curve covering extreme working conditions is generated. Then, the Lagrange mean value theorem is used to recursively segment the gentlest ECC / EDC curve to construct a conservative inner approximate boundary. Finally, the computational complexity and accuracy are balanced by dynamically adjusting the segment density and error threshold. In discharge scenarios, priority is given to allocating flexible resources to low-SoC systems with shorter discharge times, mathematically expressed as: For a cluster consisting of N flexible resource units, the necessary and sufficient condition for the slowest rate of decay of the overall ECC curve slope is the charging time of each unit. Reaching the maximum value, where, It is about The function expression, It is about The function expression, It is the energy in the current state. It is the maximum power of a single resource. It is the maximum energy of a single resource. .
[0014] Furthermore, the present invention also provides a heterogeneous flexible resource aggregation device for power systems based on limiting charge-discharge curves, the device comprising: The data acquisition and processing module is used to obtain the real-time operating parameters and status information of each flexible resource; The resource modeling module is used to perform the construction of a refined regulation capacity model and a unified modeling of virtual energy storage forms in step (1); The curve calculation module is used to perform the mathematical modeling and conservative internal approximation of the limit charge-discharge curve in step (2); The aggregation optimization module is used to perform the construction of the equivalent energy storage aggregation model in step (3); The communication and control module is used to exchange and aggregate capability information with the power grid dispatch center and issue control commands to subordinate flexible resources.
[0015] Furthermore, the present invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the above-described method for heterogeneous flexible resource aggregation in a power system based on a limit charge-discharge curve.
[0016] The beneficial effects of this invention are as follows: This invention solves the problems of low efficiency and low accuracy in scheduling calculations involving heterogeneous resources, and provides an efficient and reliable tool for power system scheduling. Through a unified modeling method for virtual energy storage, heterogeneous resources such as battery energy storage, electric vehicles, and temperature-controlled loads are transformed into standardized scheduling objects, which greatly simplifies the computational complexity. Based on the mathematical modeling of the extreme charge-discharge curve (ECC / EDC) combined with the Lagrange mean value theorem approximation algorithm, the computational resource requirements are significantly reduced while ensuring accuracy, and the problem that existing single-unit modeling methods cannot meet the scheduling requirements of large-scale clusters is solved. Attached Figure Description
[0017] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation
[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0019] Please see Figure 1 In this embodiment of the invention, a method and apparatus for heterogeneous flexible resource aggregation in a power system based on limiting charge-discharge curves are disclosed. The method specifically includes the following steps: (1) Construct a refined regulation capability model for multiple types of flexible resources (battery energy storage system, electric vehicle, temperature-controlled load), and propose a unified modeling of virtual energy storage forms for various types of resources.
[0020] (1-1) For battery energy storage systems, an energy storage power allocation strategy based on dynamic weight coefficients is proposed.
[0021] The initial energy storage is ;in, It is the initial state of charge. This is the maximum energy limit. The integral model for the dynamic energy storage capacity changing over time is: ;in, This refers to the charging and discharging power. The total stored energy can be calculated using the following expression: .
[0022] Among these, the charging and discharging power and energy must meet the constraints. ; For maximum discharge power, This is the lower limit of energy.
[0023] (1-2) A Monte Carlo-Particle Swarm Hybrid Optimization Model was established for electric vehicles.
[0024] Charging behavior modeling: The formula for charging duration is shown below. Wherein, It refers to the charging duration. It is the initial state of charge. It refers to battery capacity. It's the charging power. It refers to charging efficiency; The formula for the probability of selecting a charging mode is shown below. Where, It is in charging mode. This is the charging start time.
[0025] (1-3) A high-order RC equivalent model was established for temperature-controlled loads.
[0026] Because different buildings have varying thermal characteristics (such as wall insulation performance and air conditioning power) and users' temperature tolerance ranges, a unified Temperature Offset Ratio (TOR) value is defined to ensure that all buildings participating in regulation contribute load regulation at the same level of thermal comfort compromise, avoiding deterioration of user experience due to over-regulation in some buildings. The unified definition of TOR is as follows. It is the total load adjustment target. It is the building sensitivity coefficient. This is the maximum permissible temperature offset.
[0027] (1-4) Unified Modeling of Virtual Energy Storage. Considering the adjustment characteristics of various flexible resources such as battery energy storage systems, electric vehicles, and temperature-controlled loads, three-dimensional equivalent parameters are defined for virtual energy storage: power dimension, energy dimension, and time dimension. Among them, , and These represent the instantaneous upper limit of adjustable power, the equivalent dispatchable energy capacity, and the continuous adjustment time window, respectively. It is the time when resources are saturated.
[0028] (2) A mathematical modeling method for the limiting charge-discharge curve (ECC / EDC) is proposed, and a conservative internal approximation of ECC / EDC is realized based on the Lagrange mean value theorem.
[0029] (2-1) ECC / EDC Model for a Single Flexible Resource. The Limiting Charge Curve (ECC) and Limiting Discharge Curve (EDC) are core characteristic curves describing the charging and discharging behavior of a distributed energy storage system (DES). ECC is the energy accumulation curve when the energy storage system starts charging at maximum power from the initial state of charge (SoC0) until it reaches the upper energy limit (SoC0=1); EDC is the energy release curve when the energy storage system starts discharging at maximum power from the initial SoC0 until it reaches the lower energy limit (SoC0=0). Multi-state refers to the heterogeneous distribution of the initial state of charge of each unit in the energy storage system, and the resulting differences in dynamic charging and discharging behavior.
[0030] For a single flexible resource, the mathematical expression for its limiting charge / discharge ECC / EDC curve is derived based on the power-energy-time relationship as follows: in, It is the upper limit of energy. It is the initial state of charge. This is the maximum charging power of the energy storage system. It is the maximum discharge power of the energy storage system. It is the absolute value of the maximum discharge power. , It is a time interval; The ECC / EDC curves can intuitively reflect the power constraints (curve slope) and energy constraints (curve inflection points) of energy storage, providing a simplified representation for aggregation modeling.
[0031] (2-2) Overall characteristic modeling of multiple flexible resources. For a cluster containing N flexible resources, its overall characteristic curve is generated by superimposing the ECC / EDC of each unit. The slope of the overall characteristic curve of the system's charging power aggregation and discharging power aggregation satisfies the following relationship with the energy limit.
[0032] in, It is the maximum charging power of aggregated resources. It is the maximum discharge power of the aggregated resource. It is the slope of the k-th segment of the overall ECC. It is the slope of the k-th segment of the overall EDC. M It is the number of segments; (2-3) ECC / EDC approximation method based on Lagrange's mean value theorem. First, the ECC curve is approximated from t=0 to t= The time corresponding to SoC=1 is divided into two segments, and the midpoint is determined using the Lagrange Mean Value Theorem. This midpoint divides the ECC curve into two segments with different slopes. Then, the mean square theorem is applied repeatedly to each sub-curve to further subdivide it to a predetermined number of segments (e.g., five). This results in an equivalent ECC curve composed of multiple linear segments. The segmentation method for the EDC curve is similar, ultimately yielding the ECC / EDC curve. .
[0033] (3) An equivalent energy storage aggregation model considering extreme charge and discharge conditions is proposed, and the theory is constructed by the gentlest ECC / EDC curve to cover extreme working conditions such as sudden power shortage and resource heterogeneity.
[0034] (3-1) Optimal Equivalent Curve Construction Framework Based on the Slowest ECC / EDC Curve. In the aggregation modeling of distributed flexible resource clusters, the construction of the equivalent curve needs to meet two core requirements: conservatism and flexibility. Conservatism means that the equivalent curve must be strictly within the actual cluster charging and discharging capacity boundary to avoid scheduling instructions exceeding physical constraints. Flexibility means that under the conservatism constraint, the equivalent curve should be as close as possible to the actual capacity boundary to maximize the utilization of scheduling resources.
[0035] This invention constructs an equivalent model that combines safety and economy by combining the gentlest ECC / EDC curve with an approximation based on the Lagrange mean value theorem. First, based on the initial SoC optimization allocation strategy, the gentlest ECC / EDC curve covering extreme operating conditions is generated. Then, the Lagrange mean value theorem is used to recursively segment the gentlest ECC / EDC curve, constructing a conservative inner approximation boundary. Finally, by dynamically adjusting the segment density and error threshold, computational complexity and accuracy are balanced.
[0036] (3-2) Optimal Equivalent Curve Construction Method Based on Conservative Constraints. Since the SoC allocation of high-power flexible resources significantly affects the curve shape, while the SoC allocation of low-power flexible resources has a negligible impact, in charging scenarios, high SoC is prioritized for flexible resources with short charging times, allowing them to quickly saturate and exit charging; in discharging scenarios, low SoC is prioritized for flexible resources with short discharging times. Mathematically, this can be expressed as: For a cluster consisting of N flexible resource units, the necessary and sufficient condition for the slowest rate of decay of the overall ECC curve slope is the charging time of each unit. Reaching the maximum value, where, It is about The function expression, It is about The function expression, It is the energy in the current state. It is the maximum power of a single resource. It is the maximum energy of a single resource. It is a time interval.
[0037] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.
[0038] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.
Claims
1. A method for heterogeneous flexible resource aggregation in power systems based on limiting charge-discharge curves, characterized in that, Includes the following steps: (1) Construct a refined adjustment capability model for multiple types of flexible resources such as battery energy storage systems, electric vehicles, and temperature-controlled loads, and propose a unified modeling method for virtual energy storage for the aforementioned multiple types of flexible resources; (2) A mathematical modeling method for the limiting charge / discharge ECC / EDC curve is proposed, and a conservative internal approximation of the limiting charge / discharge ECC / EDC curve is achieved based on the Lagrange mean value theorem. (3) The theory of the gentlest ECC / EDC curve is used to cover extreme working conditions and form an equivalent energy storage aggregation model.
2. The method for heterogeneous flexible resource aggregation in a power system based on limiting charge-discharge curves according to claim 1, characterized in that, The method for constructing the refined regulation capability model of the battery energy storage system in step (1) is as follows: The initial energy storage is ;in, It is the initial state of charge. It is the maximum energy limit; The integral model for the change of dynamic energy storage capacity over time is as follows: ;in, It is the charging and discharging power; The total energy storage expression is calculated as follows: Among these, the charging and discharging power and energy must meet the constraints. The relationship between total charge and discharge power is expressed as follows: ,in For maximum discharge power, Maximum charging power, This is the lower limit of energy.
3. The method for heterogeneous flexible resource aggregation in a power system based on limiting charge-discharge curves according to claim 2, characterized in that, The method for constructing the refined adjustment capability model of electric vehicles in step (1) is as follows: Charging behavior modeling: The formula for charging duration is as follows; where, It refers to the charging duration. It is the initial state of charge. It refers to battery capacity. It's the charging power. It refers to charging efficiency; ; The formula for the probability of selecting a charging mode is shown below; where, It is in charging mode. This is the charging start time; 。 4. The method for heterogeneous flexible resource aggregation in a power system based on limiting charge-discharge curves according to claim 3, characterized in that, The method for constructing the refined regulation capability model of the temperature-controlled load in step (1) is as follows: For temperature-controlled loads, a high-order RC equivalent model is established; A uniform temperature offset ratio (TOR) is defined to ensure that all buildings involved in regulation contribute load adjustment at the same level of thermal comfort compromise. The uniform definition of the temperature offset ratio (TOR) is as follows; where, It is the total load adjustment target. It is the building sensitivity coefficient. This is the maximum permissible temperature offset; 。 5. The method for heterogeneous flexible resource aggregation in a power system based on limiting charge-discharge curves according to claim 4, characterized in that, The unified modeling method for virtual energy storage in step (1) is as follows: Considering the flexible adjustment characteristics of various resources such as battery energy storage systems, electric vehicles, and temperature-controlled loads, three-dimensional equivalent parameters are defined for virtual energy storage, namely, power dimension, energy dimension, and time dimension. , and These represent the instantaneous upper limit of adjustable power of aggregated resources, the equivalent schedulable energy capacity, and the continuous adjustment time window, respectively. It refers to the adjustable power of a single resource. It is the resource saturation time; 。 6. The method for heterogeneous flexible resource aggregation in a power system based on limiting charge-discharge curves according to claim 5, characterized in that, The mathematical modeling method for the extreme charge / discharge ECC / EDC curves in step (2) is as follows: For a single flexible resource, the mathematical expression for its limiting charge / discharge ECC / EDC curve is derived based on the power-energy-time relationship as follows: in, It is the upper limit of energy. It is the initial state of charge. That is the maximum charging power. It is the maximum discharge power of the energy storage system. It is the absolute value of the maximum discharge power. This is the extreme charging time curve. This is the limiting discharge time curve. It is a time interval; For a cluster containing N flexible resources, its overall characteristic curve is generated by superimposing the limit charge / discharge ECC / EDC curves of each unit. The slopes of the overall characteristic curves of charging power aggregation and discharging power aggregation satisfy the following relationship with the energy limit: in, It is the maximum charging power of aggregated resources. It is the maximum discharge power of the aggregated resource. It is the slope of the k-th segment of the overall ECC. It is the slope of the k-th segment of the overall EDC. M It is the number of segments.
7. The method for heterogeneous flexible resource aggregation in a power system based on limiting charge-discharge curves according to claim 6, characterized in that, The conservative internal approximation of the limiting charge / discharge ECC / EDC curve based on the Lagrange mean value theorem in step (2) is as follows: First, change the ECC / EDC curve from t=0 to t= Divide into two segments and determine the midpoint using Lagrange's Mean Value Theorem. This midpoint divides the ECC / EDC curve into two segments with different slopes. Then, the mean value theorem is repeatedly applied to each sub-curve to further subdivide it to a predetermined number of segments, ultimately yielding an equivalent ECC / EDC curve composed of multiple linear broken lines. in, It is energy The derivative with respect to time at this moment, yes The energy of moments It is the energy at the initial moment.
8. The method for heterogeneous flexible resource aggregation in a power system based on limiting charge-discharge curves according to claim 7, characterized in that, It also includes the following steps: First, based on the initial SoC optimization allocation strategy, the gentlest ECC / EDC curve covering extreme working conditions is generated. Then, the Lagrange mean value theorem is used to recursively segment the gentlest ECC / EDC curve to construct a conservative inner approximate boundary. Finally, the computational complexity and accuracy are balanced by dynamically adjusting the segment density and error threshold. In discharge scenarios, priority is given to allocating flexible resources to low-SoC systems with shorter discharge times, mathematically expressed as: For a cluster consisting of N flexible resource units, the necessary and sufficient condition for the slowest rate of decay of the overall ECC curve slope is the charging time of each unit. Reaching the maximum value, where, It is about The function expression, It is about The function expression, It is the energy in the current state. It is the maximum power of a single resource. It is the maximum energy of a single resource. It is a time interval.
9. An apparatus for implementing the method of any one of claims 1-8, characterized in that, The device includes: The data acquisition and processing module is used to obtain the real-time operating parameters and status information of each flexible resource; The resource modeling module is used to perform the construction of a refined regulation capacity model and a unified modeling of virtual energy storage forms in step (1); The curve calculation module is used to perform the mathematical modeling and conservative internal approximation of the limit charge-discharge curve in step (2); The aggregation optimization module is used to perform the construction of the equivalent energy storage aggregation model in step (3); The communication and control module is used to exchange and aggregate capability information with the power grid dispatch center and issue control commands to subordinate flexible resources.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1-8.
Citation Information
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