A hierarchical multi-dimensional availability evaluation method and system for a road area high-entropy energy system based on fuzzy entropy

Abstract

The evaluation method and system for the layered multi-dimensional availability of the road area high-entropy energy system based on fuzzy entropy of the application evaluate from three aspects of time availability, spatial coverage and power quality, innovatively combine three dimensions of time, space and quality for evaluation, comprehensively reflect the comprehensive support capability of the system in the real road area dynamic environment, so as to accurately locate the problem, which is caused by single point equipment failure, regional coordination failure or system level regulation failure, make the operation and optimization have pertinence, the evaluation method of the application can also be deconstructed from the order and coordination of the energy system, so as to quantify the availability of the road area high-entropy energy system, for quantifying the order degree of the output behavior of the unit equipment, the concept of fuzzy entropy is introduced in the model, which can effectively measure the complexity and irregularity of the time sequence, and provide an index for evaluating the quality of such non-stationary and intermittent signals.

Description

Technical Field

[0001] This invention relates to the field of high-entropy energy availability evaluation, specifically to a hierarchical multidimensional availability evaluation method and system for road-region high-entropy energy systems based on fuzzy entropy. Background Technology

[0002] As the cornerstone of modern society, the ability of energy systems to continuously and stably provide energy services can be quantitatively assessed using the indicator of "availability." Generally, energy system availability refers to the probability or proportion of time that the system can perform its intended functions (i.e., be in an available state) within a specified external condition and time frame. This indicator reflects not only the reliability of the energy system against failures but also its maintainability for rapid recovery after a failure. Its steady-state mathematical model can be expressed as:

[0003] A = MTTF + MTTR (7.1)

[0004] Wherein, MTTF is the Mean Time To Failure, which is the average uptime of the system from the time of repair to the time of the next failure; MTTR is the Mean Time To Repair, which is the average time required for the system to recover from a faulty state to a usable state. Correspondingly, instantaneous availability is defined as the probability that the system is in an available state at a specific time t.

[0005] In typical energy systems such as power systems, the concept of availability has been further specified and standardized. For example, the IEEE Std 762 standard defines indicators such as the Equivalent Availability Factor (EAF) and the Equivalent Forced Outage Rate (EFOR) for generating units. EAF comprehensively considers actual operating conditions such as planned maintenance, forced outages, and partial output operation in its calculations, more realistically reflecting the availability level of units throughout the complete commercial operating cycle. These standardized indicators provide a unified basis for availability evaluation for power generation companies, grid operators, and regulatory agencies. At the system planning level, traditional reliability assessments typically model components such as generators and transmission lines as probabilistic components with specific availability and unavailability levels. Then, methods such as recursive convolution and Monte Carlo simulations are used to assess the probability that the system will meet load demand within a given period, providing quantitative support for grid planning and reserve capacity determination.

[0006] As the energy transition deepens, the integration of a high proportion of renewable energy sources poses new challenges to traditional availability assessment methods based on deterministic components. To quantify the availability of stochastic power sources such as wind and solar power, derivative concepts such as capacity reliability and effective carrying capacity have been proposed to measure the equivalent replacement capacity of conventional generating units under the same reliability standards. In recent years, the focus of energy availability research has shifted from single-site assessments to refined modeling of system-level capacity adequacy under high renewable energy penetration, and is gradually incorporating the synergistic effects analysis of flexible resources such as energy storage and demand response. Simultaneously, the large-scale development of distributed energy resources, energy storage systems, and electric vehicles is driving the evolution of energy systems from centralized, unidirectional transmission architectures to decentralized, bidirectional interactive complex networks.

[0007] In this context, availability analysis is no longer limited to the failure-repair process of power generation equipment, but must be extended to the level of integrated energy systems, and further considerations are needed:

[0008] (1) The impact of information and communication system failures on distributed resource coordination and control;

[0009] (2) The role of the interconnection and mutual assistance between the distribution network and the microgrid group in improving the local and overall power supply availability;

[0010] (3) The impact of electric vehicle charging and discharging behavior and user-side energy storage strategies on aggregate availability through market mechanisms.

[0011] Against the backdrop of the integrated development of transportation and energy, the availability evaluation of roadside high-entropy energy systems (such as heterogeneous energy networks composed of roadside photovoltaics, vibration energy harvesting, charging facilities, and smart streetlights) exhibits significant unique characteristics. These characteristics include diversified energy sources, highly random load behavior, dynamic changes in energy configuration, complex and harsh operating environments, and close coupling with traffic flow patterns. Availability analysis of these systems must not only consider the reliability and maintainability of traditional equipment but also characterize the supply-demand matching capability under the dual uncertainties of transportation and energy, and consider the impact of new features such as infrastructure sharing and multi-energy complementarity on the system's continuous energy supply capability. Existing technologies, such as the paper "Early Warning Method for Road Microgrid Operation Status Based on High-Entropy Energy Availability Assessment" published by Liu Baozhu et al. of North China Electric Power University in the China Journal of Highway and Transport, involve a hierarchical assessment model for high-entropy energy availability. It provides calculation methods for high-entropy energy availability at the equipment layer, cluster layer, and microgrid layer. When evaluating the availability of the equipment layer, it uses equipment reliability assessment and equipment anomaly assessment. However, it is a equipment reliability assessment model based on competitive failure and a high-entropy energy capture equipment anomaly detection model based on group characteristic quantities. The model does not introduce fuzzy entropy to quantify the orderliness of the output behavior of unit equipment.

[0012] Considering that road space is evolving into an integrated energy complex encompassing photovoltaics, wind power, high-entropy roadside energy, energy storage devices, and smart loads, its internal energy types, spatiotemporal characteristics, and energy quality exhibit high heterogeneity and strong coupling. The system's operating state far exceeds the traditional binary description of "operation / outage," displaying complex intermittency, randomness, and multi-scale characteristics. Existing evaluation methods have three main limitations when dealing with such high-entropy systems:

[0013] (1) Lack of characterization of high entropy characteristics

[0014] Traditional reliability or efficiency metrics (such as mean time between failures and conversion efficiency) cannot quantify the disorder and predictability of system output, which is the core factor affecting the availability of distributed high-entropy energy in road areas.

[0015] (2) Fragmentation of evaluation dimensions

[0016] Existing methods often analyze time availability, spatial coverage, or power quality in isolation, lacking a unified measurement framework that can integrate time, space, and quality, making it difficult to fully reflect the comprehensive support capabilities of the system in real-world dynamic road environments.

[0017] (3) Insufficient diagnostic depth

[0018] Traditional methods struggle to pinpoint the source of system performance degradation—whether it stems from single-point device failure, regional coordination malfunction, or system-level control failure—leading to a lack of targeted operation and maintenance optimization.

[0019] To this end, we propose a hierarchical multidimensional availability evaluation method and system for road-region high-entropy energy systems. The system is deconstructed hierarchically from the perspectives of energy system order and synergy to quantify the availability of road-region high-entropy energy systems. Summary of the Invention

[0020] The technical problem to be solved by this invention is to provide a hierarchical multidimensional availability evaluation method for road-domain high-entropy energy systems based on fuzzy entropy, the evaluation method comprising the following steps:

[0021] I. Unit-level Availability Evaluation:

[0022] Unit devices Overall availability The definition is shown in equation (7.2):

[0023]

[0024] In the formula:

[0025] For unit-based devices Fuzzy entropy for output power time series calculation;

[0026] For behavioral orderliness factor;

[0027] This is the output capacity factor;

[0028] II. Availability Evaluation of Regional Layers:

[0029] Regional Collaborative Availability The definition is shown in equation (7.16):

[0030]

[0031] In the formula:

[0032] B represents the foundation of health; C represents the temporal coordination degree of the region; C represents the spatial coordination consistency coefficient.

[0033] in,

[0034]

[0035]

[0036]

[0037] In the formula:

[0038] This represents the total number of isomorphic energy units within the region. It is the arithmetic mean, and is calculated according to formula (7.13); The mean of the elements in the set; Let R be the standard deviation of the elements in the set; for a region containing N energy units, its optimal alignment similarity matrix is ​​R; define the cooperative potential set of this region. Let R be the set of all off-diagonal elements in matrix R: The total number of elements in this set is Each element Characterized the unit With unit The maximum possible synergy potential between them;

[0039]

[0040] III. System-level Availability Evaluation:

[0041] System layer availability The definition is shown in equation (7.19):

[0042]

[0043] in,

[0044] The static average capacity is calculated according to equation (7.18).

[0045]

[0046] in,

[0047] This represents the total number of regions within the system. For the first Cooperative availability in each region; For the first The weight coefficients of each region satisfy the following conditions. ; For dynamic and collaborative flexibility; Assigning weights based on the importance of mutual assistance .

[0048] Preferably, the unit layer availability evaluation step includes:

[0049] 1.1 Data Preprocessing and Feature Extraction:

[0050] Set unit equipment Within the evaluation period T, its output power is sampled at equal intervals to obtain an original sequence of length N; this sequence is then transformed into a normalized power sequence: ,in

[0051]

[0052] For unit devices No. Measured power at each sampling point For unit devices Reference power, It is the k-th element in the normalized power sequence of unit device i; 1≤k≤N; subsequently, the normalized sequence is... Data preprocessing is performed, including outlier removal and data smoothing. The preprocessed sequence is denoted as... ,in These are the cleaned and valid data points. This sequence will serve as the input for all subsequent calculations;

[0053] From sequence Two key features were extracted: average normalized output force. and sequence standard deviation ,in It is a sequence The kth element:

[0054]

[0055] This value directly reflects the average output level of the unit equipment during the evaluation period;

[0056]

[0057] This value will be used for the adaptive setting of the similarity tolerance parameter r in subsequent fuzzy entropy calculations;

[0058] 1.2 Calculation of output capacity factor:

[0059] Output capacity factor Calculate according to formula (7.5):

[0060]

[0061] The range of values ​​is ;

[0062] 1.3 Calculation of behavioral orderliness factor:

[0063] Behavioral orderliness factor The calculation is divided into two sub-steps: first, based on the preprocessed sequence Calculate fuzzy entropy Then, it is transformed into a normalized orderliness score through a mapping function;

[0064] 1.4 Unit equipment availability calculation:

[0065] Unit devices The overall availability is determined by , Synthesize according to formula (7.2).

[0066] Preferably, the system-level availability evaluation steps include:

[0067] First, divide the collaborative and mutually supportive clusters, assuming they are divided into... Each cluster; then the guarantee level of a single cluster is calculated. Definition: Cluster weight For clusters The proportion of critical loads to total critical loads in the system: cluster internal weights Indicates the region The load accounts for a portion of the load of its cluster. The proportion; the guarantee level of a single cluster. for:

[0068]

[0069] in,

[0070] It is a cluster The weighted average of the availability of the inner area, i.e. its static capacity;

[0071] It is a cluster The highest area availability within;

[0072] It is the collaborative gain strength coefficient, used to reward differences in availability within the cluster;

[0073] Finally, the protection levels of all clusters in the system are weighted and summarized:

[0074]

[0075] in,

[0076] It refers to the number of collaborative and mutually supportive clusters;

[0077] It is a cluster The weights;

[0078] It is the system mutual assistance gain factor, which characterizes the best overall protection level that the system can achieve by optimizing power support under a given mutual assistance network topology and capacity constraints.

[0079] Preferably, based on the preprocessed sequence Calculate fuzzy entropy The steps are as follows:

[0080] definition:

[0081] Embedding dimension m: used to reconstruct the phase space;

[0082] Similarity tolerance Adaptive value ;

[0083] Gradient parameter n: used to define the shape of the fuzzy membership function;

[0084] The first step is to reconstruct the phase space, transforming the one-dimensional sequence... Reconstructed into an m-dimensional vector:

[0085] ,

[0086] The second step is to calculate any two m-dimensional reconstruction vectors. and The Chebyshev distance between them, which characterizes the absolute difference between two power output sequences of length m at their least dissimilar moments:

[0087]

[0088] in It is the k-th element of the a-th reconstruction vector of unit device i. It is the k-th element of the b-th reconstructed vector of unit i;

[0089] Then the fuzzy similarity is

[0090]

[0091] It is a similarity tolerance. The gradient parameter is used to control the rate of similarity decay;

[0092] The third step is to calculate the average similarity:

[0093] For each vector Calculate its relationship with all other vectors. The average value of the fuzzy similarity. Defined as the vector within a tolerance of Local similarity at time:

[0094]

[0095] The fourth step involves averaging the local similarities of all vectors to obtain an embedding dimension of m with a tolerance of [value missing]. Global average similarity at time:

[0096]

[0097] Step 5: Dimensional Enhancement Calculation Increase the embedding dimension to m+1, repeat steps one through four, and calculate the corresponding fuzzy similarity. and global average similarity ;

[0098] Step 6: Calculate the fuzzy entropy Fuzzy entropy is defined as the negative of the difference between the logarithms of the global average similarity in two adjacent dimensions.

[0099]

[0100] Less than or equal to ;

[0101] The seventh step transforms the fuzzy entropy into a normalized orderliness evaluation in the range [0,1] using a monotonically decreasing mapping function, employing a negative exponential function:

[0102]

[0103] The scale parameter is obtained by calibrating the entropy distribution of typical sequences. .

[0104] Preferably, The value is [0.1, 0.2]. According to the mutual assistance matrix G, the elements... Indicates the region arrive The mutual support capability divides the areas that can provide direct or indirect power support into a collaborative mutual support cluster.

[0105] Preferably, equation (7.11) ensures that: when E(i)→0 (the sequence is completely ordered), F(E(i))→1; when E(i) increases (the disorder of the sequence increases), F(E(i)) decreases smoothly; when E(i) is very large, F(E(i))→0.

[0106] Preferably, regional time coordination The calculation is as follows:

[0107] Step 1: Perform a critical feasibility check to ensure that the maximum number of discrete delay points K and the sequence length T satisfy the following conditions. conditions;

[0108] Step 2: Create Time co-similarity matrix , This represents the total number of cells within the region; this matrix is ​​used to store the optimal alignment similarity of all cell pairs within the region; then, all unique cell pairs are traversed; assuming the cells... , The normalized output sequence is and Time shift In the interval The values ​​are taken at all integer time-shift points, for each time-shift... Calculate the sequence With overall time shift The following sequence Pearson correlation coefficient over the entire effective overlap interval Based on different time shifts All calculated In the middle, the one with the largest absolute value is the unit. and unit Optimal alignment similarity:

[0109] .

[0110] Preferably, .

[0111] Preferably, n=2 and m=2.

[0112] Preferably, it also includes a hierarchical multidimensional availability evaluation system for road-domain high-entropy energy systems based on fuzzy entropy, which includes a processor and a readable storage medium, wherein a computer program is stored in the readable storage medium, and the processor executes the readable storage medium to implement the steps of the method.

[0113] The data hierarchical model in this system combines the characteristics of multi-source, high-frequency, strong time-series, and re-analysis of high-entropy energy data in the road domain. Due to the application of the above technical solutions, this invention has the following advantages compared with existing technologies:

[0114] 1. Unit-level availability evaluation aims to comprehensively characterize the actual operational quality of unit equipment in a high-entropy road environment from two dimensions: static output capacity and behavioral orderliness. The fundamental difference between this evaluation method and traditional methods is that it upgrades from the static "whether it is usable" to the dynamic "whether it is easy to use and reliable". Unit-level evaluation not only inherits the focus on static capacity of traditional availability, but also innovatively incorporates the dynamic quality of unit equipment by introducing behavioral orderliness, thus forming a unit availability definition and calculation method applicable to high-entropy energy scenarios in road environments.

[0115] 2. The evaluation method of this application innovatively integrates time, space, and quality dimensions to evaluate the system from three aspects: time availability, spatial coverage, and power quality. This comprehensively reflects the system's overall support capability in a real-world dynamic environment. Furthermore, since the evaluation method of this invention includes progressive availability evaluation from the unit level to the regional level and then to the system level, it also encompasses evaluation parameters for time, space, and quality. This allows for precise identification of whether the problem stems from single-point equipment failure, regional coordination failure, or system-level control failure. This makes operation and maintenance optimization more targeted, abandoning the isolated evaluation of the reliability of a single device or a single moment, and instead focusing on the system's collaborative support capability in a dynamic, heterogeneous, and interconnected high-entropy environment. The evaluation method of this invention can also perform layered deconstruction from the perspectives of energy system order and coordination to quantify the availability of the high-entropy energy system in the road area.

[0116] 3. To quantify the orderliness of the output behavior of unit devices, this model introduces the concept of fuzzy entropy. This choice is primarily based on two major evaluation needs of high-entropy energy systems in road regions and the shortcomings of traditional methods: First, the system needs to evaluate the quality of its output, not just average power. Fuzzy entropy, as a development of information entropy theory, can effectively measure the complexity and irregularity of time series, providing an indicator for evaluating the quality of such non-stationary, intermittent signals. Second, the system requires continuous spectrum state evaluation to characterize intermediate states such as performance degradation, and the continuous entropy value scale provided by fuzzy entropy meets this need. Furthermore, entropy-based methods typically possess inherent robustness in dealing with data noise, enhancing their applicability in engineering field data environments. Therefore, fuzzy entropy is established as the quantitative basis for the orderliness of behavior in this model.

[0117] 4. In calculating the regional temporal synergy, this invention introduces optimal alignment similarity to evaluate the degree of matching between the global shapes of the output curves of the two units. This refers to the degree of matching between the overall trend of change and the waveform profile of the two output sequences throughout the entire evaluation period, such as the power curve of a photovoltaic unit throughout the day, or the long-term envelope energy curve of a piezoelectric unit. Under the premise of understanding the inherent phase difference between the output curves of the two units, within the maximum time difference allowed by engineering, all possible offsets are traversed, and the two complete output curves are aligned according to each offset. The similarity of their shapes during the overlapping period is calculated, and finally, the value with the highest similarity is selected as the measure of the synergy potential between the two units. Attached Figure Description

[0118] Figure 1 This is a schematic diagram of the hierarchical multidimensional availability evaluation method of this application;

[0119] Figure 2 This is a schematic diagram illustrating the specific process of the unit-level availability evaluation steps in this application;

[0120] Figure 3 This is a schematic diagram illustrating the specific process of the regional layer availability evaluation steps in this application. Detailed Implementation

[0121] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0122] Example 1

[0123] like Figure 1-3 As shown, the boundary conditions and operating conditions for the availability evaluation of the high-entropy energy system in the road region are first defined:

[0124] (1) Evaluation Object Assumption: The direct evaluation object of this evaluation method is the high-entropy energy production unit in the road area (such as photovoltaic modules, wind turbines, piezoelectric modules, etc.) and the area and system it constitutes. The reliability of auxiliary facilities such as energy routing, transmission lines, power equipment, communication networks, and control system hardware is not evaluated at this time. The reliability of auxiliary facilities is regarded as a prerequisite or external environment for this evaluation method.

[0125] (2) Information Completeness Assumption: This evaluation method assumes that, within the evaluation period, the output power time-series data and related status information of each evaluation object can be reliably obtained through a data acquisition and monitoring system or equivalent means. That is, the availability and accuracy of the data required for the evaluation are not within the evaluation scope of this evaluation method itself.

[0126] (3) Definition of operating conditions: This evaluation method aims to evaluate the system's performance under given operating conditions and objectives. The level of availability is a relative evaluation result obtained under constraints such as specific environmental stimuli, scheduling instructions, and network topology, rather than an absolute physical limit.

[0127] The evaluation model of this method adopts a three-tiered progressive structure of "unit-region-system". Each tier undertakes a specific evaluation function and outputs quantitative conclusions upwards, forming a complete evaluation chain. The unit-level evaluation not only measures the static output capacity of individual devices but also characterizes the stability of device operation and the predictability of state evolution through the orderliness of its output sequence. The region-level evaluation focuses on energy aggregates composed of multiple homogeneous units, quantifying the dynamic synergy and collective behavioral order among units, revealing the regional availability determined by the interaction and output synergy between units. The system-level evaluation focuses on the overall energy network composed of multiple heterogeneous regions, comprehensively assessing the system's ability to continuously and stably guarantee energy services under complex time-varying excitations. The core algorithms and physical significance of this three-tiered evaluation model will be explained in detail below.

[0128] (1) Unit-level availability evaluation

[0129] Traditional energy unit availability assessments primarily focus on the static health of equipment or its maximum output under rated conditions. However, the energy sources of high-entropy energy systems in road regions (such as traffic flow, wind speed, and solar radiation) are highly random, volatile, and unpredictable. Under such strong uncertainty, the stability, regularity, and predictability of equipment output power are just as important as the maximum output capacity of the unit itself for ensuring microgrid stability and achieving efficient dispatch. Equipment with high output but drastic, unpredictable fluctuations will have significantly reduced actual availability.

[0130] According to the modeling principle of "series systems" in reliability engineering, when a function of a system depends on multiple independent conditions, and all of these conditions must be satisfied, its overall availability can be expressed as the product of the availability corresponding to each condition. Considering that the actual value of a unit device to a system depends on both its sufficient output capacity and reliable, orderly output behavior—both are indispensable—insufficient output capacity or severely disordered behavior will lead to a sharp decline in its overall availability. This is consistent with the logic that the failure of any link in a series connection leads to the failure of the entire function.

[0131] To quantify the orderliness of the output behavior of unit devices, this model introduces the concept of fuzzy entropy. This choice is primarily based on two major evaluation needs of high-entropy energy systems in road regions and the shortcomings of traditional methods: First, the system needs to evaluate the quality of its output, not just average power. Fuzzy entropy, as a development of information entropy theory, can effectively measure the complexity and irregularity of time series, providing an indicator for evaluating the quality of such non-stationary, intermittent signals. Second, the system requires continuous spectrum state evaluation to characterize intermediate states such as performance degradation, and the continuous entropy value scale provided by fuzzy entropy meets this need. Furthermore, entropy-based methods typically possess inherent robustness in dealing with data noise, enhancing their applicability in engineering field data environments. Therefore, fuzzy entropy is established as the quantitative basis for the orderliness of behavior in this model.

[0132] Based on this, this model proposes a unit device. Overall availability Defined as its output capacity factor With behavioral orderliness factor The product of is shown in equation (7.2):

[0133]

[0134] In the formula:

[0135] For unit-based devices The fuzzy entropy of the output power time series is used for quantization unit devices. The complexity and irregularity of the output power time series;

[0136] The behavior order factor is a function that modulates the degree of order of behavior through a monotonically decreasing function. A normalization index mapped to the [0,1] interval. The closer its value is to 1, the smaller the output fluctuation of the unit device and the more regular the time pattern, that is, the higher the orderliness and the stronger the predictability; the closer its value is to 0, the more chaotic the output of the unit device and the less identifiable the pattern, that is, the lower the orderliness and the stronger the randomness.

[0137] The output capacity factor is a normalized index that takes values ​​in the range [0,1] and is used to quantify unit equipment. The ratio of effective power output to theoretical or rated capacity under specific time periods and actual environmental conditions. The closer the value is to 1, the more the equipment can reach its theoretical maximum potential under the current conditions; the closer the value is to 0, the more its output is severely limited (such as severe shading of photovoltaic panels, equipment failure and derating).

[0138] Normalization allows the output capabilities of devices of different capacities and types to be compared and integrated on the same scale.

[0139] The objective of unit-level availability calculation is based on unit devices. Historical or real-time operational data is used to calculate the output capacity factor and behavioral orderliness factor, and finally synthesize the unit layer availability. The entire process can be divided into three steps:

[0140] ① Data preprocessing and feature extraction

[0141] Based on the information completeness assumption mentioned above, this step aims to clean and smooth the raw data to remove measurement noise and transient interference, so that subsequent analysis can focus on the operating characteristics of the equipment itself.

[0142] Set unit equipment Within the evaluation period T, its output power is sampled at equal intervals, resulting in an original sequence of length N. To eliminate the influence of differences in rated capacity between devices on the evaluation of behavioral orderliness, it is first transformed into a normalized power sequence: ,in

[0143]

[0144] For unit devices No. Measured power at each sampling point For unit devices Reference power, It is the k-th element in the normalized power sequence of unit device i; 1≤k≤N. Subsequently, the normalized sequence... Data preprocessing is performed, including outlier removal (removing obvious abnormal data points caused by non-equipment operation factors such as communication interruptions and transient interference) and data smoothing (using moving averages or low-pass filters to smooth the data, suppressing high-frequency measurement noise and retaining low-frequency fluctuations that reflect the essence of equipment operation). The preprocessed sequence is denoted as... ,in These are the cleaned and valid data points. This sequence will serve as the input for all subsequent calculations.

[0145] From sequence Two key features were extracted: average normalized output force. and sequence standard deviation ,in It is a sequence The kth element:

[0146]

[0147] This value directly reflects the average output level of the unit equipment during the evaluation period and is the basis for calculating the output capacity factor.

[0148]

[0149] This value will be used for the adaptive setting of the similarity tolerance parameter r in subsequent fuzzy entropy calculations.

[0150] ② Calculation of output capacity factor

[0151] Output capacity factor Aimed at quantifying unit devices The ratio of the average actual output to the theoretical maximum output during the evaluation period reflects the static or quasi-static power generation potential utilization level of the equipment.

[0152] Based on the average normalized output force obtained in step one It can be known that It is essentially the ratio of average actual output to reference output or full output; therefore, the output capacity factor is... :

[0153]

[0154] The range of values ​​is .

[0155] ③ Calculation of behavioral orderliness factor

[0156] Behavioral orderliness factor Aiming to quantify equipment The stationarity and predictability of the output behavior. Its computation consists of two sub-steps: first, based on the preprocessed sequence... Calculate fuzzy entropy Then, it is transformed into a normalized order score through a mapping function.

[0157] The core of fuzzy entropy calculation is the sequence Phase space reconstruction and fuzzy similarity measurement are performed, with parameter settings following general practices in the field. Definitions:

[0158] Embedding dimension m: usually m=2, used to reconstruct phase space.

[0159] Similarity tolerance Adaptive value ,in The standard deviation of the sequence is calculated in step (1).

[0160] Gradient parameter n: Usually n=2, used to define the shape of the fuzzy membership function.

[0161] The first step is to reconstruct the phase space, transforming the one-dimensional sequence... Reconstructed into an m-dimensional vector:

[0162] ,

[0163] Example: The normalized power sequence of a unit device is

[0164]

[0165] Sequence length Generally, the embedding dimension m=2 is chosen, from Begin by constructing vectors sequentially:

[0166] ,

[0167] ,

[0168] ,

[0169] ,

[0170] ,

[0171] ,

[0172] ,

[0173] ,

[0174] ,

[0175] Thus obtained Two-dimensional vectors extend the one-dimensional time series to a two-dimensional phase space. Each vector can be viewed as a state point of a unit device in the phase space, and the sequence... The state of the unit device is represented as "power 0.85 at the previous moment, power 0.87 at the current moment." This contains more dynamic information about the trend of change than the original one-dimensional sequence. The core of fuzzy entropy is calculating the similarity between these vectors. For example, vectors... and The high similarity indicates that the unit devices underwent similar evolutionary patterns in two different time segments, reflecting the inherent regularity of the sequence.

[0176] The embedding dimension *m* determines the length of historical information contained in the reconstructed vector. Parameter selection needs to strike a balance between pattern recognition capability and statistical reliability: if *m* is too small (e.g., *m=1*), the reconstructed vector is too simple and cannot effectively distinguish complex changing patterns in the sequence, leading to underfitting; conversely, with a finite data length *M*, too much *m* will significantly reduce the number of vectors that can be constructed (a total of *M−m+1* vectors can be constructed), leading to an increase in the variance of the similarity statistical estimate, causing overfitting or unstable results.

[0177] For typical engineering time series (data length M is usually in the hundreds to thousands of points), m=2 is the most commonly used and robust choice. This value, while ensuring sufficient statistical reliability, can effectively capture the first-order variation law of the series, that is, the instantaneous change trend between two consecutive sampling points. For high-entropy energy units in road areas, this variation law of power output between adjacent moments is the core basis for judging whether its output is stable, orderly, and predictable.

[0178] The second step is to calculate any two m-dimensional reconstruction vectors. and The Chebyshev distance between them, which characterizes the absolute difference between two power output sequences of length m at their least dissimilar moments:

[0179]

[0180] in It is the k-th element of the a-th reconstruction vector of unit device i. It is the k-th element of the b-th reconstructed vector of unit i;

[0181] Then the fuzzy similarity is

[0182]

[0183] It is a similarity tolerance. The gradient parameter is used to control the similarity decay rate. Equation (7.7) states that... Mapping to an interval The fuzzy similarity value within ensures that when hour, (Completely similar); with Increase It decays smoothly and continuously to 0.

[0184] The third step is to calculate the average similarity. For each vector... Calculate its relationship with all other vectors. ( The average fuzzy similarity of the vector is defined as the value of the vector within a tolerance of . Local similarity at time:

[0185]

[0186] The fourth step involves averaging the local similarities of all vectors to obtain an embedding dimension of m with a tolerance of [value missing]. Global average similarity at time:

[0187]

[0188] Step 5: Dimensional Enhancement Calculation Increase the embedding dimension to m+1, and repeat steps one through four to calculate the corresponding fuzzy similarity. and global average similarity .

[0189] Step 6: Calculate the fuzzy entropy Fuzzy entropy is defined as the negative of the difference between the logarithms of the global average similarity in two adjacent dimensions.

[0190]

[0191] Usually less than or equal to This is because higher-dimensional sequences are more difficult to maintain similarity. (Fuzzy entropy) It quantifies the rate at which sequence similarity decays as the observation scale (dimensionality) increases. The faster the decay (the smaller the ratio), the larger the entropy value, indicating that the sequence is more complex and irregular.

[0192] The seventh step transforms the fuzzy entropy into a normalized orderliness evaluation within the range [0,1] using a monotonically decreasing mapping function. This invention employs a negative exponential function:

[0193]

[0194] The scale parameter is obtained by calibrating the entropy distribution of typical sequences. Equation (7.11) ensures that:

[0195] when When the sequence is completely ordered, .

[0196] when When the sequence disorder increases, Smooth decrease.

[0197] when When it is very large, .

[0198] Unit device availability calculation

[0199] Thus, we have obtained the characterization unit device. Key indicators of output behavior stability and predictability: Behavioral orderliness factor And unit devices The overall availability is synthesized from the two according to equation (7.2). This answers the question, "What percentage of the rated power can the equipment provide on average?" This answers the question, "Is the output of this portion of power stable and predictable?" This comprehensively answers the question, "What is the proportion of effective power that the equipment can ultimately rely on and utilize by the system?" This indicates that the device possesses both high output capacity and high output order, making it a near-ideal high-entropy power supply. When This indicates that the actual availability of the equipment is close to zero, either due to severely limited output or extremely chaotic output. A low value for either factor will significantly lower the overall value, reflecting that reliable order and sufficient output are equally important in high-entropy energy systems in the road region.

[0200] (2) Regional Availability Evaluation

[0201] In the availability assessment of distributed high-entropy energy systems in road regions, the output of energy units exhibits significant spatiotemporal correlation and strong randomness (high-entropy characteristics). When multiple homogeneous units are connected to the same regional network, they do not operate independently; their output fluctuations can superimpose, cancel each other out, or resonate, thus affecting the overall regional power support capacity, predictability, and required reserve capacity of the grid. Traditional models assume that each unit operates independently, resulting in a simple summation of the unit's capabilities, failing to capture the overall effectiveness generated by collective cooperation (or conflict). Therefore, evaluating solely based on the availability of individual units can lead to an incorrect estimate of the actual dispatchable capacity of the region, resulting in systematic biases in availability assessments. To address this challenge, this paper introduces the concept of regional availability, aiming to characterize the spatiotemporal interaction effects between homogeneous units from a regional perspective. This is not only a necessary extension to the traditional reliability assessment framework but also a key approach to optimizing the operational efficiency of high-entropy energy systems in road regions.

[0202] From a systems engineering perspective, system effectiveness is determined by both "structure" and "process." The unit availability mentioned above only describes the structural health of the system. However, whether the system can collaboratively provide stable and reliable power when needed depends on the dynamic interaction process between units. The quality of this process is reflected in the synchronicity, complementarity, and consistency of output. For example, even if all units are in a high-availability state, if their peak outputs are perfectly synchronized and far exceed the line capacity, the actual effective output of the region will be constrained by the network bottleneck, rather than the sum of the unit capabilities. Conversely, if the outputs between units are well complementary in time and space, even if the availability of individual units is low, the region as a whole may still exhibit stable and reliable output characteristics. This effect is the core of what collaborative availability needs to be quantified.

[0203] Based on the above logic, the regional availability model constructed in this invention aims to quantify homogeneous energy regions from three dimensions: structural, temporal, and spatial synergy. The health baseline (the mean availability of individual units) quantifies the static structural attributes of the system, its theoretical basis stemming from the measurement standard of component basic state in traditional reliability assessment. Regional temporal synergy uses the mean of the optimal alignment similarity of the output time series of each unit within the region as the core input. It maps and quantifies the synergistic potential of units to achieve optimal output matching within the allowable time delay range through a specific function mapping. This considers the output phase difference caused by geographical dispersion, and its methodology references the renewable energy aggregation and modeling theory that considers time-shift correlation. The synergy consistency coefficient effectively characterizes the uniformity of the synergistic effect distribution and the system robustness within the region by penalizing the spatial dispersion of the optimal alignment similarity. Its significance lies in preventing pseudo-synergy or fragile synergy states caused by a few units being highly correlated while most units are unrelated. Finally, the regional synergistic availability is given by the product of these three factors. This model theoretically breaks through the assumption of "component independence" in traditional reliability assessment, and in engineering practice, it can more realistically reflect the overall availability of homogeneous high-entropy energy clusters under spatiotemporal coupling constraints.

[0204] ① Calculation of the healthy baseline

[0205] The health base aims to quantify the static structural integrity of a region, that is, the average level of the inherent availability of each unit without considering dynamic interactions. It is defined as the arithmetic mean of the overall availability of all energy units in the region.

[0206]

[0207] in:

[0208] The total number of isomorphic energy units in the region.

[0209] : No. The availability of an energy unit reflects the unit's health status and the orderliness of its historical output.

[0210] Healthy foundation It plays a fundamental role in the regional availability model, if The model itself is small, and even with excellent synergy, the overall availability of the region will be fundamentally limited. It ensures that the model does not deviate from physical reality. For example, even if the outputs of the units within the region are completely complementary and the synergy is extremely high, if most units have inherently low availability due to failure or aging, the overall performance of the region will inevitably be poor.

[0211] ② Calculation of regional time coordination

[0212] Regional time coordination This study aims to assess the potential for synergistic effects between homogeneous energy unit clusters operating within a region, synergistically generated through temporal coordination of their output sequences. Traditional evaluation methods typically employ the zero-latency Pearson correlation coefficient to measure the output correlation between units. However, for geographically dispersed, high-entropy energy systems in road regions, the peak values ​​of the excitation received by each unit exhibit an inherent time lag, i.e., a phase difference. Ignoring this fact would underestimate the system's potential spatiotemporal complementarity.

[0213] The optimal alignment similarity introduced in this invention aims to evaluate the degree of matching between the global morphology of the output curves of two units. That is, the degree of matching between the overall trend of change and waveform profile of the two output sequences throughout the entire evaluation period, such as the power curve of a photovoltaic unit throughout the day, or the long-term envelope energy curve of a piezoelectric unit.

[0214] Under the premise of understanding that there is an inherent phase difference between the output curves of the two units, within the maximum time difference allowed by the project, all possible offsets are traversed, the two complete output curves are aligned according to each offset, and the similarity of their shapes during the overlapping period is calculated, i.e., similarity. Finally, the value with the highest similarity is selected as the measure of the collaborative potential of the two units.

[0215] Take a road vibration energy harvesting unit based on piezoelectric materials as an example. The output characteristics of such units are excited by traffic flow, and the instantaneous peak output of a single piezoelectric unit corresponds precisely to the moment when a vehicle's wheel axle passes directly above it. Assume that piezoelectric units are deployed along the driving direction on the same cross-section of a lane. With piezoelectric unit The distance between them As the vehicle moves, the output of each unit is a time-varying sequence of power pulses, with each pulse corresponding to one vehicle passing by. If the vehicle travels at a certain speed... As the vehicle travels at a constant speed past these two units, ideally, the phase difference between the output pulse sequences of the two units is a time delay. Shift one of the sequences In time, the output pulse sequences of the two units will highly overlap, and the optimal alignment similarity will be close to 1, indicating that the two have extremely high synergistic potential. Their output patterns are a reproduction of the same traffic flow event at different locations, with a predictable time delay relationship.

[0216] In real-world traffic flow, vehicle speeds are generally randomly distributed within a range, not a constant. Therefore, there is no fixed speed for calculating phase difference or time delay. Furthermore, vehicles may change lanes, and not all vehicle passage will create a correlated event between two units. Different vehicle types and weights may result in mismatched waveform amplitudes even with time phase alignment. Considering the superposition of traffic flows, the entire process becomes extremely complex. The applicable method, as described earlier, is to search for the optimal alignment similarity within a maximum allowable phase difference range.

[0217] Let the maximum allowable phase difference of the project be . Assume the physical range of vehicle speed is [ If ], then the time range for single-vehicle passage is [ Select according to the upper limit of this range. And reserve a certain margin, that is... , For safety, a value of 1.2 to 1.5 is generally used. Considering abnormal situations such as oncoming traffic flow or tidal flow lanes, the value can be adjusted within the range [-]. , Search for the best alignment similarity.

[0218] For all unit pairs within a region, an optimal alignment similarity matrix can be formed through pairwise calculations. Based on this matrix, the regional average synergy potential is further calculated and ultimately mapped to the regional temporal synergy. This method is essentially derived from cross-correlation analysis in signal processing. Its advantage lies in fully considering the reasonable phase difference caused by spatial dispersion. Similar methods have been successfully applied in the aggregation efficiency evaluation of wind farms and photovoltaic power plants, enabling a more accurate assessment of the output smoothing effect and capacity reliability of distributed power plants.

[0219] The relevant physical, engineering, and mathematical parameters for calculating regional time synergy are shown in Table 7.1. At this point, the regional time synergy can be calculated step-by-step.

[0220] surface .1 Parameters used for calculating regional time coordination

[0221]

[0222] The first step, after determining the values ​​of each parameter in Table 7.1, is to perform a critical feasibility check. This is a necessary prerequisite for ensuring the correct operation of the algorithm and the reliability of the results. The core of the check stems from the basic requirement of cross-correlation analysis: the two sequences must have a sufficiently long overlap to calculate a statistically reliable cross-correlation coefficient.

[0223] If the maximum allowable number of discrete time delay points K is close to or even equal to the sequence length T, then when calculating the cross-correlation coefficient corresponding to the boundary time delay, the two waveforms will have only a very small number of overlapping data points due to the huge phase difference. In this case, the cross-correlation coefficient calculated based on the extremely short overlapping sequence will be extremely unstable, with huge variance, and lacking statistical significance. More seriously, such short sequences are prone to generating high cross-correlation coefficients due to accidental random noise or local fluctuations, causing the algorithm to find a spurious maximum near the search boundary. However, this maximum is only a local coincidence, rather than reflecting the true physical coordination relationship between the global forms of the two output sequences.

[0224] Therefore, to ensure the reliability of cross-correlation coefficient calculation and the effectiveness of global collaborative evaluation, it is necessary to verify and satisfy the following: The conditions. It is generally recommended to use... The empirical threshold ensures that the amount of overlapping data involved in the calculation is sufficient over the entire search latency, thereby obtaining stable and reliable statistical results.

[0225] Step 2: Create Time co-similarity matrix , This represents the total number of cells within the region. This matrix is ​​used to store the optimal alignment similarity of all cell pairs within the region.

[0226] Then iterate through all unique pair of cells. Assume the cell... , The normalized output sequence is and Time shift In the interval The values ​​are taken at all integer time-shift points, for each time-shift... Calculate the sequence With overall time shift The following sequence Pearson correlation coefficient over the entire effective overlap interval Based on different time shifts All calculated In the middle, the one with the largest absolute value is the unit. and unit Optimal alignment similarity:

[0227]

[0228] Example: Calculate the optimal alignment similarity between cell A and cell B.

[0229] A and B are deployed on the same single lane, with a spacing of... The vehicle's direction of travel is fixed from A to B. Minimum speed. Safety factor Sampling interval Sequence length (Assessment duration is 10s), then the maximum allowable physical delay is... Maximum number of discrete delay points The K / T value after verification is too high; in actual analysis, it should be smaller to pass the verification. Search time shift There are 53 in total.

[0230] Express: speed The passage time is 0.5s. A pulse P1_A is generated at point A (e.g., at index n=20), and a pulse P1_B is generated at point B (at index n=25, 5 points later than P1_A (corresponding to the passage time)).

[0231] Slow train: speed The passage time is 1.5 seconds. A pulse P2_A is generated at point A (index n=50), and a pulse P2_B is generated at point B (index n=65, 15 points later than P2_A, corresponding to 1.5 seconds).

[0232] Sequence of Unit A There are two pulses at n=20 and n=50, and 0 at the rest.

[0233] Sequence of Unit B There are two pulses at n=25 and n=65, and 0 at the rest.

[0234] The algorithm in Try them one by one to see which time shift will allow... and Most similar.

[0235] When the algorithm tries It calculates and The similarity. There are two pulses at n=20 and n=50, so let's look at... and Two places, There is a pulse, so at this time and It matches, and There is no pulse, only background noise, so there is no match here. Therefore, the cross-correlation coefficient r[5] is a medium value, such as 0.55.

[0236] When the algorithm tries It calculates and The similarity. There are two pulses at n=20 and n=50, so let's look at... and Two places, No pulse, so at this time and It's a mismatch, and There is a pulse, so it is matched here. Then the cross-correlation number r

[15] is also a medium value, such as 0.53.

[0237] Traversal If r[5] is found to be the maximum value among all cross-correlation coefficients, then the optimal alignment is... .

[0238] When constructing the temporal co-similarity matrix, two fundamental mathematical properties can be observed:

[0239] 1) Self-similarity: Any unit whose output sequence is completely identical to its own, therefore its similarity is defined as the maximum value, i.e. .

[0240] 2) Symmetry: Unit With unit The synergistic potential is equivalent to the unit. With unit The synergistic potential, namely .

[0241] After construction is complete, the matrix It is a real symmetric matrix, with all elements on the main diagonal being 1. For example, for a region containing 3 units, the matrix has the following form:

[0242]

[0243] The matrix will The independent scalar measurements are integrated into a matrix with explicit mathematical properties (symmetric, positive definite). The matrix's first... The lines depict the unit Temporal coordination relationships with all other units within the region. Extract the matrix. The upper triangular part (i.e., all satisfying) of ), calculate the arithmetic mean of these values. . It is a value between 0 and 1, reflecting the overall average level of regional time synergy potential.

[0244]

[0245] Finally, a monotonically increasing cooperative function is needed to... Mapped to performance factors that directly contribute to system availability The choice of function form should be based on the principle of synergistic efficiency enhancement of high-entropy energy systems in the road region.

[0246] High-entropy energy output exhibits strong random fluctuations. When units within a region are completely uncoordinated, their aggregated output is nearly the direct superposition of the independent random fluctuations of each unit, with the fluctuation variance approximately equal to the sum of the variances of each unit. The system is in a completely disordered, high-entropy state. Even with the most basic cooperative management (such as implementing simple output limiting or peak-shaving scheduling), the natural statistical independence between units can be effectively utilized to significantly reduce the fluctuation variance of aggregated output. This low-level cooperative process completes the initial entropy reduction, achieving a qualitative change from infinite chaos to finite fluctuations, demonstrating a nonlinear threshold effect.

[0247] As coordination continues to improve, the output of units becomes increasingly correlated, and the fluctuations in aggregated output are now mainly dominated by systemic factors such as regional meteorological models or macro-traffic flows, resulting in a lower system entropy. Further smoothing of residual fluctuations requires high-precision forecasting and accurate cross-regional coordinated scheduling. However, limited by spatiotemporal physical laws, the potential for further reduction in fluctuation entropy is extremely limited, and the collaborative improvement exhibits a clear saturation effect.

[0248] For example, with piezoelectric energy, when vehicles arrive randomly at varying speeds, single pulses can be smoothed and average power increased through methods such as energy buffering. During peak commuting hours, traffic flow is high and stable, and all piezoelectric units continuously and synchronously output high power; while during off-peak hours at night, all units synchronously output low power. This periodic fluctuation originates from the macroscopic laws of human social rhythms. At this point, it is impossible to change the city's commuting tides by scheduling piezoelectric units on the road; this systemic factor is the physical upper limit governing collaborative optimization.

[0249] This law of diminishing returns has been widely observed and discussed in energy system and complex engineering system research. In the field of renewable energy integration, research clearly indicates that the volatility of wind or solar power output decreases with increasing aggregation scale (equivalent to the number of cooperating units), but the marginal benefit of its smoothing effect decreases significantly with increasing aggregation scale, directly confirming the saturation characteristic of synergy gains. Other studies analyzing the learning curve of photovoltaic technology reveal a typical pattern of rapid initial cost reduction followed by a slower rate of decline. Analogizing synergy to a capability that can be acquired through technological and managerial investment, its improvement process follows a similar saturation law. Furthermore, research based on system reliability theory suggests that in complex system performance models, the impact of component performance improvements on overall system reliability often exhibits a non-linear saturation relationship due to the inherent physical limits of the system.

[0250] Common function mapping relationships mainly include the following three basic forms:

[0251] 1) Linear mapping: The mapping relationship is as follows Although it satisfies the monotonicity requirement, the linear relationship it describes does not match the significant nonlinear characteristics exhibited by the high-entropy system in the synergistic enhancement process, and therefore it is not adopted.

[0252] 2) Convex function mapping (taking power functions as an example): The mapping relationship is as follows: , . The range of values ​​is The function outputs across its entire domain. Always less than input This is equivalent to imposing a systematic discount on any level of synergistic potential, assuming that the actual achievable synergistic efficiency is always lower than its statistical potential. However, as mentioned earlier, high-entropy energy systems can achieve significant leaps in efficiency through basic management in the low synergistic potential region, meaning that in this region, the actual synergistic efficiency... It should be no less than or even higher than its synergistic potential. Therefore, the power function clearly cannot characterize this transition process, nor can it accurately describe the saturation effect in the high-potential region. Thus, this functional form is not adopted.

[0253] 3) Concave function mapping (taking exponential saturation type as an example): , It is recommended that the value be between 2.5 and 3.5. This function is within its domain. The internal monotonically increases, and its curve shape exhibits a saturation characteristic of being steep at first and then gradual. A larger value indicates that the system is more sensitive to synergy, and a smaller potential increase can bring significant performance gains; conversely, a smaller value indicates that the system is less dependent on synergy. This provides flexibility for the model to adapt to application scenarios with different levels of rigor. Therefore, the exponential saturation function, because its mathematical form can reflect both the threshold effect of "rapid initial improvement" and the saturation law of "diminishing returns in the later stages," and its parameters have intuitive physical meaning, was chosen as the synergy function for constructing the regional temporal synergy model in this invention.

[0254]

[0255] ③ Calculation of the spatial consistency coefficient C

[0256] The spatial synergy consistency coefficient C is also a coefficient between 0 and 1, used to quantify the uniformity and stability of the spatial distribution of regional temporal synergy effects.

[0257] As mentioned earlier, even if the region has a high average synergy potential ( Even with a high similarity value, there's a possibility that this synergy is contributed by only a few pairs of highly similar units, while the majority of other units actually have very poor synergy. This uneven synergy is fragile. Once those few highly synergistic pairs fail due to faults or environmental changes, the overall synergy of the region will plummet. The spatial synergy consistency coefficient reflects this degree of unevenness.

[0258] For example, consider a wind power microgrid where the stability of the entire microgrid heavily depends on the perfect coordination of one or two pairs of units. This is a fragile cooperative structure. Once those two pairs of units fail, the overall coordination of the grid collapses. If the stability of the microgrid depends uniformly on good coordination among all units, then this is a robust cooperative structure. Even if individual units fail, the remaining units can still maintain a good overall level of coordination. Therefore, The average synchronous generation capacity of the microgrid is measured, while C measures the microgrid's ability to withstand single-point failures. A C value close to 1 indicates generally good and evenly distributed unit coordination, resulting in high system resilience. A C value close to 0 indicates that coordination is highly concentrated in a few unit pairs, the system's coordination structure is fragile, and its ability to withstand disturbances is poor.

[0259] The spatial synergy consistency coefficient is introduced to quantify the uniformity of temporal synergy distribution and structural robustness across the spatial dimension. This coefficient is based on network science and system reliability theory: the overall robustness of a system depends not only on the average performance of its components, but more critically on the uniformity of performance distribution among the components. System structures reliant on a few critical components often exhibit significant vulnerability to random component failures or specific attacks.

[0260] In the field of renewable energy integration, relevant research provides direct evidence for this. When quantifying wind power volatility and its costs, related studies clearly point out that the spatial correlation structure of output is a key factor affecting system stability; the more uniform the spatial distribution of correlation, the more stable the system. Other studies have further explicitly considered the spatial correlation structure of renewable energy output in dispatch models and demonstrated that the uniformity of the correlation structure directly affects dispatch economics and system adequacy.

[0261] Therefore, relying solely on temporal synergy to evaluate regional synergy is insufficient. It is necessary to introduce a spatial synergy consistency coefficient to measure the uniformity of synergy distribution, thereby ensuring the robustness of regional availability evaluation results.

[0262] For a region containing N energy units, its optimal alignment similarity matrix is ​​R. Define the set of cooperative potential for this region. Let R be the set of all off-diagonal elements (i.e., all unique pairs of elements) in matrix R: The total number of elements in this set is Each element. Characterized the unit With unit The maximum possible synergy potential between them. Based on the synergy potential set The spatial coherence coefficient C is defined as follows: :

[0263]

[0264] in:

[0265] The mean of the elements in this set represents the average level of regional synergy potential. The larger the value, the better the general foundation for inter-unit collaboration;

[0266] Let be the standard deviation of the elements in this set. The larger the value, the more uneven the coordination capabilities, and the more likely the system is to rely on a few highly coordinated unit pairs.

[0267] If only the mean μ is used to assess the spatial distribution quality of synergy potential, it only reflects the average strength of synergy and cannot distinguish between a system that is "generally moderate" and one that is "a few extremely high and most extremely low." The latter is relatively more fragile. Furthermore, the standard deviation σ only reflects the absolute amplitude of fluctuations and cannot determine whether the fluctuations are acceptable in engineering. Therefore, it is necessary to construct a coupling mechanism. and The composite index.

[0268] When the mean is high, the system is more tolerant of fluctuations. For example... , relative fluctuations Within acceptable limits, at this time The system, with its strong overall collaborative foundation, is able to absorb and digest certain internal imbalances without seriously compromising its consistency rating.

[0269] When the mean is low, the system's tolerance for fluctuations decreases sharply. For example... , relative fluctuations It becomes very noticeable at this time. This means that the system's already fragile collaborative foundation cannot withstand any significant internal differences; even slight imbalances will expose and amplify the system's structural flaws.

[0270] The design of Equation (7.15) sets a higher "alarm threshold" for high-mean systems, so that the overall advantages are not negated by minor unevenness; and sets a lower "alarm threshold" for low-mean systems, so that any unevenness will be amplified.

[0271] Mathematically, the numerator must be 0. This implies the cooperative potential of all unit pairs in the region. A total of zero values ​​is a scenario that is virtually impossible in a real-world energy system. Furthermore... It is also a normalized, dimensionless value, which allows it to serve as a reasonable attenuation factor and directly participate in the calculation of regional collaborative availability.

[0272] Previous studies have investigated the collaborative resilience of multi-microgrid systems under extreme weather conditions, constructing a two-layer optimization model. The core evaluation factor in the upper layer is the overall system resilience improvement level (measured by the reduction ratio of load shedding), while the lower layer focuses on evaluating the maximum mutual assistance power between microgrids. Researchers found that simply possessing a high average maximum mutual assistance capacity is insufficient; if this mutual assistance capacity is highly concentrated in a few interconnections, the system resilience remains fragile. Although the researchers did not explicitly use the same spatial coordination consistency coefficient as in this paper, their analysis is essentially an assessment of mutual assistance capacity, providing direct evidence for introducing index C into the collaborative evaluation of energy systems in this invention.

[0273] In summary, regional collaborative availability is defined as the product of three factors: the health baseline, the regional temporal collaborativeness, and the spatial collaborative consistency coefficient, forming a hierarchical, multi-dimensional evaluation framework.

[0274]

[0275] The model shows that the overall synergistic effectiveness of a region depends on the health level of the units themselves, the degree of scheduling matching between units in the time dimension, and the robustness of the distribution of this temporal synergistic effect in the spatial topology.

[0276] (3) System-level availability evaluation

[0277] System-level evaluation aims to quantify the overall reliability of a roadside energy system under conditions where inter-regional energy sharing is permitted. Its core idea is that the overall system performance is jointly determined by "static average capacity" and "dynamic collaborative resilience." Static average capacity refers to the reliability level of each region in islanded operation mode, representing the baseline of system performance. Dynamic collaborative resilience refers to the ability of high-availability regions to support low-availability regions through a mutual support network, thereby enhancing the overall resilience of the system. System-level availability is a comprehensive reflection of these two capabilities, and its general model is a weighted sum of the two:

[0278]

[0279] Static average capability characterizes the performance baseline of a system without mutual assistance:

[0280]

[0281] in,

[0282] Total number of regions within the system.

[0283] : No. The collaborative availability of each region is calculated by the region-level model.

[0284] : No. The weight coefficients of each region satisfy the following conditions. The weight can be determined according to the proportion of the region's rated capacity in the system, so as to reflect its importance in the system.

[0285] Dynamic cooperative elasticity, also known as system mutual benefit gain factor It represents the higher level of security that the system can achieve after making full use of the mutual assistance network.

[0286] First, it is necessary to divide the collaborative and mutually supportive clusters, based on the mutual support relationship matrix G (elements). Indicates the region arrive (mutual support capability), dividing areas capable of direct or indirect power support into a cooperative mutual support cluster, assuming it is divided into... A cluster.

[0287] Next, the guarantee level of a single cluster is calculated. .definition:

[0288] Cluster weight For clusters The proportion of critical loads to total critical loads in the system: cluster internal weights Indicates the region The load accounts for a portion of the load of its cluster. The proportion; the guarantee level of a single cluster. for:

[0289]

[0290] in,

[0291] It is a cluster The weighted average of the availability of the inner area, i.e. its static capacity;

[0292] It is a cluster The highest area availability within;

[0293] This is the collaborative gain strength coefficient (recommended value: 0.1~0.2), used to reward differences in availability within the cluster. The greater the difference, the greater the potential and value of optimizing scheduling through mutual assistance and compensating for lower availability with higher availability.

[0294] Finally, the protection levels of all clusters in the system are weighted and summarized:

[0295]

[0296] in,

[0297] It refers to the number of collaborative and mutually supportive clusters;

[0298] It is a cluster The weights;

[0299] It is the system mutual assistance gain factor, which characterizes the best overall protection level that the system can achieve by optimizing power support under a given mutual assistance network topology and capacity constraints.

[0300] Importance weight of mutual assistance , These are parameters set by the evaluators to balance the relative importance of "individual strength" and "collaborative assistance" in the final evaluation. When this occurs, it indicates that the evaluation system considers system performance to depend entirely on the basic capabilities of each region, ignoring mutual support. In this case, the system-level evaluation degenerates into a simple average of regional performance. When the evaluation system considers the system's performance to depend entirely on its mutual support and synergy potential, it indicates that the evaluation system believes the system's performance depends entirely on its mutual support and synergy potential. Taking the middle value reflects a comprehensive consideration that balances both aspects.

[0301] Therefore, the integrated evaluation formula for system-level availability is:

[0302]

[0303] Example: Suppose there is a road energy system consisting of three regions (R1, R2, R3). The regional evaluation result is as follows: , , Regional critical loads , , The total critical load of the system is Regional weight , , .

[0304] Regions capable of providing power support to each other form a collaborative and mutually supportive cluster. Within this cluster, resources can be shared, therefore the overall effectiveness of the cluster is determined by all its members.

[0305] In this example, the mutual aid matrix between regions is:

[0306]

[0307] This indicates that R1 and R2 can mutually support each other, while R3 is isolated. Any region within a cluster can provide support (directly or indirectly) to other regions within the cluster. Therefore, in this example, there are two cooperative clusters: cluster 1 {R1, R2} and cluster 2 {R3}.

[0308] For cluster 1, the cluster weight is Internal weights , Static average ability Highest regional availability ,when , Cluster security level .

[0309] For cluster 2, the cluster weight is Internal weights Static average ability Highest regional availability ,when , Cluster security level .

[0310] The static protection capability of the system .

[0311] System resilience potential .

[0312] System layer availability is .

[0313] Without any mutual assistance, the system availability is 0.58. With mutual assistance, the system availability increases, with a relative improvement of approximately 1.03%. If the weighting is more biased towards mutual assistance capabilities, then this availability can be further improved.

[0314] Example 2

[0315] It also includes a hierarchical multidimensional availability evaluation system for road-domain high-entropy energy systems based on fuzzy entropy, which includes a processor and a readable storage medium. The readable storage medium stores a computer program, and the processor executes the fuzzy entropy storage medium to implement the steps of the hierarchical multidimensional availability evaluation method for road-domain high-entropy energy systems based on fuzzy entropy described in Embodiment 1 above.

[0316] In summary, this invention constructs a hierarchical, progressive availability evaluation system from unit to system. Its core lies in abandoning the isolated evaluation of the reliability of a single device or at a single moment, and instead focusing on the collaborative assurance capabilities of the system in a dynamic, heterogeneous, interconnected, and high-entropy environment.

[0317] The present invention has been described in detail above, with the aim of enabling those skilled in the art to understand and implement the invention. However, this description should not be construed as limiting the scope of protection of the invention. All equivalent changes or modifications made in accordance with the spirit and essence of the invention should be included within the scope of protection of the invention.

Claims

1. A hierarchical multidimensional availability evaluation method for road-region high-entropy energy systems based on fuzzy entropy, characterized in that: The evaluation method includes the following steps: I. Unit-level Availability Evaluation: Unit devices Overall availability The definition is shown in equation (7.2): In the formula: For unit-based devices Fuzzy entropy for output power time series calculation; For behavioral orderliness factor; This is the output capacity factor; II. Availability Evaluation of Regional Layers: Regional Collaborative Availability The definition is shown in equation (7.16): In the formula: B represents the foundation of health; C represents the temporal coordination degree of the region; C represents the spatial coordination consistency coefficient. in, In the formula: This represents the total number of isomorphic energy units within the region. It is the arithmetic mean, and is calculated according to formula (7.13); The mean of the elements in the set; Let R be the standard deviation of the elements in the set; for a region containing N energy units, its optimal alignment similarity matrix is ​​R; define the cooperative potential set of this region. Let R be the set of all off-diagonal elements in matrix R: The total number of elements in this set is Each element Characterized the unit With unit The maximum possible synergy potential between them; III. System-level Availability Evaluation: System layer availability The definition is shown in equation (7.19): in, The static average capacity is calculated according to equation (7.18). in, This represents the total number of regions within the system. For the first Cooperative availability in each region; For the first The weight coefficients of each region satisfy the following conditions. ; For dynamic and collaborative flexibility; Assigning weights based on the importance of mutual assistance .

2. The hierarchical multidimensional availability evaluation method for road-domain high-entropy energy systems based on fuzzy entropy according to claim 1, characterized in that: The unit layer availability evaluation steps include: 1.1 Data Preprocessing and Feature Extraction: Set unit equipment Within the evaluation period T, its output power is sampled at equal intervals to obtain an original sequence of length N; this sequence is then transformed into a normalized power sequence: ,in For unit devices No. Measured power at each sampling point For unit devices Reference power, It is the k-th element in the normalized power sequence of unit device i; 1≤k≤N; subsequently, the normalized sequence is... Data preprocessing is performed, including outlier removal and data smoothing. The preprocessed sequence is denoted as... ,in These are the cleaned and valid data points. This sequence will serve as the input for all subsequent calculations; From sequence Two key features were extracted: average normalized output force. and sequence standard deviation ,in It is a sequence The kth element: This value directly reflects the average output level of the unit equipment during the evaluation period; This value will be used for the adaptive setting of the similarity tolerance parameter r in subsequent fuzzy entropy calculations; 1.2 Calculation of output capacity factor: Output capacity factor Calculate according to formula (7.5): The range of values ​​is ; 1.3 Calculation of behavioral orderliness factor: Behavioral orderliness factor The calculation is divided into two sub-steps: first, based on the preprocessed sequence Calculate fuzzy entropy Then, it is transformed into a normalized orderliness score through a mapping function; 1.4 Unit equipment availability calculation: Unit devices The overall availability is determined by , Synthesize according to formula (7.2).

3. The hierarchical multidimensional availability evaluation method for road-domain high-entropy energy systems based on fuzzy entropy according to claim 1, characterized in that: The system-level availability evaluation steps include: First, divide the collaborative and mutually supportive clusters, assuming they are divided into... Each cluster; then the guarantee level of a single cluster is calculated. Definition: Cluster weight For clusters The proportion of critical loads to total critical loads in the system: cluster internal weights Indicates the region The load accounts for a portion of the load of its cluster. The proportion; the guarantee level of a single cluster. for: in, It is a cluster The weighted average of the availability of the inner area, i.e. its static capacity; It is a cluster The highest area availability within; It is the collaborative gain strength coefficient, used to reward differences in availability within the cluster; Finally, the protection levels of all clusters in the system are weighted and summarized: in, It refers to the number of collaborative and mutually supportive clusters; It is a cluster The weights; It is the system mutual assistance gain factor, which characterizes the best overall protection level that the system can achieve by optimizing power support under a given mutual assistance network topology and capacity constraints.

4. The hierarchical multidimensional availability evaluation method for road-domain high-entropy energy systems based on fuzzy entropy according to claim 2, characterized in that: Based on the preprocessed sequence Calculate fuzzy entropy The steps are as follows: definition: Embedding dimension m: used to reconstruct the phase space; Similarity tolerance Adaptive value ; Gradient parameter n: used to define the shape of the fuzzy membership function; The first step is to reconstruct the phase space, transforming the one-dimensional sequence... Reconstructed into an m-dimensional vector: ， The second step is to calculate any two m-dimensional reconstruction vectors. and The Chebyshev distance between them, which characterizes the absolute difference between two power output sequences of length m at their least dissimilar moments: in It is the k-th element of the a-th reconstruction vector of unit device i. It is the k-th element of the b-th reconstructed vector of unit i; Then the fuzzy similarity is It is a similarity tolerance. The gradient parameter is used to control the rate of similarity decay; The third step is to calculate the average similarity: For each vector Calculate its relationship with all other vectors. The average value of the fuzzy similarity. Defined as the vector within a tolerance of Local similarity at time: The fourth step involves averaging the local similarities of all vectors to obtain an embedding dimension of m with a tolerance of [value missing]. Global average similarity at time: Step 5: Dimensional Enhancement Calculation Increase the embedding dimension to m+1, repeat steps one through four, and calculate the corresponding fuzzy similarity. and global average similarity ; Step 6: Calculate the fuzzy entropy Fuzzy entropy is defined as the negative of the difference between the logarithms of the global average similarity in two adjacent dimensions. Less than or equal to ; The seventh step transforms the fuzzy entropy into a normalized orderliness evaluation in the range [0,1] using a monotonically decreasing mapping function, employing a negative exponential function: The scale parameter is obtained by calibrating the entropy distribution of typical sequences. .

5. The hierarchical multidimensional availability evaluation method for road-domain high-entropy energy systems based on fuzzy entropy according to claim 3, characterized in that: The value is [0.1, 0.2]. According to the mutual assistance matrix G, the elements... Indicates the region arrive The mutual support capability divides the areas that can provide direct or indirect power support into a collaborative mutual support cluster.

6. The hierarchical multidimensional availability evaluation method for road-domain high-entropy energy systems based on fuzzy entropy according to claim 4, characterized in that: Equation (7.11) ensures that: when E(i)→0 (the sequence is completely ordered), F(E(i))→1; when E(i) increases (the disorder of the sequence increases), F(E(i)) decreases smoothly; when E(i) is very large, F(E(i))→0.

7. The hierarchical multidimensional availability evaluation method for road-domain high-entropy energy systems based on fuzzy entropy according to claim 1, characterized in that: Regional time coordination The calculation is as follows: Step 1: Perform a critical feasibility check to ensure that the maximum number of discrete delay points K and the sequence length T satisfy the following conditions. conditions; Step 2: Create Time co-similarity matrix , This represents the total number of cells within the region; this matrix is ​​used to store the optimal alignment similarity of all cell pairs within the region; then, all unique cell pairs are traversed; assuming the cells... , The normalized output sequence is and Time shift In the interval The values ​​are taken at all integer time-shift points, for each time-shift... Calculate the sequence With overall time shift The following sequence Pearson correlation coefficient over the entire effective overlap interval Based on different time shifts All calculated In the middle, the one with the largest absolute value is the unit. and unit Optimal alignment similarity: 。 8. The hierarchical multidimensional availability evaluation method for road-domain high-entropy energy systems based on fuzzy entropy according to claim 7, characterized in that: 。 9. A hierarchical multidimensional availability evaluation method for road-domain high-entropy energy systems based on fuzzy entropy according to claim 4, characterized in that: Let n=2 and m=2.

10. A hierarchical multidimensional availability evaluation system for road-domain high-entropy energy systems based on fuzzy entropy, comprising a processor and a readable storage medium, wherein the readable storage medium stores a computer program, characterized in that: The processor executes the readable storage medium to implement the steps of the method as claimed in any one of claims 1-9.

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