A power distribution system planning method for coping with seasonal imbalance and year-by-year strengthening of heat wave

Abstract

The application discloses a power distribution system planning method for coping with seasonal imbalance and year-by-year strengthening of heat wave, and belongs to the field of power system planning and operation optimization. The method first collects multi-year hourly meteorological data and power distribution system basic data of a target city, generates a multi-time scale heat wave meteorological trajectory containing short-term seasonal fluctuations and long-term strengthening trends; then converts meteorological variables into building cooling load amplification coefficients and green power output correction coefficients through source-load-meteorological sensitivity mapping to obtain node net injection power; calculates a heat wave source-load imbalance risk index and screens key heat wave scenarios based on the index, constructs a node net injection power envelope and a heat wave disturbance budget, forms a compact composite uncertainty set, and establishes a progressive two-stage robust planning model for solution. The application can reduce the solution complexity brought by high-dimensional heat wave scenarios, and improve the planning adaptability, operation safety and engineering implementability of the urban power distribution system under heat wave conditions.

Description

Technical Field

[0001] This invention belongs to the field of power system planning and operation optimization technology, specifically relating to a robust planning method for urban power distribution systems that addresses seasonal imbalances and year-on-year intensification caused by heat waves. In particular, it relates to an investment planning and operation verification method for urban power distribution systems based on a heat wave source-load imbalance risk index, progressive screening of key scenarios, and a compact composite uncertainty set. Background Technology

[0002] In recent years, global warming and the urban heat island effect have jointly exacerbated the frequency, intensity, and duration of urban heat waves. Unlike sudden disasters such as typhoons, rainstorms, and freezing rain, heat waves typically exhibit distinct seasonal cycles and a multi-year intensification trend. Their impact is not a single shock but rather acts on urban energy systems in a continuous, cumulative, and trend-like manner.

[0003] The impact of heat waves on urban power distribution systems exhibits a clear source-load coupling characteristic. On the load side, sustained high temperatures and enhanced solar radiation cause a rapid increase in cooling loads in residential buildings, commercial buildings, and public facilities, leading to higher peak loads and longer durations in summer. On the power supply side, high temperatures cause photovoltaic modules to heat up and reduce conversion efficiency, while calm or low-wind-speed weather reduces wind power output, decreasing the capacity of distributed renewable energy to support peak load periods. On the grid side, high temperatures can also reduce the operational margin of lines and equipment, further amplifying the risks of voltage overruns, line overloads, and load shedding.

[0004] Existing power distribution system planning methods typically allocate capacity based on typical days, historical average operating conditions, or a fixed number of scenarios, making it difficult to simultaneously reflect both the short-term seasonal fluctuations and long-term, year-by-year intensification trends of heat waves. Currently, numerous patents and research studies both domestically and internationally focus on power distribution network planning, optimization, and dispatch under extreme weather conditions, which can be mainly categorized into three types: The first category comprises operation and scheduling technologies under extreme high temperatures / heat waves. For example, Chinese patent application CN117131982A discloses a user-side energy optimization method to ensure reliable load supply under extreme high-temperature events. This scheme only manages user-side loads for short-term extreme high temperatures and does not consider the intraday cycle, seasonal fluctuations, and multi-year intensity evolution of heat waves. It also ignores the output attenuation problem of distributed power sources such as photovoltaics and wind power under high-temperature conditions and is only applicable to post-event scheduling, unable to support medium- and long-term planning of distribution networks. Patent CN122052005A proposes a source-grid-load-storage optimization scheduling method under extreme weather conditions, focusing on solving the system supply and demand balance problem under extreme weather conditions. However, its core is an operation and scheduling model, which does not involve planning aspects such as distributed resource site selection and capacity determination, nor does it perform meteorological modeling for the multi-timescale characteristics of heat waves.

[0005] The second category is robust planning / resilience enhancement technology for distribution networks under general extreme weather conditions. This type of technology is aimed at scenarios such as typhoons, freezing, and comprehensive natural disasters. Representative patents include Chinese patent applications CN115062833A, CN116667424A, CN119005560A, and CN120338443A. Among them, CN115062833A, which plans mobile energy storage resources for extreme weather, uses stochastic meteorological scenarios to describe uncertainties and fails to distinguish the source-load coupling characteristics and evolution patterns specific to heat waves; CN116667424A and CN119005560A use a traditional two-stage robust architecture and a general uncertainty set to handle source-load fluctuations, which suffers from high scenario dimensionality, complex solutions, and strong conservatism, and fails to establish a mapping relationship between meteorological variables and load and renewable energy output; CN120338443A constructs a robust planning model by searching for the most severe natural disaster scenario, using only load loss as a single risk assessment indicator, which cannot quantify the comprehensive imbalance risk of "load surge, renewable energy attenuation, and load spatial aggregation" during heat waves, and the scenario selection method is simple and does not support dynamic iterative updates. Another Chinese patent application, CN122136843A, conducts distribution network zoning planning for typhoon disasters, which is suitable for instantaneous impact meteorological disasters but completely unsuitable for persistent and seasonal heat wave scenarios.

[0006] The third category is conventional source-load uncertainty distribution network planning technology. This type of scheme often uses stochastic optimization and traditional robust optimization to handle load and new energy fluctuations. It directly inputs massive meteorological trajectories or power scenarios into the optimization model without splitting the meteorological scenarios into time scales, ranking and compressing risks. This results in problems such as unclear identification of key risk scenarios, poor algorithm interpretability, and low computational efficiency.

[0007] In summary, existing technologies suffer from the following common shortcomings: First, they cannot simultaneously characterize the multi-timescale evolutionary features of heat waves, including intraday fluctuations, seasonal imbalances, and multi-year intensifications; second, they lack risk quantification indicators and efficient scenario screening mechanisms for the coupling characteristics of heat wave source and load, resulting in severe redundancy in high-dimensional meteorological scenarios; third, traditional robust uncertainty sets have high dimensionality, are difficult to solve, and lead to overly conservative planning schemes; and fourth, general decomposition algorithms do not incorporate risk priority iteration, resulting in a lack of directionality in planning scheme corrections, making it difficult to meet the requirements for interpretability, feasibility, and computational efficiency in engineering pre-approval and practical planning applications.

[0008] Therefore, it is necessary to propose a robust planning method for power distribution systems that takes into account the evolution characteristics of urban heat waves. This method transforms complex meteorological trajectories and source-load response processes into risk information that can be sorted, filtered, and progressively verified, thereby reducing algorithm complexity while improving the adaptability of planning schemes to future heat wave risks. Summary of the Invention

[0009] The purpose of this invention is to overcome at least one deficiency of the prior art and provide a two-stage robust planning method for urban power distribution systems that addresses seasonal imbalances and year-on-year intensifications caused by heat waves.

[0010] The technical solution adopted in this invention is: A power distribution system planning method to address seasonal imbalances and year-on-year intensification of heat waves includes the following steps: (1) Collect multi-year hourly meteorological data and basic data of power distribution system of target city. The meteorological data includes ambient temperature, wind speed and solar radiation intensity. The basic data of power distribution system includes node topology, line parameters, installation location of candidate resources, building load access relationship and distributed power access relationship. (2) Generate multi-timescale heat wave meteorological trajectories based on the multi-year hourly meteorological data, including the periodic changes of heat waves on intraday and seasonal scales, the changes of heat waves in intensity, duration and frequency of occurrence on multi-year scales, and generate multi-scenario heat wave meteorological trajectories in the future planning period through adaptive fusion. (3) Based on the multi-scenario heat wave meteorological trajectory, perform source-load meteorological sensitivity mapping, convert meteorological variables into building cooling load amplification factor, photovoltaic power output correction factor and wind power output correction factor, and further obtain the node net injection power of each node and each time period; (4) Calculate the heat wave source load imbalance risk index based on the net injected power of the node, sort and screen the heat wave meteorological scenarios according to the heat wave source load imbalance risk index, and construct a key heat wave scenario pool; (5) Based on the key heat wave scenario pool, construct the node net injection power envelope and heat wave disturbance budget to form a compact composite uncertainty set; (6) Establish a progressive two-stage robust planning model, in which the first stage determines the investment location and capacity configuration of distributed resources, and the second stage performs operation verification in the compact composite uncertainty set and key heat wave scenario pool to determine the operational feasibility and economy of the investment scheme under heat wave conditions. (7) The progressive two-stage robust planning model is solved by using the risk ranking-driven progressive Benders decomposition algorithm. Based on the running verification results, the running cost correction constraint or running infeasibility correction constraint is generated, and the investment plan is iteratively updated to output the optimal investment layout plan, capacity configuration plan, key risk scenarios and corresponding robust operation strategies.

[0011] In some instances, the generation process of the multi-timescale heat wave meteorological trajectory includes: Ambient temperature, wind speed, and solar radiation intensity are combined into a meteorological variable vector. ; Extract the intraday cycle term, the seasonal cycle term, and the short-term random disturbance term to obtain the seasonal fluctuation term; The trend terms of heat wave intensity, duration, and frequency over multiple timescales are extracted to obtain the long-term trend term; The fusion weights are determined through adaptive fusion based on the month, heat wave level, or historical forecast error, and the seasonal fluctuation term and long-term trend term are fused into a heat wave meteorological trajectory for the future planning period.

[0012] In some instances, the source-load meteorological sensitivity mapping includes: The building cooling load amplification factor is determined based on ambient temperature and solar radiation intensity; the photovoltaic output correction factor is determined based on solar radiation intensity and component temperature rise; and the wind power output correction factor is determined based on wind speed range. The building cooling load amplification factor, photovoltaic output correction factor, and wind power output correction factor are applied to the benchmark cooling load, benchmark photovoltaic output, and benchmark wind power output, respectively, to obtain the nodal net injected power under the heat wave scenario.

[0013] In some instances, the heat wave source-load imbalance risk index is jointly determined by a high temperature intensity index, a heat wave persistence index, a cooling load growth index, a renewable energy output decay index, and a node net load spatial concentration index. The high temperature intensity index is used to characterize the peak temperature and the degree to which it exceeds the heat wave threshold. The heat wave persistence index is used to characterize the number of consecutive high temperature periods. The cooling load growth index is used to characterize the increase in building cooling load relative to the baseline operating condition. The renewable energy output decay index is used to characterize the decrease in photovoltaic and wind power output relative to the baseline operating condition. The node net load spatial concentration index is used to characterize the degree of concentration of net load increments among distribution nodes under heat wave scenarios.

[0014] In some instances, heat wave scenarios are sorted in descending order according to the heat wave source load imbalance risk index, and key heat wave scenarios are selected based on preset risk thresholds, the top K scenarios in the sorting, or the cumulative risk coverage rate to form a key heat wave scenario pool. When the investment plan changes or new scenarios are added during the progressive operation verification process, causing the operation constraints to exceed the limit, the key heat wave scenario pool is updated.

[0015] In some instances, the compact composite uncertainty set consists of the nodal net injected power envelope and the heat wave disturbance budget corresponding to the key heat wave scenario; The net injected power envelope of the nodes includes the upper limit, lower limit and deviation range of the net injected power for each node and each time period; The heat wave disturbance budget is used to limit the number of nodes, time periods, or node-time period combinations that simultaneously reach extreme deviations, thereby reducing the dimension of uncertain variables in the operation verification.

[0016] In some instances, the progressive two-stage robust programming model includes an investment master problem and an operational verification subproblem; The investment master problem takes the installation status and capacity of distributed resources as the decision objects, and considers the capacity limit of candidate locations and investment budget constraints. The operational verification subproblem verifies node power balance, line capacity, voltage range, controllable power output, and load shedding constraints under given investment plans and key heat wave scenario pools, and calculates the corresponding operating costs, load shedding amounts, over-limit nodes, and over-limit lines.

[0017] In some instances, the risk-ranked, progressive Benders decomposition algorithm includes: Calculate the source-load imbalance risk index for all heat wave scenarios, and select the scenarios with the highest source-load imbalance risk to form the initial key scenario pool. Solving the principal investment problem yields candidate investment solutions; Operational verification is performed within the critical scenario pool. If the operational verification results in load shedding, voltage exceeding limits, or line exceeding limits, an operational infeasibility correction constraint is generated and returned to the investment master problem. If the operational verification satisfies the operational constraints, an operational cost correction constraint is generated based on the operational costs. Once all scenarios in the current critical scenario pool meet the operational constraints, the scenario with the highest risk index is added from the unverified scenarios until the investment plan no longer changes or the convergence threshold is met.

[0018] In some instances, the operational infeasibility correction constraints are generated based on over-limit nodes, over-limit lines, supply shortage periods, and the corresponding investment resource locations, and are used to increase the available capacity of the relevant areas or adjust the resource layout; the operational cost correction constraints are generated based on operational costs, load shedding penalties, and constraint sensitivity information under key heat wave scenarios, and are used to correct the investment master problem's estimate of the second-stage operational costs.

[0019] In some instances, the output specifically includes the installation nodes, installation capacity, key heat wave scenario numbers, operating strategies under each key scenario, heat wave source-load imbalance risk ranking results, node net injected power envelope, and the assessment results of load shedding risk, voltage over-limit risk, and line overload risk of the planning scheme under heat wave conditions.

[0020] The above features can be combined arbitrarily as long as they do not conflict with each other.

[0021] The beneficial effects of this invention are: (1) This invention compresses high-dimensional meteorological trajectories and nodal power responses into sortable risk indicators through the heat wave source-load imbalance risk index, which can prioritize the identification of key heat wave scenarios that have the greatest impact on power distribution system planning.

[0022] (2) The present invention adopts source-load meteorological sensitivity mapping to transform the complex building thermal process, photovoltaic temperature effect and wind power wind speed effect into cold load amplification coefficient, photovoltaic output correction coefficient and wind power output correction coefficient, which reduces the complexity of model expression and enhances the feasibility of engineering.

[0023] (3) This invention utilizes the net injected power envelope of nodes corresponding to key heat wave scenarios and the heat wave disturbance budget to construct a compact composite uncertainty set, avoiding the establishment of a high-dimensional uncertainty set for all meteorological scenarios and reducing the difficulty of solving.

[0024] (4) The present invention adopts a risk-ranked progressive Benders decomposition algorithm, which prioritizes the verification of high-risk scenarios and generates directional correction constraints based on the over-limit results, so that the investment scheme can be gradually improved to address the risks of load shedding, voltage over-limit and line overload under heat wave conditions.

[0025] (5) Compared with traditional power distribution planning methods based on typical days or historical average scenarios, the present invention can simultaneously consider the seasonal fluctuations and year-by-year strengthening trend of heat waves, thereby improving the safety, economy and robustness of the planning scheme under future heat wave conditions.

[0026] The purpose of this invention is to overcome at least one deficiency of the prior art and provide a two-stage robust planning method for urban power distribution systems that addresses seasonal imbalances and year-on-year intensifications caused by heat waves. Attached Figure Description

[0027] Figure 1 The diagram illustrates the overall execution flow of the method of this invention, which includes, in sequence, the acquisition of meteorological data and power distribution system data over multiple years, generation of heat wave trajectories at multiple time scales, source-load meteorological sensitivity mapping, calculation of the heat wave source-load imbalance risk index, screening of key heat wave scenarios, construction of node net injected power envelope and disturbance budget, progressive robust planning verification and scheme correction, and output of the final planning results.

[0028] Figure 2 This is a schematic diagram of the risk-ranked progressive robust planning solution process in this invention, showing the process of constructing a key scenario pool based on the risk index, solving the main investment problem, performing operational verification, generating operational cost correction constraints or operational infeasibility correction constraints, expanding the key scenario pool, and performing convergence judgment. Detailed Implementation

[0029] The purpose of this invention is to overcome the problems of high dimensionality of heat wave meteorological scenarios, difficulty in directly using source-load response coupling relationships for planning, complexity of robust optimization solutions, and insufficient identification of key risk scenarios in existing technologies. This invention provides a power distribution system planning method to address the seasonal imbalances and year-on-year intensification of heat waves. This method achieves compressed ranking of complex scenarios through a heat wave source-load imbalance risk index, reduces the dimensionality of the uncertainty set through a key scenario pool and node net injected power envelope, and progressively verifies and corrects investment plans through a risk-ranked progressive Benders decomposition algorithm.

[0030] To achieve the above objectives, this invention provides a robust planning method for urban power distribution systems. First, hourly meteorological data and basic power distribution system data for the target city are collected over multiple years. Then, a multi-timescale meteorological evolution model is used to generate multi-scenario heatwave meteorological trajectories for the future planning period. This meteorological evolution model no longer simply mixes short-term seasonal fluctuations and long-term strengthening trends; instead, it extracts both separately and adaptively fuses them to obtain heatwave meteorological trajectories that reflect intraday fluctuations, seasonal variations, and multi-year strengthening trends.

[0031] Secondly, this invention maps heat wave meteorological trajectories to source-load meteorological sensitivity, converting ambient temperature, wind speed, and solar radiation intensity into building cooling load amplification factors, photovoltaic output correction factors, and wind power output correction factors, respectively. By applying these correction factors to the baseline cooling load, baseline photovoltaic output, and baseline wind power output, and aggregating them according to the distribution node access relationship, the net injected power of each node and each time period under the heat wave scenario is obtained.

[0032] Furthermore, this invention calculates a heat wave source-load imbalance risk index for each heat wave scenario. This risk index comprehensively considers high temperature intensity, heat wave persistence, cooling load growth, renewable energy output decay, and the spatial concentration of node net load, and is used to compress complex meteorological trajectories and node net injected power sequences into a sortable risk indicator. Heat wave scenarios are then sorted according to the risk index, and high-risk scenarios are selected to construct a key heat wave scenario pool.

[0033] Furthermore, this invention constructs a node net injected power envelope and a heat wave disturbance budget based on a pool of key heat wave scenarios, forming a compact composite uncertainty set. This uncertainty set avoids directly constructing all meteorological scenarios into a high-dimensional convex hull, effectively reducing the number of uncertain variables while retaining coverage of high-risk heat wave scenarios.

[0034] Finally, this invention establishes a progressive two-stage robust programming model and solves it using a risk-ranked progressive Benders decomposition algorithm. The main investment problem determines the installation nodes and capacity of distributed resources, while the verification subproblem verifies candidate investment schemes within a critical heatwave scenario pool, considering power balance, voltage, line capacity, controllable power output, and load shedding constraints. When the verification results are infeasible, operational infeasibility correction constraints are generated based on over-limit nodes, over-limit lines, and periods of power shortage; when the verification results are feasible, operational cost correction constraints are generated based on operational cost and constraint sensitivity. Subsequently, the critical scenario pool is gradually expanded until the investment scheme stabilizes or meets the convergence threshold.

[0035] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments. It should be understood that the following embodiments are only used to illustrate the present invention and are not intended to limit the scope of protection of the present invention. (I) Data Acquisition and Generation of Multi-Timescale Heat Wave Trajectories

[0036] In this embodiment, hourly meteorological data and basic power distribution system data for the target city over several consecutive years are first collected. The meteorological data includes ambient temperature. Wind speed and solar radiation intensity The basic data of the power distribution system includes node topology, line impedance, line capacity, node voltage upper and lower limits, candidate distributed resource installation locations, building load access nodes, and distributed power source access nodes.

[0037] Organize meteorological variables into a meteorological variable vector: The raw meteorological data underwent outlier removal, missing value imputation, unit unification, diurnal period alignment, and standardization. Subsequently, the meteorological evolution process was decomposed into a seasonal fluctuation term and a long-term trend term: the seasonal fluctuation term characterizes the periodic changes of meteorological variables on intraday and seasonal scales, while the long-term trend term characterizes the changes in heat wave intensity, duration, and frequency on multi-year scales.

[0038] In one alternative implementation, the seasonal fluctuation term can be extracted from a seasonal time series model, and the long-term trend term can be extracted from a recurrent neural network, a long short-term memory network, or other trend learning models. To avoid limiting the specific model to a single mathematical form, this invention employs an adaptive fusion approach to obtain the heatwave meteorological trajectory:

[0039] in, The combined meteorological forecast results For seasonal fluctuations, For long-term trend items, For adaptive fusion weights. The weighting can be determined based on the month, heatwave severity, historical forecast errors, or meteorological variable category. When the intraday cyclical characteristics of a month are stronger, the weighting of the seasonal fluctuation term is increased; when the long-term warming trend is more pronounced, the weighting of the long-term trend term is increased.

[0040] Based on the fused meteorological forecast results, an initial set of heat wave meteorological scenarios is generated through Monte Carlo sampling, residual resampling, quantile perturbation, or historical similar day perturbation. Each heat wave meteorological scenario includes the sequence of ambient temperature, wind speed, and solar radiation intensity during the planned operation and verification period. (II) Source-load meteorological sensitivity mapping and calculation of nodal net injection power

[0041] After obtaining the meteorological trajectories of heat waves in multiple scenarios, this invention does not directly embed all the complex building heat balance equations, photovoltaic heat balance equations, and wind turbine segmented power curves into the planning model. Instead, it transforms meteorological variables into correction coefficients that can be directly used for power distribution planning through source-load meteorological sensitivity mapping.

[0042] For building cooling load, the building cooling load amplification factor is determined based on the degree to which the ambient temperature exceeds the reference temperature, the solar radiation intensity, and the building's thermal inertia parameters. For photovoltaic power generation, the photovoltaic output correction factor is determined based on the solar radiation intensity and the temperature rise of the modules caused by high temperatures. For wind turbine generators, the wind power output correction factor is determined based on the wind speed range. .

[0043] At node i and time period t, the net injection power of the node corresponding to the heat wave scenario can be expressed as:

[0044] in, , and These are the benchmark photovoltaic output, benchmark wind power output, and benchmark building cooling load, respectively. The net power injection at these nodes adopts the notation convention of "positive for power generation injection and negative for load consumption".

[0045] This source-load meteorological sensitivity mapping method can retain the main impacts of heat waves on source-side output and load-side demand, while avoiding repeated calculations of a large number of complex physical equations during the planning and solution phase, thereby improving the engineering feasibility of the algorithm. (III) Heat Wave Source-Load Imbalance Risk Index and Key Scenarios Screening

[0046] To avoid applying robustness checks indiscriminately to all heat wave meteorological scenarios, this invention further calculates a heat wave source-load imbalance risk index. For the nth heat wave scenario, five types of features are extracted: high temperature intensity, heat wave duration, cooling load growth, renewable energy output decay, and spatial concentration of node net load, and these are normalized to... , , , and .

[0047]

[0048] in, The source-load imbalance risk index for the nth heat wave scenario; It is a high-temperature intensity index used to reflect the peak temperature and the degree to which it exceeds the heat wave threshold; It serves as an indicator of heat wave duration, reflecting the number of consecutive periods of high temperatures. It is a cooling load growth indicator used to reflect the increase in building cooling load; It serves as an indicator of renewable energy output degradation, reflecting the degree of decline in photovoltaic and wind power output. It is a spatial concentration index of node net load, used to reflect the degree of concentration of net load increments among nodes; to The weighting coefficient can be determined based on the planning focus, historical failure statistics, or expert experience.

[0049] Calculate all heat wave scenarios Then, the scenarios are sorted from highest to lowest risk index. Three methods can be used to select key heatwave scenarios: first, select scenarios with a risk index exceeding a preset threshold; second, select the top K scenarios in the risk ranking; third, select scenarios with a cumulative risk coverage rate reaching a preset percentage. The selected scenarios constitute a key heatwave scenario pool, used for subsequent node net injected power envelope construction and progressive operational verification. (iv) Construction of compact composite uncertain sets

[0050] Based on a pool of key heatwave scenarios, this invention statistically analyzes the upper and lower limits and deviation range of the net injected power at each node and at each time period, forming a node net injected power envelope: in, and Let $\mathbf{i}$ be the lower and upper bounds of the net injection power of node $i$ in time period $t$, respectively. Compared with directly constructing a high-dimensional convex hull uncertainty set from the entire scene, the node net injection power envelope can significantly reduce the complexity of uncertainty set representation.

[0051] Meanwhile, to avoid excessive conservatism caused by all nodes and all time periods reaching extreme deviations simultaneously, this invention sets a heat wave disturbance budget Γ to limit the number of nodes, time periods, or node-time period combinations in extreme deviation states. A compact composite uncertainty set is formed by the node net injected power envelope and the heat wave disturbance budget. This uncertainty set covers both high-risk heat wave source-load imbalance states and reduces the difficulty of solving the operational verification subproblem. (v) Progressive two-stage robust programming model

[0052] Based on the aforementioned compact composite uncertainty set, a progressive two-stage robust programming model is established. The first stage is the investment master problem, which determines the installation status and capacity of candidate distributed resources; the second stage is the operation verification sub-problem, which verifies the operational feasibility and economic viability of key heat wave scenarios under a given investment plan.

[0053] The decision variables for the investment master problem include the installation state z of the candidate sites. j and installation capacity s j Investment constraints include upper limits on candidate site capacity, investment budget, resource type quantity limits, and node access limits. Operational verification sub-problems include node power balance, line capacity, voltage range, controllable power output, load shedding, and resource availability capacity constraints.

[0054] To facilitate project implementation, the operation verification results not only output operating costs, but also exceedance nodes, exceedance lines, periods of supply shortage, load reduction, and the location of relevant candidate resources, providing a basis for subsequent scheme generation and constraint correction. (vi) Risk-ranked progressive Benders decomposition algorithm

[0055] This invention employs a risk-ranked, progressive Benders decomposition algorithm to solve the aforementioned planning model. Unlike traditional Benders decomposition, which processes all scenarios at once, this invention prioritizes verifying key heatwave scenarios with higher risk indices and gradually expands the scenario pool based on the verification results.

[0056] Step 1: Calculate the source-load imbalance risk index for all heat wave scenarios and sort them from high to low according to the risk index.

[0057] Step 2: Select the top K0 heat wave scenarios to form the initial critical scenario pool.

[0058] Step 3: Solve the principal investment problem to obtain candidate investment solutions.

[0059] Step 4: Solve the runtime verification sub-problem in the current critical scenario pool to determine whether the candidate investment schemes meet the constraints of power balance, voltage, line capacity, controllable output, and load shedding.

[0060] Step 5: If load shedding, voltage exceeding limits, or line exceeding limits occur during the operation verification, then generate operational infeasibility correction constraints based on the exceeding node, exceeding line, supply shortage period, and relevant candidate resource locations, and return to the main investment problem.

[0061] Step 6: If the running verification satisfies the constraints, then generate running cost correction constraints based on running cost, load reduction penalty, and constraint sensitivity information, and update the upper and lower bounds.

[0062] Step 7: Once all scenarios in the current critical scenario pool meet the operational constraints, add the scenario with the highest risk index from the unverified scenarios to expand the critical scenario pool.

[0063] Step 8: When the investment plan no longer changes in continuous iterations, or when the relative errors of the upper and lower bounds meet the convergence threshold, output the final investment plan and robust operation strategy.

[0064] The convergence condition can be expressed as: Where UB is the upper bound of the currently known feasible solutions, LB is the lower bound of the investment principal problem, and ε is the convergence threshold. In power distribution system planning, ε can be taken as 10 based on the accuracy requirements. −3 Up to 10 −2 .

[0065] The improvements of this algorithm are as follows: Scenarios are sorted by risk index to avoid premature verification of low-risk scenarios; the number of sub-problem solutions is reduced by progressively expanding the key scenario pool; investment plans can be targeted to address risks of power shortages, voltage overruns, and line overloads during heat waves by using infeasibility correction constraints and operating cost correction constraints; and the dimensionality of uncertain variables is reduced by using a compact composite uncertainty set, thereby improving the feasibility of the project. (vii) Verification of implementation results

[0066] In one embodiment, a modified IEEE 33-node urban power distribution system is used for simulation verification. The system includes 33 distribution nodes, power lines, multiple candidate distributed resource installation locations, building cooling loads, photovoltaic power generation, and wind turbines. Historical meteorological data is used to generate multi-scenario heat wave meteorological trajectories, and basic power distribution system data is used to establish the node net injected power and operational verification models.

[0067] The testing process includes: First, collecting and preprocessing hourly meteorological data of the target city over the past ten years; Second, generating multi-timescale heat wave meteorological trajectories for the future planning period; Third, obtaining the net injected power of nodes using source-load meteorological sensitivity mapping; Fourth, calculating the heat wave source-load imbalance risk index and screening key heat wave scenarios; Fifth, constructing the node net injected power envelope and heat wave disturbance budget; Sixth, comparing the planning method based on historical typical scenarios with the method of this invention.

[0068] In a set of typical embodiments, a baseline planning method based on historical typical meteorological scenarios is compared with the risk ranking-driven progressive robust planning method proposed in this invention. The comparison indicators include total system cost, investment cost, operating cost, load shedding, power shortage under the most unfavorable heat wave scenario, number of voltage overruns, number of line overloads, and coverage of key heat wave scenarios. Specific results are shown in Table 1.

[0069] Table 1 Comparison of the implementation effects of different planning methods

[0070] Among them, the total system cost is the sum of investment cost, operating cost and power shortage penalty cost; the average annual load shedding is used to characterize the degree of power supply insufficiency in the system during the high-temperature season; the power shortage under the most unfavorable heat wave scenario is used to characterize the tail risk under extreme heat wave conditions; the number of voltage over-limits is the cumulative number of times the node voltage exceeds the allowable upper and lower limits in each operating segment; the number of line overloads is the cumulative number of times the line power flow exceeds the capacity limit in each operating segment; the critical heat wave scenario coverage rate is the proportion of the number of high-risk heat wave scenarios identified by the critical scenario pool and included in the operation verification to the total number of high-risk heat wave scenarios.

[0071] As shown in Table 1, although the investment cost of the method of this invention increases from RMB 920,000 / year to RMB 1,120,000 / year compared to the baseline planning method, the operating cost is reduced from RMB 380,000 / year to RMB 340,000 / year, and the supply shortage penalty cost is reduced from RMB 185,000 / year to RMB 30,000 / year, because it can identify key scenarios with severe source-load imbalance under heat wave conditions in advance and allocate distributed resources more specifically to key nodes that have a greater impact on supply-demand balance, voltage support and line power flow. The total system cost remains basically the same.

[0072] Meanwhile, the method of this invention can significantly reduce operational risks under heat wave conditions. Compared with the baseline planning method, the average annual load shedding is reduced from 95 MWh / year to 48 MWh / year, the power shortage under the most unfavorable heat wave scenario is reduced from 600 MWh / year to 380 MWh / year, the number of voltage overruns is reduced from 42 times / year to 11 times / year, and the number of line overloads is reduced from 36 times / year to 8 times / year. The above results show that this invention can not only reduce the risk of power shortages during high-temperature seasons, but also reduce voltage overruns and line overloads caused by heat waves.

[0073] Furthermore, this invention ranks heat wave scenarios using a source-load imbalance risk index and employs a progressive expansion mechanism for a key scenario pool for operational verification, increasing the coverage of key heat wave scenarios from 68.4% to 94.7%. This result demonstrates that this invention can more fully cover key heat wave scenarios characterized by high temperature intensity, long duration, significant increase in cooling load, and significant decline in renewable energy output, thereby improving the adaptability of urban power distribution systems to seasonal imbalances and the increasing trend of heat waves.

[0074] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, or combinations made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A power distribution system planning method for addressing seasonal imbalances and year-on-year intensification of heat waves, characterized in that, Includes the following steps: (1) Collect multi-year hourly meteorological data and basic data of power distribution system of target city. The meteorological data includes ambient temperature, wind speed and solar radiation intensity. The basic data of power distribution system includes node topology, line parameters, installation location of candidate resources, building load access relationship and distributed power access relationship. (2) Generate multi-timescale heat wave meteorological trajectories based on the multi-year hourly meteorological data, including the periodic changes of heat waves on intraday and seasonal scales, the changes of heat waves in intensity, duration and frequency of occurrence on multi-year scales, and generate multi-scenario heat wave meteorological trajectories in the future planning period through adaptive fusion. (3) Based on the multi-scenario heat wave meteorological trajectory, perform source-load meteorological sensitivity mapping, convert meteorological variables into building cooling load amplification factor, photovoltaic power output correction factor and wind power output correction factor, and further obtain the node net injection power of each node and each time period; (4) Calculate the heat wave source load imbalance risk index based on the net injected power of the node, sort and screen the heat wave meteorological scenarios according to the heat wave source load imbalance risk index, and construct a key heat wave scenario pool; (5) Based on the key heat wave scenario pool, construct the node net injection power envelope and heat wave disturbance budget to form a compact composite uncertainty set; (6) Establish a progressive two-stage robust planning model, in which the first stage determines the investment location and capacity configuration of distributed resources, and the second stage performs operation verification in the compact composite uncertainty set and key heat wave scenario pool to determine the operational feasibility and economy of the investment scheme under heat wave conditions. (7) The progressive two-stage robust planning model is solved by using the risk ranking-driven progressive Benders decomposition algorithm. Based on the running verification results, the running cost correction constraint or the running infeasibility correction constraint is generated, and the investment plan is iteratively updated. The optimal investment layout plan, capacity configuration plan, key risk scenarios and corresponding robust operation strategies are output. The risk-ranked, progressive Benders decomposition algorithm includes: Calculate the source-load imbalance risk index for all heat wave scenarios, and select the scenarios with the highest source-load imbalance risk to form the initial key scenario pool. Solving the principal investment problem yields candidate investment solutions; Operational verification is performed within the critical scenario pool. If the operational verification results in load shedding, voltage exceeding limits, or line exceeding limits, an operational infeasibility correction constraint is generated and returned to the investment master problem. If the operational verification satisfies the operational constraints, an operational cost correction constraint is generated based on the operational costs. Once all scenarios in the current critical scenario pool meet the operational constraints, the scenario with the highest risk index is added from the unverified scenarios until the investment plan no longer changes or the convergence threshold is met.

2. The power distribution system planning method according to claim 1, characterized in that, The generation process of the multi-timescale heat wave meteorological trajectory includes: Ambient temperature, wind speed, and solar radiation intensity are combined into a meteorological variable vector. ; Extract the intraday cycle term, the seasonal cycle term, and the short-term random disturbance term to obtain the seasonal fluctuation term; The trend terms of heat wave intensity, duration, and frequency over multiple timescales are extracted to obtain the long-term trend term; The fusion weights are determined through adaptive fusion based on the month, heat wave level, or historical forecast error, and the seasonal fluctuation term and long-term trend term are fused into a heat wave meteorological trajectory for the future planning period.

3. The power distribution system planning method according to claim 1, characterized in that, The source-load meteorological sensitivity mapping includes: The building cooling load amplification factor is determined based on ambient temperature and solar radiation intensity; the photovoltaic output correction factor is determined based on solar radiation intensity and component temperature rise; and the wind power output correction factor is determined based on wind speed range. The building cooling load amplification factor, photovoltaic output correction factor, and wind power output correction factor are applied to the benchmark cooling load, benchmark photovoltaic output, and benchmark wind power output, respectively, to obtain the nodal net injected power under the heat wave scenario.

4. The power distribution system planning method according to claim 1, characterized in that, The heat wave source-load imbalance risk index is jointly determined by the high temperature intensity index, heat wave persistence index, cooling load growth index, renewable energy output decay index, and node net load spatial concentration index. The high temperature intensity index is used to characterize the temperature peak and the degree to which it exceeds the heat wave threshold. The heat wave persistence index is used to characterize the number of consecutive high temperature periods. The cooling load growth index is used to characterize the increase in building cooling load relative to the baseline operating condition. The renewable energy output decay index is used to characterize the decrease in photovoltaic and wind power output relative to the baseline operating condition. The node net load spatial concentration index is used to characterize the degree of concentration of net load increment among distribution nodes under heat wave scenarios.

5. The power distribution system planning method according to claim 4, characterized in that, Heat wave scenarios are sorted in descending order according to the heat wave source load imbalance risk index, and key heat wave scenarios are selected based on preset risk thresholds, the top K scenarios in the sorting, or the cumulative risk coverage rate to form a key heat wave scenario pool. When the investment plan changes or new scenarios are added during the progressive operation verification process, causing the operation constraints to exceed the limit, the key heat wave scenario pool is updated.

6. The power distribution system planning method according to claim 1, characterized in that, The compact composite uncertainty set consists of the nodal net injected power envelope and the heat wave disturbance budget corresponding to the key heat wave scenario; The net injected power envelope of the nodes includes the upper limit, lower limit and deviation range of the net injected power for each node and each time period; The heat wave disturbance budget is used to limit the number of nodes, time periods, or node-time period combinations that simultaneously reach extreme deviations, thereby reducing the dimension of uncertain variables in the operation verification.

7. The power distribution system planning method according to claim 1, characterized in that, The progressive two-stage robust programming model includes the investment master problem and the operation verification subproblem; The investment master problem takes the installation status and capacity of distributed resources as the decision objects, and considers the capacity limit of candidate locations and investment budget constraints. The operational verification subproblem verifies node power balance, line capacity, voltage range, controllable power output, and load shedding constraints under given investment plans and key heat wave scenario pools, and calculates the corresponding operating costs, load shedding amounts, over-limit nodes, and over-limit lines.

8. The power distribution system planning method according to claim 1, characterized in that, The infeasibility correction constraint is generated based on over-limit nodes, over-limit lines, supply shortage periods, and the corresponding investment resource locations, and is used to increase the available capacity of the relevant areas or adjust the resource layout; the operating cost correction constraint is generated based on the operating cost, load reduction penalty, and constraint sensitivity information under key heat wave scenarios, and is used to correct the investment master problem's estimate of the second-stage operating cost.

9. The power distribution system planning method according to claim 1, characterized in that, The output specifically includes the installation nodes and capacity of the candidate distributed resources, the key heat wave scenario numbers, the operation strategies under each key scenario, the ranking results of heat wave source-load imbalance risks, the net injected power envelope of the nodes, and the assessment results of the load shedding risk, voltage over-limit risk, and line overload risk of the planning scheme under heat wave conditions.

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