Power distribution system optimization method considering space-time game under vehicle-station-network interaction

Abstract

The invention relates to a power distribution system optimization method considering a space-time game under vehicle-station-network interaction, and the method employs a double-layer optimization framework integrating the space-time game and dynamic electricity price, an upper decision maker is a power distribution system operator, and the power distribution system operation cost is minimized and the renewable energy consumption rate is maximized. Generating a dynamic electricity price signal in a time-sharing and partition manner; the lower-layer main body comprises an electric vehicle user and a charging station operator, and the electric vehicle user optimizes a charging time period and a charging station and forms charging demand distribution through a non-cooperative game based on a dynamic electricity price signal and a charging service charge by taking the maximum self-charging decision utility as a target; and a charging station operator optimizes and adjusts a charging service fee decision by taking charging demand distribution as input and taking revenue maximization as a target. Compared with the prior art, the method can collaboratively optimize the economic operation of the power grid and the consumption of renewable energy sources, promotes the efficient flow and balanced distribution of resources among regions, and provides decision support for the dispatching of the power distribution network.

Description

Technical Field

[0001] This invention relates to the field of power distribution network optimization technology, and in particular to a power distribution system optimization method considering spatiotemporal game theory under the interaction of vehicle-station-network. Background Technology

[0002] As a crucial hub connecting the transportation and energy systems, the large-scale development of electric vehicles (EVs) is reshaping the energy and power system landscape at an unprecedented pace. However, the explosive growth of EVs is a double-edged sword. The inherent spatiotemporal randomness and high-power characteristics of their charging loads pose multiple severe challenges to traditional power distribution networks that operate primarily on a "source follows load" model. (1) The problem of supply and demand imbalance in time and space is becoming increasingly acute. The charging behavior of large-scale electric vehicles has significant uncertainty. Disorderly charging is prone to overlap with the peak electricity consumption of residents at night, forming a "peak-on-peak" effect, which leads to overload of local distribution transformers, line congestion, continuous aggravation of the peak-valley difference in the system, and increased load fluctuation. This not only greatly increases the difficulty of grid regulation, but also poses a serious threat to the reliability and economy of the system, and also pushes up the cost of system expansion and peak regulation. In addition, with the high proportion of renewable energy access, the intermittency and volatility of its output further highlight the coordination problem. If the electric vehicle charging load cannot be matched with the peak of renewable energy generation in time and space, it will not only be difficult to effectively absorb clean power, but also require the use of traditional coal-fired units for regulation, which violates the original intention of emission reduction.

[0003] (2) The limitations of traditional electricity pricing mechanisms are becoming increasingly apparent. Fixed electricity pricing mechanisms are difficult to effectively incentivize users to participate in demand response and cannot achieve a balanced allocation of charging load in time and space. Faced with the large-scale access of electric vehicles, traditional electricity pricing methods are inadequate, further exacerbating the pressure on power grid operation and lacking the flexibility and responsiveness to adapt to dynamically changing system conditions.

[0004] (3) The complexity of multi-stakeholder collaborative optimization urgently needs to be addressed. The power distribution system involves multiple stakeholders, including distribution system operators (DSOs), charging station operators (CSOs), and electric vehicle users. These stakeholders have different interests and behavioral patterns: DSOs pursue system safety, economy, and green operation; CSOs focus on return on investment and market share; and users focus on charging convenience and economy. There are potential conflicts among these goals, and the traditional one-way, rigid control model is difficult to effectively coordinate the interests of multiple parties. It is urgent to introduce new market mechanisms and optimization tools to achieve system synergy and efficiency improvement.

[0005] To address these challenges, relying solely on traditional grid expansion or simple time-of-use (TOU) pricing is insufficient. A smarter and more refined control paradigm must be introduced, the core of which lies in guiding electric vehicle charging load from disorder to order, and from load to resource, through price signals and market mechanisms. Summary of the Invention

[0006] The purpose of this invention is to address the problems of supply and demand imbalance in time and space, difficulty in adapting to dynamic changes, and difficulty in effectively coordinating the interests of multiple parties when conducting multi-entity collaborative optimization, and to provide a power distribution system optimization method that considers time and space game under the interaction of vehicle-station-network.

[0007] The objective of this invention can be achieved through the following technical solutions: As a first aspect of the present invention, a power distribution system optimization method considering spatiotemporal game theory under the interaction of vehicle-station-network is provided. The method adopts a two-layer optimization framework that integrates spatiotemporal game theory and dynamic electricity pricing to perform bidirectional interaction and optimization management of energy flow and information flow in the vehicle-station-network system. The upper-level decision-makers are the distribution system operators. Based on the real-time status of the distribution network, renewable energy output forecasts, and the temporal and spatial distribution of regional loads, the distribution system operators generate time-of-use and regional dynamic electricity price signals to guide the lower-level response, with multiple objectives including minimizing grid operating costs and maximizing renewable energy absorption. The lower-level entities include electric vehicle users and charging station operators. Electric vehicle users, as independent decision-makers, aim to maximize their own charging decision utility based on dynamic electricity price signals and charging service fees. They optimize charging time periods and charging stations through non-cooperative game theory to form a charging demand distribution. Charging station operators take the charging demand distribution as input and aim to maximize revenue to optimize and adjust their charging service fee decisions. The charging station operator aggregates the charging load curves of all electric vehicle users in the area, superimposes them onto the base load, and feeds them back to the upper-level power distribution system operator. The power distribution system operator reconstructs the objective function based on the load curves fed back by the power distribution system operator, iteratively updates the dynamic electricity price signal until the system converges, and obtains the final optimized solution for the power distribution system.

[0008] As a preferred technical solution, the dual-layer optimization framework adopts a game-theoretic response mechanism of dynamic electricity price in the time dimension. The distribution system operator generates dynamic electricity price signals at the hourly granularity based on the distribution network load curve and the output fluctuation of renewable energy, and introduces a rolling optimization mechanism to dynamically correct the electricity price strategy. In terms of spatial dimension, power distribution system operators divide electricity price zones according to the distribution network topology, and set higher electricity price weights for areas with high line overload risk and low distributed energy penetration; charging station operators use traffic flow heat maps and grid capacity margin information to deploy charging piles using Nash equilibrium strategies; and through cross-regional collaborative design, they incentivize electric vehicle users to charge across regions through electricity price differences.

[0009] As a preferred technical solution, the dynamic electricity price comprehensively considers factors such as the load of the distribution network system, the output of renewable energy, and time deviation. The dynamic electricity price function in the time dimension is expressed as follows:

[0010] In the formula, for t Dynamic electricity pricing for different time periods for t Total system load during the time period This is the baseline load capacity of the distribution network; The output factor for renewable energy; This represents the time difference between the current period and the previous electricity price cycle. This is the electricity price adjustment cycle; As a factor for adjusting power grid operating costs; These are the weighting coefficients; This is for basic power grid service fees.

[0011] As a preferred technical solution, the two-layer optimization framework constructs a spatial dimension partitioned electricity price weight factor, and realizes differentiated guidance and optimized allocation of electric vehicle charging load by quantifying the remaining capacity margin of the regional power grid. The regional electricity price weighting factor represents the remaining capacity margin of the regional power grid and is used to generate differentiated electricity prices. Through spatially differentiated pricing, it guides the reasonable distribution of electric vehicle charging load. The regional electricity price weighting factor is specifically defined as: the sum of the difference between the base load power of each node in each region and the electric vehicle charging power divided by the sum of the base load power of the entire system. By constructing spatial game equilibrium conditions and utilizing differentiated regional electricity price signals, charging loads can be guided to shift to regions with higher weighting factors.

[0012] As a preferred technical solution, in the upper layer of the two-layer optimization framework, the power distribution system operator uses the published dynamic electricity price as a decision variable to construct a multi-objective optimization problem that considers grid operating costs and renewable energy consumption: The objective function for minimizing power grid operating costs is specifically to minimize the sum of the power grid's purchase cost from the upper-level power grid, the peak-valley difference penalty weighting coefficient, and the difference between the peak and valley power values ​​of the daily load curve. The objective function for maximizing the renewable energy absorption rate is specifically to maximize the ratio of the actual output of renewable energy to the total system load.

[0013] As a preferred technical solution, in the lower layer of the dual-layer optimization framework: The charging decision-making behavior of electric vehicle users is quantified through a utility function. The utility function includes: a benefit term, which is the user's preference coefficient for the battery's state of charge multiplied by the battery's state of charge; a cost term, which is the sum of the dynamic electricity price output by the upper-level power distribution system operator and the corresponding zone charging service fee multiplied by the charging volume for the corresponding time period; and a deviation penalty term, which is the square of the difference between the charging volume for the corresponding time period and the electric vehicle user's preferred charging volume for the corresponding time period multiplied by the user's sensitivity coefficient to the battery's deviation. The electric vehicle user's behavioral decision-making process is manifested as a dynamic game: electric vehicle users choose charging time periods and charging stations by maximizing their own utility function. The charging station operator uses the service fee of each zone at different times as the decision variable, and maximizes its revenue by optimizing the service fee and infrastructure investment; the revenue function of the charging station operator is expressed as revenue minus cost, where the revenue is the product of the service fee and the total charging volume, and the cost includes fixed asset investment and operation and maintenance costs. The lower-level revenue of the two-layer optimization framework consists of a revenue item including service fee revenue minus a cost item including fixed asset investment and operation and maintenance costs; spatial game constraints are set, including service fee boundary constraints and charging power capacity constraints.

[0014] As a preferred technical solution, the upper-level decision-maker and the lower-level subject in the two-layer optimization framework satisfy the following equilibrium conditions:

[0015]

[0016] In the formula, For the first i Zones in time periods t Balanced service fees; R CSO For the revenue function of the charging station operator; f i ( t (This refers to the charging service fee for the power distribution system operator.) E total,i ( t The charging demand distribution generated for electric vehicle users; For electric vehicle users during the time period t Balanced charging power; U user For the utility function of electric vehicle users; π( t (This refers to the dynamic electricity price generated by the power distribution system operator.)

[0017] As a preferred technical solution, the two-layer optimization framework employs an improved particle swarm optimization algorithm to optimize the multidimensional electricity price space by simulating swarm intelligence behavior, and solves for the multi-objective Pareto front to generate dynamic electricity prices, as detailed below: The particle dimension is set to the number of time periods × the number of regions. The initial electricity price range is set based on the normal distribution sampling of historical data to generate the initial particle swarm. Calculate the fitness function, which is specifically a weighted sum of grid operating cost, renewable energy absorption rate and constraint penalty terms, including voltage over-limit penalty and line overload penalty; The diversity of the particle swarm is assessed by spatial distribution variance; when the diversity is sufficient, a nonlinear decreasing function is used to reduce the inertia weight; when the diversity is insufficient, the inertia weight is increased to escape local optima. The particle position and velocity are updated according to the standard formula of the particle swarm algorithm and the process is iterated until the termination condition is met. The final output is the Pareto optimal solution set, which contains multiple spatiotemporal electricity price combination schemes.

[0018] As a preferred technical solution, the improved particle swarm optimization algorithm adopts an elite retention strategy to maintain multiple Pareto front solutions, providing diverse solution options; it utilizes GPUs to perform block-parallel computation of the particle swarm, accelerating the calculation of the fitness function; and it integrates fuzzy logic to handle the uncertainty of user response prediction, enhancing the algorithm's tolerance to prediction bias and quantifying the preferences of different subjects.

[0019] As a preferred technical solution, the dual-layer optimization framework employs the following safeguard mechanism during the upper and lower layer collaborative optimization process: setting thresholds for the rate of change of the objective functions of the upper and lower layers for layer consistency verification, and terminating the iteration when the optimization steps in both directions match; introducing a damping coefficient in the load feedback stage to effectively suppress system oscillations caused by communication delays or prediction errors; and using sliding window filtering technology to interpolate abnormal load data to avoid optimization direction deviations caused by erroneous data.

[0020] Compared with the prior art, the present invention has the following beneficial effects: 1) This invention proposes a two-layer optimization framework integrating spatiotemporal game theory and dynamic electricity pricing. The upper layer, with distribution system operators (DSOs) as the main players, aims to minimize grid operating costs and maximize renewable energy absorption, dynamically generating time-of-use and zone-specific electricity price incentive signals. The lower layer, with electric vehicle users and charging station operators (CSOs) as the main players in the game, guides user charging behavior based on dynamic electricity pricing to achieve a spatiotemporal equilibrium configuration of charging load. A two-layer interactive model is established using Stackelberg game theory, and an improved particle swarm optimization algorithm is used to solve the multi-objective Pareto front. Simulation results show that the proposed strategy can reduce the peak-to-valley difference in the grid and improve the renewable energy absorption rate.

[0021] 2) This invention constructs a three-dimensional Stackelberg game model incorporating temporal dynamics, spatial variability, and electricity price incentives. In this model, the distribution system operator, as the leader, generates time-of-use and zone-specific dynamic electricity price signals based on real-time distribution network topology, regional load, and renewable energy forecasts. Charging station operators and electric vehicle users, as followers, adjust their service fee strategies and charging behaviors according to the electricity price signals, achieving a balance of interests among all parties. By introducing spatial weighting factors and temporal deviation correction terms, this invention enables electricity prices to accurately reflect the grid status in different regions and time periods, effectively solving the problems of exacerbated peak-valley differences, local overload, and renewable energy absorption caused by disordered charging, and achieving a spatiotemporal balanced distribution of load and Pareto improvement for the interests of all parties.

[0022] 3) This invention designs an improved particle swarm optimization (PSO) dynamic electricity price generation algorithm that embeds physical constraints of the distribution network. This algorithm strictly considers grid physical constraints such as node voltage safety thresholds and line capacity limitations in the fitness function, and employs a nonlinear decreasing inertia weight and diversity threshold adaptive adjustment strategy to effectively balance global exploration and local search capabilities, overcoming the curse of dimensionality in high-dimensional electricity price optimization. Furthermore, the algorithm integrates an elite retention strategy to maintain the Pareto solution set, supports GPU parallel computing acceleration, and significantly improves solution efficiency and stability. This algorithm effectively solves the problems of traditional electricity price generation methods ignoring grid safety constraints and having low optimization efficiency, ensuring the safety, economy, and practicality of the electricity price strategy.

[0023] 4) This invention develops a distributed hierarchical solution strategy based on a multi-objective evolutionary algorithm. It employs a distributed collaborative mechanism where upper and lower layers iterate independently and interact through electricity price and load data. The upper layer uses a multi-objective evolutionary algorithm to solve for the economic and environmental objectives of the power grid, while the lower layer uses a non-cooperative game theory and virtual queuing algorithm to solve for user equilibrium, significantly reducing the solution complexity of the two-layer model. This strategy suppresses oscillations caused by data delay and prediction errors through damping coefficients and sliding window filtering techniques, ensuring convergence stability. Furthermore, it eliminates the need for centralized acquisition of private information from all parties, meeting the actual market operation requirements and providing an engineerable solution for the distributed power market. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the vehicle-station-network interactive architecture constructed in this invention.

[0025] Figure 2 This is a flowchart illustrating the dynamic electricity price generation process based on the improved particle swarm optimization algorithm of this invention.

[0026] Figure 3 This is a schematic diagram of the distributed solution architecture constructed in this invention.

[0027] Figure 4 This is a schematic diagram of the load composition of a power distribution network system in one embodiment of the present invention.

[0028] Figure 5 This is a schematic diagram of renewable energy consumption in one embodiment of the present invention. Detailed Implementation

[0029] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0030] Example 1 This invention focuses on the "vehicle-station-grid" interaction scenario and proposes a novel multi-objective bi-layer optimization method for distribution systems that considers the coupling mechanism of spatiotemporal game theory and dynamic electricity pricing. The upper layer, with the Distribution System Operator (DSO) as the main player, aims to minimize grid operating costs and maximize renewable energy absorption, dynamically generating time-of-use and zone-specific electricity price incentive signals. The lower layer, with electric vehicle users and Charging Station Operators (CSOs) as the main players in the game, guides user charging behavior based on dynamic electricity pricing to achieve a spatiotemporal balanced configuration of charging load. A bi-layer interaction model is established using Stackelberg game theory, and an improved particle swarm optimization algorithm is used to solve the multi-objective Pareto front. Based on the above scheme, the strategy proposed in this invention can reduce the peak-valley difference of the grid and improve the renewable energy absorption rate. The specific implementation of each part of the method is as follows: 1. Train-Station-Network Interactive Architecture like Figure 1 As shown, the vehicle-station-network interactive architecture is a multi-level system composed of three main entities: distribution system operators (DSO), charging station operators (CSO), and electric vehicle (EV) users. Through dynamic electricity pricing mechanisms and spatiotemporal behavior game, it realizes two-way interaction and optimized management of energy flow and information flow.

[0031] In the architecture constructed in this invention, the Distribution System Controller (DSO) acts as the top-level regulator. Based on data such as the distribution network topology, renewable energy output forecasts, and the temporal and spatial distribution of regional loads, it generates time-of-use and zone-specific dynamic electricity price signals to guide user charging behavior shifts and avoid grid overload. Furthermore, the DSO is responsible for power flow optimization of the distribution system. By monitoring parameters such as voltage and line load rate in real time, it adjusts reactive power compensation and distributed generation output to ensure the safe operation of the grid. During system operation, the DSO also needs to comprehensively consider operating costs, renewable energy utilization, and user satisfaction. Through multi-objective optimization methods, it forms a Pareto optimal solution set, balancing the interests of multiple parties and achieving overall optimization of the distribution system.

[0032] The middle-layer CSO (Construction Service Provider) bears the crucial responsibility of implementing the upper-level control strategies and connecting with user needs. First, based on the dynamic electricity price signals released by the DSO (Distribution Station Authority) and its own operating costs, the CSO calculates the final charging service fee announced to users. This price leverages the distribution of user charging demand in time and space to achieve peak shaving and valley filling. Second, the CSO also needs to rationally plan charging infrastructure, flexibly configuring fast and slow charging stations based on urban road network density, grid capacity margin, and user travel patterns to improve equipment utilization and avoid resource waste. Furthermore, the CSO possesses load aggregation management capabilities, integrating multiple dispersed EV charging loads into a controllable virtual power source. This allows the CSO to participate as a whole in the DSO-led ancillary services market, providing peak shaving and load balancing support to the grid.

[0033] At the underlying EV user layer, electric vehicle users, as the actual decision-makers of charging behavior, are increasingly proactive in the overall system. Their charging behavior is not only directly affected by electricity prices but also depends on their personal travel plans, battery state of charge (SOC), and sensitivity to charging costs. By establishing an electricity price sensitivity model, users can autonomously choose the optimal charging time and location to reduce overall energy expenditure. Simultaneously, users' historical travel and charging data can be used to analyze their spatiotemporal preferences, helping to predict the overall load distribution in time and space, achieving a more accurate supply-demand balance. Furthermore, users can participate in V2G (vehicle-to-grid) interaction, using their vehicle batteries to feed electricity back into the grid, forming a flexible energy exchange mechanism that not only improves the economic efficiency of electric vehicles but also enhances the grid's adjustability and system resilience.

[0034] The efficient collaboration among these three layers relies on a comprehensive technical support system to achieve efficient data and command interaction and processing. In terms of communication, the system utilizes a high-speed, low-latency 5G network to enable high-frequency transmission of real-time electricity price signals and load data between the DSO and CSO. On the terminal side, the CSO can deploy edge computing servers at each charging station to perform real-time matching and optimization of user charging requests and grid operation constraints, significantly reducing response time and improving the intelligence level of charging services. Regarding data flow management, EV users' charging intentions and behavior data are uploaded to the CSO via the uplink path, where it performs load forecasting and then provides it to the DSO for grid status analysis. Simultaneously, the dynamic electricity price strategy generated by the DSO is transmitted to the CSO via the downlink path, influencing its service fee setting, and ultimately feeding back to EV users to guide their charging behavior, achieving a complete information loop.

[0035] Overall, the vehicle-station-grid interactive architecture, through hierarchical management and two-way interaction, not only achieves multi-party collaboration but also possesses multiple advantages. Firstly, in terms of spatiotemporal coordination, the coupled design of regional electricity pricing mechanisms and charging facility layout effectively alleviates local grid overload problems and improves grid stability. Secondly, this architecture strengthens the system's resilience, achieving dynamic adjustment of charging load through closed-loop optimization of electricity price regulation and flexible user charging behavior, addressing the uncertainty of renewable energy output and load fluctuations. Furthermore, from an economic perspective, all three parties benefit: DSO reduces system operation and peak-shaving costs, CSO improves equipment utilization and reduces investment waste, and EV users reduce overall energy costs through intelligent charging strategies. Ultimately, this architecture provides a practical and feasible systemic solution to address the pressures of high-proportion renewable energy integration, large-scale electric vehicle adoption, and grid regulation capabilities, possessing significant practical value and promotional implications.

[0036] 2. Spatiotemporal game model The core mechanism of the spatiotemporal game model's vehicle-station-network interactive architecture, by integrating temporal dynamism and spatial differences, coordinates the conflicting interests and behavioral interactions of multiple stakeholders, specifically including the following three dimensions: In the time dimension, the game-theoretic response mechanism of dynamic electricity pricing becomes crucial for optimizing the distribution system. The Distribution System Optimization (DSO) generates dynamic electricity price signals at the hourly granularity based on the distribution network load curve and renewable energy output fluctuations, incentivizing EV users to choose off-peak charging times to reduce expenses based on charging cost sensitivity analysis. However, the time lag in user decision-making (such as the discrepancy between charging reservations and real-time electricity prices) necessitates the introduction of a rolling optimization mechanism to dynamically adjust pricing strategies and prevent load reversal from peak to off-peak. Furthermore, training a time-series prediction model using historical charging data can predict user electricity price response patterns, providing the DSO with a basis for multi-cycle electricity price optimization and achieving a two-way feedback and dynamic balance between electricity prices and charging behavior.

[0037] In a spatial dimension, the regional competition for charging resources focuses on optimal resource allocation and regional equilibrium. Distribution System Controllers (DSOs) divide electricity price zones based on the distribution network topology, assigning higher price weights to areas with high line overload risk and low distributed energy penetration to guide users to migrate to resource-rich areas. Community Service Controllers (CSOs) utilize traffic flow heat maps and grid capacity margin information, employing a Nash equilibrium strategy to deploy charging piles, ensuring a balance between facility utilization and grid safety boundaries. Cross-regional collaborative design incentivizes users to charge across regions through price differences, effectively alleviating local congestion and forming a spatial load equilibrium model that links "points, lines, and surfaces." This regional competition mechanism not only optimizes the layout of charging facilities but also promotes the efficient flow and balanced distribution of resources between regions.

[0038] The dynamic coupling mechanism achieves a deep integration of spatiotemporal correlation and multi-agent game theory. The temporal distribution of charging demand is constrained by spatial accessibility, while the service capacity of charging stations is affected by time-of-day electricity prices. This complex coupling relationship is quantified by constructing a spatiotemporal joint probability density function. The DSO, as the leader, issues electricity price signals, while the CSO and EV users, as followers, adjust service fees and charging plans through price games, ultimately forming a Stackelberg equilibrium solution. In this process, non-electrical factors such as road network conditions, battery degradation costs, and user psychological preferences are also comprehensively considered, and a multi-dimensional utility function is constructed to more realistically describe the decision-making logic of the game participants.

[0039] The model's features and advantages are as follows: it characterizes the nonlinear mapping relationship between electricity price signals and user behavior through a spatiotemporal game model, avoiding strategy distortion caused by traditional linear assumptions; it introduces a dynamic constraint relaxation mechanism, enabling the electricity price adjustment range and user response threshold to adapt to the grid operation status, thus enhancing the model's robustness; at the same time, it supports cross-timescale coordination of hourly electricity price optimization and minute-level load adjustment, and is compatible with city-level macro-planning and community-level microgrid dispatch, providing solid theoretical support for the construction of highly resilient distribution networks.

[0040] 2.1 Time-based dynamic electricity price model To optimize power distribution systems and address the challenges posed by the large-scale integration of electric vehicles, this invention first defines a dynamic electricity price function. This function comprehensively considers factors such as system load, renewable energy output, and time deviation. Next, the specific construction process of the time-dimensional dynamic electricity price model will be described in detail, including the mathematical expression of the dynamic electricity price function, the physical meaning of each variable, and the model design concept, providing a theoretical foundation for subsequent power distribution system optimization strategies.

[0041] Definition of dynamic electricity pricing function. The time-dimensional dynamic electricity pricing function can be expressed as: (1) In the formula, for t Dynamic electricity pricing for different time periods for t Total system load during the period (including base load and EV charging load). The baseline load capacity of the distribution network (determined by historical data statistics); The renewable energy output factor (the ratio of actual output to rated capacity). This represents the time difference between the current period and the previous electricity price cycle. This is the electricity price adjustment cycle (typically 24 hours). This is a power grid operating cost adjustment factor (related to line losses and maintenance costs). These are the weighting coefficients (satisfying the normalization constraint α+β+γ=1). This is the basic service fee for the power grid (a policy-related fixed cost).

[0042] This electricity pricing model comprises three core influencing factors: 1) The load demand factor suppresses peak demand through a superlinear electricity price response mechanism. When the real-time load exceeds the benchmark value, the electricity price rises rapidly, effectively reducing peak load by 23%; 2) The renewable energy output factor dynamically adjusts based on the penetration rate of distributed energy, automatically increasing the electricity price gradient when photovoltaic / wind power output is insufficient, reducing non-rigid electricity consumption by 14%; 3) The time deviation correction factor compensates for load forecasting errors, avoiding regulatory lag by dynamically adjusting the rate of change in electricity prices, thus improving the robustness of the strategy. These three parameters, through the coordinated configuration of α / β / γ, achieve triple regulation of "demand suppression - absorption incentive - time-series matching".

[0043] The model's core objective is supply-demand balance: the α / β weight allocation prioritizes demand suppression during peak load periods (α = 0.4-0.6) and strengthens incentives for renewable energy absorption during periods of abundant renewable energy (β = 0.2-0.3). A γ coefficient (0.1-0.2) is introduced to correct for price signal delays under load surge scenarios, reducing the reverse risk of peak-valley shift. A cost coverage mechanism (η = 1.05-1.15) ensures the recovery of fixed grid costs, with parameter settings positively correlated with line aging. This multi-dimensional coupled model achieves dynamic matching between price signals and system states, laying the foundation for spatiotemporal game analysis.

[0044] 2.2 Spatial Dimension Regional Electricity Price Weighting Factor Model To construct a refined electricity market regulation system, a spatially-based regional electricity price weighting factor model is proposed. This model quantifies the remaining capacity margin of regional power grids to achieve differentiated guidance and optimal allocation of electric vehicle charging load. Its core mechanism uses dynamic weighting factors to reflect the supply and demand relationship between baseload power and EV charging load in each region. When an increase in EV load in a region leads to a decrease in capacity margin, a differentiated electricity price adjustment strategy is automatically triggered, thereby creating a spatial transfer effect of charging load. The following sections will elaborate on the model's calculation principles, variable definitions, and operational mechanism.

[0045] Partition weighting factor ωi This represents the remaining capacity margin of the regional power grid, which is used to generate differentiated electricity prices. Through spatially differentiated pricing, it guides the rational distribution of electric vehicle (EV) charging load. Its mathematical model is defined as follows: (2) In the formula, For the first The set of nodes in a partition is determined by the distribution network topology and is usually based on differences in line capacity margin or renewable energy penetration. This represents the total number of system partitions. For nodes The base load power (inherent load excluding EV charging load) characterizes the regional basic electricity demand. For nodes The EV charging power reflects the additional load on the power grid caused by user charging behavior.

[0046] Specifically, the physical meaning of its molecular weighting factor is to calculate the first... i The sum of the differences between the base load and the EV load within a zone represents the remaining capacity margin of the power grid in that region; the weight factor in the denominator is physically the sum of the base load power of the entire system, used for normalization processing to ensure that the weight factor has cross-regional comparability.

[0047] This regional electricity price weighting factor model achieves spatial optimization of power resource allocation through a dynamic adjustment mechanism. Its core mechanism is reflected in two aspects: First, the weighting factor is directly linked to the electricity price; when the EV charging load in a certain region... When it is increased, the weight factor of that region will decrease. This could trigger an increase in electricity prices to curb localized overload; for industrial areas and other areas with high base loads... In certain regions, due to their inherently lower weighting factors, electricity price adjustments must also take into account additional factors such as line congestion rates. Secondly, by constructing spatial game equilibrium conditions, the model utilizes differentiated regional electricity price signals to guide charging loads to shift to low-load-density regions with higher weighting factors, thus creating a "spatial transfer effect."

[0048] Model characteristics and constraints: 1. Dynamic adaptability (3) In the formula: P base,j ( t ) is a node j During the period t The base load power (kW) represents the inherent power demand of this node when there is no EV charging load, which varies over time. t For time period index, t =1,2,…, T It is usually expressed in hours or minutes; j This is a node index, belonging to a certain partition. i Node set Ni .

[0049] Extending the base load power from static to a time-varying function enables it to reflect changes in base load over different time periods, supporting spatiotemporal coupling optimization.

[0050] 2. Dynamic update mechanism for weighting factors Time-varying expression for weighting factors: (4) In the formula: ωi ( t ) is the first i Zones in time periods t The weighting factor reflects the remaining capacity margin of the power grid in the region; P ev,j ( t ) is a node j During the period t EV charging power (kW); M This represents the total number of system partitions. Ni For the first i The set of nodes within a partition.

[0051] The update cycle of the weighting factor needs to be synchronized with the distribution network status estimation (such as SCADA data refresh rate). The typical update interval is 5 to 15 minutes to avoid strategy failure due to data lag.

[0052] 2. Boundary conditions Nonnegativity constraint: (5) Ensure weighting factors To avoid negative electricity price signals. To maintain the rationality and explainability of the electricity pricing mechanism.

[0053] Normalization constraints: (6) Ensure that the sum of the electricity price weights for each zone is 1, maintaining a balance in price leverage between regions. In each time period... t Standardization is performed after calculation: (7) In the formula: It updates in real time, responds to load fluctuations and changes in renewable energy output, and enables minute-level electricity price control.

[0054] 3. Two-level optimization mathematical model The two-layer optimization model constructed in this invention uses the Stackelberg game framework to describe the hierarchical decision-making relationships among multiple stakeholders in the "vehicle-station-grid" system. The upper layer, led by the Distribution System Operator (DSO), aims to minimize grid operating costs and maximize renewable energy absorption, guiding the lower layer's response by generating dynamic electricity price signals. The lower layer includes Charging Station Operators (CSOs) and electric vehicle users, who respectively aim to maximize revenue and minimize electricity costs, adjusting service fees and charging strategies based on electricity prices. The upper and lower layers form a closed-loop feedback loop through electricity prices and load response: DSO publishes electricity prices → users and CSOs make optimization decisions → load distribution is fed back to the DSO → electricity prices are iteratively updated until the system converges to Stackelberg equilibrium. This model effectively coordinates grid economics, environmental friendliness, and user satisfaction, achieving collaborative optimization across multiple time scales.

[0055] 3.1 Upper-level model (DSO) 3.1.1 Model Framework and Objective Function The upper-level model for distribution system operators (DSOs) is a multi-objective optimization problem, including economic objectives and renewable energy consumption objectives: Objective function 1: Minimize power grid operating costs (8) In the formula, To optimize the total number of time periods in the cycle (usually based on a 24-hour cycle); The dynamic electricity price issued by the DSO serves as a decision variable, influencing users' charging behavior. for t The time-of-use electricity price and the cost of purchasing electricity from the upper-level power grid. and purchased electricity Linear correlation; This is the peak-valley difference penalty weighting coefficient, used to smooth the load curve and reduce the pressure on the power grid for peak regulation; , The peak and trough power values ​​of the daily load curve are obtained through real-time load. Dynamic calculation.

[0056] Objective function 2: Maximize the renewable energy absorption rate (9) In the formula, for t The actual output of renewable energy sources (wind power, photovoltaics, etc.) during a given period; for t Total system load during the time period includes base load and EV charging load.

[0057] 3.1.2 Constraints 1. Physical constraints of the power grid (1) Node voltage safety threshold Assume the system has Nb For each busbar, the voltage deviation must meet the following requirements: (10) In the formula: Vi ( t ) is a node i During the period t Voltage amplitude; typical value: V min=0.95pu, V max=1.05pu, to prevent voltage exceeding the limit from damaging the device. When the limit is exceeded, a penalty is triggered. (11) (2) Line capacity limitation Assume the system has Nl branches. branch road l During the period t Active power: (12) Line capacity limitation: Branch power Not exceeding the rated capacity To avoid overload tripping, overload penalties apply. (13) 2. Operational strategy constraints (1) Limits on electricity price adjustment Constraints on electricity price volatility in adjacent time periods limit the magnitude of electricity price adjustments and ensure market stability. (14) In the formula: πt For time period t Dynamic electricity price; Δ π `max` represents the maximum permissible volatility (typically 20%, or 0.2), and the electricity price for the first period. π 1. Initialize based on historical electricity prices.

[0058] (2) Budget constraints on electricity purchase costs Total electricity purchase costs shall not exceed the financial threshold: (15) In the formula: C buy ( t (Time period) t The unit price of electricity (yuan / kWh); P buy ( t (Time period) t Electricity purchased (kWh); B `max` is the financial threshold for DSO (set based on operational data).

[0059] This model features three main characteristics: multi-objective coordination, spatiotemporal correlation, and robust design. First, it employs the Pareto front method to solve the trade-off between economic efficiency and green energy utilization, and introduces a fuzzy satisfaction function to quantify the preferences of different stakeholders, improving the acceptability of the scheme. Second, it achieves dynamic adjustment of renewable energy absorption rate through a closed-loop feedback mechanism of electricity price signals and load response. Finally, it uses interval optimization methods to handle the uncertainty of renewable energy output and generate dispatch strategies with different risk preferences. Overall, this model drives user behavior through dynamic electricity price strategies, effectively coordinating and optimizing the economic operation of the power grid and the absorption of renewable energy, providing scientific decision support for smart distribution network dispatch.

[0060] 3.2 Lower-level model (CSO and EV users) 3.2.1 User Utility Function Model EV users' charging decisions are quantified using the following utility function: (16) In the formula: U user For users in time periods t Utility value; SOC ( t )for t The battery state of charge during a given period reflects user charging satisfaction, and its value range is [0,1]. π ( t (Time period) t The dynamic electricity price (yuan / kWh) is output by the upper-level DSO model; f i For the first i The charging service surcharge for each zone (RMB / kWh) is set by the CSO; E char ( t (Time period) t The charging capacity (kWh); θ This is a user preference coefficient for battery status, representing the rigidity of charging demand; γ This is a sensitivity coefficient for users to battery level deviations, reflecting the degree of user aversion to unplanned charging; E pref ( t For users in time periods t Preferred charging capacity (kWh) can be predicted based on historical behavior or travel plans.

[0061] This utility function consists of three parts: the benefit term. θ ⋅SOC( t ) represents user satisfaction gained due to increased battery capacity; cost item [π( t )+ f i ]⋅ E char (t) represents the electricity price and service fee paid by the user; deviation penalty item, γ ⋅( E char ( t )− E pref ( t )) 2 Used to depict user dissatisfaction with charging behavior that deviates from expectations.

[0062] By maximizing their utility function, users intelligently choose charging times and locations under the combined influence of electricity prices and service fees, thus responding to upper-level electricity price signals. The user behavior decision-making process manifests as a dynamic game: users intelligently select charging times and locations by maximizing their own utility function, thereby generating market feedback on grid electricity price signals. When charging station service fees are too high, resulting in negative utility, users will spontaneously adjust their strategies, either by changing charging stations or delaying charging. This flexible response mechanism effectively maintains the supply and demand balance in the charging market.

[0063] 3.2.2 CSO Revenue Model Charging station operators (CSOs) maximize revenue by optimizing service fees and infrastructure investment; their revenue function is as follows: (17) In the formula: R CSO Total revenue for CSO; f i ( t ) is the first i Zones in time periods t The service fee (RMB / kWh) is a decision variable for the CSO; E total,i (t) is the th i Zones in time periods t The total charging capacity (kWh) is affected by user response;C invest The infrastructure investment costs for CSOs include the construction, operation and maintenance of charging stations and equipment depreciation. M The total number of partitions operated by the CSO; T This represents the total number of time periods in the scheduling cycle.

[0064] Investment cost modeling: (18) In the formula: N is the total number of charging piles; k is the unit construction cost of charging pile (yuan / pile). c om Maintenance cost per unit of charging capacity (RMB / kWh).

[0065] 3.2.3 Model Features and Constraints 3.2.3.1. Revenue Composition Income items: f i ( t )⋅ E total,i ( t This reflects service fee revenue; however, it should be noted that excessively high service fees may suppress user demand. Cost items: C invest The costs include fixed asset investment and operation and maintenance, which need to be amortized through charging volume.

[0066] 3.2.3.2. Spatial Game Constraints Service fee boundary constraints: (19) In the formula: and These are the upper and lower limits of service fees under government guidance or market competition, respectively.

[0067] Charging power capacity constraint: (20) In the formula: For the first i Total capacity of zoned charging equipment (kW), Δ t This represents the length of the time period.

[0068] 3.3 Joint Optimization Framework 3.3.1 Two-layer interaction mechanism In the two-layer optimization model constructed in this invention, the upper-layer decision-maker (DSO) and the lower-layer entities (CSO and EV users) form a closed-loop interaction mechanism through electricity price signals and load response, as detailed below: Lower-level feedback mechanism: EV users based on dynamic electricity price π ( t) and charging service fee f i ( t ), optimizing charging behavior with the goal of maximizing its own utility, and forming a charging demand distribution. E total,i ( t This distribution, as an input to the CSO revenue model, influences its service fee decision. Upper-level control mechanism: DSO issues dynamic electricity price signals π ( t This guides lower-level users' charging behavior and indirectly influences the CSO's service fee strategy. f i ( t This feedback is then fed back to the upper-level objective function (operating cost and renewable energy absorption rate) through load response, forming a closed-loop optimization.

[0069] 3.3.2 Equilibrium Conditions Nash equilibrium: Neither the CSO nor the user can gain higher returns through unilateral policy changes, satisfying the following: (twenty one) (twenty two) In the formula: For the first i Zones in time periods t Balanced service fee (RMB / kWh); For EV users during the time period t Balanced charging capacity (kWh); R CSO For the CSO's revenue function; U user Let be the user's utility function. This equilibrium indicates that, under the optimal policy, neither party can gain a higher benefit by unilaterally changing their decision. Due to the nonlinear and high-dimensional nature of the model, iterative algorithms (such as particle swarm optimization, alternating direction multiplier method, etc.) are required for solving it.

[0070] The key parameters in the model and their value ranges are shown below (all based on actual surveys and historical data calibration): User preference coefficient θ The value ranges from 0.5 to 1.2. Commuters usually choose a higher value, reflecting their relatively rigid charging needs. User price sensitivity coefficient γ The value ranges from 0.3 to 0.8. Users in commercial areas are usually more price-sensitive because they have more charging options. Service fee adjustment coefficient κ The value ranges from 0.8 to 1.5, and the specific value needs to be dynamically adjusted according to the level of competition in the regional charging market. Charging pile investment cost coefficient k The value ranges from 104 to 105 yuan per charging pile. Fast charging piles have a significantly higher value than slow charging piles due to their high technical complexity and equipment cost.

[0071] This model provides a theoretical basis and decision support for dynamic pricing strategies and charging infrastructure planning in the electric vehicle charging market by quantifying the game relationship between user utility and CSO revenue.

[0072] 4. Solution Algorithm Design To effectively address the power distribution system optimization problem under the interaction of "vehicle-station-network", this invention designs an innovative solution algorithm. This algorithm dynamically generates electricity prices based on an improved particle swarm optimization (IPSO) algorithm and achieves multi-objective, two-level optimization through a distributed solution architecture. The dynamic electricity price generation mechanism and the multi-objective, two-level optimization process are described in detail below, ensuring the algorithm's efficiency, robustness, and feasibility for practical application.

[0073] 4.1 Dynamic Electricity Price Generation Mechanism The improved dynamic electricity price generation mechanism of the Particle Swarm Optimization (IPSO) algorithm achieves multi-dimensional electricity price space optimization through three key steps: First, the particle dimension is defined as a combination of "number of time periods × number of regions" (e.g., 24 hours × 5 regions = 120 dimensions), and an initial electricity price range is set based on historical data to ensure algorithm convergence; second, a fitness function is designed with grid operating costs and renewable energy absorption rate as the core, and multi-objective optimization is achieved through dynamic weight adjustment and constraint penalty terms; finally, a nonlinear decreasing inertial weight adaptive strategy is adopted to enhance global search capabilities in the early stage, focus on local optimization in the later stage, and dynamically adjust weights in combination with particle swarm diversity indicators to avoid local optima.

[0074] This algorithm features three major improvements: maintaining the Pareto front solution through an elite retention strategy, providing decision-makers with a multimodal optimization scheme; utilizing GPU parallel computing to accelerate the solution of large-scale power grid scenarios; and integrating fuzzy logic to handle the uncertainty of user behavior prediction, significantly improving the algorithm's robustness. These innovations enable IPSO to effectively balance power grid operating efficiency with renewable energy consumption needs, providing intelligent support for dynamic electricity pricing decisions.

[0075] A dynamic electricity price generation mechanism based on an improved particle swarm optimization (IPSO) algorithm optimizes the multidimensional electricity price space by simulating swarm intelligence behavior, such as... Figure 1 As shown. Its core process is as follows: 4.1.1) Particle Swarm Initialization Define the dimension; the particle dimension is set to "number of time periods × number of regions", that is... For example, on a 24-hour timescale, if divided into 5 regions, the particle dimension is 24 × 5 = 120 dimensions. Each particle represents a complete spatiotemporal electricity price combination.

[0076] Set an initial electricity price range and sample based on a normal distribution of historical data to ensure a reasonable particle distribution and avoid algorithm divergence.

[0077] Generate initial particle swarm, population size To balance computational efficiency and search capability.

[0078] 4.1.2) Fitness Function Design Economic objectives, power grid operating costs It is linearly related to time-of-use electricity pricing and the amount of electricity purchased.

[0079] Environmental goals: Renewable energy integration rate This reflects the power grid's utilization of green energy.

[0080] Constraint penalties include: voltage over-limit penalty Ensure bus voltage is within safe thresholds; line overload penalty. To prevent branch power from exceeding rated capacity; the fitness function comprehensively considers economy, environmental protection and constraints, and evaluates the quality of particles through a weighted sum.

[0081] 4.1.3) Inertia weight adaptive strategy.

[0082] Particle diversity is calculated by assessing the particle swarm diversity through spatial distribution variance. Weight adjustment is performed: when diversity is sufficient, a nonlinear decreasing function is used to reduce the inertia weight, enhancing local optimization ability. When diversity is insufficient, the inertia weight is increased to escape local optima and maintain population diversity.

[0083] 4.1.4) Algorithm Improvement Features. Multimodal optimization employs an elitist retention strategy to maintain multiple Pareto front solutions, providing decision-makers with diverse options. Parallel computing utilizes GPUs for block-based parallel computation of the particle swarm optimization, accelerating the fitness function calculation process and improving algorithm efficiency. Enhanced robustness integrates fuzzy logic to handle the uncertainty of user response predictions, enhancing the algorithm's tolerance to prediction bias and ensuring stable and reliable optimization results.

[0084] 4.1.5) Iterative Optimization. Update particle position and velocity: Update particle position and velocity according to the standard formula of particle swarm optimization to realize the movement of particles in the solution space. Iterate repeatedly until the termination condition is met (such as reaching the maximum number of iterations or the rate of change of the fitness function is lower than the threshold).

[0085] 4.1.6) Output Results: Output the Pareto optimal solution set, which includes multiple spatiotemporal electricity price combinations. This supports decision-makers in selecting the optimal solution based on their preferences, achieving economical and efficient grid operation and maximizing the absorption of renewable energy.

[0086] Key parameter explanation: Particle dimension D is 120, indicating that each particle represents a complete spatiotemporal electricity price combination. Its dimension is determined by the product of the number of time periods and the number of regions (e.g., 24 hours × 5 regions = 120 dimensions); Population size N pop Typically set to 50-100, this balances computational efficiency with global search capability. The inertia weight ω employs a non-linear decreasing strategy, gradually decreasing from 0.9 to 0.4, enhancing global exploration capability in the early iterations and focusing on refined local search in later stages. The cognitive coefficient c1 is set to 1.5 to adjust the particle's dependence on its own historical best position; the social coefficient c2 is also set to 1.5 to adjust the particle's response to the group's historical best position; the diversity threshold δdiv is set to 0.1 × particle dimension (i.e., 12), used to determine the degree of particle swarm aggregation. When the population diversity falls below this threshold, the inertia weight is adaptively adjusted to maintain search vitality. These parameters work together to improve the particle swarm optimization (IPSO) algorithm, ensuring its effective multi-objective optimization in high-dimensional electricity price optimization problems while maintaining convergence and robustness.

[0087] A flowchart illustrating the dynamic electricity price generation process based on the improved particle swarm optimization (IPSO) algorithm. (See attached diagram.) Figure 2 As shown, the entire process from initialization to result output is fully presented, highlighting the innovative design of IPSO in solving the high-dimensional electricity price optimization problem. In particular, through the triple mechanism of multimodal maintenance, parallel acceleration, and fuzzy correction, it effectively overcomes the curse of dimensionality problem of traditional algorithms.

[0088] Through the above steps and characteristics, the dynamic electricity price generation mechanism based on the improved particle swarm optimization (IPSO) algorithm can effectively optimize in the multi-dimensional electricity price space, generate reasonable dynamic electricity price signals, guide the charging behavior of electric vehicle users, and achieve the economical and efficient operation of the power distribution system and the maximum absorption of renewable energy.

[0089] 4.2 Multi-objective two-layer optimization process The distributed solution architecture achieves collaborative optimization between upper and lower layers through hierarchical iteration. Its core process includes three key steps: First, the distribution system operator (DSO) broadcasts electricity price signals containing spatiotemporal parameters to the charging station operator (CSO) and electric vehicle users at a cycle of 15-30 minutes. Second, electric vehicle users, based on a non-cooperative game model, aim to minimize charging costs and form a Nash equilibrium solution through a virtual queuing algorithm to achieve the spatiotemporal transfer of charging load. Finally, the CSO feeds back the aggregated regional charging load curve to the upper-level model, triggering a new round of iterative optimization based on the particle swarm optimization algorithm until the system converges.

[0090] To ensure system convergence and stability, the architecture employs multiple safeguards: hierarchical consistency checks are performed by setting thresholds for the rate of change of the objective functions at the upper and lower levels, terminating iteration when the optimization strides in both directions match; a damping coefficient is introduced in the load feedback stage to effectively suppress system oscillations caused by communication delays or prediction errors; and a sliding window filtering technique is used to interpolate abnormal load data, avoiding optimization direction shifts caused by erroneous data. These mechanisms collectively ensure the reliability and robustness of the distributed solution process.

[0091] The distributed solution architecture achieves collaborative optimization between upper and lower layers through layered iteration, and the specific process is as follows: Figure 3 As shown: In the "vehicle-station-network" interactive architecture, the layered interaction mechanism is the core for achieving multi-entity collaborative optimization. This mechanism ensures the efficient operation and optimal resource allocation of the power distribution system through three main stages: upper-level electricity price signal transmission, lower-level user game equilibrium solution, and load data feedback and iteration. The following is a detailed refinement of the layered interaction mechanism: 4.2.1. Issuance of upper-level electricity price signals Distribution System Operator (DSO) electricity price broadcasts: Based on the real-time status of the distribution network, renewable energy output forecasts, and regional load distribution, the DSO dynamically generates electricity price vectors that include spatiotemporal parameters. These price signals not only reflect price differences at different times but also consider spatial price zoning to guide the charging behavior of electric vehicle (EV) users.

[0092] Broadcast frequency: The electricity price update frequency is set to 15-30 minutes to match the distribution network condition estimation cycle. This high-frequency electricity price update ensures the timeliness and accuracy of the electricity price signal, responds promptly to changes in grid load, and effectively guides user charging behavior.

[0093] 4.2.2. Solving the Game Equilibrium of Lower-Level Users Non-cooperative game theory modeling: After receiving the electricity price signal from the DSO, EV users, as independent decision-makers, construct a charging strategy response model with the goal of minimizing charging costs. Users compare charging costs at different times and locations to select the optimal charging time and charging station.

[0094] Nash equilibrium solution: Since multiple users participate in charging decisions simultaneously, a virtual queuing algorithm is used to simulate the process of users competing for charging resources. Through a marginal cost adjustment mechanism, a balanced distribution of load in time and space is achieved, avoiding local overload and congestion.

[0095] 4.2.3. Load Data Feedback and Iteration CSO Data Aggregation and Feedback: The Charging Station Operator (CSO) is responsible for aggregating the charging load curves of all EV users within its area, superimposing them onto the base load, and then feeding them back to the upper-level DSO model. This process enables information transfer from the bottom-level users to the top-level DSO, providing the DSO with real-time load data support.

[0096] Upper-level model iterative optimization: Based on the load curve fed back by the CSO, the DSO reconstructs the objective function (including minimizing grid operating costs and maximizing renewable energy absorption rate) and triggers a new round of particle swarm optimization. By continuously adjusting the electricity price signal, it gradually approaches the optimal solution, achieving overall optimization of the distribution system.

[0097] Example 2 To verify the effectiveness of the proposed "vehicle-station-network" interaction optimization strategy, this embodiment constructs a simulation environment based on the IEEE 33-bus distribution system. The simulation period is 24 hours, the time resolution is 1 hour, and the key parameters are set as follows: Distribution system: Base load 1000 kW, peak renewable energy 800 kW (mixed photovoltaic and wind power), voltage tolerance ±0.08 pu; Regional division: Residential area (nodes 0–17), commercial area (nodes 18–22), industrial area (nodes 23–32); Electric vehicles: 100 vehicles in total, penetration rate 25%, V2G participation rate 30%, battery capacity 60 kWh, charging / discharging power 7 / 5 kW respectively; Electricity pricing mechanism: dynamic electricity price range [0.3, 1.2] yuan / kWh, service fee range [0.1, 0.3] yuan / kWh. The load composition of the distribution network system is as follows: Figure 4 As shown.

[0098] 1. Load optimization effect analysis The overall optimization effect of the proposed dynamic electricity pricing strategy on system load characteristics is quantitatively evaluated. Through comparative analysis of key indicators with those under a fixed electricity pricing strategy, the strategy's significant effectiveness in achieving peak shaving and valley filling, smoothing the load curve, and promoting green energy consumption is comprehensively verified from multiple dimensions, including peak-valley load, peak-valley difference, and renewable energy absorption rate. This provides core data support for the strategy's effectiveness. To evaluate the effectiveness of the proposed strategy in load regulation, Table 1 compares the load indicators under the traditional fixed electricity pricing strategy and the dynamic electricity pricing strategy proposed in this invention. Table 1 Comparison of Load Optimization Effects

[0099] Analysis shows that the proposed dynamic electricity pricing strategy effectively regulates user electricity consumption behavior through price levers, demonstrating significant advantages in a 24-hour simulation of the IEEE 33-bus system. It effectively optimizes the temporal distribution of load through precise price signals. During peak electricity consumption periods (e.g., 18:00–22:00), higher electricity prices (e.g., RMB 1.15 / kWh) significantly suppress user charging demand, reducing peak load from 1850 kW to 1680 kW, a decrease of 9.2%. Conversely, during off-peak periods such as early morning (e.g., 00:00–06:00), lowering electricity prices (RMB 0.3–0.5 / kWh) successfully attracts users to shift their charging behavior, increasing off-peak load from 350 kW to 520 kW, an increase of 48.6%. This "peak shaving and valley filling" effect significantly reduces the system's peak-to-valley difference by 22.7%, from 1500 kW to 1160 kW, significantly smoothing the daily load curve, alleviating grid peak-shaving pressure, and improving equipment utilization and operational stability.

[0100] In promoting the consumption of renewable energy, the dynamic electricity pricing mechanism demonstrates good green synergy characteristics. For example... Figure 5 As shown, by reducing electricity prices during peak renewable energy output periods (e.g., 10:00–14:00), the strategy effectively guides charging load to synchronize with peak photovoltaic power generation, increasing the renewable energy absorption rate from 83.5% to 95.8%. The correlation coefficient between the load curve and renewable energy output also significantly increased from 0.42 to 0.86, indicating that the system has achieved good load tracking of renewable energy fluctuations, greatly improving the green operation level of the power grid and the efficiency of clean energy utilization.

[0101] In summary, the strategy proposed in this invention achieves spatiotemporal coordinated optimization through a three-dimensional coupling mechanism of "time-space-electricity price". Temporally, electricity price differences successfully guide load shifting and valley filling; spatially, regional electricity pricing mechanisms (such as high electricity prices in residential areas and low electricity prices in industrial areas) promote the transfer of load from high-price areas to low-price areas, optimizing the overall spatial distribution. Ultimately, the system achieves significant results in load optimization, economic operation, and grid security, fully validating the effectiveness and practical value of the proposed strategy in improving the flexibility, economy, and environmental friendliness of the distribution system.

[0102] 2. Economic Benefit Analysis Economic viability is key to evaluating the feasibility of a strategy. This section conducts a detailed financial analysis from the cost-benefit perspective of three main stakeholders: Distribution System Operators (DSOs), Charging Station Operators (CSOs), and electric vehicle users. The aim is to clarify whether the proposed optimization strategy can create a win-win profit-sharing structure for all parties, thereby validating its economic advantages and market potential. Table 2 shows the economic benefits for each participant: Table 2 Comparison of Economic Benefits

[0103] Economic analysis shows that the proposed strategy achieves a win-win situation for all parties through dynamic electricity pricing and load aggregation mechanisms: Distribution operators (DSOs) reduce their electricity purchase costs by 13.0% (from RMB 12,580 to RMB 10,950) due to peak shaving and valley filling effects, while alleviating grid peak-shaving pressure; Charging service operators (CSOs) increase their total revenue by 20.3% (from RMB 3,200 to RMB 3,850) by optimizing service fees and load management, and significantly improve charging pile utilization to 78%; total energy costs for users decrease by 13.2% (from RMB 15,780 to RMB 13,700), and users participating in vehicle-to-grid (V2G) interaction can obtain an additional 18% benefit. These results validate the strategy's synergistic optimization capabilities in reducing system costs, improving operational efficiency, and optimizing user benefits, forming a sustainable electricity market benefit distribution mechanism.

[0104] 3. Power Grid Security Performance Analysis Ensuring the safe and stable operation of the power grid is the cornerstone of all optimization strategies. This section focuses on analyzing the improvement effect of the proposed strategy on key safety indicators of the distribution system (such as node voltage deviation and line load factor). By comparing the changes in the power grid operating status before and after optimization, the positive role of this strategy in improving system voltage stability, preventing equipment overload, and enhancing power supply reliability is demonstrated. Table 3 shows a comparison of power grid safety indicators before and after optimization: Table 3 Comparison of Power Grid Security Indicators

[0105] The power grid's safety performance has been systematically improved: overall voltage stability has increased by 32%, peak evening voltage in residential areas has significantly improved from 0.85 pu to 0.92 pu, and the load rate of industrial lines has decreased from 121% to the safe threshold of 95%, completely eliminating voltage over-limit nodes (from 5 to 0). Key indicators have improved significantly: line overload rate has decreased by 74.4% (12.5% ​​→ 3.2%), and maximum voltage deviation has decreased by 46.7% (0.15 pu → 0.08 pu). These data collectively verify the substantial breakthrough in the safety and reliability of the power distribution system.

[0106] 4. Analysis of the characteristics of spatiotemporal game This section delves into the interactive responses and game-theoretic characteristics exhibited by users and operators across time and space under the guidance of dynamic electricity pricing signals. By decoupling and analyzing the spatiotemporal transfer patterns and distribution changes of load, it reveals the intrinsic working principle of the three-dimensional coupling mechanism of "time-space-electricity price," clarifying how it coordinates the behaviors of multiple stakeholders to achieve system-level collaborative optimization.

[0107] 4.1) Time-dimensional response characteristics The time-dimensional response characteristics demonstrate the guiding role of dynamic electricity pricing in influencing user charging behavior over time. By setting time-of-use differentiated electricity price signals, the system can effectively incentivize users to charge during off-peak hours and reduce electricity consumption or participate in V2G discharge during peak hours, thereby achieving peak shaving and valley filling and promoting the consumption of renewable energy. This mechanism relies on electricity price elasticity and user psychological expectations to optimize load distribution in time sequence, enhancing the economic efficiency and stability of grid operation.

[0108] Figure 5 This demonstrates the guiding effect of electricity prices during typical time periods: Based on 24-hour simulation results from the IEEE 33-bus system, dynamic pricing demonstrates a significant ability to guide user behavior over time. During the morning peak (08:00), the price of 0.95 yuan / kWh successfully guided 120 kW of charging load to shift from peak hours to periods with lower prices, effectively alleviating grid pressure. At noon (12:00), the price dropped to 0.75 yuan / kWh, attracting not only 80 kW of charging load but also stimulating 150 kW of V2G discharge response, which matched the peak photovoltaic output during this period well, improving the local consumption level of renewable energy. During the evening peak (19:00), the price rose to 1.15 yuan / kWh, significantly suppressing charging demand to 210 kW and triggering 95 kW of V2G reverse transmission, greatly alleviating grid load pressure during this period. The above responses indicate that users' sensitivity to electricity price signals varies significantly over time. The more significant the change in electricity price gradient, the stronger the load shift and V2G participation in the response. This fully demonstrates the effectiveness and practicality of the time-dimensional electricity price mechanism in regulating electricity consumption behavior, smoothing load curves, and enhancing system flexibility.

[0109] 4.2) Spatial Dimension Load Distribution Table 4 shows the changes in load distribution in each region before and after optimization.

[0110] Table 4. Changes in load distribution in each region before and after optimization.

[0111] Regarding spatial load distribution, the proposed zoning electricity pricing mechanism demonstrates significant regulatory effects. Case studies show that the optimized load distribution across regions changes markedly: the load share in residential areas decreases from 42% to 35%, in commercial areas it increases from 38% to 40%, and in industrial areas it rises from 20% to 25%. This change stems from the effective guidance of the zoning electricity pricing mechanism. Residential areas, with their higher electricity price weighting, suppress some charging demand, while commercial and industrial areas, with their lower electricity prices, successfully attract load transfers, creating a clear "spatial transfer effect." This mechanism not only alleviates the overload risk of local power grids in residential areas and optimizes resource allocation between regions, but also achieves spatially balanced allocation of charging loads through differentiated regional electricity price signals, improving the overall stability and economy of the power grid operation.

[0112] 6. Typical Scenario Analysis To more clearly demonstrate the dynamic control process and effects of the strategy, this section selects typical scenarios such as peak renewable energy output and peak electricity load for detailed analysis. By presenting the linkage data of electricity price signals, load shifting, V2G response, and regional interaction during key periods, it concretely illustrates how the strategy achieves the goals of load optimization and maximizing renewable energy consumption in actual operation.

[0113] In the constructed typical scenario simulation, the dynamic electricity pricing strategy demonstrated excellent optimization performance through time-of-use and zone-based regulation. During the evening peak period (18:00-22:00), the system increased the electricity price from 0.9 yuan / kWh to 1.2 yuan / kWh, successfully reducing the charging load in residential areas by 35%, with 28% of the load shifting to the off-peak period in the early morning, and 7% achieving reverse power supply through V2G discharge. At the same time, the load in commercial areas increased by 12%, effectively utilizing the surplus photovoltaic power during this period. During the critical period for renewable energy consumption (10:00-14:00), the strategy reduced the electricity price to the range of 0.65-0.75 yuan / kWh, significantly enhancing the correlation between charging load and photovoltaic output curves, and achieving a V2G participation rate of 45% in industrial areas. This coordinated regulation not only achieved optimized temporal and spatial load allocation but also effectively enhanced the grid's peak-shaving capacity and operational flexibility, demonstrating the dual benefits of the dynamic electricity pricing mechanism in improving the system's renewable energy consumption level and operational economy.

[0114] This invention constructs a multi-objective, two-layer optimization model under the interaction of "vehicle-station-grid," integrating spatiotemporal game theory and dynamic electricity pricing mechanisms to systematically solve problems such as spatiotemporal imbalance of supply and demand, exacerbated peak-valley differences, and multi-stakeholder collaborative optimization brought about by the large-scale integration of electric vehicles into the distribution network. Simulation results show that the proposed strategy achieves significant results in load optimization, economic operation, and grid security: the peak-valley difference is reduced by 22.7%, the renewable energy absorption rate is increased to 95.8%, and a win-win situation is achieved for DSO, CSO, and EV users. This research not only provides theoretical support and algorithmic tools for distribution network optimization under high-proportion renewable energy and electric vehicle integration, but also provides a feasible path for the scheduling decision-making and market mechanism design of future smart distribution systems. Future research will further explore the deep integration mechanism of V2G and the electricity market to improve system flexibility and responsiveness.

[0115] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0116] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A power distribution system optimization method considering space-time game under vehicle-station-network interaction, characterized in that, The method constructs a double-layer optimization framework of fusing space-time game and dynamic electricity price; an upper-layer decision maker is a power distribution system operator, generates a dynamic electricity price signal in a time zone and a partition, according to a real-time state of a power distribution network, renewable energy output and time-space distribution of regional load, with a target of minimizing power grid operation cost and maximizing renewable energy consumption rate; a lower-layer subject includes an electric vehicle user and a charging station operator, the electric vehicle user is an independent decision subject, optimizes a charging time period and a charging station based on the dynamic electricity price signal and a charging service fee, with a target of maximizing self charging decision utility, forms a charging demand distribution through non-cooperative game; the power distribution system operator reconstructs a target function according to a load curve fed back by the charging station operator, iteratively updates the dynamic electricity price signal until the system converges, and obtains an optimized scheme of the power distribution system.

2. The power distribution system optimization method considering space-time game under vehicle-station-network interaction according to claim 1, characterized in that, The double-layer optimization framework adopts a game response mechanism of dynamic electricity price in a time dimension, the power distribution system operator generates a dynamic electricity price signal in an hourly granularity according to a load curve of the power distribution network and output fluctuation of renewable energy, and introduces a rolling optimization mechanism to dynamically correct the electricity price strategy; In a space dimension, the power distribution system operator divides the electricity price into partitions according to a topology structure of the power distribution network, sets a higher electricity price weight for a region with high line overload risk and low distributed energy penetration rate; the charging station operator uses a traffic flow heat map and grid capacity margin information, and deploys charging piles by using a Nash equilibrium strategy; Through cross-regional collaborative design, the electric vehicle user is encouraged to charge across regions through price difference.

3. The power distribution system optimization method considering space-time game under vehicle-station-network interaction according to claim 2, characterized in that, The dynamic electricity price comprehensively considers factors of power distribution network system load, renewable energy output and time bias, and a time dimension dynamic electricity price function is expressed as: , wherein, is t dynamic electricity price of the time period, is t total system load of the time period, is the base load capacity of the distribution network; is the renewable energy output coefficient; is the time deviation of the current time period and the previous electricity price cycle; is the electricity price adjustment cycle; is the grid operation cost adjustment factor; is the weight coefficient; is the grid basic service fee.

4. The power distribution system optimization method considering space-time game under vehicle-station-network interaction according to claim 2, characterized in that, The double-layer optimization framework constructs a partition electricity price weight factor in a space dimension, realizes differentiated guidance and optimized configuration of electric vehicle charging load by quantifying residual capacity margin of a regional power grid; The partition electricity price weight factor represents residual capacity margin of a regional power grid, is used to generate a differentiated electricity price, and guides reasonable distribution of electric vehicle charging load through spatial differentiated pricing, and the partition electricity price weight factor is specifically defined as: a total sum of differences between base load power and electric vehicle charging power of nodes in each partition divided by a total sum of base load power of the whole system; By constructing a space game equilibrium condition, the charging load is guided to shift to a region with a higher weight factor by using a differentiated regional electricity price signal.

5. The power distribution system optimization method considering space-time game under vehicle-station-network interaction according to claim 1, characterized in that, In the upper layer of the double-layer optimization framework, the power distribution system operator takes the published dynamic electricity price as a decision variable, constructs a multi-objective optimization problem considering power grid operation cost and renewable energy consumption: A target function of minimizing the power grid operation cost is specifically a sum of a purchase cost of the power grid from a superior power grid and a peak-valley difference penalty weight coefficient multiplied by a peak value and a valley value power difference of an intra-day load curve; A target function of maximizing the renewable energy consumption rate is specifically a quotient of actual output of renewable energy and total load of the system.

6. The power distribution system optimization method considering space-time game under vehicle-station-network interaction according to claim 1, characterized in that, In the lower layer of the double-layer optimization framework: The charging decision behavior of the electric vehicle user is quantified by a utility function; the utility function includes: a benefit item, a preference coefficient of the user for the state of charge multiplied by the state of charge of the battery; a cost item, the sum of the dynamic electricity price output by the upper distribution system operator and the corresponding partition charging service fee multiplied by the charging power of the corresponding period; a deviation penalty item, the square of the difference between the charging power of the corresponding period and the preferred charging power of the electric vehicle user in the corresponding period multiplied by the sensitivity coefficient of the user to the power deviation; the behavior decision process of the electric vehicle user is represented as a dynamic game: the electric vehicle user selects a charging period and a charging station by maximizing the utility function of itself; The charging station operator takes the service fee of each partition in each period as a decision variable, and maximizes the revenue by optimizing the service fee and infrastructure investment; the revenue function of the charging station operator is represented as the income item minus the cost item, wherein the income item is the product of the service fee and the total charging power, and the cost item includes fixed asset investment and operation and maintenance cost; The lower layer revenue of the double-layer optimization framework is composed of the income item including service fee income minus the cost item including fixed asset investment and operation and maintenance cost; spatial game constraints are set, including service fee boundary constraints and charging power capacity constraints.

7. The power distribution system optimization method considering space-time game under vehicle-station-network interaction according to claim 1, characterized in that, The upper layer decision maker and the lower layer subject in the double-layer optimization framework satisfy the following equilibrium conditions: , , where, is the i equilibrium service fee of the partition in time period t ; R CSO is the revenue function of the charging station operator; f i is the charging service fee of the distribution system operator; t E total,i is the charging demand distribution generated by the electric vehicle users; t is the equilibrium charging electricity of the electric vehicle users in time period t ; U user is the utility function of the electric vehicle users; and t is the dynamic electricity price generated by the distribution system operator.​​ 8. The power distribution system optimization method considering space-time game under vehicle-station-network interaction according to claim 1, characterized in that, The double-layer optimization framework uses an improved particle swarm algorithm to optimize the multi-dimensional electricity price space by simulating the behavior of group intelligence, solves the multi-objective Pareto frontier to generate dynamic electricity prices, and specifically as follows: The particle dimension is set as the number of periods x the number of regions, the initial electricity price range is set based on normal distribution sampling of historical data, and the initial particle swarm is generated; Calculate the fitness function, which is specifically the weighted sum of the grid operation cost, the renewable energy consumption rate and the constraint penalty term, and the constraint penalty term includes the voltage out-of-limit penalty and the line overload penalty; Evaluate the diversity of the particle swarm by the spatial distribution variance; when the diversity is sufficient, use a nonlinear decreasing function to reduce the inertia weight; when the diversity is insufficient, increase the inertia weight to jump out of the local optimal solution; Update the particle position and velocity according to the standard formula of the particle swarm algorithm and perform cyclic iteration until the termination condition is met; Finally, output the Pareto optimal solution set obtained by optimization, which includes multiple spatiotemporal electricity price combination schemes.

9. The power distribution system optimization method considering space-time game under vehicle-station-network interaction according to claim 8, characterized in that, The improved particle swarm algorithm uses an elite preservation strategy to maintain multiple Pareto frontier solutions and provides diversified scheme selection; uses GPU to perform block parallel calculation on the particle swarm to accelerate the fitness function calculation; integrates fuzzy logic to handle the uncertainty of user response prediction, enhances the tolerance of the algorithm to prediction deviation, and quantifies different subject preferences.

10. The power distribution system optimization method of claim 1, wherein, The double-layer optimization framework adopts the following safeguard mechanisms during the collaborative optimization process of the upper and lower layers: set the threshold of the change rate of the upper and lower objective functions for hierarchical consistency testing, and terminate iteration when the optimization step of both directions matches; introduce a damping coefficient in the load feedback link to effectively suppress system oscillation caused by communication delay or prediction error; use sliding window filtering technology to interpolate abnormal load data to avoid deviation of the optimization direction caused by incorrect data.

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