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

Abstract

The application relates to a power distribution system optimization method considering space-time game under station-network interaction, adopting a double-layer optimization framework fusing space-time game and dynamic electricity price, the upper-layer decision maker is a power distribution system operator, the minimum power grid operation cost and the maximum renewable energy consumption rate are taken as targets, and a dynamic electricity price signal in time and area is generated; the lower-layer subject includes electric vehicle users and charging station operators, the electric vehicle users take the maximum charging decision utility as the target based on the dynamic electricity price signal and charging service fees, the charging time period and the charging station are optimized through non-cooperative game, and charging demand distribution is formed; the charging station operator takes the charging demand distribution as input, takes the maximum revenue maximization as the target, and optimizes and adjusts the charging service fee decision. Compared with the prior art, the application can cooperatively optimize power grid economic operation and renewable energy consumption, promotes efficient flow and balanced distribution of resources among regions, and provides decision support for power distribution network dispatching.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power distribution network optimization, in particular to a power distribution system optimization method considering space-time game under vehicle-station-network interaction. BACKGROUND

[0002] As a key hub connecting the two systems of transportation and energy, the large-scale development of electric vehicles (EV) is reshaping the pattern of energy power systems at an unprecedented speed. However, the explosive growth of electric vehicles, like a double-edged sword, brings many serious challenges to the traditional power distribution network with the main operation mode of "source following load", due to the inherent space-time randomness and high power characteristics of its charging load:

[0003] (1) The imbalance between supply and demand in space and time is increasingly acute. The charging behavior of large-scale electric vehicles has significant uncertainty, and disordered charging is easy to superimpose on the evening peak of residential electricity, forming a "peak on peak" effect, leading to local power distribution transformer overload, line congestion, and increasing system peak valley difference and load fluctuation. This not only greatly increases the difficulty of grid regulation, but also poses a serious threat to system reliability and economy, and also increases the cost of system expansion and peak shaving. In addition, with the high proportion of renewable energy access, its intermittency and volatility further highlight the coordination problem. If the electric vehicle charging load cannot be matched with the peak of renewable energy generation in space and time, it is difficult to effectively consume clean power, and traditional coal-fired units need to be relied on for adjustment, which goes against the initial intention of emission reduction.

[0004] (2) The limitations of traditional electricity pricing mechanism gradually appear. The fixed electricity pricing mechanism cannot effectively encourage users to participate in demand response, and cannot achieve the balanced allocation of charging load in space and time. In the face of large-scale electric vehicle access, traditional electricity pricing methods are not up to the task, further exacerbating the pressure on the power grid, and lack of flexibility and response speed to adapt to the dynamically changing system conditions.

[0005] (3) The complexity of multi-agent collaborative optimization needs to be solved. In the power distribution system, there are multiple subjects such as power distribution system operators (DSO), charging station operators (CSO) and electric vehicle users, and there are differences in the interests and behavior patterns of each subject: DSO pursues safe, economic and green operation of the system, CSO focuses on investment return and market share, and users focus on charging convenience and economy. There is a potential conflict between these goals, and the traditional one-way and rigid control mode cannot effectively coordinate the interests of multiple parties, and new market mechanisms and optimization tools need to be introduced to achieve system coordination and efficiency improvement.

[0006] To address the above challenges, simply relying on traditional grid expansion or simple time-of-use (TOU) pricing is not enough. A more intelligent and refined regulation paradigm must be introduced, the core of which is to guide the charging load of electric vehicles from disorder to order and from load to resource through price signals and market mechanisms. SUMMARY

[0007] The purpose of the present application is to solve the problems of temporal and spatial imbalance between supply and demand, difficulty in adapting to dynamic changes, and difficulty in effectively coordinating the interests of multiple parties when performing multi-agent collaborative optimization in the current optimization method, and to provide a power distribution system optimization method considering temporal and spatial game under vehicle-station-grid interaction.

[0008] The purpose of the present application can be achieved by the following technical solutions:

[0009] As a first aspect of the present application, a power distribution system optimization method considering temporal and spatial game under vehicle-station-grid interaction is provided, which adopts a double-layer optimization framework integrating temporal and spatial game and dynamic pricing to perform bidirectional interaction and optimization management of energy flow and information flow in the vehicle-station-grid system.

[0010] The upper decision maker is a power distribution system operator, which generates a dynamic pricing signal for different time zones to guide the response of the lower layer, with the objectives of minimizing the operation cost of the power grid and maximizing the renewable energy consumption rate, based on the real-time state of the power distribution grid, renewable energy output prediction, and temporal and spatial distribution of regional load.

[0011] The lower layer includes electric vehicle users and charging station operators. The electric vehicle users, as independent decision makers, optimize the charging period and charging site through non-cooperative game based on the dynamic pricing signal and charging service fee, with the objective of maximizing their charging decision utility, and form a charging demand distribution. The charging station operators optimize and adjust the charging service fee decision with the objective of maximizing the revenue, taking the charging demand distribution as input.

[0012] The charging station operators aggregate the charging load curves of all electric vehicle users in the region and superimpose them on the basic load before feeding them back to the upper power distribution system operator. The power distribution system operator reconstructs the objective function based on the load curve fed back by the power distribution system operator, iteratively updates the dynamic pricing signal until the system converges, and obtains the final optimization scheme of the power distribution system.

[0013] As a preferred technical solution, the double-layer optimization framework adopts a game response mechanism of dynamic pricing in the time dimension. The power distribution system operator generates a dynamic pricing signal by hour granularity based on the load curve of the distribution network and the output fluctuation of renewable energy, and introduces a rolling optimization mechanism to dynamically correct the pricing strategy.

[0014] 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.

[0015] 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:

[0016]

[0017] 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.

[0018] 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.

[0019] 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.

[0020] 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.

[0021] 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:

[0022] 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.

[0023] 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.

[0024] As a preferred technical solution, in the lower layer of the dual-layer optimization framework:

[0025] 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 a dynamic game: electric vehicle users choose charging time periods and charging stations by maximizing their own utility function.

[0026] 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.

[0027] 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.

[0028] 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:

[0029]

[0030]

[0031] 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) generating charging demand distribution for electric vehicle users; ) balancing charging energy for electric vehicle users in time period t ) balancing charging energy for electric vehicle users in time period U user ) utility function for electric vehicle users; π( t ) generating dynamic electricity price for distribution system operator.

[0032] As a preferred technical solution, the double-layer optimization framework adopts an improved particle swarm algorithm to optimize a multi-dimensional electricity price space by simulating group intelligence behavior, solve a multi-objective Pareto frontier to generate a dynamic electricity price, and specifically as follows:

[0033] The particle dimension is set as the number of time periods x the number of regions, an initial electricity price range is set based on normal distribution sampling of historical data, and an initial particle swarm is generated;

[0034] A fitness function is calculated, and the fitness function is specifically a weighted sum of grid operation cost, renewable energy consumption rate and constraint penalty term, and the constraint penalty term includes voltage out-of-limit penalty and line overload penalty;

[0035] The particle swarm diversity is evaluated by spatial distribution variance; when the diversity is sufficient, a non-linear decreasing function is used to reduce the inertia weight; when the diversity is insufficient, the inertia weight is increased to jump out of a local optimal solution;

[0036] The particle position and velocity are updated according to the standard formula of the particle swarm algorithm and are iterated cyclically until the termination condition is met;

[0037] The final output is a set of Pareto optimal solutions obtained by optimization, and the set of Pareto optimal solutions includes multiple sets of spatio-temporal electricity price combination schemes.

[0038] As a preferred technical solution, the improved particle swarm algorithm adopts an elite reservation strategy to maintain multiple Pareto frontier solutions and provide diversified scheme selection; uses GPU to perform block parallel calculation on the particle swarm to accelerate fitness function calculation; integrates fuzzy logic to process the uncertainty of user response prediction, enhances the tolerance of the algorithm to prediction deviation, and quantifies different subject preferences.

[0039] As a preferred technical solution, the double-layer optimization framework adopts the following safeguard mechanisms during the collaborative optimization process of the upper and lower layers: setting a threshold for the change rate of the upper and lower layer objective functions for hierarchical consistency testing, terminating iteration when the optimization step of the two directions matches; introducing a damping coefficient in the load feedback link to effectively suppress system oscillation caused by communication delay or prediction error; using a sliding window filtering technology to interpolate abnormal load data to avoid deviation of the optimization direction caused by false data.

[0040] Compared with the prior art, the present application has the following beneficial effects:

[0041] 1) The invention proposes a bi-level optimization framework that fuses space-time game and dynamic pricing. The upper layer takes the distribution system operator (DSO) as the main body, minimizes the grid operation cost and maximizes the renewable energy consumption rate, and dynamically generates time-division and regional price incentive signals. The lower layer takes the electric vehicle user and charging station operator (CSO) as the game main body, guides the user charging behavior based on dynamic pricing, and realizes the space-time balanced configuration of charging load. A bi-level interactive model is established based on Stackelberg game theory, and an improved particle swarm optimization algorithm is used to solve the multi-objective Pareto front. The simulation results show that the proposed strategy can reduce the peak-valley difference of the power grid and improve the renewable energy consumption rate.

[0042] 2) The invention constructs a three-dimensional Stackelberg game model that includes time dynamics, spatial differences, and price incentives. In this model, the distribution system operator acts as the leader and generates dynamic pricing signals based on real-time topology, regional load, and renewable energy forecasts. Charging station operators and electric vehicle users act as followers and adjust service fees and charging behavior based on price signals to achieve a balance of interests among multiple parties. By introducing spatial weight factors and time sequence bias correction terms, the price accurately reflects the grid state in different regions and time periods, effectively addressing the problems of increasing peak-valley differences, local overload, and renewable energy consumption caused by disordered charging, and achieving a balanced distribution of loads in time and space and a Pareto improvement of interests among multiple parties.

[0043] 3) The invention designs an improved particle swarm dynamic pricing generation algorithm embedded with physical constraints of the distribution network. The algorithm strictly considers node voltage safety thresholds, line capacity limits and other grid physical operation constraints in the fitness function, and uses a nonlinear decreasing inertia weight and a diversity threshold adaptive adjustment strategy to effectively balance global exploration and local search capabilities, overcoming the dimension disaster problem in high-dimensional pricing optimization. In addition, the algorithm integrates an elite preservation strategy to maintain the Pareto solution set and supports GPU parallel computing to accelerate, significantly improving the solution efficiency and stability. This algorithm effectively addresses the problems of ignoring grid safety constraints and low optimization efficiency in traditional pricing generation methods, ensuring the safety, economy and practicality of the pricing strategy.

[0044] 4) The invention develops a distributed hierarchical solution strategy based on a multi-objective evolutionary algorithm. The strategy uses a distributed collaborative mechanism that iterates independently in the upper and lower layers and interacts through price and load data. The upper layer uses a multi-objective evolutionary algorithm to solve grid economic and environmental objectives, and the lower layer uses a non-cooperative game and virtual queuing algorithm to solve user equilibrium, significantly reducing the complexity of solving the bi-level model. This strategy uses damping coefficients and sliding window filtering techniques to suppress oscillations caused by data delays and prediction errors, ensuring convergence stability, and does not require centralized access to private information, meeting the actual market operation needs and providing an engineering solution for distributed power markets. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 The vehicle-station-grid interaction architecture constructed by the present application is shown in the figure.

[0046] Figure 2 The dynamic electricity price generation flowchart based on the improved particle swarm algorithm of the present application is shown in the figure.

[0047] Figure 3 The distributed solution architecture constructed by the present application is shown in the figure.

[0048] Figure 4 The load composition diagram of the power distribution grid system in one embodiment of the present application is shown in the figure.

[0049] Figure 5 The renewable energy consumption situation diagram in one embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0050] The present application will be described in detail below with reference to the accompanying drawings and specific embodiments. The embodiments are implemented on the premise of the technical solutions of the present application, and detailed implementation methods and specific operation processes are given, but the protection scope of the present application is not limited to the following embodiments.

[0051] Embodiment 1

[0052] The present application focuses on the “vehicle-station-grid” interaction scenario, and proposes a new multi-objective double-layer optimization method for power distribution systems considering the coupling mechanism of space-time game and dynamic electricity price. The upper layer takes the power distribution system operator (DSO) as the main body, and minimizes the power grid operation cost and maximizes the renewable energy consumption rate as the target, and dynamically generates time-zone electricity price incentive signals. The lower layer takes the electric vehicle user and the charging station operator (CSO) as the game main body, guides the user charging behavior based on the dynamic electricity price, and realizes the space-time balanced configuration of charging load. A double-layer interaction model is established by the Stackelberg game theory, and an improved particle swarm algorithm is used to solve the multi-objective Pareto frontier. Based on the above scheme, the strategy proposed by the present application can reduce the power grid peak-valley difference and improve the renewable energy consumption rate. The specific implementation of each part of the method is as follows:

[0053] 1. Vehicle-station-grid interaction architecture

[0054] As shown in Figure 1 , the vehicle-station-grid interaction architecture is a multi-level system composed of three main bodies of the power distribution system operator (DSO), the charging station operator (CSO) and the electric vehicle (EV) user. Through the dynamic electricity price mechanism and the space-time behavior game, the bidirectional interaction and optimized management of energy flow and information flow are realized.

[0055] In the architecture constructed by the application, the DSO as the top regulator generates dynamic electricity price signals according to the topological structure of the distribution network, renewable energy output prediction and regional load time and space distribution, etc., to guide the user charging behavior shift to avoid the overload of the power grid. In addition, the DSO is also responsible for the power flow optimization of the distribution system, and adjusts the reactive power compensation and distributed power output by monitoring the voltage, line load rate and other parameters in real time, so as to ensure the safe operation of the power grid. In the system operation, the DSO also needs to balance the operation cost, renewable energy utilization rate and user satisfaction, form a Pareto optimal solution set through a multi-objective optimization method, balance the interests of all parties, and realize the overall optimization of the distribution system.

[0056] The CSO in the middle layer undertakes the key responsibility of landing the upper regulation strategy and interfacing user demand. First, the CSO calculates the final charging service fee published to users according to the dynamic electricity price signal issued by the DSO and its own operation cost, adjusts the distribution of user charging demand in time and space through the price lever, so as to achieve the purpose of load peak clipping and valley filling. Second, the CSO also needs to reasonably plan the charging infrastructure, flexibly configure fast and slow charging piles according to the density of urban traffic network, the capacity margin of the power grid and the user travel behavior law, improve the utilization rate of equipment and avoid resource waste. Further, the CSO has the function of load aggregation management, integrates multiple dispersed EV charging loads into a controllable virtual power source, participates in the auxiliary service market led by the DSO as a whole, and provides peak shaving, load balancing and other support for the power grid.

[0057] At the bottom of the EV user layer, the electric vehicle user as the actual charging behavior decision maker gradually enhances the initiative in the whole system. Their charging behavior is not only directly affected by the electricity price, but also depends on the individual travel plan, the current state of charge (SOC) and the sensitivity to charging cost. By establishing a price sensitivity model, users can independently select the optimal charging time and site to reduce the overall energy expenditure. At the same time, the historical travel and charging data of users can be used to analyze their time and space preferences, which helps to predict the distribution of overall load in time and space dimensions, and realize more accurate supply and demand balance. In addition, users can also participate in the V2G (vehicle-to-grid) mode, use the vehicle battery to send electricity back to the grid, form a flexible energy exchange mechanism, not only improve the economic benefit of electric vehicles, but also enhance the adjustability and system flexibility of the power grid.

[0058] The efficient coordination between the three layers requires a complete technical support system to realize efficient interaction and processing of data and instructions. In terms of communication, the system relies on high-speed and low-latency 5G networks to achieve high-frequency transmission of real-time electricity price signals and load data between DSO and CSO. At the terminal side, CSO can deploy edge computing servers at each charging station to match and optimize user charging requests and grid operation constraints in real time, significantly reducing response time and improving the intelligence level of charging services. In terms of data flow management, EV user charging intentions and behavior data are uploaded to CSO along the uplink path, and after load forecasting, they are provided to DSO for grid state analysis; at the same time, the dynamic electricity price strategy generated by DSO is transmitted to CSO along the downlink path and affects its service pricing, ultimately feeding back to EV users to guide their charging behavior, realizing a complete information closed loop.

[0059] Overall, the vehicle-station-grid interaction architecture, through hierarchical management and two-way interaction, not only realizes multi-party collaboration, but also has multiple advantages. First, in terms of time and space coordination, through the coupled design of zonal pricing mechanism and charging facility layout, the problem of local area power grid overload is effectively alleviated, and the stability of power grid operation is improved. Second, the architecture strengthens the system's flexible response capability, through the closed-loop optimization of price regulation and user flexible charging behavior, realizing dynamic adjustment of charging load, coping with the uncertainty of new energy output and load volatility. In addition, from the economic point of view, all three participants 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 systematic solution to the challenges of high proportion of new energy access, large-scale popularization of electric vehicles, and the pressure on power grid regulation capabilities, and has important practical value and promotional significance.

[0060] 2. Time-space game model

[0061] The time-space game model is the core mechanism of the vehicle-station-grid interaction architecture, which coordinates the interests of multiple parties and behavior interaction by integrating time dynamics and spatial differences, specifically including the following three dimensions:

[0062] In the time dimension, the game response mechanism of dynamic electricity price becomes the key to optimize the distribution system. According to the load curve of distribution network and the output fluctuation of renewable energy, the DSO generates dynamic electricity price signal by hour granularity, and encourages EV users to select low valley period charging based on charging cost sensitivity analysis to reduce expenditure. However, the time lag of user decision (such as charging reservation and real-time price deviation) requires the introduction of rolling optimization mechanism to dynamically modify the electricity price strategy to prevent load peak-valley reverse transfer. In addition, by training time series prediction model through historical charging data, the user's electricity price response mode can be predicted to provide the basis for multi-period electricity price optimization for DSO, realizing the two-way feedback and dynamic balance of electricity price and charging behavior.

[0063] In the spatial dimension, the regional game of charging resources focuses on the optimal allocation and regional balance of resources. The DSO divides the electricity price zones according to the topology structure of distribution network, and sets higher electricity price weight for the areas with high risk of line overload and low penetration rate of distributed energy, to guide users to migrate to areas with abundant resources. The CSO uses traffic flow heat map and power grid capacity margin information to deploy charging piles using Nash equilibrium strategy to balance the utilization rate of facilities and the safety boundary of power grid. Cross-regional collaborative design encourages users to charge across regions through price difference, effectively alleviating local congestion and forming a "point-line-surface" linkage spatial load balancing mode. This regional game mechanism not only optimizes the layout of charging facilities, but also promotes the efficient flow and balanced allocation of resources between regions.

[0064] The dynamic coupling mechanism realizes the deep integration of time and space correlation and multi-agent game. The time distribution of charging demand is constrained by spatial accessibility, while the service capacity of charging stations is affected by time-based electricity price. By constructing a spatio-temporal joint probability density function, the complex coupling relationship is quantified. The DSO as the leader publishes the electricity price signal, and the CSO and EV users as followers adjust the service fee and charging plan through price game to form a Stackelberg equilibrium solution. In this process, non-power factors such as road network state, battery degradation cost, and user psychological preference are also considered to construct a multi-dimensional utility function to more realistically describe the decision logic of game participants.

[0065] The model is characterized by the following features and advantages: The spatio-temporal game model describes the nonlinear mapping relationship between electricity price signal and user behavior, avoiding the strategy distortion caused by traditional linear assumption; the dynamic constraint relaxation mechanism is introduced to make the electricity price adjustment range and user response threshold adapt to the state of power grid, enhancing the robustness of the model; at the same time, it supports the cross-time scale cooperation of hourly electricity price optimization and minute-level load adjustment, and is compatible with urban-level macro planning and community-level micro-grid dispatching, providing a solid theoretical support for the construction of high flexibility distribution network.

[0066] 2.1, Dynamic Electricity Price Model in Time Dimension

[0067] 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.

[0068] Definition of dynamic electricity pricing function. The time-dimensional dynamic electricity pricing function can be expressed as:

[0069] (1)

[0070] 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).

[0071] 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".

[0072] The model takes supply-demand balance as the core target: the α / β weight allocation makes the electricity price focus on demand suppression during the peak load period (α takes 0.4-0.6) and strengthens the consumption incentive during the renewable energy abundant period (β takes 0.2-0.3). By introducing the γ coefficient (0.1-0.2), the price signal delay in the load mutation scenario is corrected, and the reverse risk of peak-valley transfer is reduced. The cost coverage mechanism (η = 1.05-1.15) ensures the recovery of grid fixed costs, and the parameter setting is positively related to the degree of line aging. The multi-dimensional coupled model realizes the dynamic matching of the electricity price signal and the system state, laying the foundation for the time-space game analysis.

[0073] 2.2, Spatial dimension partitioned electricity price weight factor model

[0074] In order to build a refined power market regulation system, a spatial dimension partitioned electricity price weight factor model is proposed. This model quantifies the remaining capacity margin of regional power grids to achieve differentiated guidance and optimized allocation of electric vehicle charging loads. The core mechanism is to reflect the supply-demand relationship between the base load power and EV charging load in each partition through dynamic weight factors. When the EV load in a certain region increases and the capacity margin decreases, differentiated price adjustment strategies are automatically triggered, thereby forming a spatial transfer effect of charging load. The calculation principle, variable definition and operation mechanism of the model will be described in detail below.

[0075] Partitioned weight factor ωi The remaining capacity margin of regional power grids is used to generate differentiated electricity prices to guide the rational distribution of electric vehicle (EV) charging loads through spatial differentiation pricing. Its mathematical model is defined as follows:

[0076] (2)

[0077] In the formula, is the node set of the th partition, which is divided based on the distribution network topology structure, usually determined based on line capacity margin or renewable energy penetration rate difference; is the total number of system partitions; is the base load power of node , which represents the regional basic power demand; is the EV charging power of node , which reflects the additional load of the power grid caused by user charging behavior.

[0078] Specifically, the physical meaning of the numerator weight factor is to calculate the difference sum of the base load and EV load in the i th partition, which represents the remaining capacity margin of the regional power grid; the physical meaning of the denominator weight factor is the total base load power of the whole system, which is used for normalization to ensure the comparability of the weight factor across regions.

[0079] ‌The partitioned electricity price weight factor model realizes the spatial optimization of power resources through a dynamic adjustment mechanism. Its core mechanism is reflected in two aspects: first, the weight factor is directly linked to the electricity price. When the EV charging load in a certain partition increases, the weight factor of that area will decrease, triggering an increase in the electricity price to suppress local overload. For high-base-load areas such as industrial zones, the electricity price adjustment needs to consider additional factors such as line congestion rates, as these areas naturally have a lower weight factor. Second, the model uses differentiated regional electricity price signals to guide the transfer of charging load to areas with higher weight factors and lower load density, forming a "spatial transfer effect."

[0080] Model characteristics and constraints:

[0081] 1. Dynamic adaptability

[0082] (3)

[0083] where: P base,j ( t ) is the base load power (kW) of node j in period t , representing the inherent power demand of the node without EV charging load, which varies over time; t is the period index, t =1,2,…, T , usually in hours or minutes; j is the node index, belonging to a node set i of a certain partition Ni .

[0084] Extending the base load power from static to time-varying function allows it to reflect the changes in basic load at different times, supporting spatio-temporal coupling optimization.

[0085] 2. Dynamic weight factor update mechanism

[0086] Weight factor time-varying expression:

[0087] (4)

[0088] where: ωi ( t ) is the weight factor of the i th partition in period t , reflecting the remaining capacity margin of the regional power grid; P ev,j ( t ) is the base load power (kW) of node j in 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.

[0089] 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.

[0090] 2. Boundary conditions

[0091] Nonnegativity constraint:

[0092] (5)

[0093] Ensure weighting factors To avoid negative electricity price signals. To maintain the rationality and explainability of the electricity pricing mechanism.

[0094] Normalization constraints:

[0095] (6)

[0096] 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:

[0097] (7)

[0098] 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.

[0099] 3. Two-level optimization mathematical model

[0100] 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.

[0101] 3.1 Upper-level model (DSO)

[0102] 3.1.1 Model Framework and Objective Function

[0103] The upper-level model for distribution system operators (DSOs) is a multi-objective optimization problem, including economic objectives and renewable energy consumption objectives:

[0104] Objective function 1: Minimize power grid operating costs

[0105] (8)

[0106] 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.

[0107] Objective function 2: Maximize the renewable energy absorption rate

[0108] (9)

[0109] 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.

[0110] 3.1.2 Constraints

[0111] 1. Physical constraints of the power grid

[0112] (1) Node voltage safety threshold

[0113] Assume the system has Nb For each busbar, the voltage deviation must meet the following requirements:

[0114] (10)

[0115] In the formula: Vi ( t ) is a node i During the periodt Voltage amplitude; typical value: V min = 0.95 p.u., V max = 1.05 p.u., prevent voltage excursion leading to equipment damage, penalty triggered when excursion:

[0116] (11)

[0117] (2) Line capacity constraints

[0118] Let the system have Nl branches, be the branch l active power in time period t : P

[0119] (12)

[0120] Line capacity constraints: branch power not exceed rated capacity , avoid overload trip, overload penalty:

[0121] (13)

[0122] 2. Operating strategy constraints

[0123] (1) Price adjustment amplitude limit

[0124] Adjacent time period price fluctuation rate constraint, limit price adjustment amplitude, guarantee market stability:

[0125] (14)

[0126] Where: πt is the dynamic price in time period t ; Δ π max is the maximum allowed fluctuation rate (typical value 20%, i.e. 0.2), first time period price π 1 Based on historical price initialization.

[0127] (2) Purchase cost budget constraint

[0128] Total purchase cost does not exceed financial threshold:

[0129] (15)

[0130] Where: C buy ( t ) is the purchase unit price (yuan / kWh) in time period t ; P buy ( t ) is the total purchase cost in time periodt Purchased electricity volume (kWh); B `max` is the financial threshold for DSO (set based on operational data).

[0131] 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.

[0132] 3.2 Lower-level model (CSO and EV users)

[0133] 3.2.1 User Utility Function Model

[0134] EV users' charging decisions are quantified using the following utility function:

[0135] (16)

[0136] 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 tThe preferred charging energy (kWh) of the user can be predicted according to historical behavior or travel plan.

[0137] The utility function is composed of three parts: the revenue term θ ⋅SOC( t ) represents the satisfaction of the user due to the improvement of the battery level; the cost term [π( t )+ f i ]⋅ E char (t) represents the electricity price and service fee paid by the user; the deviation penalty term, γ ⋅( E char ( t )− E pref ( t )) 2 is used to depict the dissatisfaction of the user to the deviation from the expected charging behavior.

[0138] The user intelligently selects the charging time and charging station under the joint influence of the electricity price and service fee by maximizing the utility function, forming a response to the upper electricity price signal. The user behavior decision-making process is a dynamic game: the user intelligently selects the charging time and location by maximizing the utility function, thereby forming market feedback to the grid electricity price signal. When the service fee of the charging station is too high to cause negative utility, the user will spontaneously adjust the strategy, or replace the charging station or delay the charging, and this flexible response mechanism effectively maintains the balance of supply and demand in the charging market.

[0139] 3.2.2 CSO revenue model

[0140] The charging station operator (CSO) maximizes the revenue by optimizing the service fee and infrastructure investment, and the revenue function is:

[0141] (17)

[0142] In the formula: R CSO is the total revenue of the CSO; f i ( t ) is the service fee (yuan / kWh) of the i th zone in the time period t , which is the decision variable of the CSO; E total,i (t) is the total charging energy (kWh) of the i th zone in the time period t , which is affected by the user response; C invest is the infrastructure investment cost of the CSO, including charging pile construction, operation and maintenance, and equipment depreciation, etc.M Total number of subareas for CSO operation; T Total number of dispatching periods.

[0143] Investment cost modeling:

[0144] (18)

[0145] Where: N Total number of charging piles; k is the unit charging pile construction cost (yuan / pile); c om Unit operation and maintenance cost of charging (yuan / kWh).

[0146] 3.2.3 Model characteristics and constraints

[0147] 3.2.3.1. Revenue composition

[0148] Revenue items: f i ( t )⋅ E total,i ( t )reflects service fee income, which needs to be noted that too high service fee will inhibit user demand;

[0149] Cost items: C invest Including fixed asset investment and operation and maintenance cost, which needs to be allocated through charging capacity.

[0150] 3.2.3.2. Spatial game constraints

[0151] Service fee boundary constraints:

[0152] (19)

[0153] Where: and are the upper and lower limits of service fee under government guidance or market competition, respectively.

[0154] Charging power capacity constraints:

[0155] (20)

[0156] Where: is the total capacity of charging equipment in the i th subarea (kW), and Δ t is the period length.

[0157] 3.3, Joint optimization framework

[0158] 3.3.1 Double-layer interaction mechanism

[0159] In the double-layer optimization model constructed by the present application, the upper decision maker (DSO) and the lower subjects (CSO and EV users) form a closed-loop interaction mechanism through the electricity price signal and load response, as follows:

[0160] Lower feedback mechanism: EV users optimize charging behavior based on dynamic electricity price t ) and charging service fee f i t , with the goal of maximizing their own utility, to form the charging demand distribution E total,i t , which serves as the input of the CSO revenue model to affect its service fee decision;

[0161] Upper regulation mechanism: DSO guides the charging behavior of the lower users by issuing dynamic electricity price signal π t , indirectly affecting the service fee strategy of CSO f i t , and then feeding back to the upper objective function (operating cost and renewable energy consumption rate) through load response, forming a closed-loop optimization.

[0162] 3.3.2 Equilibrium condition

[0163] Nash equilibrium: CSO and users cannot obtain higher revenue by changing their strategies unilaterally, satisfying:

[0164] (21)

[0165] (22)

[0166] In the formula: is the equilibrium service fee of the i th sub-area in time period t (yuan / kWh); is the equilibrium charging capacity of EV users in time period t (kWh); R CSO is the revenue function of CSO; U user is the utility function of users. This equilibrium shows that under the optimal strategy, neither party can obtain higher revenue by changing their decisions unilaterally. Due to the nonlinearity and high dimensionality of the model, iterative algorithms (such as particle swarm optimization, alternating direction multiplier method, etc.) are required for solving.

[0167] The key parameters in the model and their value ranges are as follows (all based on actual investigation and historical data calibration):

[0168] ​​​​User preference coefficient θ : Value range is 0.5-1.2, and the commuter usually takes a higher value, reflecting that the charging demand is more rigid;

[0169] User price sensitivity coefficient γ : Value range is 0.3-0.8, and the user in the business district usually has higher price sensitivity because of more charging options;

[0170] Service fee adjustment coefficient κ : Value range is 0.8-1.5, and the specific value needs to be dynamically adjusted according to the degree of competition in the regional charging market;

[0171] Charging pile investment cost coefficient k : Value range is 104-105 yuan / pile, and the value of fast charging pile is significantly higher than that of slow charging pile due to its high technical complexity and high equipment cost.

[0172] The model quantifies the game relationship between user utility and CSO revenue, providing a theoretical basis and decision support for dynamic pricing strategies in the electric vehicle charging market and planning of charging infrastructure.

[0173] 4. Solution algorithm design

[0174] To effectively solve the optimization problem of the distribution system under the interaction of "vehicle-station-network", the application designs an innovative solution algorithm. The algorithm dynamically generates electricity price based on the improved particle swarm algorithm (IPSO), and realizes multi-objective double-layer optimization through a distributed solution architecture. The dynamic electricity price generation mechanism and multi-objective double-layer optimization process are described in detail below to ensure the efficiency, robustness and feasibility of the algorithm in practical applications.

[0175] 4.1 Dynamic electricity price generation mechanism

[0176] The dynamic electricity price generation mechanism of the improved particle swarm algorithm (IPSO) realizes multi-dimensional electricity price space optimization through three key steps: first, define the particle dimension as the combination of "number of time periods x number of regions" (such as 24 hours x 5 regions = 120 dimensions), and set the initial electricity price range based on historical data to ensure algorithm convergence; second, design a fitness function with grid operation cost and renewable energy consumption rate as the core, realize multi-objective optimization through dynamic weight adjustment and constraint violation penalty term; finally, adopt a nonlinear decreasing inertia weight adaptive strategy to enhance global search ability in the early stage and focus on local optimization in the later stage, and combine particle swarm diversity index to dynamically adjust the weight to avoid local optimum.

[0177] The algorithm has three major improvements: through the elite preservation strategy to maintain the Pareto front solution, to provide multi-modal optimization scheme for decision makers; using GPU parallel computing to accelerate large-scale power grid scenario solution; integrating fuzzy logic to handle the uncertainty of user behavior prediction, significantly improving the robustness of the algorithm. These innovations enable IPSO to effectively balance power grid operation efficiency and renewable energy consumption demand, providing intelligent support for dynamic pricing decisions.

[0178] The dynamic pricing generation mechanism based on improved particle swarm optimization (IPSO) optimizes the multi-dimensional price space by simulating swarm intelligence behavior, as shown in Figure 1 The core process is as follows:

[0179] 4.1.1) Particle swarm initialization

[0180] Define the dimension, set the particle dimension as "number of time periods x number of regions", i.e. For example, under a 24-hour time scale, if divided into 5 regions, the particle dimension is 24 x 5 = 120. Each particle represents a complete spatiotemporal price combination.

[0181] Set the initial price range, based on normal distribution sampling of historical data to ensure reasonable particle distribution and avoid algorithm divergence.

[0182] Generate the initial particle swarm, population size to balance the calculation efficiency and search ability.

[0183] 4.1.2) Fitness function design

[0184] Economic objective, power grid operation cost , linearly related to time-of-use pricing and electricity purchase volume.

[0185] Environmental protection objective: renewable energy consumption rate , reflecting the use of green energy by the power grid.

[0186] Constraint penalty term, including: voltage out-of-limit penalty to ensure that the bus voltage is within the safety threshold; line overload penalty to prevent branch power from exceeding the rated capacity; the fitness function considers economic, environmental and constraint conditions, and evaluates the pros and cons of particles through weighted sum.

[0187] 4.1.3) Inertia weight adaptive strategy.

[0188] Calculate particle diversity, evaluate particle swarm diversity through spatial distribution variance; weight adjustment, when diversity is sufficient, use a nonlinear decreasing function to reduce inertia weight, enhance local optimization ability. When the diversity is insufficient, increase the inertia weight to jump out of the local optimal solution and maintain population diversity.

[0189] 4.1.4) Algorithm improvement features. Multi-modal optimization, with elitist preservation strategy to maintain multiple Pareto front solutions, providing diverse options for decision makers; parallel computing, using GPU to block particle swarm parallel computing, accelerating the fitness function calculation process, improving algorithm efficiency. Robustness enhancement, integrating fuzzy logic to handle the uncertainty of user response prediction, enhancing the tolerance of algorithm to prediction deviation, ensuring the stability and reliability of optimization results.

[0190] 4.1.5) Iterative optimization. Update particle position and velocity: update particle position and velocity according to standard formula of particle swarm algorithm, realize the movement of particle in solution space. Loop iteration until the termination condition is met (such as reaching the maximum number of iterations or the change rate of fitness function is lower than the threshold).

[0191] 4.1.6) Output results, output the Pareto optimal solution set, including multiple sets of space-time price combination schemes. Support decision makers to select the optimal scheme according to preference, realize the economic and efficient operation of power grid and the maximum consumption of renewable energy.

[0192] Key parameter description: particle dimension D is 120, representing a complete set of space-time price combination represented by each particle, whose dimension is determined by the product of time period and region number (for example, 24 hours x 5 regions = 120 dimensions); population size N pop Usually set to 50~100, to balance between calculation efficiency and global search ability; inertia weight ω adopts nonlinear decreasing strategy, its value gradually decreases from 0.9 to 0.4, enhances global exploration ability in early iteration, focuses on local fine search in later period; cognitive coefficient c1 is set to 1.5, used to adjust the dependence degree of particle on its own historical optimal position; social coefficient c2 is also set to 1.5, used to adjust the response degree of particle to the group historical optimal position; diversity threshold δdiv takes the value of 0.1 x particle dimension (i.e. 12), used to judge the aggregation degree of particle swarm, when the population diversity is lower than the threshold, adaptively adjust the inertia weight to maintain search vitality. These parameters work together to improve particle swarm algorithm (IPSO), ensure its effective multi-objective optimization in high-dimensional price optimization problem, while maintaining the convergence and robustness of the algorithm.

[0193] Flow chart of dynamic price generation based on improved particle swarm algorithm (IPSO). As Figure 2 shown, the complete process from initialization to result output is presented, highlighting the innovative design of IPSO in solving high-dimensional price optimization problem, especially through the triple mechanism of multi-modal maintenance, parallel acceleration and fuzzy correction, effectively overcoming the dimension disaster problem of traditional algorithm.

[0194] Through the above steps and characteristics, the dynamic price generation mechanism based on improved particle swarm algorithm (IPSO) can effectively optimize in the multi-dimensional price space, generate reasonable dynamic price signals to guide electric vehicle users' charging behavior, and achieve economic and efficient operation of the distribution system and maximization of renewable energy consumption.

[0195] 4.2, Multi-objective double-layer optimization process

[0196] The distributed solution architecture realizes the collaborative optimization of the upper and lower layers through hierarchical iteration. Its core process includes three key links: first, the distribution system operator (DSO) broadcasts the price signal containing the time and space dimension parameters to the charging station operator (CSO) and electric vehicle users at a cycle of 15-30 minutes; second, the electric vehicle users form a Nash equilibrium solution based on the non-cooperative game model to achieve the time and space transfer of charging load by minimizing the charging cost through a virtual queuing algorithm; finally, the CSO feeds back the aggregated regional charging load curve to the upper model to trigger a new round of iterative optimization based on the particle swarm algorithm until the system converges.

[0197] To ensure the convergence and stability of the system, the architecture adopts multiple safeguard mechanisms: hierarchical consistency test is conducted by setting the upper and lower target function change rate threshold, and the iteration is terminated when the optimization step of the two directions matches; a damping coefficient is introduced in the load feedback link to effectively suppress system oscillation caused by communication delay or prediction error; at the same time, sliding window filtering technology is used to interpolate abnormal load data to avoid the deviation of the optimization direction caused by false data. These mechanisms together ensure the reliability and robustness of the distributed solution process.

[0198] The distributed solution architecture realizes the collaborative optimization of the upper and lower layers through hierarchical iteration. The specific process is as shown in Figure 3

[0199] Under the "vehicle-station-network" interactive architecture, the hierarchical interaction mechanism is the core of realizing multi-agent collaborative optimization. This mechanism ensures the efficient operation of the distribution system and the optimal allocation of resources through the three main links of upper price signal issuance, lower user game equilibrium solution, and load data feedback and iteration. The following is a detailed improvement of the hierarchical interaction mechanism:

[0200] 4.2.1. Upper price signal issuance

[0201] DSO price broadcast: The distribution system operator (DSO) dynamically generates a price vector containing time and space dimension parameters based on the real-time state of the distribution network, renewable energy output prediction, and regional load distribution. These price signals not only reflect the price difference at different times, but also consider the spatial price zoning to guide the charging behavior of electric vehicle (EV) users.

[0202] ​Broadcast frequency: The frequency of electricity price updates is set to 15-30 minutes to match the state estimation period of the power distribution network. This high-frequency electricity price update can ensure the timeliness and accuracy of the electricity price signal, timely respond to changes in grid load, and effectively guide user charging behavior.

[0203] 4.2.2. Lower user game equilibrium solution

[0204] Non-cooperative game modeling: After receiving the electricity price signal issued by the DSO, the EV user acts as an independent decision maker and builds a charging strategy response model with the goal of minimizing charging cost. The user selects the optimal charging period and charging station by comparing the charging costs at different times and locations.

[0205] 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, the load is evenly distributed in time and space, avoiding local overload and congestion.

[0206] 4.2.3. Load data feedback and iteration

[0207] CSO data aggregation and feedback: The charging station operator (CSO) is responsible for aggregating the charging load curves of all EV users in the region and superimposing them on the base load before feeding them back to the upper DSO model. This process realizes the information transmission from the bottom user to the top DSO, providing real-time load data support for the DSO.

[0208] Upper model iteration optimization: The DSO reconstructs the objective function (including minimizing grid operation cost and maximizing renewable energy consumption rate) according to the load curve feedback from the CSO and triggers a new round of particle swarm iteration optimization. By continuously adjusting the electricity price signal, the optimal solution is gradually approached, achieving overall optimization of the distribution system.

[0209] Example 2

[0210] To verify the effectiveness of the "vehicle-station-network" interactive optimization strategy proposed in the present application, a simulation environment is constructed based on the IEEE 33-node distribution system in this embodiment. The simulation period is 24 hours, with a time resolution of 1 hour, and the key parameters are set as follows:

[0211] Power distribution system: reference load 1000 kW, renewable energy peak 800 kW (mixed photovoltaic and wind power), voltage allowed deviation ±0.08 p.u.; regional division: residential area (nodes 0-17), commercial area (nodes 18-22), industrial area (nodes 23-32); electric vehicles: 100 in total, penetration rate 25%, V2G participation rate 30%, battery capacity 60 kWh, charging / discharging power 7 / 5 kW respectively; electricity price mechanism: dynamic electricity price interval [0.3, 1.2] yuan / kWh, service fee interval [0.1, 0.3] yuan / kWh. The load composition of the power distribution network system is as shown in Figure 4

[0212] 1. Load optimization effect analysis

[0213] The overall optimization effect of the proposed dynamic electricity price strategy on the load characteristics of the system is quantitatively evaluated. By comparing key indicators under the fixed electricity price strategy, the strategy's significant achievements in achieving "peak load shifting", smoothing the load curve, and promoting green energy consumption are comprehensively verified from multiple dimensions such as peak-valley load, peak-valley difference, and renewable energy consumption rate, providing core data support for the effectiveness of the strategy. To evaluate the effect of the proposed strategy on load regulation, Table 1 compares the load indicators under the traditional fixed electricity price strategy and the proposed dynamic electricity price strategy:

[0214] Table 1 Comparison of load optimization effects

[0215]

[0216] The analysis shows that the proposed dynamic electricity price strategy effectively regulates user electricity consumption through the price lever, and in the 24-hour simulation of the IEEE 33-node system, it exhibits significant advantages. Through precise price signals, it effectively optimizes the time distribution of the load. During the peak electricity consumption period (e.g., 18:00-22:00), the higher electricity price (e.g., 1.15 yuan / kWh) significantly suppresses the charging demand of users, reducing the peak load from 1850 kW to 1680 kW, a decrease of 9.2%. During the low valley period (e.g., 00:00-06:00), by lowering the electricity price (0.3-0.5 yuan / kWh), it successfully attracts users to shift their charging behavior, increasing the low valley load from 350 kW to 520 kW, an increase of 48.6%. This "peak load shifting" effect significantly reduces the system peak-valley difference by 22.7%, from 1500 kW to 1160 kW, significantly smoothing the daily load curve, reducing the pressure on the power grid peak shaving, and improving equipment utilization and operational stability.

[0217] In promoting renewable energy consumption, the dynamic electricity price mechanism exhibits good green synergy characteristics. For example, Figure 5 ​As shown, by reducing the electricity price during the peak renewable energy output period (e.g., 10:00-14:00), the strategy effectively guides the charging load to synchronize with the peak photovoltaic power generation, increasing the renewable energy consumption rate from 83.5% to 95.8%. The correlation coefficient between the load curve and renewable energy output also significantly increases from 0.42 to 0.86, indicating that the system achieves good following of new energy fluctuations by load, greatly improving the green operation level and clean energy utilization efficiency of the power grid.

[0218] In summary, the strategy proposed in the present application realizes time-space optimization through a three-dimensional coupling mechanism of "time-space-price". In terms of time, price differences successfully guide load to peak shaving; in terms of space, the zoned electricity price mechanism (e.g., high price in residential areas and low price in industrial areas) promotes 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 safety, fully verifying the effectiveness and practical value of the proposed strategy in improving the flexibility, economy, and greenness of the distribution system.

[0219] 2、Economic benefit analysis

[0220] Economic efficiency is the key to measuring the feasibility of the strategy. This section conducts a detailed financial analysis from the cost-benefit perspective of the distribution system operator (DSO), charging station operator (CSO), and electric vehicle user, aiming to clarify whether the proposed optimization strategy can build a multi-win benefit distribution pattern, thereby verifying its economic superiority and market promotion potential. Table 2 shows the benefits of each participant in terms of economic efficiency:

[0221] Table 2 Economic benefit comparison

[0222]

[0223] The economic analysis shows that the proposed strategy achieves a multi-win through dynamic pricing and load aggregation mechanisms: the distribution operator (DSO) reduces the electricity purchase cost by 13.0% (from 12,580 yuan to 10,950 yuan) due to peak shaving, while reducing the pressure on grid peak shaving; the charging service operator (CSO) increases total revenue by 20.3% (from 3,200 yuan to 3,850 yuan) through optimizing service fees and load management, and charging pile utilization rate significantly increases to 78%; the user side reduces total energy cost by 13.2% (from 15,780 yuan to 13,700 yuan), and users participating in vehicle-to-grid (V2G) can additionally obtain an 18% benefit. This result verifies the collaborative optimization capability of the strategy in reducing system cost, improving operational efficiency, and optimizing user benefits, forming a sustainable electricity market benefit distribution mechanism.

[0224] 3、Analysis of grid safety performance

[0225] 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 rate. By comparing the changes in the power grid operation state before and after optimization, it is confirmed that the strategy has a positive effect on improving system voltage stability, preventing equipment overload, and enhancing power supply reliability. Table 3 shows the comparison of power grid safety indicators before and after optimization:

[0226] Table 3 Comparison of power grid safety indicators

[0227]

[0228] The power grid safety performance is systematically improved: the overall voltage stability is enhanced by 32%, the voltage in the residential area during the evening peak is significantly improved from 0.85 p.u. to 0.92 p.u., the line load rate in the industrial area is reduced from 121% to the safety threshold of 95%, and the voltage overrun nodes are completely eliminated (from 5 to 0). Key indicators are significantly improved: line overload rate is reduced by 74.4% (12.5% → 3.2%), maximum voltage deviation is reduced by 46.7% (0.15 p.u. → 0.08 p.u.), and these data collectively verify the substantial breakthrough in the safety and reliability of the distribution system.

[0229] 4. Analysis of time and space game characteristics

[0230] This section analyzes the interactive response and game characteristics of users and operators in the time and space dimensions under the guidance of dynamic electricity price signals. By decoupling the analysis of the time and space transfer rules and distribution changes of the load, the internal action principle of the "time-space-price" three-dimensional coupling mechanism is revealed, and how it coordinates the behavior of multiple parties to achieve system-level collaborative optimization is clarified.

[0231] 4.1 Time dimension response characteristics

[0232] The time dimension response characteristics reflect the guiding effect of dynamic electricity price on the charging behavior of users over time. By setting time-differentiated electricity price signals, the system can effectively encourage users to charge during low-load periods and reduce electricity consumption or participate in V2G discharging during peak periods, thereby achieving peak shaving and promoting new energy consumption. 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 the power grid.

[0233] Figure 5 The typical period electricity price guiding effect is shown:

[0234] 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.

[0235] 4.2) Spatial Dimension Load Distribution

[0236] Table 4 shows the changes in load distribution in each region before and after optimization.

[0237] Table 4. Changes in load distribution in each region before and after optimization.

[0238]

[0239] 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.

[0240] 6. Typical Scenario Analysis

[0241] To more clearly show the dynamic regulation process and effect of the strategy, this section selects typical scenarios such as renewable energy output peak and electricity load peak for detailed analysis. By presenting the linkage data of key period electricity price signal, load transfer, V2G response and regional interaction, the strategy is concretely interpreted as to how to achieve the goal of load optimization and maximum renewable energy consumption in actual operation.

[0242] In the constructed typical scenario simulation, the dynamic electricity price strategy shows excellent optimization performance through time and zone regulation. During the evening peak period (18:00-22:00), the system increases the electricity price from 0.9 yuan / kWh to 1.2 yuan / kWh, successfully reducing the residential charging load by 35%, of which 28% is transferred to the early morning valley period and 7% is achieved through V2G discharging for reverse power supply; at the same time, the commercial district load increases by 12%, effectively utilizing the excess photovoltaic power during this period. In the key period of renewable energy consumption (10:00-14:00), the strategy reduces the electricity price to the range of 0.65-0.75 yuan / kWh, significantly enhancing the correlation between charging load and photovoltaic output curve, with an industrial V2G participation rate of 45%. This coordinated regulation not only realizes the spatio-temporal optimization of load distribution, but also effectively enhances the peak regulation capacity and operational flexibility of the power grid, proving the dual benefits of the dynamic electricity price mechanism in improving the system's renewable energy consumption level and operational economy.

[0243] The present application solves the problems of spatio-temporal imbalance of supply and demand, aggravation of peak-valley difference and multi-agent collaborative optimization caused by large-scale access of electric vehicles to distribution networks by constructing a multi-objective double-layer optimization model under the interaction of "vehicle-station-grid", integrating spatio-temporal game and dynamic electricity price coupling mechanism. The simulation results show that the proposed strategy achieves significant results in load optimization, economic operation and power grid safety: the peak-valley difference is reduced by 22.7%, the renewable energy consumption rate is increased to 95.8%, and the three-way win of DSO, CSO and EV users is achieved. This research not only provides theoretical support and algorithm tools for the optimization of distribution networks with high proportion of new energy and electric vehicles, but also provides a feasible path for the dispatching decision and market mechanism design of future smart distribution systems. Future research will further explore the deep integration mechanism of V2G and electricity market to improve the system flexibility and response capability.

[0244] If the above functions are realized in the form of software function units and sold or used as independent products, they can be stored in a computer readable storage medium. Based on this understanding, the technical solutions of the present application or the parts of the present application that essentially contribute to the prior art or the parts of the technical solutions can be embodied in the form of software products. The computer software product is stored in a storage medium and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in the various embodiments of the present application. The aforementioned storage medium includes a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and various media that can store program codes.

[0245] The preferred embodiments of the present application are described in detail above. It should be understood that those skilled in the art can make many modifications and changes without creative labor based on the concept of the present application. Therefore, any technical solutions obtained by logical analysis, reasoning, or limited experiments based on the prior art according to the concept of the present application shall be within the protection scope determined by the claims.

Claims

1. A power distribution system optimization method under vehicle-station-network interaction considering space-time game, 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 subarea according to a real-time state of a power distribution network, renewable energy output and time-space distribution of regional load, and aims to minimize power grid operation cost and maximize 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, aims to maximize self charging decision utility, forms a charging demand distribution through non-cooperative game, and optimizes and adjusts the charging service fee decision based on the charging demand distribution; The double-layer optimization framework adopts a game response mechanism of dynamic electricity price in a time dimension, the power distribution system operator generates the dynamic electricity price signal in an hourly granularity according to a power distribution network load curve and renewable energy output fluctuation, 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 subarea according to a power distribution network topology structure, sets a higher electricity price weight for a region with high line overload risk and low distributed energy penetration rate, the charging station operator deploys charging piles by using a Nash equilibrium strategy based on traffic flow thermal map and power grid capacity margin information, and excites the electric vehicle user to charge across regions through price difference by cross-regional coordination design; The double-layer optimization framework constructs a subarea electricity price weight factor in the space dimension, quantifies a regional power grid remaining capacity margin, and realizes differentiated guidance and optimized configuration of electric vehicle charging load; The subarea electricity price weight factor represents the regional power grid remaining capacity margin, is used to generate a differentiated electricity price, guides the electric vehicle charging load to be reasonably distributed through space differentiated pricing, and is specifically defined as a sum of differences between base load power and electric vehicle charging power of nodes in each subarea divided by a sum of total base load power of the whole system; the space game equilibrium condition is constructed, the differentiated regional electricity price signal is used to guide the charging load to shift to a region with a higher weight factor; The power distribution system operator reconstructs an objective 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 dynamic electricity price comprehensively considers factors of power distribution network system load, renewable energy output and time deviation, and a time dimension dynamic electricity price function is represented 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.

3. 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, and aims to minimize the power grid operation cost and maximize the renewable energy consumption rate. The objective function of minimizing the power grid operation cost is specifically a sum of a power purchase cost of the power grid from a higher-level power grid and a peak-valley difference penalty weight coefficient multiplied by a difference between a peak value and a valley value of the load curve in a day; The objective function of maximizing the renewable energy consumption rate is specifically a quotient of actual output of the renewable energy and total load of the system.

4. 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.

5. 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 t is the charging service fee of the distribution system operator; E total,i t is the charging demand distribution generated by the electric vehicle users; is the equilibrium charging power of the electric vehicle users in time period t ; U user is the utility function of the electric vehicle users; π( t ) is the dynamic price generated by the distribution system operator.​​ 6. 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.

7. The power distribution system optimization method considering space-time game under vehicle-station-network interaction according to claim 6, 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.

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 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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