Multi-objective optimization method for transmission and distribution price based on multi-objective genetic algorithm

Abstract

A kind of multi-objective genetic algorithm-based transmission and distribution price multi-objective optimization method belongs to the technical field of power system operation and energy economy cross.The purpose of the present application is to parameterize five categories of policy levers into eight decision variables, construct a three-party multi-objective collaborative optimization model, and introduce a price-load-carbon emission coupling model to quantify the dynamic influence of time-of-use price structure on system carbon emission intensity. The present application proposes a multi-objective parameterized optimization framework for transmission and distribution price policy deduction, introduces NSGA-III algorithm to solve the high-dimensional trade-off problem in transmission and distribution price regulation, and extracts three types of scenario schemes, namely economic priority, balanced development and low-carbon priority, through clustering and multi-criteria decision analysis. The present application can reveal the nonlinear interaction and non-dominated trade-off relationship among multiple levers, generate a set of Pareto optimal solutions with uniform distribution in high-dimensional objective space using the reference point mechanism, avoid the subjectivity and solution set degeneration of traditional weighted method, and achieve strict Pareto improvement of price, cost recovery deviation and carbon emission intensity for balanced development scheme compared with the current mechanism.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of power system operation and energy economics. Background Technology

[0002] Against the backdrop of energy transition and deep decarbonization of the power system, transmission and distribution networks are shifting from "passive load-bearing" to "active support," with their investment scale, operational complexity, and system service demands continuously increasing. Countries with high proportions of renewable energy, such as Germany, need to secure funding for grid expansion and upgrades while achieving emission reduction targets. Germany is promoting energy transition and has proposed a phased emission reduction and long-term carbon neutrality vision, but the huge investment and upgrade needs for grid infrastructure make the simultaneous achievement of "user affordability—sustainable grid operation—low-carbon transition" a core challenge in transmission and distribution pricing mechanism reform. Therefore, how to design transmission and distribution pricing to form an explainable and implementable compromise among multiple objectives is an important topic in energy policy and power economics research.

[0003] The contradictions in Germany's current transmission and distribution pricing mechanism are concentrated in two aspects: First, significant regional differences in network costs result in some high-renewable-energy regions bearing excessively high network costs, leading to unfair cost sharing and decreased policy acceptance. Second, the existing structure lacks direct carbon signals and green guidance; the generation side bears almost no conventional transmission and distribution costs, resulting in insufficient incentives for "polluter pays" and difficulty in passing on low-carbon benefits through the price mechanism. With the continued growth of renewable energy and a significant increase in demand for inter-regional grid transmission and flexibility, these structural problems will be further amplified: on the one hand, pushing up grid fees, and on the other hand, weakening the guiding role of electricity prices in addressing system congestion, carbon intensity differences, and investment efficiency.

[0004] The aforementioned dual dilemma indicates that the design of transmission and distribution pricing mechanisms has transcended the scope of simple cost recovery or efficiency incentives, transforming into a typical high-dimensional, multi-objective governance problem: controlling end-user electricity prices to ensure social acceptability, guaranteeing reasonable revenue for grid companies to maintain investment capacity, and internalizing the externalities of carbon emissions to drive deep decarbonization of the system. In this process, various policy levers, such as regional allocation, generation-consumption sharing, capacity-power structure, time-of-use differences, and low-carbon incentives, are not independent but interact through a complex coupling relationship between electricity prices, load, and carbon emissions. However, existing research mostly focuses on a single entity or a single policy lever, and generally uses fixed weights to aggregate multiple objectives into a single-objective optimization problem, making it difficult to characterize the inherent non-dominant trade-offs between objectives and lacking a unified model for the interconnected effects of the aforementioned multiple policy levers. Therefore, systematically reviewing the theoretical foundations, policy practices, modeling methods, and multi-objective optimization algorithms of transmission and distribution pricing mechanisms is fundamental for constructing a pricing optimization framework capable of simultaneously addressing multiple conflicting objectives. Summary of the Invention

[0005] The purpose of this invention is to parameterize five major categories of policy levers into eight decision variables, construct a three-party multi-objective collaborative optimization model, and introduce an electricity price-load-carbon emission coupling model to quantify the dynamic impact of time-of-use electricity price structure on the system's carbon emission intensity. This is based on a multi-objective genetic algorithm for multi-objective optimization of transmission and distribution prices.

[0006] The steps of this invention are: S1. A multi-objective parameterized optimization framework for the derivation of transmission and distribution pricing policies is proposed: five major categories of policy levers, namely regional sharing, generation and consumption sharing, capacity-electricity structure, time-of-use differences and low-carbon incentives, are uniformly parameterized into eight continuous decision variables, and a multi-objective optimization model covering government regulation, consumer welfare and coordination of the diverse interests of grid operators is constructed. S2. Introduce the NSGA-III algorithm to solve the high-dimensional trade-off problem in transmission and distribution price regulation; S3. Generate interpretable typical policy solutions based on actual data: Three scenario solutions were extracted through clustering and multi-criteria decision analysis: economic priority, balanced development and low-carbon priority.

[0007] Construction of the multi-objective optimization model of this invention: Let the typical day set be These represent the four seasons: spring, summer, autumn, and winter, with each season corresponding to a weighted number of days in the year. Set according to the convention of a macro-level flat year in the power system, to meet The initial baseline load curves for typical days in each season are as follows: Peak-valley electricity price ratio and energy storage discount Stimulated by price signals, the intraday time-of-use electricity price signal strength Maintain consistency across all seasons: (6) The average daily price signal strength for typical days in each season is ; 1) Objective 1: To minimize the overall average electricity price for all users in society, a load transfer and energy storage charge / discharge balance model with daily electricity consumption conservation constraints was constructed: (13) In the formula, Typical daytime period The initial baseline total load, This refers to the load reduction during periods when prices are above average. To reduce the amount of electricity redistributed to off-peak hours during off-peak periods, To increase the load for charging energy storage systems during off-peak hours, This effectively reduces the load during peak discharge periods of the energy storage system. The objective function is to minimize the comprehensive average electricity price for all users in society. Defined as the ratio of weighted total cost for all four seasons to total electricity consumption: (14) In the formula, The system calculates the seasonal and time-of-use real-time power load for various user groups, based on the total net load for each season. It was obtained by shifting and deconstructing according to the historical electricity consumption ratio of various types of users; This represents the time-of-use electricity price settlement value for each season. 2) Objective 2: Minimize the deviation in time-sharing cost recovery for operators, and construct a weighted system based on seasonal days. Weighted annual time-sharing cost recovery absolute and relative deviation objective function : (15) In the formula, the dimension conversion coefficient is... Used to standardize the conversion between the product of electricity price and power load. This represents the target baseline cost that the operator needs to recover in any single hour. 3) Objective 3: Minimize the system's carbon emission intensity; the objective function for the system's annual actual average carbon emission intensity. Expressed as the ratio of total weighted carbon emissions to total electricity consumption for the year: (20) In the formula, This represents the baseline total electricity consumption during off-peak hours in each season. In summary, the NSGA-III multi-objective optimization model for transmission and distribution pricing design is as follows: (twenty one).

[0008] This invention introduces the multi-objective solution process of the NSGA-III algorithm: 1) Population initialization and boundary reflection: Based on the legal boundaries of 8 decision variables, an initial population with high spatial uniformity is generated using Sobol pseudo-random sequences. In subsequent evolution, if crossover mutations produce individuals that cross the boundaries, the reflection boundary method is used to force them back into the feasible region to ensure genetic diversity. 2) Temporal Coupling and Electricity Price-Load Reconfiguration: This involves integrating the data carried by individual populations... to Policy-related factors are substituted into a structured two-part mapping model to calculate the comprehensive benchmark electricity price and time-of-use electricity price for various types of users. Subsequently, these are input into a load transfer and energy storage charge-discharge balance model to reconstruct the dynamic net load curves for typical days in the four seasons. ; 3) Objective Calculation and Soft Constraint Normalization: Based on the reconstructed physical-temporal boundary, calculate the three core fitness objectives of the individual. , , Simultaneously, based on the absolute violation of each soft constraint and divided by the 95th quantile normalization constant, the overall constraint violation rate for that individual is generated. ; 4) Non-dominated sorting based on the constraint dominance principle: Abandoning the traditional static large constant penalty function, this method strictly enforces the constraint dominance principle during the environment selection phase, and compares... Based on the size and feasibility, priority should be given to guiding the population to converge toward the physically and financially feasible domain; 5) Reference point association and environment selection: For individuals at the critical non-dominated level, calculate their vertical distances to the associated rays of each reference point in the three-dimensional target space; 6) Genetic Operators and Iteration Termination: The population generates offspring through simulated binary crossover and polynomial mutation. The above evaluation, sorting, and selection process is repeated until the maximum number of iterations is reached. Output the final Pareto optimal policy solution set.

[0009] The soft constraints described in this invention include the following four types of policy regulatory red lines: ① Constraints on the rationality of electricity price structure and hierarchy: (twenty four) (25) ② Regulatory price red line and adjustment rate constraints: (26) (27) ③ Weighted average price and short-run marginal cost constraint of the system: (28) ④ Constraints on power grid investment returns and asset structure rationality: (29) (30) In the formula, This is the annual equivalent value of the total network fee revenue generated by the system throughout the day on both sides. ⑤ Low-carbon transition and macroeconomic policy constraints: (31) (32) (33) In the formula, This is the power curtailment adjustment factor.

[0010] Overall constraint violation rate of this invention as follows: (36) In the formula, This represents the normalized form of inequalities for each conventional soft constraint. and is the normalization constant for each constraint.

[0011] This invention reveals the nonlinear interactions and non-dominated trade-offs among multiple levers. It utilizes a reference point mechanism to generate a uniformly distributed Pareto optimal solution set in a high-dimensional target space, avoiding the subjectivity and solution set degradation of the traditional weighted method. It also systematically compares with benchmark algorithms such as NSGA-II, verifying its superiority in convergence and solution set diversity. Within the model boundary, the balanced development scheme achieves strict Pareto improvements in electricity price, cost recovery bias, and carbon emission intensity compared to the current mechanism. Attached Figure Description

[0012] Figure 1 This is the overall framework diagram; Figure 2 Solve the logic diagram for the NSGAIII algorithm; Figure 3 A performance comparison chart of NSGA-II and NSGA-III; Figure 4 Convergence curve for objective 1; Figure 5 The convergence curve for objective 2; Figure 6 Convergence curve for objective 3; Figure 7 NSGA-II Pareto 3D front plot; Figure 8 Pareto 3D front plot for NSGA-III; Figure 9 Box plot of decision variables; Figure 10 This is a parallel coordinate graph. Detailed Implementation

[0013] The following literature review will focus on four aspects: the theory and policy of transmission and distribution pricing mechanisms, design principles and regulatory constraints, modeling and optimization methods, and the application of high-dimensional multi-objective algorithms, thereby clarifying the methodological entry point and research positioning of this invention.

[0014] Driven by energy transition and deep decarbonization of the power system, the design of transmission and distribution pricing mechanisms has transcended the scope of simple financial accounting, evolving into a high-dimensional, multi-objective governance challenge that requires simultaneously considering user affordability, grid financial sustainability, and incentives for low-carbon transformation. Regarding this issue, the international academic community has accumulated rich achievements in areas such as transmission and distribution pricing structure restructuring, dynamic response mechanisms, electricity price forecasting technology, and multi-objective decision-making algorithms.

[0015] In the core dimension of transmission and distribution pricing mechanism design, the introduction of a multi-criteria decision-making framework has driven the transformation of tariff assessment from cost accounting to systemic effectiveness measurement. Tariff structures centered on capacity signals—such as real-time capacity pricing and Paris Metro-style capacity rates—have demonstrated a clear advantage in balancing fairness and efficiency in low-voltage distribution network congestion scenarios, and multi-criteria assessment further confirms the applicability of such schemes in balancing the interests of multiple parties. Welfare effect analysis of distributed generation grid connection pricing reveals that both fixed rates and annual cumulative net metering schemes can lead to significant efficiency losses, prompting academia to re-examine the discrepancy between the value of distributed energy and credit limits. Regarding cost sharing and congestion rent allocation, a two-tiered planning framework with coexisting nodal and fixed tariffs has proven effective in coordinating the behavioral differences between flexible and inflexible users, verifying the feasibility of marginal nodal pricing and investment cost recovery compatibility. A scheme that completely separates energy costs from network costs and adopts pre-purchase capacity charging effectively curbs excessive expansion of the distribution network through incentive-compatible design. To quantify the contribution of flexible resources under uncertain conditions, improved revenue cap price control and bi-level programming models have been used to restructure network tariffs, effectively promoting the development of incentive-compatible tariff design. Flexible pricing models have also emerged in the energy storage leasing sector, capable of maintaining the stability of energy storage revenue while ensuring the safe and economical operation of the power grid. At the level of distribution network market transactions, blockchain smart contract-driven multi-stage automatic pricing mechanisms and market participant strategy behavior analysis based on multi-agent reinforcement learning have continuously deepened the path to achieving fairness and efficiency in distributed transactions. Horizontal comparisons of different pricing mechanisms further provide important insights: if distribution system operators assign equal weight to fairness and economic efficiency, cost-sharing pricing is generally superior to marginal electricity prices at distribution locations, and the latter has an advantage in voltage quality, thus establishing a comparative benchmark for pricing decisions across energy systems.

[0016] In the field of dynamic pricing and demand response, demand-response-oriented dynamic pricing mechanisms expand the flexibility boundaries of pricing strategies. A user-behavior-based V2G multi-objective scheduling model, utilizing Monte Carlo simulation and genetic algorithms, significantly smooths load fluctuations while ensuring user benefits. A chaotic genetic algorithm incorporating chaotic mapping into population initialization is used for time-of-use pricing multi-objective optimization to enhance global search capabilities and achieve a better balance between operational profitability and grid stability. Under the constraints of new transmission and distribution pricing regulations, the NSGA-II algorithm is applied to multi-objective optimization of grid resource allocation. The resulting Pareto front clearly reveals the ternary trade-off between net present value, resource allocation weights, and compliance, highlighting the priority of decentralized configurations and short-cycle projects. Research on scheduling coupled with deep peak shaving and demand response under a carbon trading mechanism shows that price-signal-guided load shifting can alter the output periods of high-carbon marginal units, reducing overall system carbon emissions from a physical perspective. Advances in electricity price forecasting technology have provided fundamental support for the aforementioned dynamic mechanisms: sparse time-varying parameter vector error correction models, semi-structured multi-region hyperbolic bid stack models, and electricity price classification frameworks based on Bayesian extreme learning machines have all significantly improved the ability to characterize electricity price behavior in different markets, making day-ahead and real-time electricity price signals more accurate. Furthermore, a multi-attribute evaluation of the effects of transmission and distribution price reform integrates economic efficiency, security, and social welfare into a unified framework, systematically examining the comprehensive impact of the "permitted cost plus reasonable benefit" mechanism.

[0017] Faced with the increasingly prominent high-dimensional multi-objective conflicts in the aforementioned research, reference-point driven evolutionary algorithms have shown significant potential. At the theoretical level, rigorous runtime analysis of NSGA-III, adaptive reference vector update strategies, and... Control and archiving mechanisms and constraints The NSGA-III algorithm continuously improves the balance between convergence and diversity. At the application level, the NSGA-III-MR algorithm based on the maximum ranking strategy enhances Pareto selection pressure through the vertical distance between the solution and the weight vector, demonstrating a competitive advantage. In green flexible production scheduling, NSGA-III generates a uniformly distributed Pareto front within the three-dimensional objective space composed of real-time electricity prices and carbon emissions, enabling decision-makers to intuitively weigh energy costs against emission reduction targets. Addressing the conflict of interest caused by disorderly charging of electric vehicles in distribution networks, a multi-objective model using dynamic electricity prices as decision variables verifies the effectiveness of the improved NSGA-III in escaping local optima, mitigating conflicts between operators and users, and maintaining the safe operation of the distribution network. User-side microgrid energy storage optimization incorporates electricity costs, carbon emission reduction, and renewable energy consumption into a unified framework. Through the equivalent mapping of real-time carbon emission factors and dynamic electricity price signals, it significantly improves the system's adaptability and operational flexibility under different scenarios. The integrated improvement of the NSGA-III and the game theory combined weights collaborative optimization framework, the multi-objective optimal partitioning of active distribution networks, and the three-objective collaborative optimization of community integrated energy systems have further confirmed the significant advantages of NSGA-III in dealing with high-dimensional conflict objectives.

[0018] Despite the significant progress made by the aforementioned studies in their respective dimensions, several gaps remain to be filled. First, existing transmission and distribution pricing designs largely focus on single or a few policy levers, failing to incorporate the five major categories of levers—regional allocation, generation-consumption sharing, capacity-energy structure, time-of-use differences, and low-carbon incentives—into a unified, interconnected modeling framework. This makes it difficult to characterize the system response under the interaction of multiple mechanisms. Second, while high-dimensional multi-objective evolutionary algorithms have demonstrated the ability to generate uniform Pareto fronts in power dispatching and microgrid optimization, they have rarely been introduced into the high-dimensional trade-offs of transmission and distribution pricing regulatory objectives. In particular, there is a lack of systematic exploration of Pareto optimal solutions from the perspective of balancing the interests of government regulation, consumer welfare, and grid operator revenue. Third, most studies remain at the level of theoretical modeling and simulation, lacking the generation and comparison of interpretable policy solutions based on real power system data, making it difficult to directly provide decision-making support for comprehensive electricity price reforms in countries with high proportions of renewable energy.

[0019] To address the aforementioned shortcomings, this paper proposes a multi-objective optimization design framework for transmission and distribution pricing based on NSGA-III, using the German transmission and distribution pricing system as an empirical example. This framework parameterizes five categories of policy levers into eight decision variables, constructing a tripartite multi-objective collaborative optimization model encompassing government regulation, consumer welfare, and grid operator revenue. It also introduces a price-load-carbon emission coupling model to quantify the dynamic impact of time-of-use pricing structure on system carbon emission intensity. Utilizing the reference point mechanism of NSGA-III, a uniformly distributed Pareto optimal solution set is generated in a high-dimensional objective space, avoiding the subjectivity and solution set degradation problems of traditional weighted methods. Furthermore, through clustering and multi-criteria decision analysis, the solution set is categorized into three typical policy schemes: economic priority, balanced development, and low-carbon priority. A case study based on actual German data from 2024 reveals the significant impact of conservative parameter changes on average user electricity prices, operator cost recovery deviations, and system carbon emission intensity. It also finds that all Pareto optimal solutions point to a substantial reduction in the energy storage charging discount coefficient, indicating a severe inadequacy of current policy incentives for energy storage.

[0020] More specifically, the present invention has the following main contributions: (1) A multi-objective parameterized optimization framework for the derivation of transmission and distribution pricing policies is proposed: five major policy levers, namely regional allocation, generation and consumption sharing, capacity-power structure, time-of-use differences and low-carbon incentives, are parameterized into eight continuous decision variables, and a multi-objective optimization model covering government regulation, consumer welfare and coordination of multiple interests of grid operators is constructed. Under the boundary conditions of "rigid approved costs, short-term load elasticity and exogenous power structure", this framework realizes closed-loop coupled modeling of electricity price-load-carbon emissions, and can reveal the nonlinear interaction and non-dominant trade-offs among multiple levers.

[0021] (2) Introducing the NSGA-III algorithm to solve the high-dimensional trade-off problem in the regulation of transmission and distribution prices: The reference point mechanism is used to generate a uniformly distributed Pareto optimal solution set in the high-dimensional target space, avoiding the subjectivity and solution set degradation of the traditional weighted method. The algorithm is also compared with the benchmark algorithms such as NSGA-II, and its superiority in terms of convergence and solution set diversity is verified.

[0022] Based on actual German data, interpretable typical policy scenarios are generated: using Germany's 2024 power transmission and distribution system as an empirical example, three scenario scenarios—economic priority, balanced development, and low-carbon priority—are extracted through clustering and multi-criteria decision analysis. The results show that, within the model boundaries, the balanced development scenario achieves strict Pareto improvements in electricity prices, cost recovery bias, and carbon emission intensity compared to the current mechanism.

[0023] NSGA III Multi-Objective Optimization Model for Transmission and Distribution Pricing Design To address the growing conflict of interests among multiple stakeholders—government regulators, electricity users, and grid operators—in modern high-proportion renewable energy power systems, this invention constructs a novel multi-objective joint optimization model for transmission and distribution pricing. Traditional pricing models often rely on static weights or single-dimensional cost assessment, failing to capture the interplay of multiple policy levers across spatial (regional allocation) and temporal (time-of-use) dimensions. Therefore, this invention parameterizes multi-dimensional electricity pricing policy levers as continuous decision variables, reconstructs a highly sensitive nonlinear electricity price mapping proxy model, and establishes a dynamic transmission chain from "price signal - load shift - time-weighted benefits," ultimately forming a policy-oriented multi-objective spatial search method for pricing.

[0024] 1. Basic Assumptions To ensure the mathematical convergence of the multi-objective optimization framework and its transferability to regulatory practice, this model uses the integrated operation architecture of the German power transmission and distribution network as an empirical example, focusing on three typical end-user groups: residential, commercial, and industrial. The model makes the following core physical and economic assumptions at the system-wide scale: 1) Assumption of rigid cost: The annual fixed asset investment (CAPEX), operation and maintenance cost (OPEX), and system service cost of the power grid are rigidly permitted revenue bases determined by regulatory agencies (such as the German Federal Network Agency BNetzA) in accordance with the law, and do not change endogenously with the slight fluctuations in the total electricity consumption of end users within a single electricity price optimization cycle.

[0025] 2) Short-run price demand elasticity assumption: End-user electricity consumption behavior exhibits price elasticity across time periods. To accurately assess the latest technological advantages of multi-energy complementarity and flexible load-side response in Europe, referencing the meta-analysis results of Frondel et al. (2020), the comprehensive load transfer elasticity coefficient is used. The value has been increased from the traditional 0.2 to 0.4 to scientifically characterize the potential of peak electricity pricing to guide load reduction.

[0026] 3) The coupling assumption of electricity price-load-generation dispatch: The time-of-use structure of transmission and distribution prices (peak-valley price ratio, etc.) will directly affect the 24-hour daily load curve of the entire network through the load-side response mechanism. The peak shaving and valley filling of the load curve will reshape the dispatch and production plan of conventional units, thereby changing the output period and consumption share of high-carbon marginal units (such as coal-fired and gas-fired peak grids), which will ultimately be reflected in the change of the system's carbon emission intensity.

[0027] 4) Revenue Mechanism Constraints: Strictly adhere to the basic law of power grid regulation of "cost-plus and reasonable returns". The deviation between the total electricity revenue of the system and the approved total cost must be closely monitored. Operators are not allowed to obtain long-term excessive monopoly profits, and the risk of long-term financial losses due to excessively low electricity prices must be avoided.

[0028] 2. Decision Variables and Electricity Pricing Model 2.1 Definition of Decision Variables This model selects eight electricity price adjustment levers with high policy implementation relevance as control variables. Based on the German AgNeS reform discussion document and BNetzA's latest regulatory principles, the boundaries of some traditional variables were relaxed by 10% to 20%. The decision vector is expressed as: (1) The mathematical definitions, value ranges, and specific implications of each decision variable for electricity regulatory policies are shown in Table 1.

[0029] Table 1 Decision Variables Table

[0030] 2.2. A Structured Model for Two-Part Electricity Pricing Based on Allowed Revenue Sharing As demonstrated in the economics of electricity regulation, policy levers such as capacity fee ratio, regional equilibrium coefficient, and grid fee sharing rate on the generation side essentially influence the end-user electricity price structure by altering the allocation mechanism of grid permitted revenue across spatial, subject, and temporal dimensions. To completely eliminate the non-monotonicity and mechanistic gaps that may arise from heuristic agent models, this invention constructs a structured two-part electricity price mapping model based on permitted revenue allocation.

[0031] Determination of the comprehensive benchmark electricity price at the regional and entity levels: First, the rigidly permitted total revenue for the entire network is deconstructed in terms of spatial (inter-regional redistribution) and entity (sharing between generation and consumption). Various end-users (residential H, commercial G, industrial S) are affected by the regional cost equilibrium coefficient. And the sharing rate of grid fees on the power generation side Integrated benchmark electricity price after linkage adjustment The expression is as follows: , (2).

[0032] Based on the hierarchical structure of cost transmission in the German Grid Charges Ordinance (StromNEV), inter-regional equilibrium adjustments primarily apply multiplicative scaling to end-user prices, while generation-side costs are initially deducted proportionally from the system's permitted revenue. Therefore, mathematically, they exhibit independent multiplier effects, as shown in the formula. The higher the value, the more the overall electricity price borne by the user decreases monotonically. The higher the threshold, the higher the inter-regional local premium that the region bears, and the benchmark electricity price rises monotonically.

[0033] The structural decomposition and time-of-use signal coupling of two-part tariffs: Introducing capacity charge percentages under the two-part tariff system. , and the proportion of commercial transition Fixed capacity unit price for various user types With variable electricity unit price Break it down into: (3) (4).

[0034] It should be noted that in the real electricity market, fixed capacity fees are typically charged based on maximum demand (€ / kW). Let the user... The equivalent utilization hours are: (Unit: h), then the actual fixed capacity unit price The conversion relationship with the equivalent electricity unit price is as follows: Due to the equivalent utilization hours of various users In single-period macroscopic optimization, it can be considered a constant, which does not change the gradient direction of Pareto optimization. To facilitate time-series calculations on the same scale as time-of-use electricity, the [variable name] in this model... The simplified expression is uniformly represented by "Volumetric Equivalent" to ensure dimensional consistency in the objective function calculation process.

[0035] In terms of physical mechanisms, since fixed capacity fees, once determined, do not dynamically change with the time of electricity consumption, end users only exhibit cross-time-based price elasticity responses to variable demand-side electricity fees. Therefore, a time-based electricity price signal strength adjustment function with a 24-hour time resolution is needed. Various types of users Comprehensive dynamic electricity price for different time periods The final coupling can be expressed as: (5).

[0036] Interpretability analysis of the mechanism: This structured decomposition model perfectly elucidates the impact of capacity fee ratio on the system's deep emission reduction target. The inherent transmission mechanism is evident from the above formula, when the capacity fee accounts for... When the weight of the fixed components increases, the fluctuation amplitude of the variable electricity fee increases. This is actively narrowed. In economics, this is known as the "passivation effect" of two-part electricity pricing on demand-side response; that is, the more fixed costs are recovered, the smaller the absolute difference in variable price signals, thus smoothing out users' willingness to shift load across time periods. This model ensures the completeness of the economic logic and the self-consistency of the monotonicity of the partial derivative gradient, laying a robust foundation for the scientific search of multi-objective algorithms within the feasible region.

[0037] 3. Construction of multi-objective optimization model This model aims to address the inherent contradictions of traditional pricing mechanisms in achieving a balance between social welfare, financial sustainability, and low-carbon transition within a unified framework. By introducing a weighted rolling response model based on typical days across the four seasons, the optimization time domain is extended to a year-round scale (4 seasons in total). 24 = 96 typical characteristic time periods). Let the typical day set be... These represent the four seasons: spring, summer, autumn, and winter. To facilitate data reproduction, the weights of the number of days in a year corresponding to each season are... According to the conventional practice of a macro-level average year for the power system, the number of days in spring (March-May) is 92, summer (June-August) is 92, autumn (September-November) is 91, and winter (December-February of the following year) is 90, thus satisfying the requirements. The initial baseline load curves for typical days in each season are as follows: (Unit: GW). Peak-valley electricity price ratio and energy storage discount Stimulated by price signals, the intraday time-of-use electricity price signal strength Maintain consistency across all seasons: (6) The average daily price signal strength for typical days in each season is .

[0038] 3.1 Objective 1: Minimize the overall average electricity price for all users in society (social affordability) Traditional models often use a fixed annual electricity multiplier for static weighted calculation of total costs. This ignores the effect of load-side net electricity transfer across time periods caused by time-of-use price fluctuations, which can easily lead to serious distortions in social welfare assessments. To address this, this invention constructs a load transfer and energy storage charge-discharge balance model with daily electricity conservation constraints.

[0039] 1) Price response to seasonal routine load and intraday electricity conservation: On a typical day in any season Within a certain period, when the electricity price is higher than the average... At that time, the conventional load reduction amount is defined as: (7) In the formula, =0.4 is the load transfer elasticity coefficient.

[0040] The total daily electricity reduction during this season is: (8).

[0041] Based on the principle of conservation of total daily electricity consumption, the reduced electricity is transferred in equal amounts to off-peak periods within the same day and evenly distributed across all off-peak periods; the increased load during off-peak periods in this season is: (9) in =7 represents the number of hours during the valley period.

[0042] 2) Seasonal "valley charging-peak discharging" energy balance model for energy storage systems: Energy storage systems on typical days in each season The valley period is subject to the discount factor The incentive is to charge, with the charging power base being the average load during the baseline off-peak period of that season. hook up: , (10) In the formula, This represents the energy storage response intensity coefficient.

[0043] Average load during the baseline valley period in each season The formal definition of (unit: GW) is: (11).

[0044] Energy storage system The actual round-trip charging and discharging efficiency, the total energy absorbed during the off-peak period is converted into discharge power during the peak period of the same day, and the hourly discharge load (negative value, representing a reduction in direct grid supply demand) for each peak period is: (12) in, =6 represents the number of hours during peak hours.

[0045] 3) Final seasonal net load curve and social average price objective function: In summary, the system has decision variables Typical days in a specific season Intraday dynamic net load curve The expression is as follows: (13).

[0046] The objective function is to minimize the comprehensive average electricity price for all users in society. Defined as the ratio of weighted total cost for all four seasons to total electricity consumption: (14) In the formula, The unit is Euros per kilowatt-hour (€ / kWh); real-time power load of various users by season and time of day. The unit is GW, and it is the total net load of the system by season. It was obtained by shifting and deconstructing according to the historical electricity consumption ratio of various types of users; This represents the time-of-use electricity price settlement value for each season.

[0047] 3.2 Objective Two: Minimize the deviation in time-sharing cost recovery for operators (long-term financial sustainability) Because this study introduces a power generation-side grid fee sharing lever (sharing rate) into its mechanism. The net cost target that the system needs to recover from the user side will be adjusted accordingly. To ensure the rigor of the financial analysis across the time span, the simple arithmetic average method based on four typical days was abandoned, and a method based on seasonal day weighting was constructed instead. Weighted Annual Time-of-Use Cost Recovery Absolute Relative Deviation (AARD) Objective Function : (15) In the formula, the dimension conversion coefficient is... Used to standardize the conversion of the product of electricity price (€ / kWh) and power load (GW) into euros per hour (€ / h). This represents the target baseline cost that the operator needs to recover in any single hour.

[0048] The following is obtained by amortizing the approved rigid annual total cost to the average annual total number of hours: (16) This formula implicitly assumes that the grid fees shared by the power generation side are evenly distributed throughout the year, which can effectively assess and smooth out the relative fluctuations and misalignments in the operator's cash flow under different load impacts in different seasons.

[0049] 3.3 Objective 3: Minimize system carbon emission intensity (electricity price-load-generation coupling model) This objective aims to minimize the annual average carbon emission intensity of the power system under a seasonally weighted architecture (unit: kgCO2 / kWh). Typical days for each season. Peak-period high carbon load reduction is defined as: (17).

[0050] Let the total electricity consumption during the baseline peak period of each season be: (18).

[0051] Peak period mixed marginal emission factor is (19).

[0052] The system's annual actual average carbon emission intensity objective function Expressed as the ratio of total weighted carbon emissions to total electricity consumption for the year: (20) In the formula, This represents the baseline total electricity consumption during off-peak hours in each season.

[0053] In summary, the NSGA-III multi-objective optimization model for transmission and distribution pricing design is as follows: (twenty one).

[0054] 4. Constraints and Handling Strategies 4.1 Optimize the model constraint system The multi-objective optimization constraint system for transmission and distribution prices constructed in this model is divided into a two-level architecture of hard constraints and soft constraints: 1) Hard constraints (spatial direct filtering layer) Hard constraints are rigid deadlock lines at the boundary between physics and mathematics, and are absolutely exclusive in the exploration of the solution space: ① Boundary constraints of decision variables: (twenty two) Decision vector The physical value range of each continuous variable is strictly limited to the policy legal boundaries listed in Table 1.

[0055] ② Non-negativity constraint on electricity prices: (twenty three) Ensure the physical and economic feasibility of electricity pricing for each time period within the day; Note: The system's daily total power conservation and the energy balance of "valley charging-peak discharging" for energy storage have been internalized in the load response model in Section 3.1. This is a self-consistent structure and does not require additional external equation hard constraints.

[0056] 2) Soft constraints (algorithm optimization guidance layer) Soft constraints allow for moderate violations in the early stages of algorithm iteration to ensure the breadth of exploration of high-dimensional Pareto fronts, and include the following four types of policy regulatory red lines: ① Constraints on the rationality of electricity price structure and hierarchy: To avoid price inversions among electricity users and maintain the strength of time-of-use incentives, soft constraints are introduced regarding electricity price sequence and peak-valley transmission and distribution price differences: (twenty four) (25).

[0057] ② Regulatory price red line and adjustment rate constraints: To ensure the affordability of public welfare and prevent dumping pricing, a comprehensive benchmark electricity price will be set. Imposing upper limits, lower limits for industrial production, and interannual steady transition rate constraints: (26) (27).

[0058] ③ Weighted average price and short-run marginal cost constraints of the system: Ensure that the weighted average price of electricity consumption for transmission and distribution across society is not lower than the short-term marginal cost red line of the power system, and maintain the financial bottom line: (28).

[0059] ④ Constraints on power grid investment returns and asset structure rationality: In accordance with basic regulatory principles, reasonable ranges for return on investment (ROI) and the proportion of power transmission and distribution network assets for operators are limited: (29) (30) In the formula, This is the annual equivalent value of the total network fee revenue generated by the system throughout the day on both sides.

[0060] ⑤ Low-carbon transition and macroeconomic policy constraints: Based on the Climate Act and the phase-out policy of coal, the following constraints are imposed: an annual total carbon emissions cap, a lower limit on the proportion of renewable energy (RES) consumption, total coal-fired power generation control, and a feasible lower bound on carbon emission intensity. (31) (32) (33) In the formula, This is the power curtailment adjustment factor. , (34) (35).

[0061] 4.2 Standardization strategies based on the principle of constraint dominance To address the Pareto dominance distortion problem caused by differences in objective dimensions in multi-objective optimization, this paper abandons the traditional static large constant penalty term accumulation method and calculates the normalized global constraint violation degree of each individual objective separately. : (36) In the formula, This represents the normalized form of inequalities for each conventional soft constraint. and These are the normalization constants for each constraint. To eliminate the subjectivity of parameter setting, the above normalization constants are calculated by performing 1000 random samplings (with decision variables uniformly distributed within the value range) to determine the violation amount of each constraint, and then taking the 95th percentile. This setting ensures that the individual violation degree of the vast majority of exploratory solutions stably falls within the [0,1] interval.

[0062] During population reproduction and the generation of new individuals by evolutionary operators, variables exceeding the boundary are forcibly corrected using the reflection method (reflecting back the excess portion) to ensure statistical diversity of the population. In the non-dominated ranking phase of environmental selection, the comparison of individual merits strictly follows the constrained dominance principle: If both solutions are feasible ( Then, based on the objective function... Perform a standard Pareto dominance comparison; If one solution is feasible while the other is infeasible ( ( ), feasible solutions absolutely dominate infeasible solutions; If both solutions are infeasible, then the normalized global constraint violation degree is... The smaller one dominates the larger one.

[0063] This strategy completely decouples the constraint penalty from the target value algebraically, avoids the distortion of high-dimensional dominance relations, and all soft constraint violations are only used to guide the optimization direction in the infeasible region, without affecting the final Pareto front target value.

[0064] 5. Multi-objective solution strategy based on NSGA-III 5.1 Principle of the Reference Point-Driven NSGA-III Algorithm The established three-dimensional conflict objective space of "social welfare, financial stability, and low-carbon transition" constitutes a typical high-dimensional multi-objective optimization problem. Traditional non-dominated ranking algorithms (such as NSGA-II) are prone to losing optimization pressure due to the "surge in the proportion of non-dominated solutions" when the objective dimension increases to three dimensions or more. Therefore, this framework adopts the reference-point based NSGA-III algorithm for global optimization. Its core lies in introducing the Das-Dennis systematic method to generate a uniformly distributed hyperplane of reference points in the three-dimensional objective space, replacing the crowding distance calculation of traditional algorithms, and fundamentally ensuring that the obtained policy set can broadly cover all extreme policy preferences and intermediate compromise zones.

[0065] 5.2 Customized Solution Process for Multi-Objective Optimization of Transmission and Distribution Prices The NSGA-III closed-loop solver execution flow designed for this invention is as follows: 1) Population Initialization and Boundary Reflection: Based on the legal boundaries of the eight decision variables in Section 2.1 (Table 1), an initial population with high spatial uniformity is generated using a Sobol pseudo-random sequence. In subsequent evolution, if crossover mutations produce individuals that cross the boundary, a boundary reflection method is used to forcibly pull them back into the feasible region to ensure genetic diversity.

[0066] 2) Temporal Coupling and Electricity Price-Load Reconfiguration: This involves integrating the data carried by individual populations... to The policy-related data is substituted into the structured two-part mapping model in Section 2.2 to calculate the comprehensive benchmark electricity price and time-of-use electricity price for various types of users. Subsequently, it is input into the load transfer and energy storage charge-discharge balance model defined in Section 3 to reconstruct the dynamic net load curves for typical days in the four seasons. .

[0067] 3) Objective Calculation and Soft Constraint Normalization: Based on the reconstructed physical-temporal boundary, calculate the three core fitness objectives of the individual. Simultaneously, based on Section 4.2, the absolute violation amount of each soft constraint is calculated and divided by the 95th quantile normalization constant to generate the overall constraint violation degree for that individual. .

[0068] 4) Non-dominated sorting based on the constraint dominance principle: This method abandons the traditional static large constant penalty function and strictly enforces the constraint dominance principle outlined in Section 4.2 during the environment selection phase. (By comparison...) The size and feasibility of the population should be considered to guide it towards the physically and financially feasible domain.

[0069] 5) Reference Point Association and Environment Selection: For individuals at the critical non-dominated level, calculate their vertical distances to the associated rays of each reference point in the three-dimensional target space. Prioritize retaining the solution that is closest to the ray of a specific policy preference and has the fewest associated individuals to carry over to the next generation, in order to maintain the extreme homogeneity of the Pareto front in high-dimensional space.

[0070] 6) Genetic Operators and Iteration Termination: The population produces offspring through simulated binary crossover (SBX) and polynomial mutation. The above evaluation, sorting, and selection process is repeated until the maximum number of iterations is reached. Output the final Pareto optimal policy solution set.

[0071] Data Analysis and Results Discussion This invention is based on the constructed NSGA-III multi-objective optimization framework and uses actual data from Germany's power transmission and distribution system in 2024 to solve and verify the model. First, it compares the performance of NSGA-III and NSGA-II in high-dimensional objective spaces. Second, it systematically analyzes the distribution characteristics of the Pareto front, revealing the nonlinear trade-offs among the three objectives, and focuses on explaining the extremely narrow physical constraint of carbon emission intensity variation. Finally, through statistical analysis of decision variables and parallel coordinate plots, it conducts global sensitivity analysis of parameters, dissecting the optimization direction and emission reduction effectiveness of eight policy levers, laying the foundation for extracting typical policy solutions.

[0072] 1. Experimental setup 1.1 Data Source Using the German power transmission and distribution system as an empirical example, the specific parameter values ​​required for the model solution (including grid cost, benchmark electricity price, carbon emission parameters, and elasticity coefficients) are detailed in the appendix. The main data sources are explained below: Permitted revenue for transmission and distribution networks (TSO) and total system service costs: Annual permitted revenue for transmission networks (TSO) and distribution networks (DSO) is derived from the regulatory report published by the German Federal Network Agency (BNetzA) in 2024, and the target benchmark cost per hour for grid operators is calculated accordingly.

[0073] Load curve sequence: 24-hour baseline load data for typical days in spring, summer, autumn and winter, taken from the European Transmission Network Operators Alliance (ENTSO-E) 2024 Transparency Platform, covering the actual historical load of the entire German grid.

[0074] Electricity price benchmarks by user category: The comprehensive electricity price benchmark values ​​for three types of end users—residential, commercial, and industrial—are taken from the official energy price statistics of the Federal Statistical Office of Germany (Destatis) for 2024.

[0075] System carbon emission parameters: marginal carbon emission factors of coal-fired and gas-fired units, average baseline emission factors during off-peak periods, proportion of coal-fired power during peak periods, and maximum annual power generation of renewable energy, etc., are comprehensively referenced from macroeconomic statistical reports of the German Federal Environment Agency (UBA) and the German Energy Balance Working Group (AG Energiebilanzen).

[0076] Soft constraint normalization constant: It is obtained by performing 1000 uniform random samplings of the decision variables within the boundary interval, calculating the violation amount of each constraint, and calibrating it using the 95th percentile.

[0077] 1.2 Algorithm Parameters and Tools Optimization Algorithms: Both NSGA-III and the comparative algorithm NSGA-II were implemented using a self-programmed approach on the MATLAB R2024b platform. NSGA-III uses the Das-Dennis method to generate reference points, dividing the 3D target space into H=91 reference points. The population size was set to... Maximum number of generations The genetic operator uses simulated binary crossover (SBX). ) and polynomial variation ( The constraint handling follows the constraint dominance principle described in Section 2.5.2. To eliminate the influence of randomness, each algorithm is run independently 20 times. The Pareto solution set given in the report is obtained from one run corresponding to the median IGD of the 20 runs.

[0078] 2. Algorithm Performance Comparison and Convergence Analysis To verify the superiority of NSGA-III in handling three-dimensional conflict target spaces, it was compared with the classic multi-objective evolutionary algorithm NSGA-II. Performance evaluation used three standard metrics: Inverted Generational Distance (IGD, a comprehensive indicator of solution set convergence and diversity), Spacing (a measure of the uniformity of solution set distribution), and running time. Statistical results from 20 independent runs are shown in Table 2.

[0079] Table 2 Performance Comparison of NSGA-II and NSGA-III (Statistics from 20 Independent Runs)

[0080] (1) Convergence and diversity analysis The mean IGD of NSGA-III (0.009786) is better than that of NSGA-II, and the standard deviation is smaller, indicating that NSGA-III can stably obtain a solution set that is closer to the true frontier and has a wider distribution.

[0081] Depend on Figure 4 , Figure 5 , Figure 6 It can be seen that the three objective functions of NSGA-III ( All of these decreased rapidly and stabilized within approximately 300 generations. In contrast, NSGA-II prematurely entered local optima in some runs, resulting in a higher financial deviation. The fluctuation range of ) is significantly greater than that of NSGA-III.

[0082] (2) Analysis of uniformity of solution set distribution The mean spacing of NSGA-III (0.000654) is significantly better than that of NSGA-II (0.000844). This indicates that the reference point-based environment selection mechanism effectively replaces the crowding distance in NSGA-II, avoiding the "loss of selection pressure" caused by the surge of non-dominated solutions in high-dimensional objective space.

[0083] Figure 7 and Figure 8 The scatter plot comparison further confirms that the solution set of NSGA-III is uniformly distributed in a network, while NSGA-II has obvious clusters and frontier "holes". This characteristic provides a continuous and refined selection space for multi-criteria decision-making of subsequent policy options.

[0084] (3) Computational efficiency analysis Despite the introduction of a reference point mechanism, the average runtime of NSGA-III (12.72 s) is still slightly shorter than that of NSGA-II (13.07 s), confirming the computational efficiency of its associative operations in high-dimensional non-dominated sorting. In conclusion, NSGA-III is suitable as the solution engine for this problem.

[0085] 3. Analysis of trade-offs in the Pareto front Figure 8 The paper presents a trade-off surface in three-dimensional space for three optimization objectives and its two-dimensional projection. From the spatial topological distribution characteristics of this surface, the following key nonlinear game relationships can be extracted and revealed: Carbon emission targets ( ) and economic / financial goals ( Strong nonlinear competition: "L-shaped" boundary observation and A two-dimensional projection of the plane can reveal the system's carbon emission intensity. ) and the average price of the whole society ( Cost recovery deviation () Both exhibit a highly pronounced "L-shaped" competition boundary. When the permissible carbon emission intensity... When the electricity price is slightly more lenient (above 0.312230 kg CO2 / kWh), Financial Deviation All can remain stable at a low, flat tail; however, when attempting to... When the limiting pressure drops below 0.312225 kgCO2 / kWh, and All experienced a steep, exponential deterioration. It climbed sharply towards 0.06288 € / kWh. (Surges to above 0.128). This profoundly reveals the dramatic marginal cost effect of deep decarbonization: after breaking through a certain point, if the load is forcibly transferred by simply relying on extreme electricity price leverage (such as maximizing the peak-valley price difference), it will not only significantly increase the electricity settlement cost of the whole society, but also seriously distort the time-series revenue structure of the power grid, triggering uncontrollable financial risks.

[0086] Average electricity price ( ) and cost recovery deviation ( The squeezed, unidirectional synergistic characteristics differ from the intuitive assumption that "lower electricity prices inevitably lead to grid losses." Observation The Pareto scatter plot, when projected onto a plane, exhibits a diffuse, quasi-positively correlated distribution. This unique geometric characteristic suggests that within the constraint space of multi-objective optimization, and It exhibits high synergy. Without pursuing extreme low-carbon emissions, the system can achieve both low user electricity prices and good financial stability through a reasonable capacity / electricity cost structure configuration. (Scatter plot) and The simultaneous deterioration (spreading towards the upper right corner) is actually due to both being subjected to extreme emission reduction targets (low emissions). The squeeze. This finding provides an important basis for policymaking: regulators can confidently... and Within the collaborative safety zone, parameter fine-tuning should be carried out, primarily to prevent external shocks brought about by extreme emission reduction pressures.

[0087] Quantitative confirmation of the "physical ceiling" for emissions reduction: It is worth noting that although the leading edge surface exhibits drastic topological changes, the system... The absolute optimization margin of the dimension is only about 0.09% (extremely narrow absolute range). This is not a defect in the model's optimization ability, but rather a profound revelation of the "physical emission reduction ceiling" of demand-side electricity price leverage in the short term. Under the assumption of "exogenously fixed power structure" in this paper, demand-side price response can only change the output timing of high-carbon and low-carbon units, not the overall low-carbon installed capacity ratio of the system. According to the model's quantitative calculations, even if the peak-valley price difference leverage is pulled to the theoretical upper limit (multiplier of 3.0), the maximum amount of electricity it can drive to transfer is only a very small proportion of the total grid load. The corresponding theoretical maximum emission reduction potential is strictly limited by the marginal output share of coal-fired power at this time, which is completely consistent with the Pareto improvement of 0.09%. This quantitative finding confirms from a mathematical and physical perspective that transmission and distribution price reform must be strongly coupled with deep decarbonization investment on the supply side (such as coal phase-out plans and new energy capacity expansion). Relying solely on demand-side price response cannot cross the systemic emission reduction gap.

[0088] 4. Global sensitivity analysis of decision variables and the effectiveness of policy levers In multi-objective optimization problems, the distribution span (interquartile range, IQR) of decision variables in the Pareto solution set directly reflects the global sensitivity of the system's objectives to that parameter. The more concentrated the distribution (the narrower the box), the more sensitive the objective is to that variable, and the smaller its policy compromise space. The wider the distribution, the lower the sensitivity and the higher the policy operational flexibility. Figure 9 The statistical distribution characteristics of eight decision variables in 80 Pareto optimal solutions are presented. Figure 10 This further reveals the sensitivity correlation between each variable and the three objectives.

[0089] 1) Energy storage charging discount factor ( Extremely sensitive variables and their theoretical warnings Of all 80 optimal solutions All values ​​are taken near the absolute lower limit of its defined interval [0.01, 1.0] (median 0.0156, meaning only 1.56% transmission and distribution fee is charged). The extremely narrow distribution of this variable indicates a very high sensitivity to the system's low-carbon and economic goals. Regardless of policy preferences, the Pareto optimal strategy requires reducing energy storage charging costs to near zero. This purely theoretical optimization result profoundly reveals the current German policy (…). The complete elimination of energy storage transmission and distribution fees (without any discount) is a serious underutilization of incentives for flexible resources like energy storage. While pure mathematical optimization points to an extremely low discount, in actual regulation, a complete exemption of transmission and distribution fees for energy storage could trigger a "death spiral" in fixed cost recovery. If energy storage installations surge and consume grid capacity without sharing costs, the remaining costs will be forced to be passed on to regular users. Therefore, this extreme optimization value (without any discount) is insufficient to incentivize flexible resources like energy storage. This should be understood as a long-term theoretical optimization direction, rather than an immediate policy that can be implemented in one step.

[0090] 2) Peak-valley electricity price multiplier ( Highly sensitive rigid lever The optimized median is 2.83, and the box is also compact, significantly higher than the current level (approximately 1.8), which is high. (>2.8) corresponds to a low-carbon solution, low (<2.0) corresponds to a high-carbon scheme, but exceeding 2.95 will lead to a worsening of financial deviation, indicating that maintaining a ratio of around 2.83 is a rigid requirement to balance the demands of all parties.

[0091] 3) Regional cost equilibrium ( ) and sharing of grid fees on the power generation side ( ) The median of 0.94 indicates that moderately distributing the network costs of high-renewable energy regions across the country is Pareto optimal. The median is only 0.016, close to the lower limit and the box is extremely narrow, indicating that the system is extremely sensitive to the cost transmission to the power generation side. Excessive transmission will reduce the allowable revenue base, forcing an increase in the proportion of capacity fees, which in turn "dulls out" demand response and undermines emission reduction targets.

[0092] 4) Capacity fee percentage ( ) and scheduling coefficient ( ) Median 0.54, The median is 0.58, all within the upper-middle range with a large interquartile range. This indicates that financial and carbon emission targets are relatively insensitive to the proportion of capacity fees, giving regulators greater flexibility for structural fine-tuning. Maintaining a high proportion of fixed costs helps stabilize operator revenue (improving...). ). The median of 0.94 indicates that prioritizing the dispatch of renewable energy is a consensus among all optimal solutions.

[0093] Extraction and comparison of typical policy options To transform the Pareto optimal solution set into specific solutions that can be directly referenced by policymakers, K-means clustering and multi-criteria decision-making methods are used to extract three typical policy options, which are then compared with the current mechanism in Germany in 2024. A phased reform path is then proposed, and the limitations of the model are discussed.

[0094] 1. Extraction of typical schemes based on K-means clustering For the three objective values ​​in the Pareto optimal solution set ( After Min-Max normalization, the solution set was clustered into three classes using the K-means clustering algorithm (with K=3 determined by the elbow rule). The solution closest to the cluster center in each cluster was selected as the representative, and its decision variables and objective values ​​are shown in Table 3.

[0095] Table 3 Comparison of decision variables and target values ​​between three typical policy options and the existing German mechanism.

[0096] 2. Analysis of Typical Pareto Schemes and Policy Implications Three typical Pareto optimal solutions extracted based on K-means clustering map the regulatory deduction paths under different policy preferences. By analyzing the multidimensional mapping relationship between decision variables and objective functions, the following policy implications can be derived: Economic priority approach: a short-term strategy that sacrifices systemic sufficiency and environmental benefits. The optimization logic of this scheme tends to control the direct electricity costs for end users, setting the proportion of residential and industrial capacity fees at relatively low levels of 0.48 and 0.55 respectively, while matching a relatively conservative peak-valley electricity price multiplier. ) and a higher generation-side grid fee sharing ratio ( Although this parameter combination makes the overall average price... It drops to the lowest of the three at €0.06286 / kWh, but its systemic disadvantages are significant: the absolute deviation in time-sharing cost recovery for operators ( The carbon emission intensity (PEI) is as high as 0.1285, which, in the long term, will lead to a lag in the recovery of grid investment costs, thereby jeopardizing the system adequacy under a high proportion of renewable energy integration; at the same time, the weak electricity price signal leads to a decrease in carbon emission intensity (PEI). The CO2 / kWh level is at a high level of 0.31228 kgCO2 / kWh. Therefore, this scheme can only serve as a short-term emergency intervention benchmark to cope with extreme inflationary pressures and does not have long-term regulatory sustainability.

[0097] Low-carbon priority approach: A radical decarbonization vision driven by strong price signals This scheme aims to explore the limits of emission reduction potential in demand-side response. Within the decision space, the peak-valley electricity price multiplier (…) The average electricity price was driven up to a high of 2.95, while the proportion of residential and industrial capacity fees was significantly increased to 0.60 and 0.62 respectively to hedge against the risk of extremely volatile electricity revenue. Through the synergistic effect of these strong leverages, the system's carbon intensity was reduced to 0.31220 kgCO2 / kWh. However, achieving this environmental benefit was accompanied by significant socioeconomic frictions: the average electricity price for users... The peak price has climbed to €0.06296 / kWh, and the overly aggressive peak-to-valley price spread could impose a disproportionate financial burden on users with rigid demand who lack load shifting capabilities. This scheme is more suitable as a long-term policy reserve for Germany's deep decarbonization phase by 2035.

[0098] Balanced Development Approach: A Feasible Regulatory Compromise for Synergistic Optimization of Multi-Dimensional Objectives This plan exhibits a significant "compromise" characteristic in its various policy levers, demonstrating excellent marginal effectiveness. Compared to the economy-first plan, its end-user electricity price... The price increased only slightly to €0.06292 / kWh, but this resulted in a slight deviation in cost recovery. The scheme sets a peak-to-valley ratio (the lowest among the three categories) and a significant improvement in carbon emission intensity. ) and energy storage discount ( This approach effectively activates the flexibility resources on the load side. Comprehensive evaluation shows that the scheme effectively internalizes the tripartite conflict between user affordability, grid financial soundness, and low-carbon incentives, and is recommended as the core benchmark for the next cycle of grid fee reform.

[0099] 3. Comparative Analysis of the Optimized Plan and the Current Regulatory Mechanism (2024 Benchmark) To quantify the empirical value of this multi-objective optimization framework, a horizontal comparison is made between the Pareto optimal solution and the actual transmission and distribution price structure in Germany in 2024. Based on the annual regulatory report of the German Federal Network Agency (BNetzA), the estimated baseline parameters for 2024 are as follows: The comparison and optimization results reveal the following structural characteristics and areas for improvement in the current policy: 1) Empirical calculations of the Pareto improvement potential of multi-dimensional regulatory objectives show that, in 2024, the current mechanism's user electricity price burden, cost recovery deviation, and carbon emission intensity have not reached the optimal frontier. Compared to the current benchmark, the "balanced development scheme" proposed in this paper theoretically achieves a Pareto improvement of 1.38% in average price, 10.9% in cost recovery deviation, and 0.09% in carbon emission intensity. Crucially, this small carbon emission reduction of 0.09% quantifies at the physical level that, under the rigid boundary of a fixed short-term installed capacity structure on the power supply side, the emission reduction efficiency relying solely on demand-side electricity price leverage has a strict physical ceiling.

[0100] 2) Structural gap in incentives for flexible resources such as energy storage: Under the current mechanism, the discount coefficient for energy storage charging ( There are almost no substantial benefits. Furthermore, the global optimization results of the NSGA-III algorithm show that, regardless of whether the priority is economic or low-carbon, all Pareto optimal solutions will... The parameter space is strongly pushed towards the lower limit of its feasible region (approximately 0.015 within the range [0.01, 1.0]). This huge contrast in parameter space profoundly reveals that Germany's current two-part grid tariff system has a significant incentive-suppression effect on energy storage participation in system regulation, and there is an urgent need to introduce a deep-targeted discount rate in the next regulatory cycle.

[0101] 3) Insufficient release of demand-side response price signals: Germany's current peak-valley electricity price ratio (1.85) is significantly lower than the optimized recommended value (2.33) of the balanced development scheme and the extreme value (2.78) of the low-carbon scheme. The weak time-of-use price difference cannot effectively cover the sunk costs of enterprises adjusting production shifts or residents purchasing smart home appliances, resulting in the insufficient activation of the elastic potential of demand-side response. Appropriately widening the peak-valley transmission and distribution price difference is a necessary prerequisite for realizing the spatial and temporal transfer of load and smoothing peak grid investment.

[0102] in conclusion This invention focuses on the triple conflict between user affordability, grid financial sustainability, and low-carbon transition incentives faced by transmission and distribution pricing mechanisms in high-proportion renewable energy power systems. It constructs a multi-objective optimization framework based on NSGA-III and, using the German transmission and distribution pricing system as an empirical benchmark, systematically analyzes the trade-offs of eight policy levers in a high-dimensional objective space under specific model boundary assumptions. The main research conclusions are as follows: First, there are clear nonlinear competitive boundaries among the multiple objectives. The average user electricity price and cost recovery deviation exhibit an "L-shaped" competitive relationship; excessively lowering electricity prices will severely erode time-of-use cost matching and jeopardize the financial soundness of the power grid. Carbon emission intensity and cost recovery deviation, on the other hand, have an approximately linear trade-off; widening the time-of-use price difference can encourage load shifting to low-carbon off-peak periods, but it will drastically disrupt the fare base distribution. Furthermore, due to the physical rigidity of the power supply structure in the short term, the emission reduction effect relying solely on demand-side electricity price leverage has a strict upper limit. In the short to medium term, with a fixed supply-side power supply structure, the absolute emission reduction effect relying solely on transmission and distribution prices—a demand-side lever—has a strict physical upper limit (less than 0.1% in this empirical calculation). This finding reveals that demand response plays a more "auxiliary smoothing" rather than an "absolutely dominant" role in emission reduction, providing quantitative evidence for policymakers to avoid unrealistic carbon reduction expectations based solely on price mechanisms.

[0103] Second, under the closed-system model, the sensitivity of policy levers exhibits significant differentiation. Global sensitivity analysis shows that peak-valley electricity price ratios and energy storage charging discount coefficients are highly sensitive rigid levers. Model optimization results show that all Pareto optimal solutions point to reducing energy storage transmission and distribution price discounts and widening peak-valley ratios. This theoretically reveals the problem that the lack of discount mechanisms and smooth time-of-use pricing are insufficient incentives for flexible resources such as energy storage, pointing to potential optimization directions for future mechanism design.

[0104] Third, the extraction of typical scenarios provides a quantitative reference for extrapolating different preferences. Based on the three scenarios generated by clustering—economic priority, balanced development, and low-carbon priority—the compromise trajectories among different objectives are shown. Among them, the balanced development scenario, under the model calculation, achieves strict Pareto improvements compared to the baseline in terms of average user price (reduction of 1.38%), cost recovery deviation (improvement of 10.9%), and carbon emission intensity (reduction of 0.09%), and can serve as a theoretical baseline scenario for balancing the interests of multiple parties.

[0105] Based on the above conclusions and considering the model's boundary constraints, this invention proposes the following policy implications: Transmission and distribution pricing reform should not pursue a single, extreme approach, but rather explore a gradual, coordinated evolution path. Model results suggest that, while preventing the loss of fixed grid costs (i.e., the risk of a "death spiral"), regulatory agencies could consider introducing tiered transmission and distribution pricing discounts for energy storage in stages, and appropriately widening the peak-valley price difference, using controllable financial shocks to activate initial demand-side response. Simultaneously, given that electricity price leverage faces physical emission reduction limits, transmission and distribution pricing reform must be coordinated with deep decarbonization investment on the supply side and the coal phase-out process to ensure the achievement of carbon reduction targets.

[0106] Finally, it must be emphasized that this study has limitations. The specific numerical optimization results obtained (such as extremely low energy storage discount coefficients or specific peak-valley ratios) should not be directly regarded as immediate adjustment suggestions for current policies. This model is based on a single-node closed grid and a typical daily static architecture, and has not yet incorporated the mutual benefit effect of cross-border green electricity trading in the European Internal Energy Market. Furthermore, the model does not consider the long-term dynamic investment response of extreme electricity price leverage to energy storage capacity installation and grid expansion, does not characterize the micro-level heterogeneous behavioral biases of different end-user groups in price response, and does not employ a long-term time-series simulation of 8760 hours per year. Future research needs to incorporate Dynamic Stochastic General Equilibrium (DSGE) analysis, multi-regional interconnected networks, and multi-agent game theory into the optimization framework to comprehensively assess the long-term macroeconomic effects and physical operational safety of extreme electricity price leverage in complex real-world systems.

[0107] To address the challenge of synergistically balancing the three heterogeneous objectives of user affordability, grid financial sustainability, and low-carbon transition incentives in the energy transition and deep decarbonization of the power system, previous studies have largely focused on single actors or single policy levers, and generally adopted fixed weights to aggregate multiple objectives into a single-objective optimization problem. However, such methods fail to reveal the inherent non-dominant trade-offs between objectives and lack a unified model for the interconnected effects of multiple policy levers. To solve these problems, this invention proposes a multi-objective optimization design framework for transmission and distribution pricing based on NSGA-III. Using the German transmission and distribution pricing system as an empirical benchmark, this method parameterizes five categories of policy levers into eight decision variables, constructing a multi-objective optimization model that coordinates the interests of government regulation, consumer welfare, and grid operators. Simultaneously, a price-load-carbon emission coupling model is introduced to quantify the dynamic impact of time-of-use pricing structure on the system's carbon emission intensity. Utilizing the reference point mechanism of NSGA-III, this invention generates a uniformly distributed Pareto optimal solution set, which is summarized into three typical scenario schemes: economic priority, balanced development, and low-carbon priority. Case studies based on the model specification show that, compared to the current baseline estimate, the balanced development scheme theoretically achieves a Pareto improvement of 1.38% in average price, 10.9% in cost recovery deviation, and 0.09% in carbon emission intensity. Further global sensitivity analysis reveals that the optimal solutions in the model all point to a significant reduction in the energy storage charging discount coefficient and a widening of the peak-valley electricity price multiplier, suggesting that under the closed-system assumption, there is theoretical room for optimization in the current mechanism's incentive for flexible resources. Since the model does not yet incorporate macroeconomic factors such as cross-border electricity trading, micro-level heterogeneity, and long-term investment response, the multi-objective optimization framework and specific parameter optimization results obtained in this invention mainly provide theoretical reference and sandbox decision-making support for the comprehensive reform of transmission and distribution prices in countries with high proportions of renewable energy, oriented towards scenario simulation.

[0108] name: .

Claims

1. A multi-objective optimization method for transmission and distribution prices based on a multi-objective genetic algorithm, characterized in that: The steps are as follows: S1. A multi-objective parameterized optimization framework for the derivation of transmission and distribution pricing policies is proposed: five major categories of policy levers, namely regional sharing, generation and consumption sharing, capacity-electricity structure, time-of-use differences and low-carbon incentives, are uniformly parameterized into eight continuous decision variables, and a multi-objective optimization model covering government regulation, consumer welfare and coordination of the diverse interests of grid operators is constructed. S2. Introduce the NSGA-III algorithm to solve the high-dimensional trade-off problem in transmission and distribution price regulation; S3. Generate interpretable typical policy solutions based on actual data: Three scenario solutions were extracted through clustering and multi-criteria decision analysis: economic priority, balanced development and low-carbon priority.

2. The multi-objective optimization method for transmission and distribution prices based on a multi-objective genetic algorithm according to claim 1, characterized in that: Construction of a multi-objective optimization model: Let the typical day set be These represent the four seasons: spring, summer, autumn, and winter, with each season corresponding to a weighted number of days in the year. Set according to the convention of a macro-level flat year in the power system, satisfying ; The initial baseline load curves for typical days in each season are as follows: Peak-valley electricity price ratio and energy storage discount Stimulated by price signals, the intraday time-of-use electricity price signal strength Maintain consistency across all seasons: （6） The average daily price signal strength for typical days in each season is ; 1) Objective 1: To minimize the overall average electricity price for all users in society, a load transfer and energy storage charge / discharge balance model with daily electricity consumption conservation constraints was constructed: （13） In the formula, Typical daytime period The initial baseline total load, This refers to the load reduction during periods when prices are above average. To reduce the amount of electricity redistributed to off-peak hours during off-peak periods, To increase the load for charging energy storage systems during off-peak hours, This effectively reduces the load during peak discharge periods of the energy storage system. The objective function is to minimize the comprehensive average electricity price for all users in society. Defined as the ratio of weighted total cost for all four seasons to total electricity consumption: （14） In the formula, The system calculates the seasonal and time-of-use real-time power load for various user groups, based on the total net load for each season. It was obtained by shifting and deconstructing according to the historical electricity consumption ratio of various types of users; This represents the time-of-use electricity price settlement value for each season. 2) Objective 2: Minimize the deviation in time-sharing cost recovery for operators, and construct a weighted system based on seasonal days. Weighted annual time-sharing cost recovery absolute and relative deviation objective function : （15） In the formula, the dimension conversion coefficient is... Used to standardize the conversion between the product of electricity price and power load. This represents the target baseline cost that the operator needs to recover in any single hour. 3) Objective 3: Minimize the system's carbon emission intensity; the objective function for the system's annual actual average carbon emission intensity. Expressed as the ratio of total weighted carbon emissions to total electricity consumption for the year: （20） In the formula, This represents the baseline total electricity consumption during off-peak hours in each season. In summary, the NSGA-III multi-objective optimization model for transmission and distribution pricing design is as follows: （21）。 3. The multi-objective optimization method for transmission and distribution prices based on a multi-objective genetic algorithm according to claim 1, characterized in that: The multi-objective solution process of introducing the NSGA-III algorithm: 1) Population initialization and boundary reflection: Based on the legal boundaries of 8 decision variables, an initial population with high spatial uniformity is generated using Sobol pseudo-random sequences. In subsequent evolution, if crossover mutations produce individuals that cross the boundaries, the reflection boundary method is used to force them back into the feasible region to ensure genetic diversity. 2) Temporal Coupling and Electricity Price-Load Reconfiguration: This involves integrating the data carried by individual populations... to Policy-related factors are substituted into a structured two-part mapping model to calculate the comprehensive benchmark electricity price and time-of-use electricity price for various types of users. Subsequently, these are input into a load transfer and energy storage charge-discharge balance model to reconstruct the dynamic net load curves for typical days in the four seasons. ; 3) Objective Calculation and Soft Constraint Normalization: Based on the reconstructed physical-temporal boundary, calculate the three core fitness objectives of the individual. , , Simultaneously, based on the absolute violation of each soft constraint and divided by the 95th quantile normalization constant, the overall constraint violation rate for that individual is generated. ; 4) Non-dominated sorting based on the constraint dominance principle: Abandoning the traditional static large constant penalty function, this method strictly enforces the constraint dominance principle during the environment selection phase, and compares... Based on the size and feasibility, priority should be given to guiding the population to converge toward the physically and financially feasible domain; 5) Reference point association and environment selection: For individuals at the critical non-dominated level, calculate their vertical distances to the associated rays of each reference point in the three-dimensional target space; 6) Genetic Operators and Iteration Termination: The population generates offspring through simulated binary crossover and polynomial mutation. The above evaluation, sorting, and selection process is repeated until the maximum number of iterations is reached. Output the final Pareto optimal policy solution set.

4. The multi-objective optimization method for transmission and distribution prices based on a multi-objective genetic algorithm according to claim 3, characterized in that: The aforementioned soft constraints include the following four types of policy regulatory red lines: ① Constraints on the rationality of electricity price structure and hierarchy: （24） （25） ② Regulatory price red lines and adjustment rate constraints: （26） （27） ③ Weighted average price and short-run marginal cost constraint of the system: （28） ④ Constraints on power grid investment returns and asset structure rationality: （29） （30） In the formula, This is the annual equivalent value of the total network fee revenue generated by the system throughout the day on both sides. ⑤ Low-carbon transition and macroeconomic policy constraints: （31） （32） （33） In the formula, This is the power curtailment adjustment factor.

5. The multi-objective optimization method for transmission and distribution prices based on a multi-objective genetic algorithm according to claim 3, characterized in that: Overall constraint violation rate as follows: （36） In the formula, This represents the normalized form of inequalities for each conventional soft constraint. and is the normalization constant for each constraint.

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