Power grid planning equalization optimization method and device based on GAN driving learning

Abstract

The invention belongs to the technical field of power grid optimization, and particularly relates to a GAN driven learning-based power grid planning equalization optimization method and device, and the method comprises the steps: constructing a physical constraint-based space-time generative adversarial network PI-ST-GAN, building a composite risk index, and screening out a high-risk scene from a generated source-load probabilistic time sequence scene; constructing a risk-cost balanced double-layer optimization model; reconstructing the double-layer optimization model into a single-layer mixed integer programming (MIP) model based on a strong dual theory, and setting constraint conditions of the single-layer mixed integer programming (MIP) model; based on a single-layer mixed integer programming MIP model, a solver is utilized to carry out joint solution on a line investment scheme and operation scheduling variables, PI-ST-GAN is dynamically guided to enhance high-risk scene generation according to a solution result, an optimization-generation-feedback closed-loop collaborative iteration solution process is realized, and finally an optimal power grid planning scheme is output. The method can improve the toughness and economical efficiency of a power grid under the high permeation of renewable energy sources.

Description

Technical Field

[0001] The present invention belongs to the technical field of power grid optimization, and specifically relates to a method and device for balanced optimization of power grid planning based on GAN-driven learning, which is particularly suitable for risk-cost balanced optimization in power grid planning. Background Art

[0002] Because renewable energy output is highly random and volatile in both time and space, and loads themselves exhibit random variations, traditional transmission network planning methods are particularly vulnerable to source-load uncertainty when faced with high renewable energy penetration. Therefore, deeply exploring the complex uncertainties of source and load, and rationally coordinating the relationships between renewable energy, loads, and the transmission network, is crucial for achieving precise investment and enhancing the resilience of the transmission system.

[0003] In recent years, many scholars have adopted methods such as stochastic programming based on static scenario sets, robust optimization based on boundary sets, and distributionally robust optimization (DRO) to study the problem of transmission network expansion planning under high penetration of renewable energy. Although these methods have improved the robustness and adaptability of planning to a certain extent, they still have many shortcomings. Traditional scenario generation and reduction methods, such as static sampling based on historical data, are difficult to effectively cover low-probability, high-impact extreme scenarios, resulting in system planning schemes easily ignoring potential vulnerabilities. Robust optimization models based on boundary assumptions are overly conservative and waste resources. Although distributionally robust optimization introduces probabilistic information, it still relies on static distribution modeling and lacks dynamic updating capabilities, making it impossible to proactively discover rare scenarios that have the greatest impact on grid planning.

[0004] The large-scale integration of renewable energy into the grid not only presents planning challenges but also provides a rich data resource for intelligent, data-driven transmission system optimization. By jointly modeling renewable energy output, load demand, and the transmission network investment and operation process, and fully leveraging their synergistic advantages, it is expected that the planning accuracy and operational resilience of the transmission system will be significantly improved. However, existing technologies for transmission network expansion planning often use static scenario sets for optimization, ignoring the complex temporal correlations between renewable energy and load. This leads to deviations in the planning results' description of the system's probabilistic operating state at all times, affecting the scientific and economic viability of system investment decisions. Summary of the Invention

[0005] In view of the above shortcomings in the existing technology, the purpose of the present invention is to provide a power grid planning and balancing optimization method and device based on GAN-driven learning, which integrates the spatiotemporal generative adversarial network (PI-ST-GAN) and a two-layer optimization framework to dynamically generate high-risk source-load scenarios and guide power grid planning investment decisions, thereby improving the resilience and economy of the power grid under high penetration of renewable energy.

[0006] To achieve the above objectives, the present invention provides a GAN-driven learning-based power grid planning and balancing optimization method, comprising the following steps: S1. Construct a physical constraint-based spatiotemporal generative adversarial network (PI-ST-GAN). This generates probabilistic time-series scenarios of source and load that meet physical, spatial, and temporal constraints based on historical data training. A composite risk indicator is then established to screen out high-risk scenarios from the generated probabilistic time-series scenarios of source and load. S2. Construct a two-layer optimization model for risk-cost balance. The upper layer aims to minimize the sum of transmission line investment costs and worst-case scenario operating risk costs, while the lower layer optimizes power generation scheduling, curtailment management, and load shedding strategies for high-risk scenarios. S3. Based on the strong duality theory, the two-level optimization model is reconstructed into a single-level mixed integer programming (MIP) model, and its constraints are set. S4. Based on a single-layer mixed integer programming (MIP) model, a solver is used to jointly solve the line investment plan and operation scheduling variables. Based on the solution results, the PI-ST-GAN is dynamically guided to enhance the generation of high-risk scenarios, realizing an optimization-generation-feedback closed-loop collaborative iterative solution process, and ultimately outputting the optimal power grid planning solution.

[0007] As a preferred embodiment of the present invention, in S1, the training objective and generator loss of PI-ST-GAN are expressed as: (1); Where, Represents the network parameter set of generator G; Represents the network parameter set of the discriminator D; Represents a sample of historical real source load scenarios; represents the empirical distribution of source-load scenarios obtained from historical samples; Represents the latent space mid-sampled latent variables as noise variables; Indicates expected value; represents the generator neural network, which generates fake scenes based on the input; The discriminator neural network determines whether the input scene is real or fake; The loss function of the generator G Expressed as: (2); Where, represents the risk-reward coefficient; Represents the composite risk indicator corresponding to the scenario generated by generator G, including the expected energy shortage EENS, load loss probability LOLP, and marginal congestion cost MCC; Classification loss of the discriminator D Expressed as: (3); Risk regression loss of the discriminator D Expressed as: (4); Where, represents the predicted value of the composite risk index of the generated scenario by the discriminator risk regression head; Physical constraint regularization loss of generator G Expressed as: (5); Where, Representation node In time of renewable energy output; 、 Represents nodes respectively Maximum and minimum output boundary values; For nodes Regularization coefficient of the physical boundary regularization term; Spatial correlation regularization loss of generator G Expressed as: (6); Where, 、 Node ,node At time step The normalized output of For node pairs The spatial regularization coefficient of ; is the indicator function, if the node pair If it belongs to a long-distance pair, the value is 1, otherwise it is 0; Temporal smoothness regularization loss of generator G Expressed as: (7); Where, is the total number of time steps; For nodes The temporal smoothing regularization coefficient of ; Representation node In time of renewable energy output; Comprehensive loss function of generator G Expressed as: (8); Where, 、 、 They are 、 、 The weight coefficient of Obtaining the comprehensive loss function Finally, high-risk scenarios are screened, expressed as: (9); Where, Represents the potential noise variable selected high-risk latent variables; A set of scenarios that meet physical and statistical feasibility requirements; The corresponding generated scenario is a high-risk scenario.

[0008] As a preferred solution of the present invention, in S2, the upper layer of the two-layer optimization model takes the transmission network planner as the decision-making body, and its goal is to optimize the selection from several candidate transmission lines under budget constraints to minimize the sum of the total investment cost of the power system and the operating risk cost under the worst-case scenario; the lower layer takes the grid operator as the main body, and optimizes the power system's power generation scheduling, renewable energy curtailment management and load shedding strategy for the high-risk scenarios selected by PI-ST-GAN.

[0009] As a preferred solution of the present invention, the upper layer optimization objective function is expressed as: (10); In the formula, the decision vector Encoded candidate routes Binary expansion decision , the unit investment cost of the corresponding line is , is the set of candidate routes; uncertainty set By distributing around experience The Wasserstein distance sphere is constructed, represents the candidate distribution; is a collection of nodes; For the scene ,time Next, node Loss load penalty factor at ; For the scene ,time Next, node The amount of load loss at For the scene ,time Next, node Penalty coefficient for curtailment of renewable energy power; For the scene ,time Next, node renewable energy curtailment; For the scene ,time Next, line The amount of line congestion at For the scene ,time Next, line Congestion price at Representation and Node A collection of connected lines.

[0010] As a preferred solution of the present invention, the lower layer optimization objective function is expressed as: (11); Where, Representation scene The set of all operating variables that need to be optimized includes unit output, power curtailment, load loss, power flow and voltage angle; For the scene ,time Next, node The cost of electricity generation at Indicates the scene ,time Next, node Conventional power generation at Representation node The cost factor of fuel for electricity generation; For the scene ,time Next, node Penalties for curtailing renewable energy generation, Representation node Penalty costs per unit of renewable energy curtailment; For the scene ,time Next, node Load loss at Representation node Unit load reduction costs; Indicates the scene of the upper layer transmitting ,time Next, line Congestion price; For the line In time , scene The current power under .

[0011] As a preferred solution of the present invention, in the S3, when reconstructing, the scene Corresponding composite risk indicators Expressed as: (12); Where, For the scene ,time Next, node The amount of electricity at the location is less than expected; For the scene Next node In time The probability of load loss; For the line In time , scene The marginal congestion cost under 、 、 They are 、 、 The weight coefficient of The single-level mixed integer programming MIP model reconstructed based on strong duality theory is expressed as: (13); Where, represents the set of adversarial generation scenarios.

[0012] As a preferred solution of the present invention, in S3, the constraints include node power balance constraints, line flow constraints, conventional power generation and renewable energy constraints, load reduction constraints, line capacity constraints, budget constraints, line operation status constraints, complementary relaxation conditions and Wasserstein fuzzy set constraints.

[0013] As a preferred solution of the present invention, the node power balance constraint is expressed as: (14); Where, Representation scene Next node and The node admittance matrix between ; Representation scene Next node In time The voltage phase angle; For the scene ,time Next, node renewable energy output at the site; Represents the node The collection of lines that transmit power; Indicates that in the scene ,time Next, node Total load demand at The line power flow constraint is expressed as: (15); Where, For the line The line reactance, line Connecting Nodes and ; For the scene ,time Next, node The voltage phase angle at For the scene ,time Next, node The voltage phase angle at is a binary variable, if the line If it has been built, the value is 1, otherwise it is 0; The constraints of conventional power generation and renewable energy are expressed as: (16); Where, For nodes the upper limit of conventional power generation; For the scene ,time Next, node the available upper limit of renewable energy at the site; The load reduction constraint is expressed as: (17); Where, Represents a collection of scenes; The line capacity constraint is expressed as: (18); Where, is a collection of lines; Indicates line The upper limit of the power flow capacity; The budget constraint is expressed as: (19); Where, Indicates line Unit investment cost; Due to budget constraints; The line operation status constraint is expressed as: (20); The complementary slack condition is expressed as: (twenty one); (twenty two); Wasserstein fuzzy set constraints are expressed as: (twenty three); (twenty four); (25); Where, express and Wasserstein distance between them; is the allowable deviation range; Representation scene The corresponding power system operation loss under is the cost metric function used in the Wasserstein distance sphere, Indicates another scene; 、 represents the dual variable; sup and inf represent the supremum and infimum respectively; Indicates the most risky scenario selected; represents the set of physical feasibility constraints; represents the set of statistical plausibility constraints.

[0014] As a preferred embodiment of the present invention, in S4, the solution process is: S4.1. Input historical wind power, photovoltaic, and load data and calculate empirical distribution ; S4.2. Initialize the network parameters of the generator G and the network parameters of the discriminator D ; S4.3. Initialize the line investment variable, i.e. ; S4.4. Set the Wasserstein distance sphere range ; S4.5. Set the maximum number of iterations and convergence criterion , initialize the iteration count ; S4.6. Generating Potential Noise Samples ; S4.7. Noise variables Input generator neural network, i.e. , the total is calculated by forward propagation of the neural network The wind power output, photovoltaic output and load demand of each time step constitute the source-load timing scenario ; S4.8. Calculate the classification loss of the discriminator D and risk regression loss ; S4.9. Calculate the loss of the generator G ; S4.10. Calculate the physical constraint regularization loss , spatial correlation regularization loss , temporal smoothness regularization loss ; S4.11. Combined generator loss ; S4.12. Determine the generated scene Is it satisfied 、 and If the constraints are satisfied, Put into the feasible scenario set and continue; if not satisfied, return to step S4.6; S4.13, determine whether all noise samples If the traversal has been completed, continue; otherwise, return to step S4.6; S4.14. From the feasible scenario set Select the maximum composite risk indicator Corresponding scenarios ; S4.15. Enter the current scene ; S4.16, solve the upper optimization objective function; S4.17, determine whether the budget constraint and Wasserstein fuzzy set constraint are satisfied. If yes, continue; otherwise, return to S4.16; S4.18, generate the current line operation status, that is, ; S4.19, the worst risk distribution in the upper optimization objective, that is, The upper bound optimization of is reconstructed into a single-level mixed integer programming through duality theory, and the dual variable is introduced. 、 and the distance cost ; S4.20, MIP solver according to Dynamically define line flow constraints, i.e. ; S4.21. Calculate the node power balance equation, i.e., equation (14); Calculate the line power flow equation, which is equation (15); Calculate the complementary relaxation conditions, i.e., Equation (21) and Equation (22); S4.22, determine whether the line flow exceeds the capacity limit , whether the upper and lower limits of power generation, load, and renewable output are met, i.e., equations (16) and (17); If satisfied, continue; otherwise, return to S4.16; S4.23. Output the current total running cost , dual variables, power flow results; S4.24. Calculate the current scene Corresponding composite risk indicators And pass it back to the generator neural network as a reward signal; S4.25. Calculate risk feedback gradient , represents the comprehensive loss About the network parameters of the generator G gradient; S4.26. Update the network parameters of the generator G and the network parameters of the discriminator D ; S4.27, determine whether the convergence conditions are met ,in 、 Respectively represent sequence The composite risk index at the iteration; if satisfied, continue; otherwise, update , return to step S4.6; S4.28. Output the optimal line construction plan , corresponding to the worst risk scenario and convergence curve ; S4.29, the solution process ends.

[0015] A power grid planning and balancing optimization device based on GAN-driven learning includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The above method is implemented by executing the computer program by the processor.

[0016] The beneficial effects of the present invention are: This paper proposes a method for generating probabilistic time-series scenarios for sources and loads based on a physically constrained spatiotemporal generative adversarial network (PI-ST-GAN). This method dynamically learns the complex uncertainties of sources and loads and, guided by optimized feedback, proactively generates high-risk scenarios that pose the greatest impact on transmission network operations. This closed-loop optimization-generation collaborative mechanism effectively overcomes the limitations of traditional static scenario sampling methods.

[0017] This paper constructs a two-tiered optimization planning model with a risk-cost trade-off. By coupling upper-tier infrastructure investment optimization with lower-tier operational response optimization for dynamic scenarios, this model achieves highly resilient transmission network planning solutions to high renewable energy penetration and load uncertainty. This two-tiered optimization architecture combines the concept of distributed robust optimization with dynamic scenario-generated feedback.

[0018] The present invention designs a composite risk index ( ), comprehensively considers the expected energy shortage (EENS), load loss probability (LOLP), and marginal congestion cost (MCC), and embeds them into the PI-ST-GAN training process to form a risk-driven adversarial scenario generation strategy, which effectively improves the adaptability of the planning scheme to the vulnerable state of the system.

[0019] The present invention constructs a year-round operational probability state calculation and simulation process, combines GAN dynamically generated time series scenarios with iterative training of optimization models, and forms an integrated optimization-generation-simulation solution process, which can achieve high-precision performance evaluation and optimization of planning schemes within the year-round operational cycle. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a schematic diagram of the process of the present invention; Figure 2 It is a complete optimization flow chart of the present invention. DETAILED DESCRIPTION

[0021] The embodiments of the present invention are further described below with reference to the accompanying drawings: Example 1: Figure 1 As shown in FIG, a power grid planning and balancing optimization method based on GAN-driven learning includes the following steps: S1. Construct a physical constraint-based spatiotemporal generative adversarial network (PI-ST-GAN). This generates probabilistic time-series scenarios of source and load that meet physical, spatial, and temporal constraints based on historical data training. A composite risk indicator is then established to screen out high-risk scenarios from the generated probabilistic time-series scenarios of source and load. S2. Construct a two-layer optimization model for risk-cost balance. The upper layer aims to minimize the sum of transmission line investment costs and worst-case scenario operating risk costs, while the lower layer optimizes power generation scheduling, curtailment management, and load shedding strategies for high-risk scenarios. S3. Based on the strong duality theory, the two-level optimization model is reconstructed into a single-level mixed integer programming (MIP) model, and its constraints are set. S4. Based on a single-layer mixed integer programming (MIP) model, a solver is used to jointly solve the line investment plan and operation scheduling variables. Based on the solution results, the PI-ST-GAN is dynamically guided to enhance the generation of high-risk scenarios, realizing an optimization-generation-feedback closed-loop collaborative iterative solution process, and ultimately outputting the optimal power grid planning solution.

[0022] Wind power and photovoltaic power output and loads have high spatiotemporal uncertainty, making traditional static scenario generation methods ineffective in reflecting high-risk, low-probability extreme scenarios. This embodiment uses a physically constrained spatiotemporal generative adversarial network to dynamically generate source-load time-series scenarios with high-risk impact.

[0023] In S1, the training objective and generator loss of PI-ST-GAN are expressed as: (1); Where, Represents the network parameter set of generator G; Represents the network parameter set of the discriminator D; Represents a sample of historical real source load scenarios (i.e. the scenarios mentioned later) ); represents the empirical distribution of source-load scenarios obtained from historical samples, Represents the empirical distribution Sampling the scene ; Represents the latent space mid-sampled latent variables as noise variables; Indicates expected value; represents the generator neural network, which generates fake scenes based on the input; The discriminator neural network determines whether the input scene is real or fake; For example, Represents a generator with As input, generate fake scenes; Represents the input scenario Determine whether it is genuine or forged; Indicates the scene From the empirical distribution Calculation of expected value during sampling; represents the expected value calculation of the noise variable z; This goal defines and A min-max game between Synthesize realistic renewable energy and load scenarios The discriminator maximizes its classification accuracy, while the generator learns to deceive the discriminator, thus laying an adversarial foundation for generating realistic yet unpredictable scenarios.

[0024] The loss function of the generator G Expressed as: (2); Where, represents the risk-reward coefficient; Represents the composite risk indicator corresponding to the scenario generated by generator G, including the expected energy shortage EENS, load loss probability LOLP, and marginal congestion cost MCC; A stress-guided reward term is added to the generator’s loss function , and through the coefficient This design forces the generator to not only learn to deceive the discriminator but also to generate scenarios with high operational risks, thus closely linking the GAN training process directly with the downstream optimization results.

[0025] Expected Energy Shortage (EENS), Loss of Load Probability (LOLP), and Marginal Congestion Cost (MCC) are existing and commonly used indicators in power systems, among which: Expected Energy Not Supplied (EENS) is the expected reduction in load demand due to generation capacity shortages or grid constraints within a given timeframe. It comprehensively expresses the expected reduction in load demand due to generation capacity shortages or grid constraints within a given timeframe by combining the number, average duration, and average outage power of power outages. This metric measures the expected power supply shortfall in the power system, reflecting the energy supply gap caused by forced generator outages or grid issues. Its calculation is typically based on a generator outage capacity probability model and hourly load curves, accounting for both generation capacity shortages and duration.

[0026] Loss of Load Probability (LOLP) is a core probabilistic metric in power system reliability assessment. It is defined as the probability that the available capacity of a power generation system will not be able to meet the system's annual maximum load demand. Traditionally, this is the probability that the available capacity of a power generation system will not be able to meet the system's annual maximum load demand. In the power market, it is also closely related to the available transmission capacity and reliability of the transmission system, reflecting the impact of transmission failures or congestion on the available generation capacity of the power system. LOLP directly reflects the supply and demand situation in the power market and quantifies the risk of insufficient power system capacity.

[0027] Marginal congestion cost (MCC) refers to the additional costs incurred due to transmission network congestion. When transmission lines are congested, electricity cannot flow freely between different regions according to the principles of economic dispatch, resulting in increased generation costs. MCC reflects the additional costs incurred when generation resources in the power system are not optimally allocated due to transmission line constraints and is commonly used to assess the operational efficiency and economic viability of transmission networks.

[0028] Classification loss of the discriminator D Expressed as: (3); The discriminator's classification loss penalizes incorrect true or false labels, making it a powerful gatekeeper for scene authenticity. This loss helps shape the optimization space during GAN training, especially in the early stages of training, when stress feedback has not yet become a dominant factor, effectively guiding model learning.

[0029] Risk regression loss of the discriminator D Expressed as: (4); Where, represents the predicted value of the composite risk index of the generated scenario by the discriminator risk regression head; The discriminator is also trained as a regressor for the risk indicator, constructing a differentiable mapping from generated scenarios to operational stresses. This allows the generator to receive a smooth gradient signal from the stresses without relying on a discrete two-level optimization process for evaluation.

[0030] Physical constraint regularization loss of generator G Expressed as: (5); Where, Representation node In time of renewable energy output; 、 Represents nodes respectively Maximum and minimum output boundary values; For nodes Regularization coefficient of the physical boundary regularization term; If the generator generates renewable energy (RES) output that exceeds the physical constraints, it will be softly penalized. Ensure that the generated output trajectory remains realistic and can be actually executed by power system dispatchers.

[0031] Spatial correlation regularization loss of generator G Expressed as: (6); Where, 、 Node ,node At time step The normalized output of For node pairs The spatial regularization coefficient of ; is the indicator function, if the node pair If the distance is long (greater than or equal to 30 km), the value is 1, otherwise it is 0; This spatial regularization enables the generated renewable energy configuration Aligns between adjacent busbars, preserving the spatial correlation structure of the real world. Extreme differences between geographically connected nodes are suppressed by using a distance-based penalty.

[0032] Temporal smoothness regularization loss of generator G Expressed as: (7); Where, is the total number of time steps; For nodes The temporal smoothing regularization coefficient of ; Representation node In time of renewable energy output; A temporal smoothness constraint is introduced via a ramp rate penalty term, forcing the generator to avoid unrealistically sudden changes in renewable energy (RES) availability. This constraint mimics the operational forecast constraints used in real-world independent system operator (ISO) procedures.

[0033] Comprehensive loss function of generator G Expressed as: (8); Where, 、 、 They are 、 、 The weight coefficient of The complete generator loss function is a weighted combination of adversarial learning, physical realism, spatial correlation, and temporal smoothness objectives. These components balance creative diversity with feasibility constraints, enabling the generator to produce operationally plausible scenarios with high-risk characteristics.

[0034] Obtaining the comprehensive loss function Finally, high-risk scenarios are screened, expressed as: (9); Where, Represents the potential noise variable selected high-risk latent variables; A set of scenarios that meet physical and statistical feasibility requirements; Meaning is defined as; The corresponding generated scenario is a high-risk scenario.

[0035] In S2, the upper layer of the two-layer optimization model is based on the transmission network planner as the decision-maker. Its goal is to optimize the selection from several candidate transmission lines under budget constraints, minimize the sum of the total investment cost of the power system and the operating risk cost under the worst-case scenario, and ensure that the investment plan is both economical and resilient. The lower layer is based on the grid operator as the main body. For the high-risk scenarios selected by PI-ST-GAN, it optimizes the power system's power generation scheduling, renewable energy curtailment management, and load shedding strategies to achieve the economy and feasibility of power system operation.

[0036] The upper optimization objective function is expressed as: (10); The upper-level objective function reflects the strategic planning decisions faced by transmission expansion planning agencies, which aims to minimize the sum of infrastructure investment costs and worst-case operational performance losses under a distributed robust uncertainty model.

[0037] In the formula, the decision vector Encoded candidate routes Binary expansion decision , the unit investment cost of the corresponding line is , is the set of candidate routes; the second term in the formula measures the worst-case operating loss, the uncertainty set By distributing around experience The Wasserstein distance sphere is constructed to ensure the robustness of the model under sample error. represents the candidate distribution; is a collection of nodes; the inner expectation item evaluates the scenario-related operating costs, including: For the scene ,time Next, node Loss load penalty factor at ; For the scene ,time Next, node The amount of load loss at For the scene ,time Next, node Penalty coefficient for curtailment of renewable energy power; For the scene ,time Next, node renewable energy curtailment; For the scene ,time Next, line The amount of line congestion at For the scene ,time Next, line Congestion price at Representation and Node A collection of connected lines.

[0038] The lower-level optimization objective function is expressed as: (11); In the lower model, the objective function describes the Under these circumstances, the power system dispatcher aims to minimize a comprehensive cost function that includes multiple factors. This layer of the model embodies a distributed yet coordinated dispatch mechanism that can adapt to the uncertainty of net load and renewable energy injection, reflecting the real-time resilience of the power system under adversarial pressure.

[0039] Where, Representation scene The set of all operating variables that need to be optimized includes unit output, power curtailment, load loss, power flow and voltage angle; For the scene ,time Next, node The cost of electricity generation at Indicates that in the scene ,time Next, node Conventional power generation at Representation node The power generation fuel cost coefficient; For the scene ,time Next, node Penalties for curtailing renewable energy generation, Representation node Penalty costs per unit of renewable energy curtailment; For the scene ,time Next, node Load loss at Representation node Unit load reduction costs; Indicates the scene of the upper layer transmitting ,time Next, line Congestion price; For the line In time , scene The current power under .

[0040] In S3, during reconstruction, in order to guide the adversarial generator to identify high-impact scenarios, the scenario Corresponding composite risk indicators Expressed as: (12); Where, For the scene ,time Next, node The amount of electricity at the location is less than expected; For the scene Next node In time The probability of load loss; For the line In time , scene The marginal congestion cost under 、 、 They are 、 、 The weight coefficients are used to reflect the importance differences of each risk dimension. This composite risk indicator serves as a differentiable proxy objective function for the scenario generator to optimize, thereby guiding the generator to generate scenarios in the direction of pressure trajectories that are more critical to operations and more challenging for planned infrastructure. The single-level mixed integer programming MIP model reconstructed based on strong duality theory is expressed as: (13); Where, represents the set of adversarial generation scenarios.

[0041] In S3, the constraints include: Node power balance constraints: (14); Where, Representation scene Next node and The node admittance matrix between ; Representation scene Next node In time The voltage phase angle; For the scene ,time Next, node renewable energy output at the site; Represents the node The collection of lines that transmit power; Indicates the scene ,time Next, node Total load demand at The power balance equation ensures that in the scenario The energy conservation of the lower node is the power generation , renewable energy output The sum of the flow injected into the node equals the total load demand , the adjustment includes load loss and renewable energy curtailment The left side of the equation represents the node injection power based on the DC power flow model, using the admittance matrix and voltage phase angle The results show that the real-time feasibility of scheduling decisions in transmission networks is feasible.

[0042] Line flow constraints: (15); Where, For the line The line reactance, line Connecting Nodes and ; For the scene ,time Next, node The voltage phase angle at For the scene ,time Next, node The voltage phase angle at is a binary variable, if the line If it has been built, the value is 1, otherwise it is 0; The line power flow constraint linearly maps the voltage phase angle difference to the voltage along the line. The power flow on the line is mapped by the line reactance Scaling. Binary variables Control the activation status of the line. If the line has been built, , thus ensuring that only constructed lines participate in energy transmission. This constraint, which embodies Kirchhoff’s law, plays a central role in determining congestion patterns, especially in scenarios with antagonistically generated high-voltage stresses.

[0043] Conventional power generation and renewable energy constraints: (16); Where, For nodes The upper limit of power generation; For the scene ,time Next, node the available upper limit of renewable energy at the site; This set of constraints on conventional power generation , renewable energy output and renewable energy curtailment Physical feasibility boundary constraints are imposed. The upper limit of renewable energy output is determined by the scenario-dependent availability profile. curtailment is only allowed within the achieved renewable energy output limit, thus ensuring the integrity of the energy balance.

[0044] Load reduction constraints: (17); Where, Represents a collection of scenes; This inequality constraint specifies the permissible load loss range for each node and time step, ensuring that the load loss does not exceed the actual load. This constraint is crucial for ensuring the physical plausibility of the operational response and helps avoid unrealistic loss scenarios, especially when facing GAN-generated peak demand shocks.

[0045] Line capacity constraints: (18); Where, is a collection of lines; Indicates line The upper limit of the power flow capacity; This constraint is activated by a binary variable To achieve the control of transmission line capacity, limit the flow value allowed on each line. ), its power flow capacity will degenerate to zero, thus ensuring that the optimization logic does not use unbuilt lines to form infeasible “shortcut” paths.

[0046] Budget Constraint: (19); Where, Indicates line Unit investment cost; Due to budget constraints; Budget constraints limit the total amount of transmission investment, ensuring that planners' decisions meet financial constraints. Each binary variable Incurring costs , forming a feasible region similar to the knapsack problem. This constraint introduces a strategic tension between transmission grid expansion and resilience under stress.

[0047] Line operation status constraints: (20); The activation variables for each candidate transmission line is a binary variable used to implement discretized investment decisions. This modeling form supports an exact solution strategy based on MIP (mixed integer programming) and can efficiently represent combinatorial infrastructure design problems.

[0048] Complementary slack conditions: (twenty one); The complementary slack condition will increase the line congestion price Linked to power flow constraints, this ensures that price signals only emerge when capacity constraints become a constraint. This lays the foundation for capturing economic dispatch feedback and incorporating dual prices into pressure signals.

[0049] (twenty two); These complementary conditions ensure that the associated penalty prices are activated only when renewable energy curtailment and load loss reach their respective constraint limits. These constraints emulate the design principle of incentive compatibility—penalizing only those deviations that materially violate energy adequacy expectations.

[0050] Wasserstein fuzzy set constraints: (twenty three); This constraint defines the Wasserstein fuzzy set , restricting any candidate distribution Relative to the empirical distribution The allowable deviation of The robustness level of the control model directly affects the conservatism of the final transmission planning scheme.

[0051] (twenty four); By dualizing the DRO inner layer problem, the worst-case expectation problem can be transformed into a solvable convex optimization problem, which relies on strong duality theory. Representation scene The corresponding power system operation loss is: is the cost metric function used in the Wasserstein distance sphere. Dual variable Control the trade-off between model conservatism and scenario penalization.

[0052] (25); Finally, the adversarial scenario screening rule selects the scenario that can maximize the system pressure from all the scenarios generated by GAN. This rule contains the physical feasibility filter and statistical plausibility screening conditions to ensure that only high-impact scenarios with practical significance and high impact can influence infrastructure planning outcomes.

[0053] Where, express and Wasserstein distance between them; is the allowable deviation range; Representation scene The corresponding power system operation loss under is the cost metric function used in the Wasserstein distance sphere, Indicates another scene; 、 represents the dual variable; sup and inf represent the supremum and infimum respectively; Indicates the most risky scenario selected; represents the set of physical feasibility constraints; represents the set of statistical plausibility constraints.

[0054] This embodiment dynamically generates and screens source-load probabilistic time series scenarios under the condition of high penetration of renewable energy access to the transmission network by constructing a physical constraint-based spatiotemporal generative adversarial network (PI-ST-GAN). First, PI-ST-GAN is trained with historical wind power, photovoltaic, and load data to generate source-load probabilistic time series sequences that meet the constraints of physical feasibility, spatial correlation, and temporal smoothness. The impact of the generated scenarios on the system operation is calculated, and the most risky scenarios are selected as the lower-level optimization input. In the optimization model, a two-layer optimization framework of risk-cost balance is adopted. The upper-layer optimization model takes minimizing the sum of the transmission line investment cost and the system operation risk cost under the worst scenario as the optimization goal, and the lower-layer optimization model takes minimizing the scenario-related power generation cost, load loss cost, renewable energy curtailment cost and congestion cost under a given line construction plan as the goal, and fully describes the coupling relationship between transmission network planning and operation. In order to improve the solution efficiency and accuracy, this paper uses strong duality theory to reconstruct the original two-layer optimization problem into a single-layer mixed integer programming (MIP) model, and uses the solver to solve the line investment plan. and operation scheduling variables for joint solution, and dynamically guide PI-ST-GAN to enhance the generation of high-risk scenarios through the optimization feedback mechanism, realizing a closed-loop collaborative iterative solution process of optimization-generation-feedback.

[0055] In S4, the solution process is: S4.1. Input historical wind power, photovoltaic, and load data and calculate empirical distribution ; S4.2. Initialize the network parameters of the generator G and the network parameters of the discriminator D ; S4.3. Initialize the line investment variable, i.e. ; S4.4. Set the Wasserstein distance sphere range ; S4.5. Set the maximum number of iterations and convergence criterion , initialize the iteration count ; S4.6. Generating Potential Noise Samples ; S4.7. Noise variables Input generator neural network, i.e. , the total is calculated by forward propagation of the neural network The wind power output, photovoltaic output and load demand of each time step constitute the source-load timing scenario ; S4.8. Calculate the classification loss of the discriminator D and risk regression loss ; S4.9. Calculate the loss of the generator G ; S4.10. Calculate the physical constraint regularization loss , spatial correlation regularization loss , temporal smoothness regularization loss ; S4.11. Combined generator loss ; S4.12. Determine the generated scene Is it satisfied 、 and If the constraints are satisfied, Put into the feasible scenario set and continue; if not satisfied, return to step S4.6; S4.13, determine whether all noise samples If the traversal has been completed, continue; otherwise, return to step S4.6; S4.14. From the feasible scenario set Select the maximum composite risk indicator Corresponding scenarios ; S4.15. Enter the current scene ; S4.16, solve the upper optimization objective function; S4.17, determine whether the budget constraint and Wasserstein fuzzy set constraint are satisfied. If yes, continue; otherwise, return to S4.16; S4.18, generate the current line operation status, that is, ; S4.19, the worst risk distribution in the upper optimization objective, that is, The upper bound optimization of is reconstructed into a single-level mixed integer programming through duality theory, and the dual variable is introduced. 、 and the distance cost ; S4.20, MIP solver according to Dynamically define line flow constraints, i.e. ; S4.21. Calculate the node power balance equation ; Calculate the line power flow equation ; Computing complementary slack conditions 、 、 ; S4.22, determine whether the line flow exceeds the capacity limit , whether the upper and lower limits of power generation, load, and renewable output are met 、 、 、 ; If satisfied, continue; otherwise, return to S4.16; S4.23. Output the current total running cost , dual variables, and power flow results; S4.24. Calculate the current scene Corresponding composite risk indicators And pass it back to the generator neural network as a reward signal; S4.25. Calculate risk feedback gradient , represents the comprehensive loss About the network parameters of the generator G gradient; S4.26. Update the network parameters of the generator G and the network parameters of the discriminator D ; S4.27, determine whether the convergence conditions are met ,in 、 Respectively represent sequence The composite risk index at the iteration; if satisfied, continue; otherwise, update , return to step S4.6; S4.28. Output the optimal line construction plan , corresponding to the worst risk scenario and convergence curve ; S4.29, the solution process ends.

[0056] Combining the above content, the complete balance optimization process is as follows Figure 2 shown.

[0057] Example 2: A power grid planning and balancing optimization device based on GAN-driven learning, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor, and the method in Example 1 is implemented by executing the computer program by the processor.

Claims

1. A GAN-driven learning-based power grid planning and balancing optimization method, characterized by The following steps are involved: S1. Construct a physical constraint-based spatiotemporal generative adversarial network (PI-ST-GAN). This generates probabilistic time-series scenarios of source and load that meet physical, spatial, and temporal constraints based on historical data training. A composite risk indicator is then established to screen out high-risk scenarios from the generated probabilistic time-series scenarios of source and load. S2. Construct a two-layer optimization model for risk-cost balance. The upper layer aims to minimize the sum of transmission line investment costs and worst-case scenario operating risk costs, while the lower layer optimizes power generation scheduling, curtailment management, and load shedding strategies for high-risk scenarios. S3. Based on the strong duality theory, the two-level optimization model is reconstructed into a single-level mixed integer programming (MIP) model, and its constraints are set. S4. Based on a single-layer mixed integer programming (MIP) model, a solver is used to jointly solve the line investment plan and operation scheduling variables. Based on the solution results, the PI-ST-GAN is dynamically guided to enhance the generation of high-risk scenarios, realizing an optimization-generation-feedback closed-loop collaborative iterative solution process, and ultimately outputting the optimal power grid planning solution.

2. A GAN-driven learning-based power grid planning and balancing optimization method according to claim 1, characterized in that: In S1, the training objective and generator loss of PI-ST-GAN are expressed as: （1）； Where, Represents the network parameter set of generator G; Represents the network parameter set of the discriminator D; Represents a sample of historical real source load scenarios; represents the empirical distribution of source-load scenarios obtained from historical samples; Represents the latent space mid-sampled latent variables as noise variables; Indicates expected value; represents the generator neural network, which generates fake scenes based on the input; The discriminator neural network determines whether the input scene is real or fake; The loss function of the generator G Expressed as: （2）； Where, represents the risk-reward coefficient; Represents the composite risk indicator corresponding to the scenario generated by generator G, including the expected energy shortage EENS, load loss probability LOLP, and marginal congestion cost MCC; Classification loss of the discriminator D Expressed as: （3）； Risk regression loss of the discriminator D Expressed as: （4）； Where, represents the predicted value of the composite risk index of the generated scenario by the discriminator risk regression head; Physical constraint regularization loss of generator G Expressed as: （5）； Where, Representation node In time of renewable energy output; 、 Represents nodes respectively Maximum and minimum output boundary values; For nodes Regularization coefficient of the physical boundary regularization term; Spatial correlation regularization loss of generator G Expressed as: （6）； Where, 、 Node ,node At time step The normalized output of For node pairs The spatial regularization coefficient of ; is the indicator function, if the node pair If it belongs to a long-distance pair, the value is 1, otherwise it is 0; Temporal smoothness regularization loss of generator G Expressed as: （7）； Where, is the total number of time steps; For nodes The temporal smoothing regularization coefficient of ; Representation node In time of renewable energy output; Comprehensive loss function of generator G Expressed as: （8）； Where, 、 、 They are 、 、 The weight coefficient of Obtaining the comprehensive loss function Finally, high-risk scenarios are screened, expressed as: （9）； Where, Represents the potential noise variable selected high-risk latent variables; A set of scenarios that meet physical and statistical feasibility requirements; The corresponding generated scenario is a high-risk scenario.

3. A GAN-driven learning-based power grid planning and balancing optimization method according to claim 1, characterized in that: In S2, the upper layer of the two-layer optimization model takes the transmission network planner as the decision-making subject, whose goal is to optimize the selection from several candidate transmission lines under budget constraints to minimize the sum of the total investment cost of the power system and the operating risk cost under the worst-case scenario; The lower layer is mainly based on the grid operator, and optimizes the power system's power generation scheduling, renewable energy curtailment management, and load shedding strategies for high-risk scenarios screened by PI-ST-GAN.

4. A GAN-driven learning-based power grid planning and balancing optimization method according to claim 2, characterized in that: The upper optimization objective function is expressed as: （10）； In the formula, the decision vector Encoded candidate routes Binary expansion decision , the unit investment cost of the corresponding line is , is the set of candidate routes; uncertainty set By distributing around experience The Wasserstein distance sphere is constructed, represents the candidate distribution; is a collection of nodes; For the scene ,time Next, node Loss load penalty factor at ; For the scene ,time Next, node The amount of load loss at For the scene ,time Next, node Penalty coefficient for curtailment of renewable energy power; For the scene ,time Next, node renewable energy curtailment; For the scene ,time Next, line The amount of line congestion at For the scene ,time Next, line Congestion price at Representation and Node A collection of connected lines.

5. A GAN-driven learning-based power grid planning and balancing optimization method according to claim 4, characterized in that: The lower-level optimization objective function is expressed as: （11）； Where, Representation scene The set of all operating variables that need to be optimized includes unit output, power curtailment, load loss, power flow and voltage angle; For the scene ,time Next, node The cost of electricity generation at Indicates the scene ,time Next, node Conventional power generation at Representation node The cost factor of fuel for electricity generation; For the scene ,time Next, node Penalties for curtailing renewable energy generation, Representation node Penalty costs per unit of renewable energy curtailment; For the scene ,time Next, node Load loss at Representation node Unit load reduction costs; Indicates the scene of the upper layer transmitting ,time Next, line Congestion price; For the line In time , scene The current power under .

6. A GAN-driven learning-based power grid planning and balancing optimization method according to claim 5, characterized in that: In the S3, when reconstructing, the scene Corresponding composite risk indicators Expressed as: （12）； Where, For the scene ,time Next, node The amount of electricity at the location is less than expected; For the scene Next node In time The probability of load loss; For the line In time , scene The marginal congestion cost under 、 、 They are 、 、 The weight coefficient of The single-level mixed integer programming MIP model reconstructed based on strong duality theory is expressed as: （13）； Where, represents the set of adversarial generation scenarios.

7. A GAN-driven learning-based power grid planning and balancing optimization method according to claim 6, characterized in that: In the aforementioned S3, the constraints include node power balance constraints, line flow constraints, conventional power generation and renewable energy constraints, load reduction constraints, line capacity constraints, budget constraints, line operation status constraints, complementary slack conditions, and Wasserstein fuzzy set constraints.

8. A method for power grid planning and balancing optimization based on GAN-driven learning according to claim 7, characterized in that: The node power balance constraint is expressed as: （14）； Where, Representation scene Next node and The node admittance matrix between ; Representation scene Next node In time The voltage phase angle; For the scene ,time Next, node renewable energy output at the site; Represents the node The collection of lines that transmit power; Indicates the scene ,time Next, node Total load demand at The line power flow constraint is expressed as: （15）； Where, For the line The line reactance, line Connecting Nodes and ; For the scene ,time Next, node The voltage phase angle at For the scene ,time Next, node The voltage phase angle at is a binary variable, if the line If it has been built, the value is 1, otherwise it is 0; The constraints of conventional power generation and renewable energy are expressed as: （16）； Where, For nodes the upper limit of conventional power generation; For the scene ,time Next, node the available upper limit of renewable energy at the site; The load reduction constraint is expressed as: （17）； Where, Represents a collection of scenes; The line capacity constraint is expressed as: （18）； Where, is a collection of lines; Indicates line The upper limit of the power flow capacity; The budget constraint is expressed as: （19）； Where, Indicates line Unit investment cost; Due to budget constraints; The line operation status constraint is expressed as: （20）； The complementary slack condition is expressed as: （21）； （22）； Wasserstein fuzzy set constraints are expressed as: （23）； （24）； （25）； Where, express and Wasserstein distance between them; is the allowable deviation range; Representation scene The corresponding power system operation loss under is the cost metric function used in the Wasserstein distance sphere, Indicates another scene; 、 represents the dual variable; sup and inf represent the supremum and infimum respectively; Indicates the most risky scenario selected; represents the set of physical feasibility constraints; represents the set of statistical plausibility constraints.

9. A GAN-driven learning-based power grid planning and balancing optimization method according to claim 8, characterized in that: In the above S4, the solution process is: S4.

1. Input historical wind power, photovoltaic, and load data and calculate empirical distribution ; S4.

2. Initialize the network parameters of the generator G and the network parameters of the discriminator D ; S4.

3. Initialize the line investment variable, i.e. ; S4.

4. Set the Wasserstein distance sphere range ; S4.

5. Set the maximum number of iterations and convergence criterion , initialize the iteration count ; S4.

6. Generating Potential Noise Samples ; S4.

7. Noise variables Input generator neural network, i.e. , the total is calculated by forward propagation of the neural network The wind power output, photovoltaic output and load demand of each time step constitute the source-load timing scenario ; S4.

8. Calculate the classification loss of the discriminator D and risk regression loss ; S4.

9. Calculate the loss of the generator G ; S4.

10. Calculate the physical constraint regularization loss , spatial correlation regularization loss , temporal smoothness regularization loss ; S4.

11. Combined generator loss ; S4.

12. Determine the generated scene Is it satisfied 、 and If the constraints are satisfied, Put into the feasible scenario set and continue; if not satisfied, return to step S4.6; S4.13, determine whether all noise samples If the traversal has been completed, continue; otherwise, return to step S4.6; S4.

14. From the feasible scenario set Select the maximum composite risk indicator Corresponding scenarios ; S4.

15. Enter the current scene ; S4.16, solve the upper optimization objective function; S4.17, determine whether the budget constraint and Wasserstein fuzzy set constraint are satisfied. If yes, continue; otherwise, return to S4.16; S4.18, generate the current line operation status, that is, ; S4.19, the worst risk distribution in the upper optimization objective, that is, The upper bound optimization of is reconstructed into a single-level mixed integer programming through duality theory, and the dual variable is introduced. 、 and the distance cost ; S4.20, MIP solver according to Dynamically define line flow constraints, i.e. ; S4.

21. Calculate the node power balance equation, i.e., equation (14); Calculate the line power flow equation, which is equation (15); Calculate the complementary relaxation conditions, i.e., Equation (21) and Equation (22); S4.22, determine whether the line flow exceeds the capacity limit , whether the upper and lower limits of power generation, load, and renewable output are met, i.e., equations (16) and (17); If satisfied, continue; otherwise, return to S4.16; S4.

23. Output the current total running cost , dual variables, and power flow results; S4.

24. Calculate the current scene Corresponding composite risk indicators And pass it back to the generator neural network as a reward signal; S4.

25. Calculate risk feedback gradient , represents the comprehensive loss About the network parameters of the generator G gradient; S4.

26. Update the network parameters of the generator G and the network parameters of the discriminator D ; S4.27, determine whether the convergence conditions are met ,in 、 Respectively represent sequence The composite risk index at the iteration; if satisfied, continue; otherwise, update , return to step S4.6; S4.

28. Output the optimal line construction plan , corresponding to the worst risk scenario and convergence curve ; S4.29, the solution process ends.

10. A power grid planning and balancing optimization device based on GAN-driven learning, characterized by: The method comprises a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the method according to any one of claims 1 to 9 is implemented by executing the computer program by the processor.

Images