A wind and light containing transient stability optimal power flow control method based on PGMSPCE

Abstract

A wind and light transient stability optimal power flow control method based on PGMSPCE, step 1: based on wind and light historical data, the uncertainty of wind speed and light intensity is modeled by Weibull and Beta distribution respectively; Step 2: for wind and light uncertainty, the transient stability optimal power flow (Chance Constrained Transient Stability Constrained Optimal Power Flow, CC-TSCOPF) is constructed by using opportunity constraint, and the rotor angle deviation relative to the center of inertia (Center of Inertia, COI) is used as the transient stability criterion; Step 3: based on the partial gradient-enhanced multi-output sparse polynomial chaos expansion (Partial Gradient-Enhanced Multi-output Sparse Polynomial Chaos Expansion, PGMSPCE) model, the CC-TSCOPF model is converted into a deterministic model by combining Galerkin projection; Step 4: the Marine Predators Algorithm (Marine Predators Algorithm, MPA) is used to solve the reconstructed CC-TSCOPF model. The wind and light transient stability optimal power flow control method based on PGMSPCE proposed in the application not only considers the wind and light uncertainty, but also considers the analysis of transient stability, so that the power system can be safely and stably operated.

Description

Technical Field

[0001] This invention relates to the fields of power systems and new energy technologies, and particularly to the fields of power system transient stability analysis and optimal power flow calculation, specifically to a method for optimal power flow control with wind and solar transient stability based on PGMSPCE. Background Technology

[0002] Due to the clean and renewable advantages of wind power and photovoltaic power, their installed capacity and power generation have continued to rise, and they have gradually become an important part of the power supply. However, the inherent intermittency, volatility and randomness of wind and solar power generation significantly increase the uncertainty of the power system's operating state and raise the risk of transient stability. Therefore, conducting research on transient stability-constrained optimal power flow that takes into account the uncertainties of wind and solar power is of great significance for balancing the safety and efficiency of the power system and promoting the large-scale grid connection and consumption of new energy sources.

[0003] Patent document CN109698511A discloses a transient stability prevention and control optimization algorithm based on adjoint sensitivity. This method uses the minimum fuel cost of the entire system as the objective function, and establishes a TSCOPF model with constraints including line power flow constraints, node voltage constraints, unit output upper and lower limits constraints, initial equations of system state variables during faults, and unit power angle stability constraints after faults. The process constraint of unit power angle stability after a fault is transformed into an integral constraint through constraint transformation. The first-order gradient information of the integral constraint is calculated using adjoint sensitivity analysis, and then an optimization layer is employed. The simulation layer's program framework solves nonlinear optimization problems. However, this method has certain limitations, failing to consider the impact of uncertainties in renewable energy output on the system, which may lead to deviations between the calculation results and actual operating conditions. Patent document CN115829258A discloses a power system economic dispatch method based on polynomial chaotic approximate dynamic programming. This method constructs an approximate value function distribution using a polynomial chaotic surrogate model and achieves decoupled solution for multi-period economic dispatch through dynamic programming, providing a surrogate model approach for power system optimization under uncertainty. However, this method has certain limitations in terms of applicable scenarios and model performance: its core is the economic dispatch problem, without introducing transient stability constraints, which cannot meet the transient safety requirements of the system under high-proportion renewable energy grid connection; furthermore, traditional polynomial chaotic models do not consider gradient information and multi-output characteristics, making it difficult to balance sparsity and fitting accuracy when dealing with multivariate uncertainties in wind and solar power.

[0004] In summary, the applicant proposes an optimal power flow control method based on PGMSPCE with transient stability, which comprehensively considers transient safety and efficiency, ensuring the safe and efficient operation of the wind and solar grid-connected system under transient stability constraints, and providing reliable technical support for new power systems. Summary of the Invention

[0005] The purpose of this invention is to address the problems of existing optimal power flow calculation methods in power systems when facing the high-dimensional uncertainties of wind and solar renewable energy. Traditional surrogate models, such as conventional polynomial chaotic expansion, do not fully utilize gradient information and multi-output characteristics, making it difficult to ensure model fitting accuracy while taking into account the sparsity of basis functions. Furthermore, existing scheduling methods often fail to introduce transient stability constraints or oversimplify them. As a result, existing optimal power flow control methods face technical problems such as computational dimensionality explosion, low solution efficiency, and difficulty in accurately balancing high system energy efficiency and transient dynamic security defenses in scenarios with a high proportion of renewable energy grid connection. Therefore, this invention is proposed.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A power flow control method based on PGMSPCE with transient stability including wind and solar power includes the following steps: Step 1: Based on historical data, Weibull and Beta distributions are used to model the uncertainties of wind speed and light intensity, respectively, and finally obtain the wind and solar uncertainty input sources containing the probability density function of wind speed and the probability density of light intensity; in order to establish the independent probability distribution characteristics of wind and solar resources, and provide basic data that fits the actual operating conditions for system optimization; Step 2: For the uncertain input sources of wind and solar power obtained in Step 1, construct an opportunity-constrained transient stability optimal power flow model, and use the rotor angle deviation relative to the center of inertia as the transient stability criterion. Finally, obtain the original system mathematical model containing the comprehensive operation objective function, power flow balance constraints and transient stability opportunity constraints. This transforms the complex system dynamic calculus process into strict probabilistic safety constraints, and achieves rapid and accurate quantification of transient stability. Step 3: Based on the multi-output sparse polynomial chaotic expansion model with partial gradient enhancement, the original system mathematical model obtained in Step 2 is transformed into a deterministic model by combining Galerkin projection. Finally, a solvable and reconstructable model containing deterministic objective function and deterministic constraint boundary is obtained. Thus, while ensuring the model fitting accuracy, gradient information is used to achieve adaptive dimensionality reduction and decoupling of high-dimensional variables, which greatly reduces the computational complexity. Step 4: Use the ocean predator algorithm to solve for the deterministic objective function and deterministic constraint boundary obtained in Step 3, and iteratively optimize to obtain the optimal power flow control strategy; to efficiently handle nonlinear constraints and avoid getting trapped in local optima, ensuring that the algorithm converges quickly and stably to the global optimum. Step 5: Generate underlying hardware drive instructions based on the optimal power flow control strategy to adjust the active and reactive power output of each grid-connected generator in the power grid in real time, so as to maintain the transient stable operation of the power grid physical system under the expected fault; thereby ensuring the safety and reliability of the real power grid physical dispatch under the high proportion of new energy access.

[0007] Step 1 specifically includes the following steps: Step 1-1: Collect historical wind speed data from wind farms for preprocessing, model wind speed using Weibull distribution, determine the wind speed probability density function, and combine it with the wind turbine operating characteristic curves to determine the wind power output. Steps 1-2: Collect historical solar irradiance data of photovoltaic power plants for preprocessing, use Beta distribution to model solar irradiance, determine the probability density function of solar irradiance, and combine it with the photoelectric conversion physical model to determine the photovoltaic output power. Finally, obtain the wind-solar uncertainty input source that includes the probability density function of wind speed and the probability density of solar irradiance.

[0008] Step 2 specifically includes the following steps: Step 2-1: Establish the comprehensive operational objective function of the system, with the goal of minimizing the expected value of the basic comprehensive operational parameters of all thermal power units in the network; Step 2-2: Establish power flow equality constraints that include the balance of active and reactive power injection at nodes, as well as chance constraint inequalities for node state variables; Step 2-3: For anticipated faults, calculate the rotor angle deviation of each thermal power unit relative to the center of inertia, construct the opportunity constraint of rotor angle deviation as a transient stability criterion, and finally combine the comprehensive operation objective function obtained in Step 2-1, the power flow equality constraint obtained in Step 2-2, the opportunity constraint inequality, and the rotor angle deviation opportunity constraint to obtain the original system mathematical model.

[0009] Step 3 specifically includes the following steps: Step 3-1: Based on the distribution information of the wind and solar uncertainty input sources, select orthogonal basis functions and construct the initial PCE surrogate model; Step 3-2: Construct a partial gradient dataset, filter out the key uncertainties that affect the system state, and use the fixed-point iteration method to filter out the key PCE terms; Step 3-3: Represent the moment information of the running variables as a deterministic function of the PCE coefficients; Steps 3-4: Based on Galerkin projection, transform the power flow equality constraints into deterministic equations for PCE coefficients; Steps 3-5: Express the integrated operation objective function as a deterministic function of the PCE coefficients, and substitute the deterministic function of the PCE coefficients into the power flow equations and transient stability constraints to finally obtain the reconstructed solvable reconstructable model containing the deterministic objective function and deterministic constraint boundaries.

[0010] Step 4 specifically includes the following steps: Step 4-1: Define the set of control variables, i.e., the PCE coefficients of the running variables, and set the population size for the marine predator algorithm. Maximum number of iterations FADs probability An initial population is randomly generated, such that each individual in the initial population represents a power system control strategy; Step 4-2: Calculate the transient stability index and the fitness of the overall objective function for each individual in the initial population, and select the strategy with the best overall fitness as the elite strategy to guide subsequent iterative search; Step 4-3: In the early stage of iteration, the control strategies within the population are extensively explored using Brownian motion to simulate the physical process of a power system adjusting control variables over a wide range after a fault. In the middle stage of iteration, half of the population strategies are used for local fine-tuning using Lévy flight, while the other half continue to explore using Brownian motion to balance high energy efficiency and stability search. In the later stage of iteration, all population strategies are fine-tuned around the aforementioned elite strategies using Lévy flight to optimize transient stability margin. Step 4-4: Using mutation probability By introducing a mutation perturbation similar to the eddy current effect of FADs, and randomly adjusting the control variables of some individuals in the population, we can simulate the scenario of sudden power system failure or load change, thus avoiding the optimization process from getting trapped in local optima. Steps 4-5: Compare the transient stability performance of the old and new strategies before and after the disturbance with the fitness of the comprehensive operating objective function, retain the better strategy, and update the current elite strategy of the system. Steps 4-3 to 4-5: Repeat steps 4-3 to 4-5 until the maximum number of iterations is reached. Alternatively, if the set convergence conditions are met, the final elite strategy is output as the optimal power flow control strategy in step 5.

[0011] In step 1-1, the formula used to determine the wind speed probability density function is as follows: (1); In the formula: Let be the wind speed probability density function; The magnitude of the wind speed; For shape parameters; For scale parameters; The formula used to determine the wind power output based on the wind turbine's operating characteristic curve is expressed as follows: (2); In the formula: Contributing to the active power of wind power; Rated power; To cut in wind speed; Rated wind speed; To cut off the wind speed.

[0012] In steps 1-2, the formula used to determine the probability density function of light intensity is as follows: (3); In the formula: Let be the probability density function of light intensity; Normalized light intensity; , These are the shape parameters; It is a gamma function; The formula used to determine the photovoltaic output power based on the photoelectric conversion physical model is expressed as follows: (4); In the formula: Contributing to the power of optoelectronics; Light intensity; The effective area of ​​the photovoltaic array; This refers to the photoelectric conversion efficiency.

[0013] In step 2-1, the formula used to establish the comprehensive operational objective function of the system is expressed as follows: (5); In the formula: Total power generation cost; This represents the total number of thermal power generators in the power grid. , , All are fuel cost coefficients; For the first The active power output of the thermal power generator; This is the expected value; In step 2-2, the established power flow equality constraints and chance constraint inequalities for nodal state variables are expressed using the following set of formulas: (6); In the formula: For an uncertain source vector, , For the first An uncertain source, , The total number of uncertain sources; For runtime variables; , They are respectively The lower and upper limits; , They are nodes The active and reactive power injected by wind power; , They are nodes The active and reactive power injected by photoelectric sensors; , They are nodes The active and reactive power of the load; , They are nodes Uncertain sources of active and reactive power injection; For nodes The reactive power injection of the thermal power generator; , They are nodes The real and imaginary parts of the voltage; , They are nodes The real and imaginary parts of the voltage; , They are nodes , between admittance The real and imaginary parts; For nodes The voltage amplitude; For nodes and Line current between; For chance constraints to violate probability, , , , , These represent the probability of violation of opportunity constraints for generator active and reactive power, node voltage, and line current, respectively. Operators for probabilistic solutions; In steps 2-3, the rotor angular deviation of each thermal power unit relative to the center of inertia is calculated, and the formula used to construct the chance constraint of the rotor angular deviation is expressed as follows: (7); In the formula: For the first The inertial time constant of a thermal power generator; For the first The rotor angle deviation of the thermal power generator relative to the center of inertia; , The first , Rotor angle of a thermal power generator; This is the unstable limit; The probability of violating the opportunity constraint for rotor angular deviation.

[0014] In step 3-1, the formula used to construct the initial PCE proxy model is expressed as follows: (8); In the formula: For runtime variables; for The PCE coefficient; For the first Term basis functions; For the PCE item count index set, , This represents the total number of PCE items. In step 3-2, the calculation formula used to construct the partial gradient dataset and select PCE key terms is expressed as follows: (9); In the formula: For the first Individual and runtime variables; For the first The relative contribution of each uncertain source; Threshold for filtering uncertain sources; , The first , The derivative sensitivity index of an uncertain source; This represents the total number of variables used in the runtime environment. For variance; for The PCE coefficient; For the first The relative importance ratio of the term coefficients; The filtering threshold; It is a 2-norm.

[0015] In step 3-3, the formula used to represent the moment information of the running variables as a deterministic function of the PCE coefficients is as follows: (10); In the formula: This is an inner product operation; For the first The inner product of the term basis functions; For runtime variables; for The zeroth PCE coefficient; for The PCE coefficient; Standard deviation; In steps 3-5, the final solvable reconstructable model containing a deterministic objective function and deterministic constraint boundaries is represented as follows: (11); (12); In the formula: , They are respectively , The PCE coefficient; , They are respectively , The PCE coefficient; , They are respectively , The PCE coefficient; For the first Term basis functions; For the active power flow equation; The reactive power flow equation; for The zeroth PCE coefficient; for The PCE coefficient; For runtime variables; , They are respectively The lower and upper limits; It is the inverse cumulative distribution function of the violation probability.

[0016] Compared with the prior art, the present invention has the following technical effects: 1) To address the problem of computational bloat that existing technologies tend to fall into when dealing with the uncertainties of multiple variables in wind and solar power, this invention introduces a multi-output sparse polynomial chaotic expansion PGMSPCE model with partial gradient enhancement. By constructing a partial gradient dataset and calculating the derivative sensitivity index, key uncertainty sources that significantly affect the system state are accurately identified. While ensuring the accuracy of the surrogate model in fitting multiple output variables, redundant high-order cross terms are adaptively eliminated, achieving an efficient and accurate representation of complex stochastic responses. 2) To address the problem of strategy distortion caused by neglecting or simplifying transient stability constraints in traditional methods, this invention establishes a transient stability constraint system based on the rotor angle deviation relative to the center of inertia (COI). Combined with chance-constrained programming theory, it allows the system to flexibly adjust its operating point within a very small probability threshold. This can more accurately reflect the relative sway characteristics between units and realize the precise quantification and control of the system's transient stability margin under uncertain wind and solar environments. 3) To address the problem of premature convergence in traditional optimization algorithms when dealing with complex models, this invention uses the Marine Predator Algorithm (MPA) to solve the reconstructed deterministic model. This utilizes a three-stage search mechanism and dynamic switching between Brownian motion and Lévy flight, combined with the built-in FADs mutation perturbation effect, to greatly enhance the algorithm's ability to escape local optima traps, ensuring the safe, stable, and energy-efficient operation of the power system under complex operating conditions. Attached Figure Description

[0017] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the IEEE 39-node system in an example of the present invention; Figure 3 This is a relative rotor angle diagram of the IEEE 39-node system in an example of the present invention without using the method of the present invention; Figure 4 This is a relative rotor angle diagram obtained by using the optimization method of this invention in the IEEE 39-bus system in an example of this invention; Figure 5 This is a flowchart of the algorithm for solving CC-TSCOPF in this invention. Detailed Implementation

[0018] like Figure 1 As shown, a power flow control method based on PGMSPCE with transient stability includes the following steps: Step 1: Based on historical wind and solar data, Weibull and Beta distributions are used to model the uncertainties of wind speed and light intensity, respectively; Step 2: To address the uncertainties of wind and solar power, a chance-constrained transient stable optimal power flow (CC-TSCOPF) is constructed, and the rotor angle deviation relative to the center of inertia (COI) is used as the transient stability criterion. Step 3: Based on the Partial Gradient-Enhanced Multi-output Sparse Polynomial Chaos Expansion (PGMSPCE) model, the CC-TSCOPF model is transformed into a deterministic model by combining Galerkin projection. Step 4: Solve the reconstructed CC-TSCOPF model using the Marine Predators Algorithm (MPA).

[0019] In step 1, based on historical wind and solar data, Weibull and Beta distributions are used to model wind speed and solar intensity, respectively.

[0020] 1) Wind speed probability model Based on historical wind speed data, the Weibull distribution is used to model wind speed, and its probability density function is: (1); In the formula: Let be the wind speed probability density function; The magnitude of the wind speed; For shape parameters; This is the scale parameter.

[0021] Wind power output can be determined from the wind speed-wind power output curve: (2); In the formula: Contributing to the active power of wind power; Rated power; To cut in wind speed; Rated wind speed; To cut off the wind speed.

[0022] 2) Probabilistic model of light intensity Based on historical light intensity data, a Beta distribution is used to model light intensity, and its probability density function is: (3); In the formula: Let be the probability density function of light intensity; Normalized light intensity; , These are the shape parameters; This is a gamma function.

[0023] Photovoltaic power can be determined by the relationship between light intensity and photovoltaic power curve: (4); In the formula: Contributing to the power of optoelectronics; Light intensity; The effective area of ​​the photovoltaic array; This refers to the photoelectric conversion efficiency.

[0024] In step 2, CC-TSCOPF is established, and the transformation of transient stability constraints is completed.

[0025] 1) Objective function: (5); In the formula: Total power generation cost; This represents the total number of thermal power generators in the power grid. , , All are fuel cost coefficients; For the first The active power output of the thermal power generator; This is the expected value.

[0026] 2) Steady-state constraints: (6); In the formula: For an uncertain source vector, , For the first An uncertain source, , The total number of uncertain sources; For runtime variables; , They are respectively The lower and upper limits; , They are nodes The active and reactive power injected by wind power; , They are nodes The active and reactive power injected by photoelectric sensors; , They are nodes The active and reactive power of the load; , They are nodes Uncertain sources of active and reactive power injection; For nodes The reactive power injection of the thermal power generator; , They are nodes The real and imaginary parts of the voltage; , They are nodes The real and imaginary parts of the voltage; , They are nodes , between admittance The real and imaginary parts; For nodes The voltage amplitude; For nodes and Line current between; For chance constraints to violate probability, , , , , These represent the probability of violation of opportunity constraints for generator active and reactive power, node voltage, and line current, respectively. For probabilistic solvers.

[0027] 4) Transient stability constraints: (7); In the formula: For the first The inertial time constant of a thermal power generator; For the first The rotor angle deviation of the thermal power generator relative to the center of inertia; , The first , Rotor angle of a thermal power generator; This is the unstable limit; The probability of violating the opportunity constraint for rotor angular deviation.

[0028] In step 3, the CC-TSCOPF model is transformed into a deterministic model based on the PGMSPCE model and combined with Galerkin projection.

[0029] Step 3-1: Based on the distribution information of the scenery, select orthogonal basis functions and construct the initial PCE proxy model: (8); In the formula: For runtime variables; for The PCE coefficient; For the first Term basis functions; For the PCE item count index set, , This represents the total number of PCE items.

[0030] Step 3-2: Construct a partial gradient dataset, filter out important sources of uncertainty, and use fixed-point iteration to filter out key PCE terms, calculated as follows: (9); In the formula: For the first One runtime variable; For the first The relative contribution of each uncertain source; Threshold for filtering uncertain sources; , The first , The derivative sensitivity index of an uncertain source; This represents the total number of variables used in the runtime environment. For variance; for The PCE coefficient; For the first The relative importance ratio of the term coefficients; The filtering threshold; It is a 2-norm.

[0031] Step 3-3: Represent the moment information of the running variables as a deterministic function of the PCE coefficients: (10); In the formula: This is an inner product operation; For the first The inner product of the term basis functions; For runtime variables; for The zeroth PCE coefficient; for The PCE coefficient; The standard deviation is denoted as .

[0032] Steps 3-4: Based on Galerkin projection, transform the power flow equations into deterministic equations for the PCE coefficients; Steps 3-5: Express the objective function as a deterministic function of the PCE coefficients, and substitute equation (10) into equations (6) and (7) to obtain the reconstructed CC-TSCOPF model: (11); (12); In the formula: , They are respectively , The PCE coefficient; , They are respectively , The PCE coefficient; , They are respectively , The PCE coefficient; For the first Term basis functions; For the active power flow equation; The reactive power flow equation; for The zeroth PCE coefficient; for The PCE coefficient; For runtime variables; , They are respectively The lower and upper limits; It is the inverse cumulative distribution function of the violation probability.

[0033] In step 4, MPA is used to solve the reconstructed CC-TSCOPF model.

[0034] Step 4-1: Define the set of control variables, i.e., the PCE coefficients of the running variables, and set the population size. Maximum number of iterations FADs probability An initial population is randomly generated, with each individual representing a control strategy; Step 4-2: Calculate the transient stability index and power flow cost of each strategy in the initial population, and select the overall optimal strategy as the elite strategy to guide subsequent searches; Step 4-3: In the early stage of iteration, the control strategy is explored extensively using Brownian motion to simulate the process of the system adjusting control variables on a large scale after a failure; in the middle stage of iteration, half of the strategies are developed locally using Lévy flight, while the other half continue to explore using Brownian motion to balance efficiency and stability search; in the later stage of iteration, the strategy is fine-tuned around the elite strategy using Lévy flight to optimize transient stability margin and efficiency. Step 4-4: Using probability By introducing sudden disturbances similar to FADs and randomly adjusting some control variables, we can simulate power system faults or load changes and avoid optimization getting trapped in local optima. Steps 4-5: Compare the transient stability performance and current flow cost of the new and old strategies, retain the better strategy, and update the elite strategy; Steps 4-6: Repeat steps 4-3 to 4-5 until the desired result is achieved. If the convergence condition is met, the elite strategy is output as the optimal control scheme.

[0035] Example: The method described in this invention was tested and verified in an improved IEEE 39-node system. For example... Figure 2 As shown, the system comprises 39 buses, 8 thermal power generators, and 46 branches. The system's baseline total active load is approximately 6097MW. Bus 34 houses a wind farm with a rated power of 300MW, and bus 37 houses a photovoltaic power station with a rated power of 200MW. The renewable energy penetration rate is approximately 8%. The load level varies in 5% increments within the range of 80% to 120% of the baseline value to simulate load fluctuations in actual operation.

[0036] The wind speed of the wind farm was modeled using a Weibull distribution fitted from historical data, and the solar irradiance of the photovoltaic power station was modeled using a Beta distribution fitted from historical data. The Ocean Predator algorithm was used to solve the models. Detailed parameter configurations for the system, wind and solar power stations, and the algorithm are shown in Table 1.

[0037] The improved IEEE 39-bus system configured in Table 1 is a widely used multi-machine test system in transient stability analysis. Its multiple generator units and tightly coupled transmission network can fully demonstrate the interaction and power angle swing characteristics between the units after a fault. After replacing the conventional units at bus 34 and bus 37 with wind farms and photovoltaic power stations, the system introduces significant power supply-side randomness while retaining the necessary synchronous regulation capability. Combined with the wide range of load fluctuations, this constitutes a test environment with dual uncertainties on both the power supply and load sides, which can effectively verify the transient stability control capability and economic dispatch performance of the method of this invention under variable operating conditions.

[0038] To verify the system transient stability of the method of this invention, a three-phase short-circuit fault was set at bus 14, with a fault start time of 0.5 seconds and a duration of 0.2 seconds, and a 10-second time-domain simulation was performed. When the traditional TSCOPF method is used for scheduling, the generator-to-rotor angle curve of the system after the fault is as follows: Figure 3 As shown, the generator rotor angle continuously increases, leading to transient instability in the system. This indicates that the traditional TSCOPF model is insufficient to guarantee the dynamic safety of the system when dealing with wind and solar uncertainties. However, after optimizing the scheduling using the method proposed in this invention, the generator relative rotor angle curve under the same fault is as follows: Figure 4As shown, the power angles of each generator remained synchronized after the fault, the system remained stable, and the transient stability margin was significantly improved. To further investigate the impact of fault duration on system transient stability, a comparative simulation was conducted by changing the fault duration of a three-phase short circuit on bus 14. The results are shown in Table 2.

[0039] As shown in Table 2, the duration of the three-phase short-circuit fault on bus 14 has a decisive impact on the system's transient stability. When using the traditional TSCOPF method for scheduling, a fault duration of 0.10 seconds can maintain critical stability, while a duration of 0.20 seconds leads to transient instability. However, when using the method of this invention, even with a fault duration of 0.20 seconds, the maximum relative power angle of the first swing after the fault is only about 81.6° and converges rapidly; a further increase in duration to 0.30 seconds still maintains critical stability. These results demonstrate that the method of this invention can significantly expand the system's transient stability margin under severe faults.

[0040] To comprehensively evaluate the performance of the method of this invention in terms of efficiency and transient stability, it was further compared with the deterministic optimal power flow method and the traditional TSCOPF method. The results are shown in Table 3:

[0041] As shown in Table 3, although the deterministic optimal power flow method has the lowest power generation cost, it fails to consider transient stability constraints, resulting in a critical disconnection time of only 0.08 seconds at bus 14, which cannot guarantee the safe operation of the system. While the traditional TSCOPF method can satisfy transient stability when the fault duration is short, its power generation cost is higher than that of the method proposed in this invention. The power generation cost of the method proposed in this invention is reduced by 1.77% compared to the traditional TSCOPF method, and the critical disconnection time at bus 14 is extended from 0.16 seconds in the traditional TSCOPF method to 0.34 seconds, significantly enhancing the transient safety of the system while ensuring operational efficiency. These advantages are mainly due to the PGMSPCE method's accurate identification of key uncertainty sources and reduction of decision-making dimensionality using gradient information, and the MPA three-stage search mechanism's dynamic balance between global exploration and local development, making the optimization results more efficient while ensuring system safety.

[0042] Compared with existing technologies, the optimal power flow control method based on PGMSPCE with wind and solar transient stability proposed in this invention has the following advantages: In handling transient stability constraints, this invention is based on the COI framework, using the rotor angle deviation of each generator relative to the COI as the transient stability criterion, which more accurately reflects the relative sway characteristics between units, thus achieving accurate assessment of system transient stability under uncertain wind and solar environments. Simultaneously, by combining chance-constrained programming theory and setting reasonable violation probabilities, the system is allowed to flexibly adjust its operating point within a very small risk threshold, making the optimization results more efficient while ensuring safety, especially suitable for grid environments with increasingly higher requirements for operational efficiency under the background of high-proportion renewable energy access. In terms of model transformation, the PGMSPCE used in this invention introduces partial gradient information to construct a sensitivity index, which can accurately identify key uncertainty sources that significantly affect the system state, significantly reducing the decision-making dimensionality. Furthermore, by employing a sparse screening strategy to ensure the surrogate model's fitting accuracy to multiple output variables, unimportant high-order PCE cross terms are eliminated, thereby achieving accurate characterization of complex stochastic responses with a minimal number of basis function combinations. Compared to traditional PCE, PGMSPCE achieves higher fitting accuracy and significantly improved computational efficiency when dealing with high-dimensional, multi-output, and strongly coupled uncertainty propagation problems in power systems, and can more reliably capture the coupling relationships between output variables. In model solving, this invention employs MPA to solve the reconstructed CC-TSCOPF model. Its three-stage search mechanism dynamically balances global exploration and local development: in the early iteration stage, Brownian motion is used to explore the solution space over a large area, simulating scenarios where the system needs global adjustment after a fault; in the middle iteration stage, half of the population uses Lévy flight for local fine-tuning, while the other half continues Brownian motion exploration, achieving parallel optimization of efficiency and stability; in the later iteration stage, Lévy flight is used for fine-tuning around an elite strategy to finely optimize transient stability margins. Furthermore, the algorithm's built-in FADs effect applies random perturbations with a certain probability, effectively simulating sudden grid faults or load changes, helping the algorithm escape local optima traps, enhancing the robustness of the optimization scheme, and thus better ensuring the safe and stable operation of the power system under wind and solar grid-connected conditions.

Claims

1. A power flow control method based on PGMSPCE with transient stability and optimality, characterized in that, Includes the following steps: Step 1: Based on historical data, perform uncertainty modeling on wind speed and light intensity respectively to obtain wind and light uncertainty input sources including wind speed probability density function and light intensity probability density function; Step 2: For the wind and solar uncertainty input sources obtained in Step 1, construct the opportunity-constrained transient stability optimal power flow model and obtain the original system model containing the comprehensive operating objective function, power flow balance constraints and transient stability opportunity constraints; Step 3: Transform the original system model obtained in Step 2 into a deterministic model to obtain a solvable and reconstructable model containing a deterministic objective function and deterministic constraint boundaries; Step 4: Solve for the deterministic objective function and deterministic constraint boundary obtained in Step 3, and iteratively optimize to obtain the optimal power flow control strategy; Step 5: Generate underlying hardware drive instructions based on the optimal power flow control strategy to adjust the active and reactive power output of each grid-connected generator in real time, so as to maintain the transient stable operation of the power grid physical system under the expected fault.

2. The method according to claim 1, characterized in that, Step 1 specifically includes the following steps: Step 1-1: Collect historical wind speed data from wind farms for preprocessing, model wind speed using Weibull distribution, determine the wind speed probability density function, and combine it with the wind turbine operating characteristic curves to determine the wind power output. Steps 1-2: Collect historical solar irradiance data of photovoltaic power plants for preprocessing, use Beta distribution to model solar irradiance, determine the probability density function of solar irradiance, and combine it with the photoelectric conversion physical model to determine the photovoltaic output power. Finally, obtain the wind-solar uncertainty input source that includes the probability density function of wind speed and the probability density of solar irradiance.

3. The method according to claim 1, characterized in that, Step 2 specifically includes the following steps: Step 2-1: Establish the comprehensive operational objective function of the system, with the goal of minimizing the expected value of the basic comprehensive operational parameters of all thermal power units in the network; Step 2-2: Establish power flow equality constraints that include the balance of active and reactive power injection at nodes, as well as chance constraint inequalities for node state variables; Step 2-3: For anticipated faults, calculate the rotor angle deviation of each thermal power unit relative to the center of inertia, construct the opportunity constraint of rotor angle deviation as a transient stability criterion, and finally combine the comprehensive operation objective function obtained in Step 2-1, the power flow equality constraint obtained in Step 2-2, the opportunity constraint inequality, and the rotor angle deviation opportunity constraint to obtain the original system mathematical model.

4. The method according to claim 1, characterized in that, Step 3 specifically includes the following steps: Step 3-1: Based on the distribution information of the wind and solar uncertainty input sources, select orthogonal basis functions and construct the initial PCE surrogate model; Step 3-2: Construct a partial gradient dataset, filter out the key uncertainties that affect the system state, and use the fixed-point iteration method to filter out the key PCE terms; Step 3-3: Represent the moment information of the running variables as a deterministic function of the PCE coefficients; Steps 3-4: Based on Galerkin projection, transform the power flow equality constraints into deterministic equations for PCE coefficients; Steps 3-5: Express the integrated operation objective function as a deterministic function of the PCE coefficients, and substitute the deterministic function of the PCE coefficients into the power flow equations and transient stability constraints to finally obtain the reconstructed solvable reconstructable model containing the deterministic objective function and deterministic constraint boundaries.

5. The method according to claim 1, characterized in that, Step 4 specifically includes the following steps: Step 4-1: Define the set of control variables, i.e., the PCE coefficients of the running variables, and set the population size for the marine predator algorithm. Maximum number of iterations FADs probability An initial population is randomly generated, such that each individual in the initial population represents a power system control strategy; Step 4-2: Calculate the transient stability index and the fitness of the overall objective function for each individual in the initial population, and select the strategy with the best overall fitness as the elite strategy to guide subsequent iterative search; Step 4-3: In the early stage of iteration, the control strategies within the population are extensively explored using Brownian motion to simulate the physical process of a power system adjusting control variables over a wide range after a fault. In the middle stage of iteration, half of the population strategies are used for local fine-tuning using Lévy flight, while the other half continue to explore using Brownian motion to balance high energy efficiency and stability search. In the later stage of iteration, all population strategies are fine-tuned around the aforementioned elite strategies using Lévy flight to optimize transient stability margin. Step 4-4: Using mutation probability By introducing a mutation perturbation similar to the eddy current effect of FADs, and randomly adjusting the control variables of some individuals in the population, we can simulate the scenario of sudden power system failure or load change, thus avoiding the optimization process from getting trapped in local optima. Steps 4-5: Compare the transient stability performance of the old and new strategies before and after the disturbance with the fitness of the comprehensive operating objective function, retain the better strategy, and update the current elite strategy of the system. Steps 4-3 to 4-5: Repeat steps 4-3 to 4-5 until the maximum number of iterations is reached. Alternatively, if the set convergence conditions are met, the final elite strategy is output as the optimal power flow control strategy in step 5.

6. The method according to claim 2, characterized in that, In step 1-1, the formula used to determine the wind speed probability density function is as follows: （1）； In the formula: Let be the wind speed probability density function; The magnitude of the wind speed; For shape parameters; For scale parameters; The formula used to determine the wind power output based on the wind turbine's operating characteristic curve is expressed as follows: （2）； In the formula: Contributing to the active power of wind power; Rated power; To cut in wind speed; Rated wind speed; To cut off the wind speed.

7. The method according to claim 2, characterized in that, In steps 1-2, the formula used to determine the probability density function of illumination intensity is as follows: （3）； In the formula: Let be the probability density function of light intensity; Normalized light intensity; , These are the shape parameters; It is a gamma function; The formula used to determine the photovoltaic output power based on the photoelectric conversion physical model is expressed as follows: （4）； In the formula: Contributing to the power of optoelectronics; Light intensity; The effective area of ​​the photovoltaic array; This refers to the photoelectric conversion efficiency.

8. The method according to claim 3, characterized in that, In step 2-1, the formula used to establish the comprehensive operational objective function of the system is as follows: （5）； In the formula: Total power generation cost; This represents the total number of thermal power generators in the power grid. , , All are fuel cost coefficients; For the first The active power output of the thermal power generator; This is the expected value; In step 2-2, the established power flow equality constraints and chance constraint inequalities for nodal state variables are expressed using the following set of formulas: （6）； In the formula: For an uncertain source vector, , For the first An uncertain source, , The total number of uncertain sources; For runtime variables; , They are respectively The lower and upper limits; , They are nodes The active and reactive power injected by wind power; , They are nodes The active and reactive power injected by photoelectric sensors; , They are nodes The active and reactive power of the load; , They are nodes Uncertain sources of active and reactive power injection; For nodes The reactive power injection of the thermal power generator; , They are nodes The real and imaginary parts of the voltage; , They are nodes The real and imaginary parts of the voltage; , They are nodes , between admittance The real and imaginary parts; For nodes The voltage amplitude; For nodes and Line current between; For chance constraints to violate probability, , , , , These represent the probability of violation of opportunity constraints for generator active and reactive power, node voltage, and line current, respectively. Operators for probabilistic solutions; In steps 2-3, the rotor angular deviation of each thermal power unit relative to the center of inertia is calculated, and the formula used to construct the chance constraint of the rotor angular deviation is expressed as follows: （7）； In the formula: For the first The inertial time constant of a thermal power generator; For the first The rotor angle deviation of the thermal power generator relative to the center of inertia; , The first , Rotor angle of a thermal power generator; This is the unstable limit; The probability of violating the opportunity constraint for rotor angular deviation.

9. The method according to claim 4, characterized in that, In step 3-1, the formula used to construct the initial PCE proxy model is expressed as follows: （8）； In the formula: For runtime variables; for The PCE coefficient; For the first Term basis functions; For the PCE item count index set, , This represents the total number of PCE items. In step 3-2, the calculation formula used to construct the partial gradient dataset and select PCE key terms is expressed as follows: （9）； In the formula: For the first Individual and runtime variables; For the first The relative contribution of each uncertain source; Threshold for filtering uncertain sources; , The first , The derivative sensitivity index of an uncertain source; This represents the total number of variables used in the runtime environment. For variance; for The PCE coefficient; For the first The relative importance ratio of the term coefficients; The filtering threshold; It is a 2-norm.

10. The method according to claim 4 or 9, characterized in that, In step 3-3, the formula used to represent the moment information of the running variables as a deterministic function of the PCE coefficients is as follows: （10）； In the formula: This is an inner product operation; For the first The inner product of the term basis functions; For runtime variables; for The zeroth PCE coefficient; for The PCE coefficient; Standard deviation; In steps 3-5, the final solvable reconstructable model containing a deterministic objective function and deterministic constraint boundaries is represented as follows: （11）； （12）； In the formula: , They are respectively , The PCE coefficient; , They are respectively , The PCE coefficient; , They are respectively , The PCE coefficient; For the first Term basis functions; For the active power flow equation; The reactive power flow equation; for The zeroth PCE coefficient; for The PCE coefficient; For runtime variables; , They are respectively The lower and upper limits; It is the inverse cumulative distribution function of the violation probability.

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