A scheduling side optimization method of a power grid safety control system and a computer device

By updating the parameters of the power grid dynamic operation model in real time and dynamically adjusting the model parameters, the problem that the power grid operation model cannot adapt to rapid changes has been solved, enabling more accurate power grid optimization scheduling and improving the stability and efficiency of the power grid.

CN119298123BActive Publication Date: 2025-12-19HAIBEI POWER SUPPLY COMPANY STATE GRID QINGHAI ELECTRIC POWER +3
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Patent Information

Application Number
CN202411286925.7
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Priority Date
2024-08-14
Filing Date
2024-09-13
Publication Date
2025-12-19
Estimated Expiration
2044-09-13

AI Technical Summary

Technical Problem

The parameters of the existing power grid operation model are fixed and cannot adapt to the rapid dynamic changes of the power grid, resulting in unreasonable optimization results.

Method used

The Kalman filter algorithm is used to update the parameters of the power grid dynamic operation model in real time, and the model parameters are dynamically adjusted by combining the reinforcement learning algorithm to construct a dynamic optimization scheduling model. The least squares support regression vector machine and deep learning model are combined to predict power generation and load, and optimize the output and input/output of new energy and energy storage equipment.

Benefits of technology

It improves the accuracy and adaptability of the power grid dynamic operation model, optimizes dispatch results to be more reasonable, enhances the stability and reliability of the power grid, reduces the need for manual intervention, and improves the system's operating efficiency and security.

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Abstract

The application belongs to the technical field of power systems, and particularly relates to a dispatch side optimization method of a power grid safety control system and a computer device. The method comprises the following steps: S1, acquiring real-time operation data of the power grid; S2, establishing a dynamic operation model of the power grid; the dynamic operation model of the power grid comprises a state space equation with power grid operation state parameters as state variables; and a Kalman filtering algorithm is used to update the state space equation in real time according to the real-time operation data; S3, constructing an optimal dispatching model with the dynamic operation model of the power grid as a constraint condition, and solving the optimal dispatching model to obtain optimal output of each new energy power generation unit and input or output power of each energy storage device in the power grid; and S4, executing the optimal output of each new energy power generation unit and the input or output power of each energy storage device. The application solves the technical problem that the model parameters of the power grid operation model constructed in the prior art are fixed and cannot adapt to rapid dynamic changes of the power grid, resulting in unreasonable optimization results.
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Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power systems, and particularly relates to a dispatch side optimization method of a power grid safety control system and a computer device. BACKGROUND

[0002] The distribution network refers to a power grid that accepts electric energy from a power transmission network or a regional power plant, and distributes the electric energy to various users through distribution facilities or step by step according to voltages. The distribution network is composed of overhead lines, cables, towers, distribution transformers, disconnectors, reactive power compensators and some auxiliary facilities, and plays an important role in distributing electric energy in the power grid.

[0003] With the construction of the ultra-high voltage network frame of the power grid, the characteristics of "strong straight and weak intersection" are obvious, and the risk of stable operation of the power grid is increasing. In order to ensure the safe and stable and economic operation of the power grid, a large number of power grid safety and stability control systems, i.e. the second safety defense line of the power grid, are configured in the sending and receiving end power grid. At present, a typical power grid safety and stability control system includes an ancillary control substation and a plurality of ancillary control operation devices. The substation collects plant station information, identifies the operation mode to realize control strategy retrieval. The execution device collects information, judges faults and realizes local control.

[0004] At present, the new energy consumption, power flow and voltage problem of the regional power grid with high penetration of distributed energy usually presents the characteristics of whole network and decentralization. Only investigating a single source and adjusting a single end device has limited adjustment capacity and cannot effectively solve the system problems in this operation scenario. On the other hand, with the continuous increase of the scale of the distribution network, the research on the corresponding control framework and the interaction mode between different levels is still lacking.

[0005] In general, the power grid optimization scheduling needs to establish a power grid operation model to reflect the actual operation state of the power grid. The power grid operation model established in the prior art is mostly offline and static. For example, the Chinese patent application publication No. CN112350380A published on February 9, 2021 discloses a dispatch side operation model construction method and system of a power grid safety and stability control system. The method for constructing the ancillary control operation model includes the following steps: constructing an offline information model; and constructing a quasi-real-time scheduling model. The constructed ancillary control operation model is offline and static, which cannot adapt to the rapid dynamic changes of the power grid, so that the optimization result is affected when the optimization scheduling is performed, resulting in unreasonable optimization result. SUMMARY

[0006] The purpose of the present application is to provide a dispatch side optimization method of a power grid safety control system and a computer device, so as to solve the technical problem that the model parameters of the power grid operation model constructed in the prior art are fixed and cannot adapt to the rapid dynamic changes of the power grid, resulting in unreasonable optimization result.

[0007] To solve the above technical problems, the technical scheme of the method for optimizing the scheduling side of the power grid safety control system provided by the application is as follows: a method for optimizing the scheduling side of the power grid safety control system, the method comprising:

[0008] S1, acquiring real-time operation data of the power grid;

[0009] S2, establishing a dynamic operation model of the power grid;

[0010] The dynamic operation model of the power grid comprises a state space equation taking power grid operation state parameters as state variables; and a Kalman filtering algorithm is used to update the state variables of the state space equation in real time according to the real-time operation data;

[0011] S3, constructing an optimal scheduling model with the dynamic operation model of the power grid as a constraint condition, and solving the optimal scheduling model to obtain optimal output of each new energy power generation unit and input or output power of each energy storage device in the power grid;

[0012] S4, executing the optimal output of each new energy power generation unit and the input or output power of each energy storage device obtained in S3.

[0013] The beneficial effects of the above technical scheme are as follows: the technical scheme of the method for optimizing the scheduling side of the power grid safety control system belongs to an improved invention. When establishing the dynamic operation model of the power grid, the Kalman filtering algorithm is used to update the model parameters in real time, achieving good dynamic tracking effect. This real-time updating capability greatly improves the actual power grid operation accuracy represented by the dynamic operation model of the power grid, providing a more accurate dynamic operation model, so that the final optimization result is more reasonable. The application solves the technical problem that the model parameters of the power grid operation model constructed in the prior art are fixed and cannot adapt to rapid dynamic changes of the power grid, resulting in unreasonable optimization results.

[0014] Further, the S4 further comprises: in the execution process, a reinforcement learning algorithm is used to adjust the power grid operation state parameters in real time to make the power grid meet the conditions for stable operation; the conditions for stable operation include that the power supply and demand of the power grid are balanced, the transmission loss of electric energy does not exceed a preset transmission loss threshold, or the load fluctuation of the power grid does not exceed a preset load fluctuation threshold.

[0015] Further, the value function in the reinforcement learning algorithm is adjusted according to the following formula:

[0016]

[0017] Wherein, s t represents the real-time operation state parameters of the power grid at time t, a t represents a control decision, and a represents a learning rate, r trepresents an immediate reward, γ represents a discount factor, a' represents all possible actions at the next time, Q(s t , a t ) represents a value function of taking action a t in running state s t ; Q(s t+1 , a t+1 ) represents a value function of taking action a t+1 in running state s t+1 ; Q(s t+1 , a') represents a value function of taking action a' in running state s t+1 .

[0018] Further, the optimization objective of the optimization scheduling model in S3 is to maximize new energy consumption in the region, and the objective function is:

[0019]

[0020] where I represents a set of new energy generation units, c i is a contribution coefficient of the i-th new energy generation unit, x i is the output of the i-th new energy generation unit; J represents a set of energy storage devices, d j is a benefit coefficient of the j-th energy storage device, y j is the input or output power of the j-th energy storage device.

[0021] Further, the grid operating state parameters include at least one of node voltage, line flow, grid frequency, harmonic current, harmonic voltage, and three-phase imbalance degree.

[0022] Further, S2 further comprises establishing a power generation prediction model of the new energy generation unit, and the input parameters of the power generation prediction model of the new energy generation unit include at least one of solar radiation intensity, environmental temperature, environmental humidity, sunshine duration, photovoltaic component performance, degree of pollution of the photovoltaic panel, and inverter parameter performance on the output side of the new energy generation unit; the constraint condition of the optimization scheduling model in S3 further comprises the power generation prediction model.

[0023] Further, the power generation prediction model is a least squares support vector machine model, and the training formula is as follows:

[0024]

[0025] s.t.y i -w T Φ(x i )-b≤ε+ζ i

[0026]

[0027] i = 1, 2, …, N

[0028] where w is a weight vector, b is a bias, Φ(x i ) is a nonlinear mapping of sample x i , y i is the true value of the i-th sample, ε is an error threshold, C is a penalty factor, ζ i and ζ i * are slack variables, and N is the number of samples.

[0029] Further, S2 further comprises establishing a load forecasting model for load forecasting, an input parameter of the load forecasting model comprising meteorological data, and the load forecasting model adopting a deep learning model; and the constraint condition of the optimization scheduling model in S3 further comprises the load forecasting model.

[0030] Further, the constraint condition of the optimization scheduling model further comprises at least one of the following: a transmission power of each line of the power grid is not greater than a maximum power allowed to be transmitted by the corresponding line, an operating voltage of each device of the power grid is not greater than a rated voltage of the corresponding device, a voltage of each node of the power grid is not greater than a maximum threshold of the corresponding node voltage and not less than a minimum threshold of the corresponding node voltage, a frequency of the power grid is not greater than a maximum threshold of the frequency and not less than a minimum threshold of the frequency, and a load of each transformer is not greater than a rated capacity of the corresponding transformer.

[0031] The present application also provides a technical solution of a computer device: a computer device comprising a processor configured to execute a computer program to implement the steps of the dispatch side optimization method of the power grid safety control system. BRIEF DESCRIPTION OF DRAWINGS

[0032] Figure 1 is a method flowchart of an embodiment of the dispatch side optimization method of the power grid safety control system. DETAILED DESCRIPTION

[0033] In the establishment of the power grid dynamic operation model, the Kalman filtering algorithm is used to update the model parameters in real time, which greatly improves the actual power grid operation accuracy represented by the power grid dynamic operation model, and makes the final optimization result more reasonable. The present application solves the technical problem that the model parameters of the power grid operation model constructed in the prior art are fixed and cannot adapt to the rapid dynamic changes of the power grid, resulting in unreasonable optimization results.

[0034] Embodiment of the dispatch side optimization method of the power grid safety control system:

[0035] A dispatch side optimization method of a power grid safety control system, comprising the following steps: Figure 1As shown, comprising the following steps:

[0036] S1, acquiring real-time operation data of the power grid.

[0037] The embodiment acquires real-time operation data through the power grid dispatching automation system, and the real-time operation data includes but is not limited to node voltage, line flow, load change, distributed power output and power grid equipment state;

[0038] Specifically, the power grid operation data is acquired in real time through sensors, measuring devices and the power grid dispatching automation system deployed at each node, and the real-time operation data includes node voltage V(n), line flow P / Q(kW / kVar), load change ΔL(kW), distributed power output DPS(kW) and power grid equipment state information E (including equipment operating state, temperature, load condition and the like). Specifically, the power grid equipment mainly includes power generation equipment, power transmission and transformation equipment and power distribution equipment on the power transmission and distribution side, such as transformer load and switch equipment state.

[0039] The real-time data is transmitted to the data center in real time through sensors, smart meters and SCADA systems. For example, the acquisition formula of a node voltage V can be simplified as: Vn(t)=f(Sensor(t)), wherein Sensor(t) represents the sensor reading of the nth node at time t, and f() represents a data processing function, such as filtering, calibration and the like.

[0040] S2, establishing a dynamic operation model of the power grid.

[0041] The dynamic operation model of the power grid includes a state space equation taking power grid operation state parameters as state variables; and a Kalman filtering algorithm is used to update the state variables of the state space equation in real time according to the real-time operation data; the power grid operation state parameters include at least one of node voltage, line flow, power grid frequency, harmonic current, harmonic voltage and three-phase imbalance degree.

[0042] The basic equation of Kalman filtering is:

[0043] x(k)=F(k-1)x(k-1)+B(k)u(k-1)+w(k-1)

[0044] z(k)=H(k)x(k)+v(k)

[0045] Wherein, x represents a state vector, i.e. a power grid operation state vector; F is a state transition matrix; B is a control input matrix; u is a control input; w is a process noise; z is an observation vector; H is an observation matrix; v is an observation noise.

[0046] Kalman filter is a recursive filtering algorithm based on statistical estimation, which mainly estimates the state of the system recursively based on observation data and system model.

[0047] The embodiment also establishes a power generation prediction model for each new energy unit. The power generation prediction model adopts a least squares support vector regression machine (LSSVR) model, and the model training formula is as follows:

[0048]

[0049] s.t.y i -w T Φ(x i )-b≤ε+ζ i

[0050]

[0051] i=1,2,...,N

[0052] where w is the weight vector, b is the bias, Φ(x i ) is the nonlinear mapping of sample x i , y i is the true value of the i-th sample, ε is the error threshold, C is the penalty factor, ζ i and ζ i * are slack variables, and N is the number of samples.

[0053] In this embodiment, x i specifically refers to a series of input parameter samples considered for new energy power generation prediction. These parameters are crucial for accurately predicting new energy (such as wind energy and solar energy) power generation. New energy power generation is highly dependent on natural conditions and other external factors, therefore, the prediction model needs to consider multiple variables, such as solar radiation intensity, environmental temperature, environmental humidity, sunshine duration, photovoltaic component performance, photovoltaic panel contamination level, and inverter parameter performance on the output side of the new energy generation unit.

[0054] The embodiment also establishes a load prediction model based on real-time data. The prediction model adopts a time series prediction method based on deep learning to improve the accuracy of load prediction.

[0055] The load forecasting model is mainly established according to the following types of data: 1. Time series historical data, load data in the past period of time, reflecting the mode of load change over time, including daily load curve, weekly load curve and seasonal variation law; 2. Weather data: temperature, humidity, wind speed and other weather conditions have a significant impact on some types of load (such as air conditioning load). For example, high temperature weather may cause the refrigeration load to increase; 3. Holidays and special events: holidays, large events, factory rest days, etc. can cause significant changes in load patterns.

[0056] S3, constructing an optimal scheduling model with the grid dynamic operation model as a constraint condition, and solving the optimal scheduling model to obtain optimal output of each new energy unit generation unit and input or output power of each energy storage device.

[0057] Once the model parameters are updated in real time by the Kalman filtering algorithm, the model can be applied to the optimization solution of the power grid safety control strategy. Specifically, a mixed integer linear programming (MILP) method is used to maximize new energy consumption while maintaining grid stability, and the standard form of the MILP problem is as follows:

[0058] min c T x

[0059] s.t.Ax=b

[0060] x l ≤x≤x u

[0061] x j ∈Z,j∈J

[0062] Wherein, c is the objective function coefficient vector, x is the decision variable vector, A and b define the linear relationship constraint, x l and x u are the lower and upper bounds of the decision variable, respectively, and J is the set of integer variables.

[0063] The optimization goal of MILP is to maximize new energy consumption while maintaining grid stability, which constitutes the core of the MILP problem. Based on this, the objective function can be summarized as maximizing the total output of new energy (assuming a part of the decision variable) while satisfying all grid stability and safety constraints. If the decision variable x includes the output of each new energy and the power of each energy storage device, whether the load side parameter is included depends on the specific problem setting. In actual application, the load forecasting result can indirectly affect the decision-making process, such as being an exogenous condition input.

[0064] In this embodiment, the goal of the MILP model is to maximize new energy consumption while ensuring stable operation of the grid, and the objective function (maximize new energy consumption) is:

[0065]

[0066] wherein I represents a set of new energy generation units, c i is a contribution coefficient of the i-th new energy unit, x i is the output of the i-th new energy unit; J represents a set of energy storage devices, d j is a benefit coefficient of the j-th energy storage device, y j is the charging and discharging power of the j-th energy storage device. The objective function aims to reflect the use of as much new energy generation as possible under the premise of ensuring grid stability.

[0067] The constraint conditions of the optimization scheduling model also include that the transmission power of each line of the power grid is not greater than the maximum power allowed to be transmitted by the corresponding line, the operating voltage of each device of the power grid is not greater than the rated voltage of the corresponding device, the voltage of each node of the power grid is not greater than the maximum threshold value of the corresponding node voltage and not less than the minimum threshold value of the corresponding node voltage, the frequency of the power grid is not greater than the maximum threshold value of the frequency and not less than the minimum threshold value of the corresponding node voltage, the load of each transformer is not greater than the rated capacity of the corresponding transformer, each transformer is not overloaded, and the above-mentioned generation capacity prediction model, load prediction model and probability prediction model are established.

[0068] S4, executing the optimal output of each new energy generation unit and the input or output power of each energy storage device obtained in S3.

[0069] In order to better adapt to the changes of the power grid environment, a reinforcement learning algorithm is introduced to dynamically adjust the model parameters. The Q-learning algorithm is used to update the control strategy of the model:

[0070] 1. Reinforcement learning environment definition: the power grid system is abstracted as a Markov decision process (MDP), state s t including the real-time running state of the power grid (such as node voltage, line flow, etc.), action a t representing control decisions (such as adjusting generator output, changing reactive power compensation, etc.).

[0071] 2. Update rule: the Q-learning algorithm is used to update the Q-table (state-action value function), and the Q-value is updated after each decision step, and the value function is adjusted according to the following formula:

[0072]

[0073] wherein s t represents the real-time running state parameters of the power grid at time t (such as node voltage, line flow, etc.), a t represents control decisions (such as adjusting generator output, changing reactive power compensation, etc.), and a represents the learning rate, r trepresents an instant reward, γ represents a discount factor, a' represents all possible actions at the next moment, Q(s t , a t ) represents a value function of taking action a t in running state s t ; Q(s t+1 , a t+1 ) represents a value function of taking action a t+1 in running state s t+1 ; Q(s t+1 , a') represents a value function of taking action a' in running state s t+1 .

[0074] After the value function is updated, the real-time running state s t+1 of the power grid corresponding to the updated value function Q(s t+1 , a t+1 ) is taken as the update target of the running state of the power grid, that is, the running state of the power grid is updated to s t+1 .

[0075] The reinforcement learning algorithm can gradually explore the optimal control strategy in an unknown environment, and dynamically adjust the model parameters to adapt to the changes of the power grid operation, thereby improving the robustness and adaptability of the entire system.

[0076] Embodiment of computer device:

[0077] A computer device comprises a processor configured to execute a computer program to implement the steps of the dispatch side optimization method of the power grid safety control system as described above. Specifically, the dispatch side optimization method of the power grid safety control system has been described in sufficient detail in the above-mentioned embodiment of the dispatch side optimization method of the power grid safety control system, and will not be repeated here.

[0078] The present application has the following characteristics:

[0079] The application realizes accurate collection of all-round real-time data such as node voltage, line flow, load change, distributed power output and power grid equipment state through the power grid dispatching automation system, which helps to more accurately reflect the actual operation state of the power grid and improve the response speed and control accuracy of the system; the multivariable dynamic modeling technology is used to update the model parameters in real time combined with the improved Kalman filtering algorithm, solving the problem that the traditional model parameters are fixed and cannot adapt to the rapid dynamic change of the power grid. The real-time updating capability greatly improves the prediction accuracy and adaptability of the model, which is crucial for the safe and stable operation of the power grid. In the traditional offline and static model, the model parameters are determined at the initial stage of model construction and are assumed to remain unchanged during the entire operation period. In the dynamic model, the state variables change with time and can be updated according to real-time data through methods such as Kalman filtering algorithm, thereby realizing more accurate estimation of the state variables to adapt to the dynamic change of the power grid, thus improving the accuracy and applicability of the model. The dynamic operation model is applied to the power grid safety control strategy, which can optimize the dispatching strategy of the power grid in real time, including voltage regulation, flow distribution, etc., thereby effectively preventing power grid overload, ensuring power quality, and improving the reliability and stability of the entire power grid system; the reinforcement learning algorithm is introduced to dynamically adjust the model parameters, which is an intelligent adaptive optimization method. When facing changes in power grid environment and load, the system can autonomously learn and adjust the control strategy, which is more adaptable to complex and unpredictable operating conditions compared to the static preset control mode.

[0080] Through the reinforcement learning algorithm, the system can accumulate experience from continuous operations, gradually optimizing and improving its control strategy, not only reducing the need for manual intervention, but also discovering and applying the best control scheme, thereby significantly improving the operation efficiency and safety of the system.

[0081] Finally, it should be noted that the above description is only a preferred embodiment of the application and is not intended to limit the application, although the application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments without creative labor, or make equivalent replacement of part of the technical features. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the application shall be included in the protection scope of the application.

Claims

1. A dispatch side optimization method for a power grid security control system, characterized in that, The method comprises the following steps: S1, acquiring real-time operation data of a power grid; S2, establishing a dynamic operation model of the power grid and a power generation prediction model of a new energy generation unit; The dynamic operation model of the power grid comprises a state space equation with power grid operation state parameters as state variables; and a Kalman filtering algorithm is used to update the state variables of the state space equation in real time according to the real-time operation data; The power generation prediction model is an LSSVR, and the training formula is: ; w is a weight vector, b is a bias, Φ x i is a nonlinear mapping of a sample x i y i is a true value of the i-th sample, i is an error threshold, ε is a penalty factor, C ζ i and is a relaxation variable, N is a number of samples;​​ S3, constructing an optimal scheduling model with the dynamic operation model of the power grid and the power generation prediction model as constraint conditions and with maximum new energy consumption in the region as a target, and solving the optimal scheduling model to obtain optimal output of each new energy generation unit in the power grid and input or output power of each energy storage device; The target function is: ; I It is a collection of new energy power generation units. c i For the first i The contribution coefficient of each new energy power generation unit. X i For the first i The output of each new energy power generation unit; J A collection of energy storage devices, d j For the first j The efficiency coefficient of an energy storage device Y j For the first j The input or output power of an energy storage device; S4, executing the solving result of S3.

2. The dispatch side optimization method of the grid security control system according to claim 1, characterized in that, The S4 further comprises: in the execution process, a reinforcement learning algorithm is used to adjust the power grid operation state parameters in real time to make the power grid meet the conditions for stable operation; the conditions for stable operation include power supply and demand balance of the power grid, transmission loss of electric energy not exceeding a preset transmission loss threshold, or load fluctuation of the power grid not exceeding a preset load fluctuation threshold.

3. The dispatch side optimization method of the grid security control system according to claim 2, wherein, The value function in the reinforcement learning algorithm is adjusted according to the following formula: ; wherein, s t denotes t the real-time operating state parameter of the power grid at the moment, a t denotes the control decision, α denotes the learning rate, r t denotes the immediate reward, γ denotes the discount factor, a’ denotes all possible actions at the next moment, Q ( s t , a t ) denotes the value function of taking action s t at the operating state a t ; Q ( s t+1 , a t+1 ) denotes the value function of taking action s t+1 at the operating state a t+1 ; Q ( s t+1 , a’ ) denotes the value function of taking action s t+1 at the operating state a’ .

4. The scheduling side optimization method of the power grid security control system according to any one of claims 1-3, characterized in that, The power grid operation state parameters include at least one of node voltage, line flow, power grid frequency, harmonic current, harmonic voltage, and three-phase imbalance degree.

5. The dispatch side optimization method of the grid security control system of claim 1, wherein, The input parameters of the power generation prediction model of the new energy generation unit include at least one of solar radiation intensity, environmental temperature, environmental humidity, sunshine duration, photovoltaic component performance, pollution degree of a photovoltaic panel, and inverter parameter performance on the output side of the new energy generation unit.

6. The dispatch side optimization method of the grid security control system of claim 1, wherein, S2 further comprises establishing a load prediction model for load prediction, the input parameters of the load prediction model include meteorological data, and the load prediction model uses a deep learning model; the constraint conditions of the optimal scheduling model in S3 further include the load prediction model.

7. The dispatch side optimization method of the grid security control system according to claim 1 or 6, characterized in that, The constraint conditions of the optimal scheduling model further include at least one of the following: transmission power of each line of the power grid is not greater than the maximum power allowed to be transmitted by the corresponding line, working voltage of each device of the power grid is not greater than the rated voltage of the corresponding device, node voltage of the power grid is not greater than the maximum threshold of the corresponding node voltage and not less than the minimum threshold of the corresponding node voltage, power grid frequency is not greater than the maximum threshold of the frequency and not less than the minimum threshold of the frequency, and load of each transformer is not greater than the rated capacity of the corresponding transformer.

8. A computer device comprising a processor, characterized in that, The processor is configured to execute a computer program to implement the steps of the scheduling side optimization method of the power grid safety control system according to any one of claims 1-7.

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