A robust preventive scheduling method considering failure probability information and dynamic thermal rating

Abstract

The application relates to a robust preventive scheduling method considering fault probability information and dynamic thermal setting, and belongs to the technical field of power system scheduling. The method comprises the following steps: obtaining cold wave weather forecast data and power grid data; calculating the line current of each power transmission line based on the power grid data; determining the line temperature of the power transmission line based on the cold wave weather forecast data and the line current of the power transmission line; obtaining the fault probability of the power transmission line based on the cold wave weather forecast data, the line temperature and the line current of the power transmission line; constructing a fault entropy constraint based on the fault probability of each power transmission line and a fault entropy threshold value, and constructing a probability-aware N-K line fault uncertainty set based on the fault entropy constraint; constructing a two-stage robust preventive scheduling model, solving the two-stage robust preventive scheduling model by using a C&CG algorithm based on the probability-aware N-K line fault uncertainty set, and obtaining a target scheduling scheme. The method can balance the economy and safety of power system operation under cold weather.

Description

Technical Field

[0001] This invention relates to the field of power system dispatching technology, and in particular to a robust preventive dispatching method that considers fault probability information and dynamic thermal setpoints. Background Technology

[0002] With the advancement of "dual-carbon" targets and the construction of new power systems, the installed capacity of new energy sources such as wind power and photovoltaics continues to increase, significantly enhancing the power system's sensitivity to meteorological conditions and extreme weather. Extreme weather events such as cold waves, freezing rain, and blizzards can easily lead to faults such as icing on transmission lines, conductor breaks, and tower collapses, potentially triggering widespread power deficits and cascading blackouts. As critical grid-side components directly exposed to the natural environment during cold waves, transmission lines are affected by meteorological factors such as icing and wind loads, as well as by line power flow, current heating, and the de-icing process. Therefore, establishing preventative dispatching methods that balance the actual transmission capacity of lines with fault risks to ensure the safe and economical operation of the power system during cold waves has become a critical issue that urgently needs to be addressed.

[0003] In existing power system dispatching methods, transmission line capacity is typically constrained using static thermal ratings (STRs). This method sets a fixed capacity for lines based on relatively conservative meteorological conditions, making it difficult to reflect the dynamic changes in line thermal stability margins under conditions such as cold waves, strong winds, and solar radiation. Dynamic thermal ratings (DTRs) can comprehensively consider factors such as ambient temperature, wind speed, solar radiation, and line temperature to dynamically assess the allowable current-carrying capacity of lines, thereby tapping into the potential transmission capacity of existing transmission channels without exceeding the maximum allowable operating temperature of the lines. However, existing DTR-related technologies mostly focus on conventional meteorological conditions, renewable energy consumption, or line capacity improvement, and do not adequately consider the coupling relationship between DTR and line icing growth, Joule heating for de-icing, and fault probability under cold waves. At the same time, traditional DC power flow models ignore the effects of reactive power and voltage deviation, making it difficult to accurately calculate line currents, which in turn affects the accuracy of line thermal state calculations, DTR constraint construction, and icing-de-icing process judgment.

[0004] Meanwhile, existing preventative scheduling and robust optimization methods for handling simultaneous multi-line failures that may occur under extreme weather conditions typically use the traditional NK line fault uncertainty set to describe the fault scenario. This assumes a system with N lines, allowing any K lines to fail simultaneously, limiting the number of simultaneously outage lines only to the number of faulty lines, K. This approach assumes different lines have similar or identical fault risks, failing to reflect the differentiated fault probabilities of different lines under cold weather conditions due to varying meteorological conditions, ice thickness, ice melting status, and ice-wind loads. As the value of K increases, the traditional NK line fault uncertainty set easily includes combinations of multi-line faults with extremely low probabilities in the robust search scope, causing the scheduling model to reserve excessive reserve capacity for low-probability, overly conservative scenarios, leading to decreased operational efficiency. Summary of the Invention

[0005] Based on the above analysis, the embodiments of the present invention aim to provide a robust preventive scheduling method that considers fault probability information and dynamic thermal setpoints, in order to solve the technical problems of inaccurate line current calculation and overly conservative backup schemes caused by the failure of the NK fault set to take into account the differentiated fault probabilities of the lines in existing scheduling methods under extreme cold wave weather.

[0006] On one hand, embodiments of the present invention provide a robust preventive scheduling method that considers fault probability information and dynamic thermal setpoints, including: Acquire cold wave weather forecast data and power grid data, use the duration of the cold wave as the scheduling period, and take multiple discrete moments within the scheduling period; For each transmission line in the power grid, the line current of the transmission line at each time moment is calculated based on the power grid data; Based on the cold wave weather forecast data and the line current of the transmission line at each time, the line temperature of the transmission line at each time is determined according to the overhead line heat balance equation. Based on the cold wave weather forecast data, the line temperature and line current of the transmission line at each time, the failure probability of the transmission line at each time is obtained. Based on the fault probability and fault entropy threshold of each transmission line at each time, a fault entropy constraint is constructed, and a probability-aware NK line fault uncertainty set is constructed based on the fault entropy constraint. Each element in the set represents the fault state vector of each transmission line at a certain time. A two-stage robust preventive scheduling model is constructed. The objective function of the two-stage robust preventive scheduling model is to minimize the total operating cost. The constraints are the preventive scheduling constraints of the first stage and the emergency scheduling constraints of the second stage. The total operating cost includes the power generation cost, start-up and shutdown cost and standby cost of the thermal power unit. Based on the probability-aware NK line fault uncertainty set, the two-stage robust prevention scheduling model is solved using the C&CG algorithm to obtain the target scheduling scheme.

[0007] A further improvement to the above method, the step of calculating the line current of the transmission line at each moment based on the power grid data, includes: Based on the node voltage amplitude and node phase angle at the beginning and end of the transmission line at each moment, calculate the active power and reactive power of the transmission line at each moment. The line current of the transmission line at each time moment is determined based on the active power and the reactive power.

[0008] A further improvement to the above method, the step of obtaining the fault probability of the transmission line at each moment based on the cold wave weather forecast data, the line temperature and line current of the transmission line at each moment, includes: The transmission line is divided into multiple sections, and the probability of failure per unit length of line in each section at each time is determined. For each segment, the line fault probability of the segment at each time time is determined based on the segment's line fault probability per unit length and the segment length. The failure probability of the transmission line at each time is determined based on the line failure probability of each section at each time.

[0009] Based on a further improvement of the above method, determining the fault probability per unit length of line in each section at each time step includes: For each section, based on the cold wave weather forecast data, the ice thickness per unit length of the line at each time point is calculated. Based on the line temperature and line current of the transmission line at each time, calculate the ice melting volume per unit length of the line in the section at each time. Based on the ice thickness, calculate the ice volume per unit length of the line in the section at each time point; Based on the ice-covered volume and the ice-melted volume, the ice load per unit length of the line in the section at each time moment is obtained. Based on the ice thickness, the wind load per unit length of the line in the section at each time moment is obtained; Based on the icing load and the wind load, the icing and wind load per unit length of the line in the section at each time moment is obtained. Based on the ice and wind load, preset design load, and preset ultimate load per unit length of the line in the section at each time, the probability of failure per unit length of the line in the section at each time is determined.

[0010] A further improvement to the above method, the step of calculating the ice thickness per unit length of the line at various times based on the cold wave weather forecast data, includes: Based on the cold wave weather forecast data, the change in ice thickness per unit length of the line at the current moment is calculated using the Jones model; The ice thickness change is summed with the ice thickness per unit length of the line at the previous moment to obtain the ice thickness per unit length of the line at the current moment, where the initial ice thickness is 0.

[0011] A further improvement to the above method involves constructing a fault entropy constraint based on the fault probability and fault entropy threshold of each transmission line at each time point, and constructing a probability-aware NK line fault uncertainty set based on the fault entropy constraint, including: For each time point, based on the fault probability of each transmission line at that time point, the overall fault entropy value of all transmission lines at that time point is obtained. The fault entropy constraint at the given time is constructed with the overall fault entropy value not exceeding the fault entropy threshold as a constraint. The fault entropy constraint at the given time is embedded into the basic NK fault uncertainty set at the same time to obtain the probability-aware NK line fault uncertainty set corresponding to the given time. The basic NK fault uncertainty set refers to the fault uncertainty set constrained only by the upper limit of the number of transmission lines that are allowed to fail simultaneously.

[0012] Based on further improvements to the above method, the preventive scheduling constraints in the first stage are constraints under normal operation of the transmission line, and the emergency scheduling constraints in the second stage are constraints under fault conditions of the transmission line. Both the preventive scheduling constraints in the first stage and the emergency scheduling constraints in the second stage include dynamic thermal setpoint constraints. The dynamic thermal setpoint constraints include: the line temperature of the transmission line at each moment does not exceed the preset maximum allowable operating temperature.

[0013] Based on a further improvement of the above method, the step of using the C&CG algorithm to solve the two-stage robust prevention scheduling model to obtain the target scheduling scheme includes: Under the condition of satisfying the prevention scheduling constraints of the first stage, optimization is performed with the objective function as the goal to obtain candidate scheduling schemes, which include the values ​​of scheduling decision variables under normal operating conditions; The values ​​of the scheduling decision variables are substituted as known parameters into the emergency scheduling constraints of the second stage; Using the emergency scheduling constraints of the second stage as verification conditions, a max-min structure is used to determine the vector with the highest degree of safety constraint violation in the probability-aware NK line fault uncertainty set. If the degree of violation of the security constraint is less than or equal to the preset security threshold, then the candidate scheduling scheme is determined to satisfy all the emergency scheduling constraints of the second stage, and the candidate scheduling scheme is taken as the target scheduling scheme. If the degree of violation of the security constraint is greater than the preset security threshold, it is determined that the candidate scheduling scheme does not meet at least one emergency scheduling constraint of the second stage, and a C&CG cut constraint is generated based on the vector with the largest degree of violation of the security constraint. The C&CG cut constraint is incorporated into the prevention scheduling constraint of the first stage, and the candidate scheduling scheme is solved again until the maximum security constraint violation is less than or equal to the preset security threshold, and the target scheduling scheme is obtained.

[0014] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: 1. By acquiring cold wave weather forecast data and power grid data, and using the duration of the cold wave as the scheduling period, multiple discrete moments are taken within the scheduling period. The line current, line temperature, and fault probability of each transmission line are calculated sequentially at each moment. A fault entropy constraint and a probability-aware NK line fault uncertainty set are constructed. Then, a two-stage robust preventive scheduling model is built with the goal of minimizing total operating cost, and the C&CG algorithm is used to solve it, yielding the target scheduling scheme. This method improves the calculation accuracy of transmission line current and temperature through dynamic thermal setpoint constraints and linearized AC power flow calculations that consider reactive power. The probability-aware NK fault uncertainty set is constructed through fault entropy constraints to filter out low-probability fault combinations. Through two-stage robust optimization and iterative solving using the C&CG algorithm, robust safety is ensured for all possible fault scenarios while minimizing total operating cost, achieving synergistic optimization of power system safety and economy under extreme weather conditions.

[0015] 2. Based on the voltage amplitude and phase angle at the first and last nodes of the transmission line, a linearized AC power flow model that considers reactive power is used to calculate the active and reactive power of the line, thereby determining the line current. Compared with the traditional DC power flow model that only considers active power and ignores the influence of reactive power and voltage deviation on the line current, resulting in insufficient accuracy of current calculation, the linearized AC power flow model in this application significantly improves the accuracy of line current calculation by introducing reactive power and voltage deviation.

[0016] 3. The Jones model is used to calculate the change in icing thickness, and the melting volume is calculated using the heat balance equation. This yields the icing volume, icing load, and wind load. The combined icing-wind load, along with the preset design load and ultimate load, determines the fault probability. This process fully considers the impact of cold wave weather conditions on icing growth and the contribution of Joule heating of line current to the melting process. It achieves accurate modeling of the dynamic icing-melting process, allowing the fault probability to change in real time with weather conditions and line operating status. Compared to the traditional fixed outage rate assumption, this approach better reflects the actual physical process and significantly improves the accuracy of fault probability assessment.

[0017] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0018] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts. Figure 1 is a flowchart of a robust preventive scheduling method that considers fault probability information and dynamic thermal setpoints in an embodiment of the present invention. Figure 2 This is a diagram of the improved IEEE-RTS79 architecture in an embodiment of the present invention; Figure 3 The following are graphs showing the start-up and shutdown results of thermal power units for four sets of calculation examples in this embodiment of the invention; Figure 4 This is a comparison chart of the transmission capacity of the line under static thermal setpoint and dynamic thermal setpoint constraints after a fault occurs in an embodiment of the present invention. Detailed Implementation

[0019] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0020] A specific embodiment of the present invention discloses a robust preventive scheduling method that considers fault probability information and dynamic thermal setpoints, such as... Figure 1 As shown, it includes the following steps: S1. Obtain cold wave weather forecast data and power grid data, take the duration of the cold wave as the scheduling period, and take multiple discrete moments within the scheduling period.

[0021] Cold wave weather forecast data consists of meteorological parameters obtained from numerical weather prediction (NWP), including at least ambient temperature, wind speed and direction, solar radiation intensity, freezing rain, and absolute humidity under cold wave conditions. Power grid data includes transmission line parameters and power grid operating status data. Transmission line parameters include at least the transmission line's resistance, reactance, conductance, susceptance, line quality, specific heat capacity, surface roughness, line alignment, outermost strand diameter, light absorption coefficient, maximum allowable operating temperature, reference temperature, temperature coefficient of resistance, resistance at the reference temperature, bare conductor radius, and span factor. Power grid operating status data includes at least the voltage amplitude, phase angle, and load at each node, as well as the output of each generating unit, such as the active and reactive power of thermal power units.

[0022] This application uses the duration of the cold wave as the scheduling period, and takes multiple discrete moments within the scheduling period. For example, in a real daytime scheduling scenario, the scheduling period is 24 hours in the future, and 24 discrete moments are taken, with a time interval of 1 hour between two adjacent discrete moments.

[0023] S2. For each transmission line in the power grid, calculate the line current of the transmission line at each time point based on the power grid data.

[0024] Specifically, including: Based on the transmission line Using a linearized AC power flow model, the active and reactive power of the transmission line at each moment are calculated based on the node voltage amplitude and node phase angle at the beginning and end of the line. The line current of the transmission line at each moment is then determined based on the active and reactive power.

[0025] The linearized AC power flow model is as follows: (1) (2) in, 、 Transmission lines Series conductance and series susceptance; 、 They represent transmission lines The first and last nodes; 、 They are respectively The voltage amplitude at the beginning and end of the node at any given time; 、 They are respectively Phase angles of the first and last nodes at any given moment; For power transmission lines active power, For power transmission lines reactive power, superscript This indicates that the system is in normal operating condition.

[0026] Based on the calculated active power of the transmission line and the reactive power The line current of the transmission line can be obtained using the following formula: (3) Traditional DC power flow models only consider active power, neglecting the impact of reactive power and voltage deviation on line current, which limits their calculation accuracy. To address this shortcoming, the linearized AC power flow model in this application significantly improves the calculation accuracy of line current by introducing reactive power and voltage deviation.

[0027] S3. Based on the cold wave weather forecast data and the line current of the transmission line at each time, determine the line temperature of the transmission line at each time according to the overhead line icing heat balance equation.

[0028] Specifically, the expression for the heat balance equation of icing on overhead power lines is:

[0029] in, For line quality; The specific heat capacity of the circuit; This is the first derivative of the line temperature with respect to time. It generates heat in joules; The heat generated by sunlight; This refers to convective heat dissipation. For radiative heat dissipation, This refers to the line temperature of the power transmission line.

[0030] Specifically, joule heat The expression is:

[0031] in, This is the maximum allowable operating temperature of the circuit. The reference temperature for the line. The resistance when the line temperature is the reference temperature. is the temperature coefficient of resistance.

[0032] Heat generated by sunlight The expression is:

[0033] in, The light absorption coefficient of the circuit surface; Solar radiation intensity; This represents the diameter of the line after it becomes icy.

[0034] Convection heat dissipation The expression is:

[0035] in,

[0036]

[0037]

[0038]

[0039]

[0040] in, Thermal conductivity of air; For the film temperature, in order to ensure convective heat dissipation Nonlinearity of the expression Take a preset fixed value; For Nusselt numbers, For power transmission lines Ambient temperature The Reynolds number is... For power transmission lines Surface roughness, , For Reynolds number and surface roughness The empirical coefficients determined jointly The angle between the route direction and the wind direction. , , For the reason The empirical coefficients determined jointly This is the diameter of the line after it becomes icy. The diameter of the outermost stranded wire in the circuit. The air density at sea level. For ambient wind speed, Altitude This is the air viscosity coefficient.

[0041] Radiative heat dissipation The expression is:

[0042] in,

[0043] in, This is the Stefan-Boltzmann constant. The surface emissivity of the line. This is an intermediate variable. Furthermore, to quickly solve for the line temperature of the transmission line, the above overhead line heat balance equation is rearranged into a first-order linear differential equation:

[0044] in, for Overall heat dissipation coefficient ， for Joule heating rate of temperature rise ， for The rate of temperature rise caused by solar radiation.

[0045] Solving the above first-order linear differential equation yields the analytical solution to the overhead power line icing heat balance equation:

[0046] in, The time interval between two adjacent discrete moments. It is an exponential decay factor; The initial temperature of the line is usually taken as the ambient temperature at the start of scheduling, but it can also be obtained through actual measurement. This application does not limit the method of obtaining the initial temperature of the line.

[0047] The line temperature of the transmission line obtained by solving the thermal balance equation for icing of overhead lines must not exceed the preset maximum allowable operating temperature. Simultaneously, a dynamic thermal setpoint constraint is constructed based on the aforementioned temperature-related formulas.

[0048] The dynamic thermal setpoint constraint in this application dynamically considers key factors affecting conductor temperature, such as Joule heat generated by line current, ambient temperature, wind speed, and solar radiation. It can dynamically reflect the thermal stability limit of the line based on cold wave weather conditions and line operating status. Compared with the traditional static thermal setpoint which uses a fixed conservative capacity, this invention makes full use of the line's heat dissipation capacity under cold wave, low temperature, and strong wind conditions. While ensuring that the line temperature does not exceed the limit, it avoids excessive reserve provisions caused by conservative thermal setpoints, reduces reserve costs, and improves the economy of the dispatching scheme.

[0049] S4. Based on the cold wave weather forecast data, the line temperature and line current of the transmission line at each time, the failure probability of the transmission line at each time is obtained.

[0050] Specifically, including: S4-1. Divide the transmission line into multiple sections and determine the fault probability per unit length of the line in each section at each time.

[0051] Specifically, the transmission lines Divided into There are 1 segment, each segment being 1000 segments long. , , ..., The probability of failure per unit length of line in each section at each time point is determined. It should be noted that the length of each section can be divided equally or unequally according to the meteorological conditions and terrain differences along the line. This application does not limit the specific method of section division.

[0052] S4-2. For each segment, determine the line fault probability of the segment at each time based on the line fault probability per unit length of the segment at each time and the segment length.

[0053] S4-3. Determine the fault probability of the transmission line at each time based on the line fault probability of each section at each time.

[0054] S4-1 includes: (1) For any segment Based on the cold wave weather forecast data, the Jones model is used to calculate the change in ice thickness per unit length of the line at the current moment.

[0055] Specifically, the Jones model is as follows:

[0056]

[0057] in, For a moment t The change in icing thickness per unit length of transmission line; , The density of ice and water; For a moment Freezing rainfall; For a moment wind speed; This refers to the absolute humidity of the air.

[0058] (2) The change in ice thickness is summed with the ice thickness per unit length of the line at the previous moment to obtain the ice thickness per unit length of the line at the current moment.

[0059]

[0060] in Indicates the current time Ice thickness per unit length of the line, where the initial ice thickness is 0.

[0061] (3) Based on the line temperature and line current of the transmission line at each time, calculate the ice melting volume per unit length of the line in the section at each time.

[0062] The de-icing process of power transmission lines follows the heat balance equation:

[0063] Substituting the heat-related formulas from (7) to (14) into formula (21), we obtain the volume of melted ice. :

[0064] The current in the formula must satisfy the following condition:

[0065] in, The critical de-icing current is given if and only if Only then will the ice begin to melt; The latent heat of fusion of ice represents the amount of heat required for a unit mass of ice to completely transform from a solid to a liquid state at its melting point.

[0066] In calculating the ice melt volume in this application, not only is the impact of meteorological forecast data on ice melt considered, but the Joule heating generated by the line current is also introduced. This allows the ice-melting volume to dynamically change in conjunction with line current and meteorological conditions. The ice-melting volume obtained through this method more closely reflects the actual operating conditions of the line, resulting in more accurate calculations.

[0067] (4) Based on the ice thickness, calculate the ice volume per unit length of the line in the section at each time. ;

[0068] (5) Based on the ice-covered volume and the ice-melted volume, the ice load per unit length of the line in the section at each time moment is obtained. :

[0069] (6) Based on the ice thickness, the wind load per unit length of the line in the section at each time moment is obtained. ;

[0070] In formulas (24) to (26): The radius of the bare conductor of the transmission line. The constant is taken as 9.8 × 10⁻⁶. -3 ; It is a constant, taken as 6.694 × 10 -3 ; Span factor; This is a preset critical ice-melting volume threshold.

[0071] (7) Based on the icing load and the wind load, obtain the icing and wind load per unit length of the line in the section at each time. ;

[0072] (8) Based on the ice wind load, preset design load and preset ultimate load of the unit length line of the section at each time, determine the failure probability of the unit length line of the section at each time. :

[0073] in, For the preset design load, The preset ultimate load.

[0074] Furthermore, any segment in S4-2 Line fault probability at each time point for:

[0075] in, For section The length.

[0076] Furthermore, in S4-3, the transmission line is determined based on the line fault probability of each section at each time point. Failure probability at each time point :

[0077] The transmission line is determined based on the line fault probability of each section at each time. Failure probability at each time point.

[0078] This application calculates the change in icing thickness using the Jones model and the melting volume using the heat balance equation, thereby obtaining the icing volume, icing load, and wind load. The synthesized icing-wind load is then combined with the preset design load and ultimate load to determine the failure probability. This process fully considers the impact of cold wave weather conditions on icing growth and the contribution of Joule heating of line current to the melting process, achieving accurate modeling of the dynamic process of icing and melting. This allows the failure probability to change in real time with weather conditions and line operating status, which is more consistent with the actual physical process than the traditional fixed outage rate assumption, significantly improving the accuracy of failure probability assessment. S5. Based on the fault probability and fault entropy threshold of each transmission line at each time, construct fault entropy constraints, and construct a probability-aware NK line fault uncertainty set based on the fault entropy constraints.

[0079] Specifically, since information entropy can be used to measure the degree of uncertainty of random events, this application introduces information entropy to quantify the degree of transmission line faults. For time... The overall fault entropy value of all transmission lines Represented as:

[0080] In the formula: A collection of transmission lines; For power transmission lines At any moment The probability of failure; For power transmission lines At any moment The operating status is indicated by a value of 1, which represents normal operation, and a value of 0, which represents a fault. For power transmission line identification. Indicates the line At any moment The amount of information about the failure The overall fault entropy value for all transmission lines, representing time. The sum of information from all faulty lines is used to quantize the time. The degree of uncertainty in the failure. The greater the total amount of information, the more accurate the representation of the time interval. The more transmission lines with lower failure probabilities included, the lower the overall probability of a combination of line fault states occurring.

[0081] Furthermore, a fault entropy threshold is introduced. : ,in, The preset truncation probability is a fixed constant. To avoid including combinations of line fault states with extremely low probabilities of occurrence into the uncertainty set, the overall fault entropy value must not exceed the fault entropy threshold, i.e., the following fault entropy constraint is constructed:

[0082] At that moment When the sum of information of all faulty lines exceeds the fault entropy threshold, the corresponding line fault state combination will be excluded from the uncertainty set. By using the fault entropy threshold, line fault state combinations whose total information exceeds the threshold can be screened out, that is, extreme combinations containing multiple low-probability faulty lines are excluded, so that only line fault state combinations with relatively high probability of occurrence are retained in the uncertainty set.

[0083] Furthermore, the aforementioned fault entropy constraints are embedded into the basic NK fault uncertainty set. In this process, the uncertainty set of probability-aware NK line faults is obtained. , is represented as:

[0084] in, This represents the total number of transmission lines. This is a preset upper limit on the number of lines that can fail simultaneously. This set Each element in the table represents a time interval. Fault state vector Each vector represents the normal operation or fault state of each transmission line at that moment, that is, each vector corresponds to a combination of line fault states.

[0085] For example, suppose there are 3 transmission lines, at time The probability-aware NK line fault uncertainty set contains two fault state vectors. This indicates that line 2 is faulty, while lines 1 and 3 are operating normally. This indicates that line 1 is operating normally, while lines 2 and 3 are faulty.

[0086] Specifically, the basic NK fault uncertainty set is the traditional NK fault uncertainty set, which is based solely on a preset upper limit on the number of lines that can simultaneously experience faults. As a constraint, the number of transmission lines that can be simultaneously shut down is limited to no more than [a certain number]. It assumes that each transmission line has the same failure probability, without considering the differentiated failure probabilities caused by different weather conditions, ice thickness, and icing loads. Therefore, the traditional NK set tends to include combinations of line failure states with extremely low probability of occurrence into the uncertainty set, resulting in scheduling schemes based on this set needing to reserve too much reserve capacity for these low-probability failure scenarios, leading to poor operational economy.

[0087] This application constructs a fault entropy constraint based on the differentiated fault probabilities of each transmission line and embeds it into the traditional NK line fault uncertainty set to build a probability-aware NK line fault uncertainty set. This set filters out line fault state combinations with extremely low probability of occurrence through fault entropy constraints, reducing the conservatism of the traditional NK set while maintaining robust safety, and avoiding reserving too much reserve capacity for low-probability fault scenarios, thus balancing the economy and safety of power system operation under extreme weather conditions.

[0088] S6. Construct a two-stage robust preventive scheduling model. The two-stage robust preventive scheduling model takes the minimum total operating cost as the objective function and the preventive scheduling constraints of the first stage and the emergency scheduling constraints of the second stage as the constraints. The total operating cost includes the power generation cost, start-up and shutdown cost and standby cost of the thermal power unit.

[0089] Specifically, the objective function of the two-stage robust prevention scheduling model is:

[0090] in, The total number of moments within the scheduling period; A collection of thermal power units; , They represent thermal power units Start-up and shutdown costs; , For thermal power units At any moment Adjusting the reserve capacity upwards and downwards; , thermal power units The application adjusts the reserve cost coefficient upwards and downwards; since the operating cost of thermal power units is a non-linear function, this application performs piecewise linearization on the operating cost of thermal power units. For thermal power units After piecewise linearization, the first... The power generation cost coefficient of the segment; For a moment thermal power units In the The power generation of the section; This represents the number of segments after piecewise linearization.

[0091] The preventive dispatch constraints in the first stage are constraints assuming all transmission lines are in normal operating condition, including: (1) Node power balance constraints

[0092]

[0093] in, , They are time points No. Active and reactive power of the thermal power units; , They are time points No. Active and reactive power of typhoon generator units; , They are time points transmission lines The active and reactive power flowing through; , They are time points node Active and reactive loads; , , , They are respectively with the busbar Connected sets of thermal power units, wind turbine units, transmission lines, and loads; superscript This indicates that the system is in normal operating condition.

[0094] (2) Linear power flow constraints of transmission lines (37) (38) (39) (40) (41) in, , They are nodes The upper and lower limits of the voltage at the point; , For power transmission lines The upper and lower limits of the phase angle difference allowed for operation; This represents the upper limit of the line's apparent power.

[0095] (3) Conventional unit constraints.

[0096] (42) (43) (44) (45) (46) (47) (48) (49) in, This is the start-up and shutdown variable for thermal power units during normal operation; 1 indicates operation, and 0 indicates shutdown. , thermal power units At any moment Continuous operating time and downtime; , These are the minimum continuous power-on time and the minimum continuous power-off time, respectively. , For thermal power units The upper and lower limits of contribution; , These are the upper and lower limits of the generator's reactive power output, respectively. , To adjust the peak reserve capacity upwards and downwards; , For thermal power units Upward and downward climbing capacity; , For thermal power units The cost of a single power-on and power-off cycle; For thermal power units In the The maximum power generation within the linearized interval of the segment.

[0097] (4) Wind farm output constraints.

[0098] (50) in, For nodes The power factor angle corresponding to the minimum power factor of the connected wind turbine unit; For wind turbine units at all times The predictions were helpful and productive.

[0099] (5) Transmission line DTR constraint.

[0100]

[0101] The emergency dispatch constraints in the second stage are the constraints under the transmission line fault state, including: (1) Node power balance constraints.

[0102] (52) (53) in, 、 They are time points No. Active and reactive power of the thermal power units; ， They are time points No. Active and reactive power of typhoon generator units; ， They are time points transmission lines The active and reactive power flowing through; ， They are time points node Active and reactive loads; superscript This represents an uncertain scenario, i.e., N occurrences. Operational status of the K transmission line after a fault.

[0103] (2) Linear power flow constraints of transmission lines.

[0104] (54) (55) (56) (57) (58) in, , They are respectively Phase angles of the first and last nodes at any given moment; , They are respectively The voltage amplitude at the beginning and end of the node at any given time; Derived from the probability-aware NK line fault uncertainty set; , For each time point transmission lines The active and reactive power flowing through, M These are preset fixed parameters.

[0105] (3) Constraints of conventional units under uncertain scenarios.

[0106] (59) (60) (61) (62) (4) Wind turbine output constraints under uncertain scenarios.

[0107] (63) (5) Transmission line DTR constraint.

[0108]

[0109] in, The line temperature of the power transmission line; This represents the rate of temperature rise caused by Joule heating.

[0110] This application sets dynamic thermal setpoint constraints in both the first-stage preventive scheduling constraints and the second-stage emergency scheduling constraints, enabling the two-stage robust scheduling model to ensure that the line temperature does not exceed the limit under all operating scenarios, thus balancing the safety and economy of the scheduling scheme.

[0111] S7. Based on the probability-aware NK line fault uncertainty set, the two-stage robust prevention scheduling model is solved using the C&CG algorithm to obtain the target scheduling scheme, specifically including the following steps: S7-1. Under the condition of satisfying the prevention scheduling constraints of the first stage, optimize with the objective function as the goal to obtain candidate scheduling schemes.

[0112] The candidate scheduling schemes include scheduling decision variable values ​​for each transmission line under normal operating conditions, specifically including thermal power unit start-up and shutdown variables. 、 Active power of thermal power units and reactive power 、 Thermal power units increase reserve capacity and reduce reserve capacity Active power of wind turbine units and reactive power .

[0113] S7-2. Substitute the values ​​of the scheduling decision variables as known parameters into the emergency scheduling constraints of the second stage.

[0114] In formulas (58) to (61) = ， The scheduling decision variables obtained in step S7-1 , , , The value is substituted into the emergency dispatch constraint formulas (58) to (61) of the second stage.

[0115] S7-3. Using the emergency scheduling constraints of the second stage as verification conditions, a max-min structure is used to determine the vector with the highest degree of safety constraint violation in the probability-aware NK line fault uncertainty set.

[0116] To verify whether the above candidate scheduling schemes satisfy all the constraints of the emergency scheduling constraints in the second stage under the worst combination of line fault states, a max-min structure is used to search for the worst combination of line fault states in the probability-aware NK line fault uncertainty set.

[0117] The max-min structure is represented as follows:

[0118] in, Represents the rescheduling decision variables; Let be a vector of slack variables, where each component represents the amount of violation of each safety constraint under a given combination of line fault states; This represents the minimum degree of safety constraint violation under the given combination of line fault states. Specifically, the degree of violation of each safety constraint refers to the extent to which the values ​​of the rescheduling decision variables cannot meet the emergency scheduling constraints of the second stage under a given combination of line fault states. This includes the power imbalance of node power balance constraints and the temperature exceeding the limit of transmission line temperature constraints. When solving, we use... Minimize as the optimization objective, determine the minimum degree of safety constraint violation and the corresponding rescheduling decision variable value under a given combination of line fault states.

[0119] Among them, the rescheduling decision variables include the active power of thermal power units under uncertain scenarios. and reactive power 、 Active power of wind turbine and reactive power ， transmission lines Active power flowing and reactive power Node voltage amplitude and phase angle and line temperature .

[0120] Specifically, the outer layer of the max-min structure searches for a combination of line fault states in the probability-aware NK line fault uncertainty set. The inner layer of the max-min structure, given a combination of line fault states, determines the minimum safety constraint violation degree of the combination of line fault states by optimizing the rescheduling decision variable in the emergency scheduling constraint of the second stage. The outer layer, by traversing different combinations, finally finds the combination of line fault states that maximizes the minimum safety constraint violation degree, which is the worst combination of line fault states.

[0121] S7-4. If the degree of violation of the security constraint is less than or equal to the preset security threshold, then the candidate scheduling scheme is determined to satisfy all the emergency scheduling constraints of the second stage, and the candidate scheduling scheme is taken as the target scheduling scheme.

[0122] Specifically, after finding the worst-case line fault state combination, if the minimum safety constraint violation degree corresponding to the worst-case line fault state combination is... ,in, To preset a safety threshold, the above candidate scheduling schemes are used as the target scheduling scheme.

[0123] S7-5. If the degree of violation of the security constraint is greater than the preset security threshold, it is determined that the candidate scheduling scheme does not meet at least one emergency scheduling constraint of the second stage, and a C&CG cut constraint is generated based on the vector with the largest degree of violation of the security constraint.

[0124] Specifically, if the minimum safety constraint violation degree corresponds to the worst-case line fault state combination Based on the worst-case line fault state combination, a C&CG cut constraint is generated. The C&CG cut constraint is: to divide the operating states of each line in the worst-case line fault state combination. Substituting the specific values ​​into the emergency scheduling constraints of the second stage yields all the emergency scheduling constraints for the second stage corresponding to the worst-case line fault state combination. It should be noted that these all the emergency scheduling constraints for the second stage corresponding to the worst-case line fault state combination involve considering the operating states of each line in the worst-case line fault state combination. The specific values, and the scheduling decision variables obtained in step S7-1. , , , The value of is substituted into formulas (52) to (64) to obtain a set of constraints.

[0125] S7-6. The C&CG cut constraint is incorporated into the prevention scheduling constraint of the first stage, and the candidate scheduling scheme is solved again until the maximum security constraint violation is less than or equal to the preset security threshold, and the target scheduling scheme is obtained.

[0126] The C&CG cut constraints generated by S7-5 are incorporated into the preventive scheduling constraints of the first stage, forming the updated preventive scheduling constraints of the first stage. Correspondingly, new variables are added to the updated preventive scheduling constraints of the first stage. , , , , , , , and ,in, This represents the number of iterations.

[0127] Based on this, under the condition of satisfying the updated first-stage preventive scheduling constraints, optimization is performed with the objective function as the goal, candidate scheduling schemes are obtained again, and steps S7-2 to S7-6 are executed again until the maximum safety constraint violation is less than or equal to the preset safety threshold, and the corresponding candidate scheduling scheme is taken as the target scheduling scheme.

[0128] This invention acquires cold wave weather forecast data and power grid data, using the duration of the cold wave as the scheduling period. Within this period, multiple discrete moments are selected, and the line current, line temperature, and fault probability of each transmission line are calculated sequentially at each moment. A fault entropy constraint and a probability-aware NK line fault uncertainty set are constructed. A two-stage robust preventive scheduling model is then built with the goal of minimizing total operating cost, and the C&CG algorithm is used to solve it, yielding the target scheduling scheme. This method improves the accuracy of transmission line current and temperature calculations through dynamic thermal setpoint constraints and linearized AC power flow calculations that consider reactive power. The fault entropy constraint constructs a probability-aware NK fault uncertainty set, filtering out low-probability fault combinations. Through two-stage robust optimization and iterative solving using the C&CG algorithm, it minimizes total operating cost while ensuring robust safety for all possible fault scenarios, achieving synergistic optimization of power system safety and economy under extreme weather conditions.

[0129] To verify the effectiveness of this invention, a numerical example analysis was performed using the improved IEEE-RTS79 system. The power system architecture diagram is attached. Figure 2As shown, the system comprises 24 nodes, 15 thermal power units, 3 wind turbine units, and 48 transmission lines. The dispatch cycle is 24 hours, with 24 discrete time points, and the time interval between two adjacent discrete time points is 1 hour. The system's baseline capacity is 100 MVA, and all active and reactive power are converted to per-unit values ​​based on this baseline capacity. Historical cold wave events in a city in Northeast China are selected as meteorological data to simulate the dynamic processes of icing and melting of transmission lines under cold wave weather. Wind turbine units are connected at nodes 17, 21, and 22, and the wind turbine capacities connected to each node are shown in Table 1. The wind turbine output prediction error is set to 20%.

[0130] Table 1 Wind Turbine Connection Locations

[0131] To verify the impact of fault entropy constraints and dynamic thermal setpoint constraints on the scheduling scheme of the two-stage robust preventive scheduling model, this paper sets up four sets of examples for comparative analysis, as shown in Table 2. Example 1 uses the traditional NK line fault uncertainty set and static thermal setpoint (STR) as the baseline example; Example 2 introduces dynamic thermal setpoint constraints based on Example 1 to analyze the impact of dynamic thermal setpoint constraints on system transmission capacity and reserve demand; Example 3 introduces a probabilistically perceived NK line fault uncertainty set based on fault entropy constraints based on Example 1 to verify the reduction effect of fault entropy constraints on the conservatism of the traditional robust model; Example 4 considers both the probabilistically perceived NK line fault uncertainty set and dynamic thermal setpoint constraints, which is the method proposed in this invention, and is used to comprehensively verify the scheduling economy and robust security under the synergistic effect of fault entropy constraints and dynamic thermal setpoint constraints.

[0132] Table 2. Case Study Scenario Settings

[0133] The system operating costs for solving the four sets of examples in Table 2 are shown in Table 3. Example 1, using the traditional NK line fault uncertainty set and STR, has the highest total operating cost of 536,827.9. This indicates that the traditional NK set assumes all transmission lines have the same fault probability, and the STR uses a fixed conservative capacity. Both factors contribute to higher reserve requirements and increased operating costs for the preventive dispatch scheme. Example 2, after introducing dynamic thermal setpoint constraints, reduces the total operating cost by 4.81% and the reserve cost by 35.36% compared to Example 1. This shows that dynamic thermal setpoint constraints can fully utilize the heat dissipation capacity of lines under cold wave, low temperature, and strong wind conditions, improving the power flow transfer capability after a fault, thereby reducing reserve requirements and lowering operating costs. Example 3, based on static thermal setpoints, introduces a probability-aware NK line fault uncertainty set, reducing the total cost by 7.83% compared to Example 1. This demonstrates that fault entropy constraints can utilize the differentiated fault probabilities of lines to filter out some low-probability line fault state combinations, weakening the conservatism of the traditional NK set and thus reducing operating costs. Example 4, considering both the probability-aware NK line fault uncertainty set and dynamic thermal setpoint constraints, further reduces the total operating cost to 485,403.7, the lowest among the four examples. Compared to Example 1, the total cost is reduced by 9.58%, the generation cost by 8.89%, and the reserve cost by 37.92%. The results show that the fault entropy constraint reduces the conservatism of the robust model at the fault scenario level, while the dynamic thermal setpoint constraint releases the transmission margin at the line thermal stability level. The synergistic effect of the two can achieve more economical unit output and reserve configuration while ensuring the robust safety of NK faults.

[0134] Table 3 Scheduling and Operation Costs

[0135] The unit combination decision for the four sets of calculation examples is as follows: Figure 3The diagram shows the start-up and shutdown status of thermal power units at various times in the four sets of examples. Comparing Examples 1 and 2, it can be seen that under the traditional NK line fault uncertainty set, after introducing dynamic thermal set constraints, some small-capacity, high-cost units shut down during low-load periods. This indicates that after the dynamic thermal set constraints release the line thermal stability margin, the system can rely more on low-cost units to complete the power flow transfer and supply after a fault, thereby reducing generation and standby costs. Comparing Examples 3 and 4, it can be seen that although the probability-aware NK line fault uncertainty set can weaken the conservatism of the fault scenario, under static thermal set constraints, the system still needs to start some high-cost units to provide local support. Further introducing dynamic thermal set constraints improves the line thermal stability margin, enhances the power flow transfer capability after a fault, and further reduces the need to start up high-cost small units. Overall, dynamic thermal set constraints not only improve the thermal stability margin of the line but also optimize the unit combination structure, reduce the preventative start-up and standby configuration of high-cost units, and enable the system to meet the robust safety requirements of multiple line faults under cold weather conditions at a lower cost.

[0136] To analyze the upper limit of the number of transmission lines that can experience simultaneous faults. This paper discusses the impact of different scheduling schemes. The total operating costs of the four sets of calculations under different values ​​are compared, and the results are shown in Table 4. As the number of variables increases, the operating costs of both Example 1 and Example 2 rise, indicating that the uncertainty set of faults on traditional NK lines increases. Adding more variables enhances the conservatism of the scheduling scheme. Compared to Example 1, Example 2 shows improvements in various aspects. The costs are lower under all the selected values, indicating that the dynamic thermal setpoint constraint can release the thermal stability margin of the line and alleviate the power flow transfer pressure after multiple line faults. The costs of Examples 3 and 4 vary with... The relatively small changes indicate that the probability-aware NK line fault uncertainty set can utilize the differentiated fault probabilities of lines to screen fault scenarios, reducing the conservatism of the traditional NK set. Specifically, Example 4 shows that... The fact that the minimum cost is maintained under all values ​​indicates that the fault entropy constraint and the dynamic thermal setpoint constraint work together to reduce the conservatism of fault scenarios while improving the power flow transfer capability after a fault, thereby improving the economy of robust preventive scheduling under cold wave weather.

[0137] Table 4 is different Operating cost under the given value

[0138] To verify the effect of dynamic thermal setpoint constraints on improving transmission capacity during cold waves, a fault scenario involving the simultaneous disconnection of lines 25, 26, and 30 was selected. This fault combination severed a crucial transmission corridor in the northern region, forcing the power originally transmitted via lines 25, 26, and 30 to be redistributed to adjacent sections. Consequently, lines 31 and 37 became the critical channels for power flow transfer after the fault. Under the same fault scenario, the apparent power changes of the critical transfer channels were compared under static and dynamic thermal setpoint constraints. The results are as follows: Figure 4 As shown. Under static thermal setpoint conditions, the transmission power of the two lines is constrained by the upper limit of static transmission capacity, and there is a significant risk of local blockage after a fault. After introducing dynamic thermal setpoint constraints, the available transmission capacity of lines 31 and 37 is significantly improved, and the capacity shows dynamic variation characteristics over time. This indicates that meteorological conditions such as cold waves and strong winds enhance the heat dissipation capacity of the conductors, allowing the lines to release additional thermal stability margins without exceeding the maximum allowable operating temperature. It can be concluded that under cold wave weather, dynamic thermal setpoint constraints can overcome the conservative limitations of traditional STRs, improve the power flow transfer capability of critical channels after a fault, and effectively alleviate line blockage, which helps to reduce standby costs and total operating costs.

[0139] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0140] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A robust preventive scheduling method considering fault probability information and dynamic thermal setpoints, characterized in that, The method includes: Acquire cold wave weather forecast data and power grid data, use the duration of the cold wave as the scheduling period, and take multiple discrete moments within the scheduling period; For each transmission line in the power grid, the line current of the transmission line at each time moment is calculated based on the power grid data; Based on the cold wave weather forecast data and the line current of the transmission line at each time, the line temperature of the transmission line at each time is determined according to the overhead line heat balance equation. Based on the cold wave weather forecast data, the line temperature and line current of the transmission line at each time, the failure probability of the transmission line at each time is obtained. Based on the fault probability and fault entropy threshold of each transmission line at each time, a fault entropy constraint is constructed, and a probability-aware NK line fault uncertainty set is constructed based on the fault entropy constraint. Each element in the set represents the fault state vector of each transmission line at a certain time. A two-stage robust preventive scheduling model is constructed. The objective function of the two-stage robust preventive scheduling model is to minimize the total operating cost, and the constraints are the preventive scheduling constraints of the first stage and the emergency scheduling constraints of the second stage. Based on the probability-aware NK line fault uncertainty set, the two-stage robust prevention scheduling model is solved using the C&CG algorithm to obtain the target scheduling scheme.

2. The method according to claim 1, characterized in that, The calculation of the line current of the transmission line at each time point based on the power grid data includes: Based on the node voltage amplitude and node phase angle at the beginning and end of the transmission line at each moment, calculate the active power and reactive power of the transmission line at each moment. The line current of the transmission line at each time moment is determined based on the active power and the reactive power.

3. The method according to claim 1, characterized in that, The method of obtaining the fault probability of the transmission line at each moment based on the cold wave weather forecast data, the line temperature and line current of the transmission line at each moment, includes: The transmission line is divided into multiple sections, and the probability of failure per unit length of line in each section at each time is determined. For each segment, the line fault probability of the segment at each time time is determined based on the segment's line fault probability per unit length and the segment length. The failure probability of the transmission line at each time is determined based on the line failure probability of each section at each time.

4. The method according to claim 3, characterized in that, Determining the fault probability per unit length of line in each section at each time point includes: For each section, based on the cold wave weather forecast data, the ice thickness per unit length of the line at each time point is calculated. Based on the line temperature and line current of the transmission line at each time, calculate the ice melting volume per unit length of the line in the section at each time. Based on the ice thickness, calculate the ice volume per unit length of the line in the section at each time point; Based on the ice-covered volume and the ice-melted volume, the ice load per unit length of the line in the section at each time moment is obtained. Based on the ice thickness, the wind load per unit length of the line in the section at each time moment is obtained; Based on the icing load and the wind load, the icing and wind load per unit length of the line in the section at each time moment is obtained. Based on the ice and wind load, preset design load, and preset ultimate load per unit length of the line in the section at each time, the probability of failure per unit length of the line in the section at each time is determined.

5. The method according to claim 4, characterized in that, The calculation of the icing thickness per unit length of the line in the section at various times, based on the cold wave weather forecast data, includes: Based on the cold wave weather forecast data, the change in ice thickness per unit length of the line at the current moment is calculated using the Jones model; The ice thickness change is summed with the ice thickness per unit length of the line at the previous moment to obtain the ice thickness per unit length of the line at the current moment, where the initial ice thickness is 0.

6. The method according to claim 1, characterized in that, The method involves constructing a fault entropy constraint based on the fault probability and fault entropy threshold of each transmission line at each time moment, and constructing a probability-aware NK line fault uncertainty set based on the fault entropy constraint, including: For each time point, based on the fault probability of each transmission line at that time point, the overall fault entropy value of all transmission lines at that time point is obtained. The fault entropy constraint at the given time is constructed with the overall fault entropy value not exceeding the fault entropy threshold as a constraint. The fault entropy constraint at the given time is embedded into the basic NK fault uncertainty set at the same time to obtain the probability-aware NK line fault uncertainty set corresponding to the given time. The basic NK fault uncertainty set refers to the fault uncertainty set constrained only by the upper limit of the number of transmission lines that are allowed to fail simultaneously.

7. The method according to claim 1, characterized in that, The first stage of preventive dispatch constraints are constraints under normal operation of the transmission line, and the second stage of emergency dispatch constraints are constraints under fault conditions of the transmission line. Both the first stage of preventive dispatch constraints and the second stage of emergency dispatch constraints include dynamic thermal setpoint constraints. The dynamic thermal setpoint constraint includes: the line temperature of the transmission line at any time does not exceed the preset maximum allowable operating temperature.

8. The method according to claim 6, characterized in that, The process of solving the two-stage robust prevention scheduling model using the C&CG algorithm to obtain the target scheduling scheme includes: Under the condition of satisfying the prevention scheduling constraints of the first stage, optimization is performed with the objective function as the goal to obtain candidate scheduling schemes, which include the values ​​of scheduling decision variables under normal operating conditions; The values ​​of the scheduling decision variables are substituted as known parameters into the emergency scheduling constraints of the second stage; Using the emergency scheduling constraints of the second stage as verification conditions, a max-min structure is used to determine the vector with the highest degree of safety constraint violation in the probability-aware NK line fault uncertainty set. If the degree of violation of the security constraint is less than or equal to the preset security threshold, then the candidate scheduling scheme is determined to satisfy all the emergency scheduling constraints of the second stage, and the candidate scheduling scheme is taken as the target scheduling scheme. If the degree of violation of the security constraint is greater than the preset security threshold, it is determined that the candidate scheduling scheme does not meet at least one emergency scheduling constraint of the second stage, and a C&CG cut constraint is generated based on the vector with the largest degree of violation of the security constraint. The C&CG cut constraint is incorporated into the prevention scheduling constraint of the first stage, and the candidate scheduling scheme is solved again until the maximum security constraint violation is less than or equal to the preset security threshold, and the target scheduling scheme is obtained.

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