A unit commitment modeling method based on bayesian filtering system frequency response

Abstract

The application discloses a unit combination modeling method based on a frequency response of a Bayesian filtering system, abstracts and equivalently takes generators with the same frequency modulation type in traditional units and new energy units as one generator unit, so that a mapping relationship between equivalent frequency modulation parameters of a power system and frequency modulation characteristics of the generator unit in operation is established, then according to the mapping relationship, a target function and constraint conditions of a unit combination model embedded with the frequency response of the Bayesian filtering system are constructed, finally, data are collected according to an actual power system condition, and the target function is solved by calling a Gurobi solver, so that the sum of unit start-stop cost and operation fuel cost of the power system is minimized, and thus the start-stop and output conditions of the traditional units and the new energy units under the optimal combination are obtained.

Description

Technical Field

[0001] This invention belongs to the field of new energy technology, and more specifically, it is a method for unit combination modeling based on the frequency response of a Bayesian filter system. Background Technology

[0002] In recent years, new energy power generation technologies, represented by wind power and photovoltaic power generation, have developed rapidly, promoting the clean and low-carbon transformation of the power industry. However, with the increase in the installed capacity of new energy, the frequency response process of the power system is increasingly affected by various uncertainties. Therefore, it is particularly necessary to explore the frequency process of the power system under uncertain conditions and the corresponding frequency regulation constraint unit combination problem.

[0003] Frequency response is a time-varying dynamic modeling problem. After a system experiences a frequency shift due to a disturbance, operating generating units compensate for the impact of the external disturbance on the system frequency by adjusting their output. Traditional frequency modeling schemes assume that operating generating units follow a specific frequency regulation control function, obtaining an analytical expression for the system frequency response through the equivalent unit modeling approach using the center of inertia. In reality, the system frequency regulation process faces various uncertainties, and with the increasing scale of renewable energy grid connection, the frequency dynamic modeling process has gradually transformed from a deterministic process based on the frequency regulation control of operating generating units to a stochastic process that implicitly contains deterministic outputs of various generating units during frequency regulation. Therefore, analyzing the frequency response and applying it to the unit combination problem is of great significance for guiding power security assurance.

[0004] In recent years, research on stochastic process modeling methods for power system frequency response and related unit combination modeling with frequency regulation constraints has mainly encountered three problems:

[0005] (1) The random variation in new energy power generation and load makes the unbalanced power during system frequency regulation always random. Although the system unbalanced power and frequency deviation show an overall downward trend as the power generation of power system units gradually increases, the impact of the uncertainty of frequency regulation power output (especially when new energy takes on the frequency regulation task) on the system frequency regulation process always exists and becomes more and more obvious with the increase of new energy installed capacity. Under such circumstances, how to quantify the impact of uncertainty on the frequency regulation process is a forward-looking issue worthy of attention.

[0006] (2) The impact of generating units withdrawing from frequency regulation due to insufficient frequency regulation capability on system frequency changes cannot be ignored. Traditional frequency response models assume that all normally operating generating units participate in primary frequency regulation through their respective frequency control functions, new energy sources participate in primary frequency regulation through virtual inertia control or droop control, and traditional generating units (such as thermal power generating units) participate in the frequency regulation process using droop control with a delay element. The hidden precondition of the traditional frequency regulation model requires that generating units have sufficient frequency regulation capability to participate in the primary frequency regulation process. As the installed capacity of new energy sources increases, new energy sources participating in frequency regulation usually reserve a portion of adjustable power as frequency regulation backup by operating at reduced capacity. Affected by both the uncertainty of power generation and the limitation of their own frequency regulation capability, new energy sources often have to withdraw from the system frequency regulation process because their frequency regulation capability has reached its limit. This means that if some generating units have to withdraw from the frequency regulation process because their own frequency regulation capability has reached its limit, the traditional frequency response model cannot effectively consider this problem.

[0007] (3) The grid connection of new energy sources leads to the probabilistic and complex operation mode of the power system. In addition to focusing on the impact of the uncertainty of new energy generation on the operation of the power system, the study of the impact of new energy grid connection on the operation of the power system also needs to focus on the modeling of system frequency security constraints and its impact on the operation of the power system. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art and provide a unit combination modeling method based on the frequency response of a Bayesian filter system, which realizes the coordinated optimization of power system frequency security and unit combination power generation under disturbance conditions of dynamic frequency changes in the power system.

[0009] To achieve the above-mentioned objectives, this invention provides a unit combination modeling method based on the frequency response of a Bayesian filter system, characterized by comprising the following steps:

[0010] (1) Constructing the frequency deviation and unbalanced power of the power system in Functional relation of the domain;

[0011] (1);

[0012] in, Indicates traditional units The frequency modulation control inertia constant, Indicates new energy power units The virtual inertial control inertia coefficient; , These represent the frequency regulation control damping coefficients of traditional generating units and new energy generating units, respectively. Indicating the frequency deviation of the power system Domain form; Indicates the power of the unbalanced disturbance; This represents the mechanical power gain coefficient of a traditional generator set; , These represent the fixed droop control coefficients for traditional generating units and new energy generating units, respectively. This indicates the percentage of high-pressure cylinder output in a traditional generator set. , These represent the time constants of traditional generating units and new energy generating units, respectively. , These represent the frequency control transfer functions for traditional generating units and new energy generating units, respectively.

[0013] (2) Perform an inverse Laplace transform on formula (1) to obtain the time-domain form of the joint probability density distribution function characterizing the state of the power system;

[0014] (2);

[0015] in, The time-domain representation of power system frequency deviation. for First derivative; This indicates that the increased power generation of new energy units is offsetting the power deficit in the power system. This represents the increased power output of a traditional generator unit during a single frequency regulation process. This indicates the increased power output of the new energy generating unit during a single frequency regulation process. , Both indicate time;

[0016] (3) Combining formula (2), the frequency response process of the power system is transformed into a recursive hidden Markov decision process;

[0017] (4) Construct according to Bayes' theorem The probability density distribution;

[0018] (4.1) Calculate the prior probability of the Bayesian filtering process;

[0019] ;

[0020] in, Indicates time The posterior probability density, The initial time of the power system disturbance. For discrete time steps, The variance and expectation of the prior probability density during the observation process, The total duration of the power system disturbance. Indicates from 0 to The sequence of observed variables at time points;

[0021] (4.2) Calculate the posterior probability of the Bayesian filtering process;

[0022] ;

[0023] in, Indicates time The prior probability density, For the variance and expectation of the posterior probability density during the observation process;

[0024] (4.3) Based on the prior probability density and posterior probability density obtained in steps (4.1) and (4.2), construct... The probability density distribution;

[0025] ;

[0026] (5) Abstract and equate the generators with the same frequency regulation type in traditional units and new energy units into a single generator unit, thereby establishing a mapping relationship between the equivalent frequency regulation parameters of the power system and the frequency regulation characteristics of the generator units in operation.

[0027] ;

[0028] in, Represents the equivalent inertia coefficient of the power system. This represents the equivalent damping coefficient of the power system. The gain coefficient represents the output power of a traditional generator unit in a power system. This represents the droop factor of a conventional power unit in a power system. This represents the droop coefficient of new energy generating units in the power system. As the reference power of the power system, and They are a combination of traditional generating units and new energy generating units. This represents a set of new energy generating units that utilize virtual inertia to participate in frequency regulation. This refers to a collection of new energy generating units that utilize droop control to participate in power system frequency regulation. For the maximum output of traditional units, For the output of new energy generating units in maximum power point tracking mode; For traditional units in The runtime state variable at any given time, when it starts. The value is 1, when it is off. The value is 0;

[0029] (6) Based on the mapping relationship in step (5), construct a unit combination model of the frequency response of the embedded Bayesian filter system;

[0030] (6.1) Construct the objective function of the unit combination model of the frequency response of the embedded Bayesian filter system;

[0031] ;

[0032] in, and These represent the start-up cost and shutdown cost of a traditional generating unit, respectively. For traditional units in The power-on decision variable at any given moment is set to 1 when a power-on decision is made, and 0 otherwise. For traditional units in The shutdown decision variable at any given time is set to 1 when a shutdown decision is made, and 0 otherwise. For random scene index numbers, A collection of scenes; For the scene The probability of the following occurring; Linearized segmented index numbering for the energy consumption curve of traditional generating units. For the set of segmented index numbers; Indicates that traditional units are In the scene Take the power generation at time 1. The value of the segment, For traditional units in the first The percentage of high-pressure cylinder output corresponding to the segment value. For the value of loss of load, For load exist In the scene The risk of constant downtime For time sets;

[0033] (6.2) Constraints for constructing a unit combination model of the frequency response of an embedded Bayesian filter system;

[0034] (6.2.1) Construct power balance constraints for the power system;

[0035] ;

[0036] in, Indicates that new energy units are in In the scene Power generation at any given moment For load exist Load value at any given time;

[0037] (6.2.2) Construct power transmission constraints for transmission lines;

[0038] ;

[0039] in, Indicates the index number of the transmission line; This is the index number of the bus node. For the set of bus nodes; These represent the components mounted on the busbar nodes. The traditional unit set, the new energy unit set, and the load set; Indicates transmission line The maximum transmittable power;

[0040] (6.2.3) Construct upward and downward rotational standby constraints for traditional units;

[0041] ;

[0042] in, and Indicates the load reserve factor. and This represents the error coefficient for new energy prediction. This is the minimum output of a traditional unit. For new energy units in the first In the scene Output in maximum power point tracking mode at any given time;

[0043] (6.2.4) Construct upper and lower limits for the output of the new energy group;

[0044] ;

[0045] (6.2.5) Construct frequency change rate constraints for the power system;

[0046] ;

[0047] in, This represents the maximum rate of change of the power system frequency deviation.

[0048] (7) Traverse all operating modes of the power system to be tested, and then calculate the frequency deviation generated under each operating mode. Calculate the corresponding probability density distribution according to step (4);

[0049] (8) Set threshold Select the probability density distribution corresponding to the largest frequency deviation, denoted as . ;

[0050] set up Confidence constraints:

[0051] ;

[0052] in, The preset confidence level;

[0053] (9) Under the constraints of steps (6.2) and (8), with the goal of minimizing the sum of unit start-up and shutdown costs and operating fuel costs, call the Gurobi solver to solve the objective function in step (6.1), thereby outputting the optimization variables of the unit combination model with embedded Bayesian filter system frequency response, and completing the unit combination optimization under the frequency dynamic response process.

[0054] The objective of this invention is achieved as follows:

[0055] This invention presents a unit combination modeling method based on the frequency response of a Bayesian filter system. It abstracts and equates generators with the same frequency regulation type in both traditional and renewable energy units into a single generator unit, thereby establishing a mapping relationship between the equivalent frequency regulation parameters of the power system and the frequency regulation characteristics of the operating generator unit. Then, based on this mapping relationship, it constructs the objective function and constraints of a unit combination model with an embedded Bayesian filter system frequency response. Finally, it collects data based on the actual power system conditions and solves the objective function using the Gurobi solver to minimize the sum of the power system unit start-up and shutdown costs and operating fuel costs. This yields the start-up, shutdown, and output characteristics of traditional and renewable energy units under the optimal combination.

[0056] Meanwhile, the unit combination modeling method based on the frequency response of a Bayesian filter system of the present invention also has the following beneficial effects:

[0057] (1) The present invention has the ability to deal with the uncertainty of unit output during frequency regulation and its effectiveness on the system frequency process through the Bayesian filtering system frequency modeling scheme. It can effectively consider the impact of the uncertainty of unit output during frequency regulation on frequency deviation and obtain the probability distribution information of frequency deviation.

[0058] (2) The present invention takes into account the system frequency factor, and the system can respond to the frequency dynamic process of power disturbance more smoothly, and has a smaller frequency change rate and a lower system frequency deviation.

[0059] (3) This invention takes frequency security into consideration. By maintaining a certain number of traditional synchronous machines in operation and giving full play to the priority participation of units with good frequency regulation performance in power balance, it ensures that the obtained start-up mode has good regulation performance for the system frequency process under power disturbance, which helps to avoid the possible frequency stability problems of low inertia system operation mode.

[0060] (4) This invention converts the probability distribution information of frequency deviation into frequency safety constraints and connects it with the traditional unit combination model to construct a frequency constraint unit combination model that takes into account both frequency safety requirements and operating economy. Attached Figure Description

[0061] Figure 1 This is a flowchart of a unit combination modeling method based on the frequency response of a Bayesian filter system according to the present invention;

[0062] Figure 2 It is a block diagram of the transfer function of the primary frequency regulation process in a power system;

[0063] Figure 3 It is the inference and decision-making process of the system's frequency response;

[0064] Figure 4 It is the probability density distribution of system frequency deviation in the MatlabSimulink environment, including two schemes: Scheme 1 (without considering wind power) and Scheme 2 (considering wind power);

[0065] Figure 5 It is the confidence interval of the system frequency deviation in the MatlabSimulink environment, which includes both Scheme 1 (without considering wind power) and Scheme 2 (considering wind power);

[0066] Figure 6 This is a comparison chart of the frequency change process of the Bayesian filter system in the Matlab Simulink environment and the traditional simulator system, including two schemes: Scheme 1 (without considering wind power) and Scheme 2 (considering wind power). Detailed Implementation

[0067] The specific embodiments of the present invention will now be described with reference to the accompanying drawings to enable those skilled in the art to better understand the invention. It should be particularly noted that in the following description, detailed descriptions of known functions and designs that might obscure the main content of the invention will be omitted here.

[0068] Example

[0069] In this embodiment, traditional units are represented by thermal power generators, while new energy units are represented by wind turbines and photovoltaic units. The optimization methods for the combination of photovoltaic and wind turbines are similar. Below, we take wind turbines as an example. This invention provides a wind turbine combination optimization method based on Bayesian filtering, which includes the following steps:

[0070] S1. Based on the impact of different generator unit frequency control on system frequency response, construct a model of power system frequency deviation and unbalanced power. Functional relation of the domain;

[0071] ;

[0072] in, Indicates thermal power generating unit The frequency modulation control inertia constant, Indicates wind turbine The virtual inertial control inertia coefficient; , These represent the frequency regulation control damping coefficients of thermal power generating units and wind power generating units, respectively. Indicating the frequency deviation of the power system Domain form; Indicates the power of the unbalanced disturbance; This represents the mechanical power gain coefficient of a thermal power generating unit; , These represent the fixed droop control coefficients for thermal power generating units and wind power generating units, respectively. This indicates the percentage of high-pressure cylinder output in a thermal power generator set; , These represent the time constants of thermal power generating units and wind power generating units, respectively. , These represent the frequency control transfer functions for thermal power generating units and wind power generating units, respectively.

[0073] In this embodiment, as Figure 2 As shown, the transfer function of the primary frequency regulation process of different units reflects the influence of the frequency control of different units on the system frequency response. Therefore, the above functional relationship was constructed on this basis.

[0074] S2. Perform an inverse Laplace transform on the formula in step S1 to obtain the time-domain form of the joint probability density distribution function characterizing the state of the power system.

[0075] ;

[0076] in, The time-domain representation of power system frequency deviation. for First derivative; This indicates that the increased power generation of new energy units is offsetting the power deficit in the power system. This represents the increased power output of a traditional generator unit during a single frequency regulation process. This indicates the increased power output of the new energy generating unit during a single frequency regulation process. , Both indicate time;

[0077] S3. Combining the formula in step S2, the frequency response process of the power system is transformed into a recursive hidden Markov decision process.

[0078] In this embodiment, as Figure 3 As shown, the system frequency process is abstracted into a hidden Markov decision process. As an observed variable, As a latent variable;

[0079] S4. Following step S3, after transforming the power system frequency response process into a stochastic process, construct the following based on Bayes' theorem: The probability density distribution;

[0080] S4.1 Calculate the prior probability of the Bayesian filtering process;

[0081] ;

[0082] in, Indicates time The posterior probability density, The initial time of the power system disturbance. For discrete time steps, The variance and expectation of the prior probability density during the observation process, The total duration of the power system disturbance. Indicates from 0 to The sequence of observed variables at time points;

[0083] S4.2 Calculate the posterior probability of the Bayesian filtering process;

[0084] ;

[0085] in, Indicates time The prior probability density, For the variance and expectation of the posterior probability density during the observation process;

[0086] S4.3. Based on the prior probability density and posterior probability density obtained in steps S4.1 and S4.2, construct... The probability density distribution;

[0087] ;

[0088] S5. Abstract and equate the generators with the same frequency regulation type in thermal power generating units and wind power generating units to a single generator unit, thereby establishing a mapping relationship between the equivalent frequency regulation parameters of the power system and the frequency regulation characteristics of the operating generator unit.

[0089] ;

[0090] in, Represents the equivalent inertia coefficient of the power system. This represents the equivalent damping coefficient of the power system. The gain coefficient represents the output power of a traditional generator unit in a power system. This represents the droop factor of a conventional power unit in a power system. This represents the droop coefficient of new energy generating units in the power system. As the reference power of the power system, and They are a combination of traditional generating units and new energy generating units. This represents a set of new energy generating units that utilize virtual inertia to participate in frequency regulation. This refers to a collection of new energy generating units that utilize droop control to participate in power system frequency regulation. For the maximum output of traditional units, For the output of new energy generating units in maximum power point tracking mode; For traditional units in The runtime state variable at any given time, when it starts. The value is 1, when it is off. The value is 0;

[0091] S6. Based on the mapping relationship in step S5, construct a unit combination model for the frequency response of the embedded Bayesian filter system;

[0092] S6.1, Construct the objective function of the unit combination model for the frequency response of the embedded Bayesian filter system;

[0093] ;

[0094] in, and These represent the start-up cost and shutdown cost of a traditional generating unit, respectively. For traditional units in The power-on decision variable at any given moment is set to 1 when a power-on decision is made, and 0 otherwise. For traditional units in The shutdown decision variable at any given time is set to 1 when a shutdown decision is made, and 0 otherwise. For random scene index numbers, A collection of scenes; For the scene The probability of the following occurring; Linearized segmented index numbering for the energy consumption curve of traditional generating units. For the set of segmented index numbers; Indicates that traditional units are In the scene Take the power generation at time 1. The value of the segment, For traditional units in the first The percentage of high-pressure cylinder output corresponding to the segment value. For the value of loss of load, For load exist In the scene The risk of constant downtime For time sets;

[0095] S6.2 Constraints for constructing a unit combination model of the frequency response of an embedded Bayesian filter system;

[0096] S6.2.1 Constructing power balance constraints for the power system;

[0097] ;

[0098] in, Indicates that new energy units are in In the scene Power generation at any given moment For load exist Load value at any given time;

[0099] S6.2.2 Constructing power transmission constraints for transmission lines;

[0100] ;

[0101] in, Indicates the index number of the transmission line; This is the index number of the bus node. For the set of bus nodes; These represent the components mounted on the busbar nodes. The traditional unit set, the new energy unit set, and the load set; Indicates transmission line The maximum transmittable power;

[0102] S6.2.3 Construct backup constraints for the upward and downward rotation of the thermal power generating unit;

[0103] ;

[0104] in, and Indicates the load reserve factor. and This represents the error coefficient for new energy prediction. This is the minimum output of a traditional unit. For new energy units in the first In the scene Output in maximum power point tracking mode at any given time;

[0105] S6.2.4 Construct upper and lower limits for wind turbine output;

[0106] ;

[0107] S6.2.5 Construct frequency change rate constraints for the power system;

[0108] ;

[0109] in, This represents the maximum rate of change of the power system frequency deviation.

[0110] S7. Iterate through all operating modes of the power system to be tested, and then calculate the frequency deviation generated under each operating mode. Calculate the corresponding probability density distribution according to step S4;

[0111] S8. Set threshold Select the probability density distribution corresponding to the largest frequency deviation, denoted as . ;

[0112] set up Confidence constraints:

[0113] ;

[0114] in, In this embodiment, the preset confidence level is used. The value is 5%;

[0115] S9. Under the constraints of steps S6.2 and S8, with the goal of minimizing the sum of unit start-up and shutdown costs and operating fuel costs, call the Gurobi solver to solve the objective function in step S6.1, thereby outputting the optimization variables of the unit combination model with embedded Bayesian filter system frequency response, and completing the unit combination optimization under the frequency dynamic response process.

[0116] In this embodiment, as Figure 4 and Figure 5 As shown, the proposed frequency modeling scheme can not only estimate the system frequency response process considering the uncertainty of increased generator power, but also provide probabilistic information on frequency deviation. Furthermore, compared to Scheme 1, Scheme 2 exhibits a smoother probability density distribution of the maximum system frequency deviation. This indicates that the introduction of uncertainty in increased generator power will lead to a certain degree of dispersion in the system frequency process. In this case, if the traditional analytical modeling approach is used, the extreme values ​​of system frequency deviation under certain adverse conditions will be ignored. Nevertheless, by combining the modeling method proposed in this chapter, the expected value and probability distribution information of the system frequency deviation can still be effectively quantified. Figure 6As shown, the frequency deviation obtained using the proposed Bayesian filter system frequency model is close to that of the traditional simulator, which verifies the effectiveness of the proposed frequency response model. Compared with Scheme 1, Scheme 2 considers the frequency support role of wind turbines in the primary frequency regulation process of the system. The system frequency process is smoother, the rate of change of frequency deviation decreases, and the maximum value of system frequency deviation is further reduced, indicating the effectiveness of introducing wind turbines into the system frequency regulation process. In addition, comparing the system frequency processes of different schemes, it can be seen that the system frequency response process is significantly affected by the uncertainty of turbine output. Specifically, the smaller the uncertainty of the increased power generation of the turbines during the frequency regulation process, the easier it is to predict the system frequency. When the influence of the uncertainty of turbine output on primary frequency regulation becomes significant, the frequency response will be transformed into a highly complex stochastic process. In this case, it is difficult to characterize the dynamic process of system frequency under uncertain conditions using traditional analytical schemes. Nevertheless, the proposed model still provides good modeling accuracy.

[0117] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of the present invention are protected.

Claims

1. A unit combination modeling method based on the frequency response of a Bayesian filter system, characterized in that, Includes the following steps: (1) Constructing the frequency deviation and unbalanced power of the power system in Functional relation of the domain; （1）； in, Indicates traditional units The frequency modulation control inertia constant, Indicates new energy power units The virtual inertial control inertia coefficient; , These represent the frequency regulation control damping coefficients of traditional generating units and new energy generating units, respectively. Indicating the frequency deviation of the power system Domain form; Indicates the power of the unbalanced disturbance; This represents the mechanical power gain coefficient of a traditional generator set; , These represent the fixed droop control coefficients for traditional generating units and new energy generating units, respectively. This indicates the percentage of high-pressure cylinder output in a traditional generator set. , These represent the time constants of traditional generating units and new energy generating units, respectively. , These represent the frequency control transfer functions for traditional generating units and new energy generating units, respectively. (2) Perform an inverse Laplace transform on formula (1) to obtain the time-domain form of the joint probability density distribution function characterizing the state of the power system; （2）； in, The time-domain representation of power system frequency deviation. for First derivative; This indicates that the increased power generation of new energy units is offsetting the power deficit in the power system. This represents the increased power output of a traditional generator unit during a single frequency regulation process. This indicates the increased power generation of the new energy unit during a single frequency regulation process. , Both indicate time; (3) Combining formula (2), the frequency response process of the power system is transformed into a recursive hidden Markov decision process; (4) Construct according to Bayes' theorem The probability density distribution; (4.1) Calculate the prior probability of the Bayesian filtering process; ； in, Indicates time The posterior probability density, The initial time of the power system disturbance. For discrete time steps, The variance and expectation of the prior probability density during the observation process, The total duration of the power system disturbance. Indicates from 0 to The sequence of observed variables at time points; (4.2) Calculate the posterior probability of the Bayesian filtering process; ； in, Indicates time The prior probability density, For the variance and expectation of the posterior probability density during the observation process; (4.3) Based on the prior probability density and posterior probability density obtained in steps (4.1) and (4.2), construct... The probability density distribution; ； (5) Abstract and equate the generators with the same frequency regulation type in traditional units and new energy units into a single generator unit, thereby establishing a mapping relationship between the equivalent frequency regulation parameters of the power system and the frequency regulation characteristics of the generator units in operation. ； in, Represents the equivalent inertia coefficient of the power system. This represents the equivalent damping coefficient of the power system. The gain coefficient represents the output power of a traditional generator unit in a power system. This represents the droop factor of a conventional power unit in a power system. This represents the droop coefficient of new energy generating units in the power system. As the reference power of the power system, and They are a combination of traditional generating units and new energy generating units. This represents a set of new energy generating units that utilize virtual inertia to participate in frequency regulation. This refers to a collection of new energy generating units that utilize droop control to participate in power system frequency regulation. For the maximum output of traditional units, For the output of new energy generating units in maximum power point tracking mode; For traditional units in The runtime state variable at any given time, when it starts. The value is 1, when it is off. The value is 0; (6) Based on the mapping relationship in step (5), construct a unit combination model of the frequency response of the embedded Bayesian filter system; (6.1) Construct the objective function of the unit combination model of the frequency response of the embedded Bayesian filter system; ； in, and These represent the start-up cost and shutdown cost of a traditional generating unit, respectively. For traditional units in The power-on decision variable at any given moment is set to 1 when a power-on decision is made, and 0 otherwise. For traditional units in The shutdown decision variable at any given time is set to 1 when a shutdown decision is made, and 0 otherwise. For random scene index numbers, A collection of scenes; For the scene The probability of the following occurring; Linearized segmented index numbering for the energy consumption curve of traditional generating units. For the set of segmented index numbers; Indicates that traditional units are In the scene Take the power generation at time 1. The value of the segment, For traditional units in the first The percentage of high-pressure cylinder output corresponding to the segment value. For the value of loss of load, For load exist In the scene The risk of constant downtime For time sets; (6.2) Constraints for constructing a unit combination model of the frequency response of an embedded Bayesian filter system; (6.2.1) Construct power balance constraints for the power system; ； in, Indicates that new energy units are in In the scene Power generation at any given moment For load exist Load value at any given time; (6.2.2) Construct power transmission constraints for transmission lines; ； in, Indicates the index number of the transmission line; This is the index number of the bus node. For the set of bus nodes; These represent the components mounted on the busbar nodes. The traditional unit set, the new energy unit set, and the load set; Indicates transmission line The maximum transmittable power; (6.2.3) Construct upward and downward rotational standby constraints for traditional units; ； in, and Indicates the load reserve factor. and This represents the error coefficient for new energy prediction. This is the minimum output of a traditional unit. For new energy units in the first In the scene Output in maximum power point tracking mode at any given time; (6.2.4) Construct upper and lower limits for the output of the new energy group; ； (6.2.5) Construct frequency change rate constraints for the power system; ； in, This represents the maximum rate of change of the power system frequency deviation. (7) Traverse all operating modes of the power system to be tested, and then calculate the frequency deviation generated under each operating mode. Calculate the corresponding probability density distribution according to step (4); (8) Set threshold Select the probability density distribution corresponding to the largest frequency deviation, denoted as . ; set up Confidence constraints: ； in, The preset confidence level; (9) Under the constraints of steps (6.2) and (8), with the goal of minimizing the sum of unit start-up and shutdown costs and operating fuel costs, call the Gurobi solver to solve the objective function in step (6.1), thereby outputting the optimization variables of the unit combination model with embedded Bayesian filter system frequency response, and completing the unit combination optimization under the frequency dynamic response process.

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