Electric power system scheduling method considering inertia and power dual adequacy

Abstract

The invention belongs to the field of power grid dispatching, and particularly discloses a power system dispatching method considering inertia and power abundance. According to the method, the frequency response model containing the load power change is established, quantitative characterization of the dynamic characteristics of the load-side inertia resources is realized, and the inertia adequacy constraint cooperating with the dynamic capability of the source and load double sides and the power adequacy constraint fusing the load power support are deduced according to the quantitative characterization of the dynamic characteristics of the load-side inertia resources. And finally, the load side recessive reserve is converted into schedulable dominant resources in optimal scheduling, the problem that the adjustment potential is limited due to the fact that a traditional scheduling model ignores load dynamic support is solved, and the system operation scheduling performance is remarkably improved while the frequency stability is guaranteed.

Description

Technical Field

[0001] The present application relates to the field of power grid dispatching, and more specifically, to a power system dispatching method taking into account both inertia and power sufficiency. Background Art

[0002] As the proportion of renewable energy sources, such as wind and solar, connected to the grid continues to rise, the inertia level of the power system continues to decline. At the same time, the uncertainty of wind and photovoltaic output power leads to an increase in the system's demand for inertia to support frequency stability. Therefore, when formulating dispatch plans for unit combinations, considering both system power adequacy and inertia adequacy to support frequency stability in new power systems is the future development direction.

[0003] Existing research primarily involves introducing frequency security indicators to optimize the start-up and shutdown status of units and their reserve capacity, ensuring the system has sufficient frequency regulation capability to maintain frequency stability. Commonly used frequency security indicators include the maximum frequency change rate after a disturbance, the lowest frequency point, and the quasi-steady-state frequency. By considering the entire process of system dynamic frequency changes and utilizing time-frequency domain analytical transformations, frequency security indicator constraints can be established. Incorporating these into unit combination models can effectively improve the system's frequency response capability and stability.

[0004] However, current research on unit commitment for frequency security primarily focuses on leveraging the inertia of generators on the source side to improve system frequency response, while insufficient consideration is given to the role of inertia on the load side, failing to achieve coordinated frequency regulation between sources and loads. Research has shown that load-side resources (such as industrial loads and temperature-controlled loads) can provide important dynamic frequency support for the system due to their rapid response characteristics. In fact, the power support characteristics of load-side inertia resources are equivalent to providing the system with "implicit reserve capacity," which can dynamically compensate for power shortfalls and suppress frequency fluctuations.

[0005] In summary, due to the lack of specific means to dynamically characterize the load-side inertia, the current power system fails to fully take into account the dynamic support capacity of inertia during the source and load frequency regulation process, resulting in the failure to fully realize the system frequency response potential, restricting the improvement of the power system frequency stability, and thus limiting the power system scheduling. Summary of the Invention

[0006] In response to the defects of the existing technology, the purpose of this application is to provide a power system scheduling method that takes into account both inertia and power sufficiency, aiming to solve the technical problem that the current power system lacks a means of dynamically characterizing the inertia on the load side, resulting in limited power system scheduling.

[0007] To achieve the above-mentioned objectives, in a first aspect, the present application provides a power system scheduling method taking into account both inertia and power sufficiency, including: determining a system frequency response model based on disturbance power, load power change, prime mover power change and equivalent inertia time constant; obtaining inertia sufficiency constraints and quasi-steady-state frequency deviation according to the system frequency response model; obtaining power sufficiency constraints based on disturbance power and quasi-steady-state frequency deviation; and outputting a scheduling plan according to the system objective function based on the inertia sufficiency constraints, power sufficiency constraints and system operation constraints.

[0008] In one embodiment, the system frequency response model is: ; ; ; ; ; ; in, is the system frequency deviation; For time; is the disturbance power; is the unit adjustment coefficient; is the equivalent inertia time constant of the unit; is the work coefficient of the prime mover's high-pressure cylinder; is the load frequency regulation effect coefficient; is the mechanical power factor; is the unit reheat time constant; is the natural oscillation angular frequency, is the damping ratio, is the damped oscillation angular frequency, and is an intermediate variable in the calculation process.

[0009] In one embodiment, the inertia adequacy constraint includes: a maximum frequency change rate constraint, a frequency minimum point constraint, and a quasi-steady-state frequency deviation constraint; obtaining the inertia adequacy constraint and the quasi-steady-state frequency deviation according to the system frequency response model, including: obtaining the descending slope of the system frequency response model at the start of the disturbance as the maximum frequency change rate, and establishing a maximum frequency change rate constraint; obtaining the time when the descending slope of the system frequency response model is 0 as the time when the frequency reaches the minimum point, and obtaining the frequency minimum point based on the time when the frequency reaches the minimum point, and establishing a frequency minimum point constraint; obtaining the continuous frequency deviation after the system frequency response model enters the quasi-steady state as the quasi-steady-state frequency deviation, and establishing a quasi-steady-state frequency deviation constraint.

[0010] In one embodiment, a power adequacy constraint is obtained based on the disturbance power and the quasi-steady-state frequency deviation, including: obtaining the reserve capacity of the power system and the disturbance power of the load, wind power output, and photovoltaic output; performing probabilistic quantization characterization on the disturbance power to obtain the disturbance power constraint; and obtaining the power adequacy constraint based on the disturbance power, the reserve capacity, the quasi-steady-state frequency deviation, and the disturbance power constraint.

[0011] In one embodiment, the disturbance power is probabilistically quantified to obtain a disturbance power constraint, including: obtaining prediction error variables for the power system load, wind power output, and photovoltaic output; constraining the disturbance power based on the prediction error variables and a preset confidence level, and obtaining a probability distribution model of the prediction error as the disturbance power constraint.

[0012] In one embodiment, based on the inertia adequacy constraint, the power adequacy constraint and the system operation constraint, a scheduling plan is output according to the system objective function, including: based on the system objective function, obtaining an upper-level target for unit combination optimization taking into account power adequacy and a lower-level target taking into account inertia adequacy verification; solving the upper-level target to obtain the decision variables of the system and inputting them into the lower-level target; when the decision variables do not meet the lower-level target, generating an optimization cut and inputting it into the upper-level target, executing the steps of solving the upper-level target to obtain the decision variables of the system and inputting them into the lower-level target; and outputting the decision variables as a scheduling plan when the decision variables meet the lower-level target.

[0013] In the second aspect, the present application provides an electric power system dispatching device that takes into account both inertia and power sufficiency, including: a model establishment module for determining a system frequency response model based on disturbance power, load power change, prime mover power change and equivalent inertia time constant; a constraint acquisition module for obtaining inertia sufficiency constraints and quasi-steady-state frequency deviation according to the system frequency response model; and also for obtaining power sufficiency constraints based on disturbance power and quasi-steady-state frequency deviation; a dispatching output module for outputting a dispatching plan according to the system objective function based on inertia sufficiency constraints, power sufficiency constraints and system operation constraints.

[0014] In a third aspect, the present application provides an electronic device comprising: at least one memory for storing programs; and at least one processor for executing the programs stored in the memory. When the program stored in the memory is executed, the processor is used to execute the method described in the first aspect or any possible implementation of the first aspect.

[0015] In a fourth aspect, the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method described in the first aspect or any possible implementation of the first aspect.

[0016] In a fifth aspect, the present application provides a computer program product, which, when executed on a processor, enables the processor to execute the method described in the first aspect or any possible implementation of the first aspect.

[0017] In general, the above technical solutions conceived by this application have the following beneficial effects compared with the existing technologies: This application introduces load power variation into the frequency response model to quantitatively characterize the dynamic characteristics of load-side inertia. This step breaks through the limitation of traditional models that rely solely on power-side parameters and establishes a complete system frequency characteristic analysis framework that includes load-side dynamic response.

[0018] Next, based on the inertia adequacy constraint derived from the above model, the dynamic support capacity of the load side is converted into a mathematical constraint condition through the quasi-steady-state frequency deviation index. This step solves the key problem that the load side inertia cannot participate in scheduling due to the lack of dynamic representation, ensuring that the system inertia constraint covers both the source and load resources. The power adequacy constraint is obtained based on the disturbance power and the quasi-steady-state frequency deviation. The reduction of the quasi-steady-state frequency deviation directly reflects the power shortage caused by the reduction of the load response, so that the new power constraint implicitly includes the equivalent reserve contribution of the load side, and converts the implicit reserve provided by the load resources into an explicit power constraint. This step breaks through the limitation of traditional power constraints relying solely on unit reserves by synergistically optimizing the load side power support capacity and conventional power reserve, thereby reducing redundant reserve configuration.

[0019] Finally, the above-mentioned dual sufficiency constraints are combined with the system operation constraints for optimization and solution. Since the load-side inertia resources participate in the optimization scheduling in the form of dynamic constraints, the system operation scheduling performance is ultimately improved while ensuring frequency safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is one of the flow charts provided in the embodiment of the power system dispatching method taking into account both inertia and power sufficiency of the present application; Figure 2 This is a system frequency response model diagram provided by an embodiment of the method of the present application; Figure 3 This is an analysis diagram of the relationship between inertia, frequency, and power provided by an embodiment of the method of this application; Figure 4 This is the second flow chart provided in the embodiment of the method of this application; Figure 5 This is the third flow chart provided in the embodiment of the method of this application; Figure 6 This is the fourth flow chart provided in the embodiment of the method of this application; Figure 7 This is a flowchart of solving the optimization model provided by the embodiment of the method of this application; Figure 8 This is a load and new energy prediction curve diagram provided by the embodiment of the method of this application; Figure 9 This is a diagram of the inertia time constants for each time period under different schemes provided in the embodiment of the method of the present application; Figure 10 This is a graph of the maximum frequency change rate in each time period under different schemes provided by the embodiment of the method of this application; Figure 11 This is a diagram of the start and stop status of the unit in each time period under different schemes provided by the embodiment of the method of this application; Figure 12 This is a graph of the lowest frequency points in each time period under different schemes provided by the embodiment of the method of this application; Figure 13 This is a diagram of the spare capacity for each time period under different solutions provided by the embodiment of the method of this application; Figure 14 A schematic diagram of the module structure provided for an embodiment of a power system dispatching device taking into account both inertia and power sufficiency of the present application; Figure 15 This is a structural diagram provided by an embodiment of the electronic device of the present application. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0022] Current unit commitment models designed to ensure frequency security primarily rely on the inertia of generators on the power source side to support system frequency, but fail to effectively characterize and utilize the dynamic inertia support capabilities of load-side resources, such as industrial and temperature-controlled loads. Due to the lack of dynamic modeling of load-side inertia, system dispatchers are unable to quantify the "implicit reserve capacity" of load resources that respond to power shortfalls and mitigate frequency fluctuations. Consequently, the potential for coordinated frequency regulation between sources and loads remains unrealized, limiting improvements in frequency stability and dispatch flexibility.

[0023] Based on this, the present application proposes a power system dispatching method that takes into account both inertia and power sufficiency. First, the necessity of considering both inertia and power sufficiency in unit combination is explained.

[0024] With the construction and development of new power systems, the power balance between sources and loads has undergone significant changes. On the one hand, the power balance relationship in the power system has shifted from deterministic matching to probabilistic balance. On the other hand, the continuous decline in the proportion of synchronous units has led to a gradual decline in the system's equivalent inertia level, and the traditional frequency stability mechanism that relies on the inertial support of synchronous units is at risk of failure. This dual dilemma of intensified random disturbances and weakened inertial support makes it difficult for traditional unit combination models that rely solely on rigid power balance to guarantee power adequacy and maintain the dynamic safety margin of the system frequency.

[0025] The power system dispatching method proposed in this application, which takes into account both inertia and power redundancy, focuses on the "inertia-frequency-power" relationship under source-load coordinated frequency regulation, and proposes a unit combination optimization model that integrates the "inertia-power" dual redundancy. Based on the traditional system frequency response model that relies on thermal power units for frequency regulation, this application considers the load frequency response, constructs a frequency response model for source-load coordinated frequency regulation, analyzes the source-load "inertia-frequency-power" relationship, and incorporates dynamic frequency safety constraints into the unit combination model: on the one hand, by utilizing the power-frequency characteristics of the load, the system is allowed to have a steady-state frequency deviation within a controllable range, thereby releasing the frequency regulation potential on the load side, balancing the disturbance power together with the unit reserve, and forming a system power redundancy constraint; on the other hand, a system frequency response model for source-load frequency regulation is established, the "inertia-frequency-power" relationship is analyzed, and based on the frequency change rate and the frequency minimum point expression, an inertia redundancy constraint is constructed to ensure system frequency safety.

[0026] Therefore, please refer to Figure 1 , Figure 1 This is one of the flow charts provided in the embodiment of the power system dispatching method taking into account both inertia and power sufficiency. In this embodiment, the power system dispatching method taking into account both inertia and power sufficiency includes steps S10 to S40.

[0027] Step S10 : determining a system frequency response model based on the disturbance power, the load power variation, the prime mover power variation, and the equivalent inertia time constant.

[0028] It should be noted that obtaining a system frequency response model (SFRM) is a core task in power system analysis, planning, and control. Its necessity stems from the fact that frequency is a key indicator of system operation. In this embodiment, the SFRM for source-load frequency regulation is obtained.

[0029] It should be noted that the system frequency response model for source-load frequency regulation is a core tool for analyzing the dynamic process of frequency regulation in power systems where both sources and loads participate. Its goal is to quantify the frequency response behavior of sources and loads under power imbalance, reveal the patterns of system frequency variation, and provide theoretical support for the design of frequency regulation control strategies. The system frequency response model for source-load frequency regulation must consider both the source-side frequency regulation capability and the load-side dynamic characteristics, such as the load frequency regulation effect.

[0030] It's understandable that the frequency response of a power system is essentially a dynamic process of power imbalance, frequency variation, frequency regulation resource activation, and frequency recovery. The four parameters selected in this application directly correspond to key aspects of this process and fully cover the frequency response. Disturbance power represents the system's initial power deficit or surplus and is the triggering source of the frequency response. Clarifying the magnitude and time-varying characteristics of disturbance power is fundamental to analyzing the initial conditions for frequency variation. Load power variation reflects the load's dynamic response to frequency variation, known as the load frequency regulation effect. This reflects the load's adaptive ability to frequency fluctuations, such as the automatic load shedding of an induction motor as the frequency decreases. This parameter is directly related to the system's inherent frequency regulation potential. Prime mover power variation represents the power source's active frequency regulation capability, achieved through a speed regulator or automatic generation control (AGC). It is the primary control mechanism for restoring system frequency stability. Its dynamic characteristics directly impact the speed and accuracy of frequency recovery. The equivalent inertia time constant measures the system's resistance to frequency variation and is determined by the rotating mass of the synchronous generator (traditional power source) and the virtual inertia of the power electronics interface power supply. The size of the inertia time constant directly determines the initial rate of frequency change and is a key indicator for evaluating the inertia level of the system.

[0031] It should be noted that according to the static frequency characteristics of the load, when the system frequency is Fluctuation to When , the corresponding load power change is as follows (1).

[0032] (1) Where, The frequency is equal to The active load of the system at time t The load is proportional to the frequency. share of is the frequency deviation; Denoted as the load frequency regulation effect coefficient, is the load part that participates in the frequency response.

[0033] Further construct the system frequency response model considering source and load frequency modulation as follows Figure 2 shown. Figure 2 middle, The disturbance power is mainly caused by the uncertainty of wind power, photovoltaic power and load; is the equivalent inertia time constant of the unit; is the damping coefficient of the unit; is the unit adjustment coefficient; is the unit reheat time constant; is the work coefficient of the prime mover's high-pressure cylinder; is the mechanical power factor; is the load frequency regulation effect coefficient.

[0034] It should be noted that, in order to simplify the functional relationship, this application does not consider the damping coefficient of the thermal power unit. The equivalent inertia time constant is related to the inertia time constant and the start-stop state of each unit, that is, the following formula (2).

[0035] (2) Where, N is the total number of units; For the crew i The inertia time constant; For the crew i Rated capacity; is the system baseline capacity; is the start and stop status of unit i at time t. Figure 3 By Laplace transform or piecewise solution, the system frequency response model of source and load frequency modulation can be obtained, which has a time domain expression of the relationship between system inertia, frequency and power, and is used as the expression of the system frequency response model of this application, namely the following formula (3).

[0036] (3) in, is the natural oscillation angular frequency, is the damping ratio, is the damped oscillation angular frequency, and is the intermediate variable in the calculation process. The expressions of each variable are as follows (4).

[0037] (4) Based on equations (3) and (4), the typical values ​​of inertia time constant and disturbance power are selected to explore the intrinsic correlation mechanism between inertia, frequency and power. The results are as follows: Figure 3 As shown, Figure 3This is an analysis chart of the relationship between inertia, frequency, and power provided by an embodiment of the method of this application. It can be seen that as the disturbance power increases, the amplitude of the system frequency changes significantly more rapidly, and the depth of the frequency drop further increases, reflecting the direct correlation between the intensity of the power disturbance and the dynamic response of the frequency. The larger the inertia time constant, the stronger the system's ability to suppress frequency fluctuations and the smaller the frequency change rate, indicating that the inertia level is a key factor in suppressing rapid frequency drops.

[0038] Therefore, the system frequency response model proposed in this embodiment conforms to the laws of nature, can well characterize the relationship between inertia, frequency and power, and includes the dynamic characterization of load-side resources, thereby improving the potential of the system frequency response model.

[0039] Step S20 : ​​obtaining an inertia sufficiency constraint and a quasi-steady-state frequency deviation according to the system frequency response model.

[0040] It's important to note that frequency security is a core element in ensuring grid stability and power supply reliability during power system operation. When the system experiences power disturbances (such as generator trips or sudden load increases), the frequency undergoes dynamic changes, and its key indicators directly influence whether the system can quickly recover stability. Inertia adequacy constraint modeling quantifies the system's ability to support frequency changes with inertia, focusing on the maximum frequency change rate, the lowest frequency point, the quasi-steady-state frequency deviation, and their constraint modeling methods.

[0041] It's important to note that the maximum frequency change rate reflects the system's inertia's ability to buffer sudden power surges. Greater inertia results in smoother frequency changes; insufficient inertia can cause a sharp drop in frequency, triggering malfunctioning protection devices or damaging equipment. The lowest frequency point determines whether the system enters an emergency state; if it falls below a critical value, it can lead to a cascading failure. Quasi-steady-state frequency deviation reflects the system's secondary frequency regulation capabilities, such as the AGC response speed. Excessive deviation can impact the normal operation of user equipment or trigger inter-regional power oscillations.

[0042] In this embodiment, the inertia adequacy constraint is derived from a system frequency response model because it can quantify the coupling relationship between system inertia, frequency regulation resources, and frequency dynamics, thereby providing theoretical support for frequency security assessments in power grids with a high proportion of renewable energy. Specifically, the expression of the system frequency response model can be substituted into the aforementioned frequency security index expression. The core logic is to directly link frequency dynamics with system parameters through mathematical derivation, thereby quantifying the constraining effect of inertia on frequency security.

[0043] It can be understood that this embodiment provides a specific implementation method for obtaining inertia adequacy constraint modeling, such as Figure 4 As shown, Figure 4 This is the second flow chart provided in the embodiment of the method of this application.

[0044] In this embodiment, step S20 includes steps S21 to S23.

[0045] Step S21 : obtaining the descending slope of the system frequency response model at the disturbance start time as the maximum frequency change rate, and establishing a maximum frequency change rate constraint.

[0046] It should be noted that the maximum frequency change rate The frequency drop slope at the initial stage of the disturbance is expressed as the following formula (5). The maximum frequency change rate should be less than the upper limit value.

[0047] (5) Step S22 , obtaining the time when the descending slope of the system frequency response model is 0 as the time when the frequency reaches the lowest point, obtaining the frequency lowest point based on the time when the frequency reaches the lowest point, and establishing a frequency lowest point constraint. It should be noted that the lowest frequency It is the lowest frequency reached before the frequency is restored. , the time when the frequency reaches the lowest point can be obtained The lowest frequency point can be calculated as the following formula (6). The lowest frequency point should be greater than the lower limit value.

[0048] (6) (7) Step S23 : obtaining a continuous frequency deviation after the system frequency response model enters the quasi-steady state as a quasi-steady-state frequency deviation, and establishing a quasi-steady-state frequency deviation constraint.

[0049] It should be noted that the quasi-steady-state frequency deviation , the continuous frequency deviation after the system enters the quasi-steady state is calculated as follows (8).

[0050] (8) It should be noted that, by limiting the obtained frequency safety index according to the system operation requirements, a dynamic inertia adequacy constraint can be constructed as a frequency safety constraint.

[0051] Step S30: obtaining a power adequacy constraint based on the disturbance power and the quasi-steady-state frequency deviation.

[0052] It can be understood that in the power system frequency security assessment, the core of step S30 is to derive the power adequacy constraint required by the system through the correlation between the disturbance power, that is, the power shortage or surplus suffered by the system and the quasi-steady-state frequency deviation, that is, the minimum spare capacity or frequency regulation resources that the system needs to reserve to ensure that the system can control the frequency deviation within a safe range after the disturbance occurs.

[0053] It should be noted that, considering the frequency regulation power support role of the load, this application will take the backup constraint that takes into account the source and load frequency regulation effect as the power adequacy constraint, and the system backup capacity must meet the regulation requirements of both the power side and the load side.

[0054] Furthermore, this embodiment provides a specific implementation method for obtaining power adequacy constraint modeling, such as Figure 5 As shown, Figure 5 This is the third flow chart provided in the embodiment of the method of this application.

[0055] In this embodiment, step S30 includes steps S31 to S33.

[0056] Step S31 , obtaining the reserve capacity of the power system and the disturbance power of the load, wind power output and photovoltaic output.

[0057] It should be noted that reserve capacity refers to the redundant resources reserved by the system to cope with sudden power shortages. It is usually divided into spinning reserve, which is the capacity of units that are connected to the grid and can respond quickly, and non-spinning reserve, which is the resources that need to be started or dispatched, such as energy storage and interruptible loads. The acquisition methods include: obtaining daily / weekly dispatch plans from the power grid dispatch center, which clearly mark the planned output and reserved reserve capacity of each unit; or collecting the unit operating status, output ceiling and current available capacity in real time through the dispatch automation system; in the power market environment, reserve capacity may be purchased through the ancillary service market; based on historical data or prediction models, the required reserve capacity is calculated through probabilistic safety assessment.

[0058] It should be noted that load disturbance refers to a sudden increase or decrease in load power, which may be caused by industrial start-up and shutdown, sudden changes in air conditioning load, etc. Disturbances in wind power output and photovoltaic output usually refer to those significantly affected by weather, and the disturbance manifests as a sudden drop or increase in output, such as a cliff-like drop in photovoltaic output caused by cloud cover. The disturbance power of load, wind power output, and photovoltaic output can be respectively collected in real time by deploying synchronized phasor measurement units to calculate the power change rate; combining anemometers with power curves to analyze abnormalities where wind speed changes suddenly but output does not follow; using irradiance sensors and sky imagers to capture cloud movement and predict cliff-like drops in output.

[0059] Step S32: Perform probability quantization characterization on the disturbance power to obtain the disturbance power constraint.

[0060] It should be noted that by quantifying the uncertainty of disturbance power through probabilistic statistical methods, such as the probability distribution of load mutations and sudden drops in wind power output, probabilistic disturbance constraints that meet system safety requirements are generated to replace traditional deterministic constraints, such as fixed thresholds, thereby improving the economy and robustness of reserve capacity configuration.

[0061] Specifically, the disturbance power is probabilistically quantified and obtained, including: obtaining prediction error variables for power system load, wind power output, and photovoltaic output; constraining the disturbance power based on the prediction error variables and preset confidence levels, and obtaining a probability distribution model of the prediction error as the disturbance power constraint.

[0062] It's understandable that the forecast error variable, the difference between the actual and predicted values, requires a different definition for different disturbance types. By collecting extensive historical data and conducting statistical analysis on the forecast error variable, we can derive its probability distribution model. For example, forecast errors for load, wind power, and photovoltaic output may follow other distributions, such as the normal distribution or the Laplace distribution. These probability distribution models serve as disturbance power constraints for subsequent power system analysis and reserve capacity allocation.

[0063] It can be understood that since the prediction errors of load, wind power and photovoltaic output are random, the disturbance power is no longer a constant. Therefore, this embodiment uses the p-effective point method to perform probabilistic quantification as the disturbance power constraint, as shown in the following equations (9) to (11).

[0064] (9) (10) (11) Where, Pr{} is the mathematical symbol for probability quantization; 、 、 are the disturbance powers caused by load, wind power and photovoltaic output forecast errors respectively. 、 、 are the prediction error variables of load, wind power output, and photovoltaic output, respectively. 、 、 is the corresponding preset confidence level.

[0065] It is understandable that the confidence level is determined based on the safety requirements and operating strategies of the power system. For example, in scenarios with higher security requirements, a confidence level of 95% or 99% might be selected. Different confidence levels correspond to different risk tolerances. A higher confidence level means a higher degree of assurance for system safety, but it may also lead to an increase in required resources such as backup capacity. For a given confidence level, the corresponding quantile can be calculated based on the probability distribution model of the prediction error. Taking the normal distribution as an example, to calculate the one-sided lower or upper confidence limit for a preset confidence level, the quantile table or related functions of the standard normal distribution can be used. Methods for calculating quantiles also exist for other distribution types. For example, for the Laplace distribution, the quantile at a given confidence level can be calculated using the properties of its probability density function and cumulative distribution function, thereby obtaining the deterministic equivalent disturbance power.

[0066] Step S33: obtaining a power adequacy constraint based on the disturbance power, the spare capacity, the quasi-steady-state frequency deviation, and the disturbance power constraint.

[0067] Combining the above contents, the power adequacy constraint can be established based on the disturbance power, spare capacity, and quasi-steady-state frequency deviation, as shown in the following equation (12).

[0068] (12) in, For the crew i The reserve capacity of the power generators is 100%, and the disturbance power should satisfy the disturbance power constraints of equations (9) to (11). The left side of the equation represents the available power regulation capability of the system. The first term on the left is the sum of the reserve capacity of all units, which can directly increase or decrease the power generation to cope with the disturbance. The second term on the left reflects the load's regulation of frequency changes in a quasi-steady state. When the frequency drops, the load power will automatically decrease, thereby helping the system to restore power balance to a certain extent.

[0069] It's important to note that the right side of the equation represents the total power disturbances faced by the system, including random load variations and uncertain fluctuations in wind and photovoltaic output. This formula requires that the system's available power regulation capacity be greater than or equal to the total power disturbances it faces to ensure stable operation after a disturbance occurs and avoid significant frequency drops or increases due to power shortages.

[0070] Step S40 : Based on the inertia adequacy constraint, the power adequacy constraint and the system operation constraint, a scheduling plan is output according to the system objective function.

[0071] It can be understood that, on the basis of considering the operating cost and standby cost of thermal power units, economic optimality is used as the objective function, as shown in the following formula (13).

[0072] (13) in, 、 、 is the power generation cost coefficient of the unit; For the crew i In the period t contribution; is the spare capacity of unit i at time t; is the start and stop status of unit i at time t; is the start and stop status of unit i at time t-1; 、 For the crew i In the period t The start and stop cost coefficient; For the crew i The backup cost coefficient is . Combining the inertia adequacy constraint, power adequacy constraint and system operation constraint, the specific expression is as follows (14).

[0073] (14) It should be noted that the first formula in (14) is the power balance constraint. 、 、 are the predicted values ​​of wind power output, photovoltaic output and system load in period t respectively; the second formula is the unit climbing constraint, 、 Respectively for units i Upward and downward climbing rates; the third formula is the unit output constraint, 、 Respectively for units i Output upper and lower limits; the fourth formula is the minimum start and stop time constraint of the unit, 、 Respectively for units i exist t Always on and off time; 、 Respectively for units i Minimum startup and shutdown time.

[0074] It should be noted that the fifth formula in (14) is the power adequacy constraint. represents the total disturbance power of the system, , is the confidence level that the system reserve capacity needs to meet; the sixth and seventh formulas are inertia adequacy constraints, and It can be calculated by formula (2) and formula (6) respectively. is the frequency change rate limit, The lowest frequency limit.

[0075] As you can understand, after obtaining the objective function and constraints, the established mathematical model is solved using optimization software, such as MATLAB's Optimization Toolbox or the Gurobi solver. The solution provides information such as the output plan and start / stop status of each unit, i.e., the dispatch plan. The solution is analyzed to verify that all constraints are met, and the economic feasibility of the dispatch plan is evaluated. If the results are unsatisfactory, the model parameters or constraints need to be adjusted and the solution repeated.

[0076] Furthermore, this embodiment provides a specific output scheduling solution implementation method, please refer to Figure 6 and Figure 7 , Figure 6 This is the fourth flow chart provided in the embodiment of the method of this application; Figure 7 This is a flowchart of the optimization model solution provided by the embodiment of the method of this application.

[0077] In this embodiment, step S40 includes steps S41 to S44.

[0078] Step S41 : Based on the system objective function, an upper target of unit commitment optimization taking into account power adequacy and a lower target taking into account inertia adequacy verification are obtained.

[0079] It should be noted that the proposed unit commitment model, or the system objective function, is decomposed into an upper-level main problem / upper-level objective and a lower-level sub-problem / lower-level objective, connected by a Benders cut. The upper-level objective focuses on power adequacy and solves the problem of outputting the start and stop states of the units in the unit commitment model. The lower-level objective, based on inertia adequacy requirements, verifies the frequency security constraints of the above solution under disturbance scenarios.

[0080] It should be noted that the Benders cut transfers information from lower-level subproblems to the upper-level main problem in the form of linear constraints, allowing the upper-level main problem to consider feedback from the lower-level subproblems in subsequent iterations, thereby optimizing the solution process. Through continuous iteration, the upper-level main problem adjusts the unit commitment plan based on the Benders cut, and the lower-level subproblems verify the adjusted plan until the economically optimal unit commitment plan that satisfies both power adequacy and inertia adequacy constraints is found. This allows for efficient solution of unit commitment optimization problems that take both power adequacy and inertia adequacy into account.

[0081] Step S42: Solve the upper-level goal to obtain the decision variables of the system and input them into the lower-level goal.

[0082] It's important to note that the upper-level objective is a unit commitment optimization problem that takes power availability into account. This is typically a mixed-integer linear programming problem, as it involves the start / stop states (discrete variables) and output conditions (continuous variables) of the units. Solvers such as Gurobi, MATLAB, or CPLEX can be directly invoked, with built-in branch-and-cut algorithms that combine branch and bound with cutting planes. This algorithm leverages the convexity of linear problems to ensure convergence to the global optimal solution.

[0083] It should be noted that after the optimization of the upper-level objectives converges, the start-up and shutdown status, output status, and standby status of each unit can be obtained as decision variables, and the obtained optimization solution is used as the input of the lower-level objectives.

[0084] Understandably, the unit start / stop status specifies the operating or shutdown status of each unit within the dispatch cycle, which is crucial for lower-level inertia adequacy verification, as only operating units can provide rotational inertia. Unit output includes the actual output values ​​of each unit at different time periods, which affects the system's total inertia calculation and frequency dynamic response. Reserve capacity includes rotating and non-rotating reserves. The allocation of reserve capacity affects the system's power balance and frequency stability under disturbances. Lower-level subproblems need to consider this reserve information to evaluate the system's inertia adequacy.

[0085] Step S43, when the decision variables do not meet the lower-level objectives, an optimized cut is generated and input into the upper-level objectives, and the steps of solving the upper-level objectives to obtain the decision variables of the system and inputting them into the lower-level objectives are executed.

[0086] It is understandable that the upper layer optimization solution is verified to see whether it satisfies the frequency safety constraint, i.e., the inertia sufficiency constraint, under disturbance conditions. If the constraint is not satisfied, an optimization cut is generated and the process returns to the upper layer and re-executes step S42.

[0087] It's understandable that an optimization cut is a special type of constraint. Based on the solutions to the lower-level subproblems, it feeds back information about unsatisfied constraints found during the lower-level verification process to the upper-level main problem, guiding the upper-level main problem to adjust the unit combination. It's typically expressed as a linear constraint. For example, based on the lower-level verification results, it determines which unit combinations or output conditions lead to insufficient inertia. Then, corresponding constraints are generated to prevent similar infeasible solutions from occurring in subsequent iterations of the upper-level main problem.

[0088] It should be noted that the optimization cut generated by this application can be an optimization cut for increasing system inertia. Generally, the optimization cut is only used to exclude infeasible solutions, while the optimization cut in this application not only excludes infeasible solutions, but also actively guides the increase of system inertia. By identifying the scenario of insufficient inertia in the lower-level verification, the generated optimization cut will require the upper-level main problem to select a unit combination that can increase the system inertia. This optimization cut helps to enhance the frequency stability of the power system, especially in scenarios with a high proportion of renewable energy access.

[0089] Step S44: output the decision variables as a scheduling solution when the decision variables meet the lower-level objectives.

[0090] It's understandable that when the decision variables meet the lower-level objectives—that is, pass the inertia adequacy check—the upper-level optimization solution not only excels in power adequacy, able to cope with uncertainties in load, wind power, and PV output, but also meets the system frequency security requirements in terms of inertia adequacy. This demonstrates that the unit combination scheme is a feasible and high-quality scheduling solution, taking into account multiple key factors such as economic efficiency, power balance, and frequency stability.

[0091] In this embodiment, by incorporating load power variation into the frequency response model, we achieve a quantitative characterization of the dynamic characteristics of load-side inertia. This step overcomes the limitations of traditional models that rely solely on power-side parameters and establishes a complete system frequency characteristic analysis framework for load-side dynamic response.

[0092] Next, based on the inertia adequacy constraint derived from the above model, the dynamic support capacity of the load side is converted into a mathematical constraint condition through the quasi-steady-state frequency deviation index. This step solves the key problem that the load side inertia cannot participate in scheduling due to the lack of dynamic representation, ensuring that the system inertia constraint covers both the source and load resources. The power adequacy constraint is obtained based on the disturbance power and the quasi-steady-state frequency deviation. The reduction of the quasi-steady-state frequency deviation directly reflects the power shortage caused by the reduction of the load response, so that the new power constraint implicitly includes the equivalent reserve contribution of the load side, and converts the implicit reserve provided by the load resources into an explicit power constraint. This step breaks through the limitation of traditional power constraints relying solely on unit reserves by synergistically optimizing the load side power support capacity and conventional power reserve, thereby reducing redundant reserve configuration.

[0093] Finally, the above-mentioned dual sufficiency constraints and system operation constraints are combined for optimization and solution. Since the load-side inertia resources participate in the optimization scheduling in the form of dynamic constraints, a more economical scheduling plan is finally generated while ensuring frequency safety.

[0094] Furthermore, the present application breaks through the limitation of traditional scheduling that only focuses on power sufficiency and source-side inertia, innovatively introduces source and load inertia as optimization variables, and constructs a unit combination model that considers both inertia and power sufficiency. As shown in the table below, the traditional unit combination model, the unit combination model considering source-load randomness, and the model considering "inertia-frequency-power" in this article are compared. From the comparison, it can be seen that the model proposed by the present invention, on the basis of considering source-load randomness, adds the consideration of the source-load inertia-frequency contribution, and incorporates the load-side frequency regulation contribution as the effective frequency regulation power capacity into the total standby resources of the system, thereby increasing the system frequency regulation power capacity. On the other hand, the "frequency-inertia" related indicator restrictions are converted into constraint conditions to ensure that the system has a sufficient inertia level.

[0095] .

[0096] It can be understood that this application comprehensively utilizes the frequency regulation potential on both the source and load sides to achieve the coordinated optimization of the system's dynamic frequency response capability and the backup (power) capacity, which can effectively enhance the frequency stability and operational economy of the power system in scenarios with a high proportion of new energy.

[0097] In order to verify the effectiveness of this method, appropriate modifications are made to the IEEE 10-machine 39-bus system, and the wind power, photovoltaic output and load forecast data are as follows: Figure 8 As shown in the figure, further discussion is given. Among them, the system base frequency is 50Hz, the frequency change rate limit is -0.5Hz / s, the frequency minimum point limit is 49Hz, the steady-state frequency deviation allowable value is set to 0.5Hz, and the setting Calculate the load frequency regulation effect coefficient. Confidence Take 0.96.

[0098] It should be noted that three schemes are set up and the scheduling results are analyzed: Scheme 1 is a conventional unit combination model that only considers power abundance; Scheme 2 is a unit combination model that considers source side inertia and power abundance, without considering the load frequency regulation effect; Scheme 3 is the unit combination model proposed in this application that considers dual abundance of source and load, inertia and power.

[0099] It should be noted that in order to clearly present the beneficial effects of this application, the following Figures 9 to 13 , a comparative analysis was carried out using the maximum frequency change rate, the lowest frequency point and the spare capacity as indicators.

[0100] It should be noted that Figure 9 This is a diagram of the inertia time constants for each period under different schemes provided by the embodiment of the method of this application. Figure 10 This is a graph of the maximum frequency change rate in each time period under different schemes provided by the embodiment of the method of this application. Figure 11 It is the start and stop status of the unit in each time period under different schemes provided by the embodiment of the method of this application.

[0101] Among them, Plan 1 only considers power sufficiency without also considering inertia sufficiency, and only aims to balance disturbance power with reserve capacity. The number of units started during the 13th to 15th period is relatively small, causing the system inertia level to fall below the minimum requirement. The maximum frequency change rate exceeds the safety threshold of -0.5Hz / s (maximum -0.53Hz / s), posing a threat to system frequency stability. Plan 2 and the present application (Scheme 3 in the figure) increase system inertia by adding units, keeping the maximum frequency change rate within a safe range, fully demonstrating the necessity of considering inertia sufficiency.

[0102] It should be noted that Figure 12 This is the lowest frequency point in each time period under the different schemes provided by the embodiments of the present invention. Compared to Scheme 1, Scheme 2 incorporates an inertia sufficiency constraint, increasing the system inertia by adding operating units during the 13-15 period, thereby raising the lowest frequency point in this period. This application further explores the potential of the load frequency regulation effect, improving the system frequency response capability without adding operating units, and increasing the lowest frequency point in each time period by an average of approximately 6.13%, enhancing system frequency stability.

[0103] It should be noted that Figure 13 It is the spare capacity in each time period under different schemes provided by the embodiment of the method of this application. Since Scheme 1 and Scheme 2 follow the same spare constraints, under the same power disturbance, both optimize the spare capacity to the minimum level that meets the requirements with the goal of cost optimization, so the spare capacity performance in each time period is consistent. In comparison, the present application takes into account the load frequency regulation effect and uses it to share part of the disturbance power, thereby reducing the dependence on spare capacity and alleviating the frequency regulation pressure of thermal power units, reducing the spare capacity in each time period by an average of 3.29%, and the total spare capacity is reduced by 3.31% compared with Scheme 2, which reduces the standby cost while improving the economic efficiency of system operation.

[0104] The power system dispatching device taking into account both inertia and power sufficiency provided in this application is described below. The power system dispatching device taking into account both inertia and power sufficiency described below and the power system dispatching method taking into account both inertia and power sufficiency described above can be referenced to each other.

[0105] It should be noted that if Figure 14As shown, the power system dispatching device taking into account both inertia and power sufficiency includes: a model building module 10, used to determine the system frequency response model based on the disturbance power, the load power change, the prime mover power change and the equivalent inertia time constant; a constraint acquisition module 20, used to obtain the inertia sufficiency constraint and the quasi-steady-state frequency deviation according to the system frequency response model; and also used to obtain the power sufficiency constraint based on the disturbance power and the quasi-steady-state frequency deviation; a dispatching output module 30, used to output a dispatching plan according to the system objective function based on the inertia sufficiency constraint, the power sufficiency constraint and the system operation constraint.

[0106] It is understood that the detailed functional implementation of each of the above-mentioned units / modules can be found in the description of the aforementioned method embodiments and will not be described in detail here. The above-mentioned device is used to execute the method in the above-mentioned embodiment. The corresponding program modules in the device have similar implementation principles and technical effects as those described in the aforementioned method. The working process of the device can be referenced to the corresponding process in the aforementioned method and will not be described in detail here.

[0107] Based on the method in the above embodiment, the embodiment of the present application provides an electronic device, such as Figure 15 As shown. The electronic device may include: a processor (Processor) 41, a communication interface (Communications Interface) 42, a memory (Memory) 43, and a communication bus 44. The processor 41, the communication interface 42, and the memory 43 communicate with each other via the communication bus 44. The processor 41 can call the logic instructions in the memory 43 to execute the method in the above embodiment.

[0108] In addition, the logic instructions in the aforementioned memory 43 can be implemented in the form of a software functional unit and, when sold or used as an independent product, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the portion that contributes to the prior art, or the portion of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a number of instructions for causing a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application.

[0109] Based on the method in the above embodiment, an embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method in the above embodiment.

[0110] Based on the method in the above embodiment, an embodiment of the present application provides a computer program product. When the computer program product runs on a processor, the processor executes the method in the above embodiment.

[0111] It is understood that the processor in the embodiments of the present application may be a central processing unit (CPU), other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA), other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. The general-purpose processor may be a microprocessor or any conventional processor.

[0112] The method steps in the embodiments of the present application can be implemented by hardware or by a processor executing software instructions. The software instructions can be composed of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, removable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be an integral part of the processor. The processor and storage medium can be located in an ASIC.

[0113] The above embodiments can be implemented in whole or in part using software, hardware, firmware, or any combination thereof. When implemented using software, they can be implemented in whole or in part in the form of a computer program product. The computer program product comprises one or more computer instructions. When loaded and executed on a computer, the computer program instructions fully or partially produce the processes or functions described in the embodiments of this application. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted via the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible by a computer or a data storage device such as a server or data center that integrates one or more available media. The available medium can be magnetic media (e.g., floppy disk, hard disk, tape), optical media (e.g., DVD), or semiconductor media (e.g., solid-state drive (SSD)).

[0114] It will be understood that the various numerical numbers involved in the embodiments of the present application are merely distinctions for the convenience of description and are not intended to limit the scope of the embodiments of the present application.

[0115] It is easy for those skilled in the art to understand that the above is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the scope of protection of the present application.

Claims

1. A power system dispatching method taking into account both inertia and power sufficiency, characterized in that: include: Determine the system frequency response model based on the disturbance power, load power change, prime mover power change and equivalent inertia time constant; Obtaining inertia sufficiency constraints and quasi-steady-state frequency deviations according to the system frequency response model; Obtaining a power adequacy constraint based on the disturbance power and the quasi-steady-state frequency deviation; Based on the inertia adequacy constraint, the power adequacy constraint and the system operation constraint, a scheduling plan is output according to a system objective function.

2. The power system dispatching method taking into account both inertia and power sufficiency according to claim 1, characterized in that: The system frequency response model is: ； ； ； ； ； ； in, is the system frequency deviation; For time; is the disturbance power; is the unit adjustment coefficient; is the equivalent inertia time constant of the unit; is the work coefficient of the prime mover's high-pressure cylinder; is the load frequency regulation effect coefficient; is the mechanical power factor; is the unit reheat time constant; is the natural oscillation angular frequency, is the damping ratio, is the damped oscillation angular frequency, and is an intermediate variable in the calculation process.

3. The power system dispatching method taking into account both inertia and power sufficiency as claimed in claim 2, characterized in that: The inertia sufficiency constraints include: maximum frequency change rate constraint, frequency minimum point constraint, and quasi-steady-state frequency deviation constraint; obtaining the inertia sufficiency constraint and quasi-steady-state frequency deviation according to the system frequency response model includes: Obtaining the descending slope of the system frequency response model at the start of the disturbance as the maximum frequency change rate, and establishing a maximum frequency change rate constraint; Obtaining the time when the descending slope of the system frequency response model is 0 as the time when the frequency reaches the lowest point, obtaining the lowest frequency point based on the time when the frequency reaches the lowest point, and establishing a frequency lowest point constraint; A continuous frequency deviation after the system frequency response model enters the quasi-steady state is obtained as a quasi-steady-state frequency deviation, and a quasi-steady-state frequency deviation constraint is established.

4. The power system dispatching method taking into account both inertia and power sufficiency as claimed in claim 3, characterized in that: The disturbance power includes the disturbance power of the load, wind power output, and photovoltaic output; obtaining the power adequacy constraint based on the disturbance power and the quasi-steady-state frequency deviation includes: Obtain the reserve capacity of the power system and the disturbance power of load, wind power output and photovoltaic output; Performing probabilistic quantization characterization on the disturbance power to obtain a disturbance power constraint; A power adequacy constraint is obtained based on the disturbance power, the spare capacity, the quasi-steady-state frequency deviation, and the disturbance power constraint.

5. The power system dispatching method taking into account both inertia and power sufficiency as claimed in claim 4, characterized in that: Probabilistically quantifying the disturbance power to obtain a disturbance power constraint includes: Obtain prediction error variables for power system load, wind power output, and photovoltaic output; The disturbance power is constrained based on the prediction error variable and a preset confidence level, and a probability distribution model of the prediction error is obtained as the disturbance power constraint.

6. The power system dispatching method taking into account both inertia and power sufficiency as claimed in claim 1, characterized in that: Based on the inertia sufficiency constraints, power sufficiency constraints, and system operation constraints, a scheduling plan is output according to the system objective function, including: Based on the system objective function, the upper-level objective of unit commitment optimization taking into account power adequacy and the lower-level objective taking into account inertia adequacy verification are obtained; Solving the upper-level goal to obtain the system's decision variables and inputting them into the lower-level goal; When the decision variables do not satisfy the lower-level objectives, an optimized cut is generated and inputted into the upper-level objectives, and the steps of solving the upper-level objectives to obtain the decision variables of the system and inputting them into the lower-level objectives are performed; When the decision variables satisfy the lower-level objectives, the decision variables are output as a scheduling solution.

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