Methods and systems for combining electric and thermal co-generation units, taking into account operational risks and frequency safety.

Abstract

This invention discloses a method and system for combining electrothermal power generation units, considering both operational risk and frequency security. Relating to the field of power system technology, the method includes: establishing full-process frequency security constraints by considering the differentiated frequency regulation characteristics of different units; using a polyhedral uncertainty set to characterize the fluctuation range of wind power output; introducing conditional risk value to quantify the risk of wind curtailment and power shortage caused by wind power output exceeding limits; constructing operational risk costs from the penalty costs of wind curtailment risk and power shortage risk, and incorporating these costs into the optimization objective; and constructing a two-stage optimization model to obtain the optimal scheduling scheme for unit start-up and shutdown, electrothermal output, and frequency regulation reserve. This achieves a synergy between frequency security and economic efficiency.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and in particular to a method and system for combining electrothermal co-generation units that takes into account operational risks and frequency safety. Background Technology

[0002] Currently, most mainstream grid-following (GFL) wind turbines lack synchronous rotational inertia and autonomous frequency regulation capabilities. Their high proportion of grid connection significantly weakens the inertial response capability of the power system, leading to a decrease in system frequency stability. Several frequency instability incidents have already occurred due to insufficient system inertia and a lack of frequency regulation resources.

[0003] Combined heat and power (CHP) units, through coordinated operation with heating networks, can leverage the heat storage characteristics of these networks to expand their operational range, providing the power system with more ample regulation capacity while ensuring heat load supply. Therefore, fully exploring the frequency support potential of diverse resources such as CHP units and wind power is a crucial measure for maintaining power system frequency security.

[0004] In terms of frequency support resource modeling, current research mostly considers only a single flexible resource, lacking coordination for multiple heterogeneous resources. Furthermore, wind farms are often treated as idealized resources capable of providing a uniform inertial response and primary frequency regulation capability, ignoring the fundamental differences in frequency response among different types of wind farms: GFLs require phase-locked loops to measure frequency, have inherent delays, and are difficult to participate in inertial response. This uniform modeling approach may lead to an overestimation of the system's frequency support capability, affecting the reliability of scheduling decisions.

[0005] For the random fluctuations in wind power output, robust optimization, with its low dependence on probability distribution and scenario samples, has become the mainstream method to improve the system's ability to withstand fluctuations. However, most current research focuses only on the inertial response and primary frequency regulation after disturbances, neglecting the secondary frequency regulation (SFR) reserve necessary to cope with the continuous power fluctuations of wind power. The few models that consider wind power uncertainties also fail to coordinate reserve capacity with dynamic frequency security constraints, resulting in scheduling schemes still facing high risks when facing actual fluctuations.

[0006] In the area of ​​coordinated power and heat dispatch, numerous studies have explored ways to enhance the operational flexibility of the power grid through horizontal energy conversion between electricity and heat. However, there are still shortcomings in applying the flexibility of the heating network to support system frequency: when CHP units participate in rapid frequency regulation, the rapid changes in heat output can impact safety constraints such as water supply temperature, and existing models do not adequately account for the impact of this impact on the safe operation of the heating network. Summary of the Invention

[0007] To address the aforementioned issues, this invention proposes a method and system for combining electrothermal units that considers both operational risks and frequency safety, thereby achieving a synergy between frequency safety and economic efficiency.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a method for combining electrothermal co-generation units, taking into account operational risks and frequency safety, comprising: Considering the differentiated frequency regulation characteristics of thermal power units, CHP units, GFM wind turbine units, and GFL wind turbine units, a full-process frequency safety constraint including inertial response, primary frequency regulation, and secondary frequency regulation is established. The polyhedral uncertainty set is used to characterize the fluctuation range of wind power output. Conditional risk value is introduced to quantify the wind curtailment risk and power shortage risk caused by wind power output exceeding the limit. The operation risk cost is composed of the wind curtailment risk penalty cost and the power shortage risk penalty cost. The first-stage optimization objective is to minimize the sum of start-up and shutdown costs, power generation costs, reserve costs of primary and secondary frequency regulation, and operational risk costs. The second-stage optimization objective is to minimize the operational risk costs under the worst-case scenario characterized by the polyhedral uncertainty set. Combining the frequency security constraints of the entire process, a two-stage optimization model is constructed to solve for the optimal scheduling scheme for unit start-up and shutdown, electrical and thermal output, and frequency regulation reserve.

[0009] As an alternative implementation method, the wind power output fluctuation range is: ; in, For wind turbines The output value; and Wind turbine exist Wind power output and wind power forecast for the specified time period; and Wind turbine exist Upward and downward adjustment margins for different time periods; and Wind turbine exist The upward and downward adjustment factors for each time period are 0 / 1 variables; and These are the spatial uncertainty parameter and the time uncertainty parameter, respectively; denoted as the number of wind turbine units; T represents the total number of time periods.

[0010] As alternative implementation methods, the risks of wind curtailment and power shortages are respectively: ; ; in, and These are the upper and lower limits of the acceptable range for wind power, respectively. and These are the risks of wind curtailment and power shortages, respectively. This is the upper limit of the wind power disturbance range at this node; For wind power random disturbances, which are random variables; Let it be the expected function; Let be the probability density function of random disturbances in wind power. Operating risk costs for: ; in, , These are the unit wind curtailment penalty cost and the unit power shortage penalty cost, respectively.

[0011] As an alternative implementation method, the optimization objective for the second stage is: ; in, and Wind turbine exist The upward and downward adjustment factors for each time period are 0 / 1 variables; T is the total number of time periods; , For the load and the number of wind turbine units; and These are the cost coefficients for the second phase of power shortage and wind curtailment at wind farms, respectively. For the second phase Time period The power shortage of each load; For the second phase Time period j The amount of wind curtailment at each wind farm.

[0012] As an alternative implementation method, the process of constructing the two-stage optimization model also considers the power balance constraints satisfied by thermal power units, CHP units and wind power units in the ground state scenario, the flexible supply constraints of heat source nodes in the disturbance scenario, and the flexible recovery constraints of the heat network after frequency response. Among them, the supply constraint of flexibility is ; In the formula: , For the upward and downward changes in heat output; , These represent the maximum upward adjustable capacity and the maximum downward adjustable capacity provided by the heating network, respectively. , All are 0–1 variables, representing the heat storage and heat release states of the heating network; To account for the water supply pipe outlet temperature after heat transfer delay; and These are the lower and upper limits of the outlet water temperature of the water supply pipeline, respectively. For a moment t unit Hot water flow rate at the outlet; For FPP cycle; This is the specific heat capacity of hot water; The heating network flexibility recovery constraint is that during the FPP period of providing frequency response, the actual water supply temperature of the CHP unit is always maintained within the safe threshold range.

[0013] As an optional implementation method, the full-process frequency security constraints include frequency change rate constraints, frequency minimum point constraints, quasi-steady-state frequency constraints, and secondary frequency modulation constraints. Specifically: The frequency change rate constraint is: ; in, This represents the total inertia of the system. This is the limit for the rate of change of frequency; This is for frequency deviation; In order to be in t Power disturbances during the time period; The minimum frequency point constraint is: frequency deviation. Satisfying the maximum frequency deviation ; ; in, This includes thermal power units, wind power units, and CHP units; For system inertia; This is the load damping coefficient; For unit e in t The primary frequency regulation reserve capacity provided during the time period; Response time to release full reserve capacity; This refers to the frequency dead zone of the speed controller; For power disturbances exceeding the frequency dead zone; The quasi-steady-state frequency constraint is that the deviation of the quasi-steady-state frequency is within the allowable deviation. The second frequency modulation constraint is: ; in, , , The number of thermal power units, wind power units, and CHP units; In order to be in t Power disturbances during the time period; thermal power units CHP unit Wind turbine During the period Reserved SFR spare capacity; This refers to the quasi-steady-state frequency deviation. and This is the equivalent primary frequency modulation droop coefficient of the system.

[0014] Secondly, the present invention provides an electrothermal co-generation unit combination system that takes into account operational risks and frequency safety, comprising: The constraint modeling module is configured to consider the differentiated frequency regulation characteristics of thermal power units, CHP units, GFM wind turbine units, and GFL wind turbine units, and establish full-process frequency safety constraints including inertial response, primary frequency regulation, and secondary frequency regulation. The wind power uncertainty characterization module is configured to use a polyhedral uncertainty set to characterize the wind power output fluctuation range, introduce conditional risk value to quantify the wind curtailment risk and power shortage risk caused by wind power output exceeding the limit, and the operation risk cost is composed of the wind curtailment risk penalty cost and the power shortage risk penalty cost. The two-stage optimization module is configured to minimize the sum of start-up and shutdown costs, power generation costs, reserve costs of primary and secondary frequency regulation, and operational risk costs as the first-stage optimization objective, and minimize the operational risk costs under the worst-case scenario characterized by the polyhedral uncertainty set as the second-stage optimization objective. Combining the frequency security constraints of the entire process, a two-stage optimization model is constructed to solve for the optimal scheduling scheme for unit start-up and shutdown, electrical and thermal output, and frequency regulation reserve.

[0015] Thirdly, the present invention provides an electronic device including a memory and a processor, and computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the method described in the first aspect.

[0016] Fourthly, the present invention provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the method described in the first aspect.

[0017] Fifthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the method described in the first aspect.

[0018] Compared with the prior art, the beneficial effects of the present invention are as follows: With a high proportion of renewable energy integration, system inertia and primary frequency regulation resources decrease, and frequency security issues become prominent after large disturbances. The strong uncertainty of wind power output further exacerbates operational risks. To address this, this invention proposes a combined electric-thermal power unit method and system that considers operational risks and frequency security. Based on the frequency deviation dynamic equation, it constructs frequency security constraints that take into account the differentiated frequency regulation characteristics of thermal power units, cogeneration units, and grid-connected / grid-linked wind power units. It deeply characterizes the differentiated frequency regulation characteristics of different types of resources and establishes a full-process frequency security constraint framework covering inertial response, primary frequency regulation, and secondary frequency regulation. Then, considering the entire process of wind power providing frequency support and the uncertainty of wind power output, it uses a polyhedral uncertainty set to describe wind power output fluctuations, introduces conditional risk value theory to quantify wind curtailment and power shortage risks, and establishes a two-stage robust optimization model. Finally, within the framework of electrothermal synergy, the dynamic characteristics and recovery process of the heating network in frequency support are characterized in detail, taking into account the impact of the rapid adjustment of heat output by the cogeneration unit on the safety constraints of the water supply temperature. The heat storage characteristics of the heating network are used to provide flexible frequency regulation backup for the system, and frequency safety and economy are synergistically achieved through two-stage robust optimization.

[0019] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0021] Figure 1 This is a flowchart of the electrothermal co-generation unit combination method considering operational risks and frequency safety provided in Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of the system frequency dynamic response process provided in Embodiment 1 of the present invention; Figure 3 This is a schematic diagram of the wind power acceptance range of the wind power access node provided in Embodiment 1 of the present invention; Figure 4 This is a flowchart of the CC&G algorithm solution provided in Embodiment 1 of the present invention; Figure 5 This is a comparison chart of the frequency change rate results for scenario 1 and scenario 2 provided in Embodiment 1 of the present invention; Figure 6This is a comparison chart of the lowest frequency results for scenario 1 and scenario 2 provided in Embodiment 1 of the present invention; Figure 7 This is a comparison chart of the total backup differences between scenario 1 and scenario 2 provided in Embodiment 1 of the present invention; Figure 8 This is a diagram showing the unit combination decision results for different scenarios provided in Embodiment 1 of the present invention; Figure 9 This is a comparison chart of the frequency change rates of scenarios 3, 4, and 5 provided in Embodiment 1 of the present invention; Figure 10 This is a comparison diagram of the lowest frequency points in scenarios 4 and 5 provided in Embodiment 1 of the present invention; Figure 11 This is a diagram of primary frequency modulation reserve capacity for scenario 4 provided in Embodiment 1 of the present invention; Figure 12 This is a diagram of primary frequency regulation reserve capacity for scenario 5 provided in Embodiment 1 of the present invention; Figure 13 This is a diagram showing the heat network storage / release power and cumulative heat storage in scenario 5 provided in Embodiment 1 of the present invention; Figure 14 This is a comparison chart of the frequency change rates of different schemes provided in Embodiment 1 of the present invention; Figure 15 The convergence curves are shown for the different scale case analysis systems provided in Embodiment 1 of the present invention. Detailed Implementation

[0022] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0023] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0024] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments of the invention. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form as well. Furthermore, it should be understood that the terms “comprising” and “including”, and any variations thereof, are intended to cover non-exclusive inclusion, for example, a process, method, system, product, or apparatus that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0025] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0026] Regarding frequency support resource modeling, some studies have considered the wind power frequency response process and proposed data-driven linear proxy constraints. These studies model the frequency response process from the perspective of multiple stakeholders, including power sources, loads, and energy storage. Other studies have considered the collaborative participation of wind power and energy storage in frequency support. Some studies have further investigated variable droop frequency control for converter-type generators, but these treat wind farms uniformly as idealized models with flexible droop control. Most of these studies only consider a single flexible resource, lacking coordination for multiple heterogeneous resources. Furthermore, they typically treat wind farms as idealized resources capable of providing a uniform inertial response and primary frequency regulation capability, ignoring the fundamental differences in frequency response between different types of wind farms: GFLs require phase-locked loops to measure frequency, have inherent delays, and are difficult to participate in inertial response. This uniform modeling approach may lead to an overestimation of the system's frequency support capability, affecting the reliability of scheduling decisions.

[0027] For the random fluctuations in wind power output, robust optimization, with its low dependence on probability distribution and scenario samples, has become a mainstream approach to improve the system's ability to withstand fluctuations. Some studies have established robust scheduling models covering the entire frequency regulation process by constructing a feasible region for prediction errors. Others have proposed a two-stage robust unit combination model by establishing a robust feasible region for wind power output; some studies have used interval uncertainty sets to characterize the fluctuation range and worst-case scenarios of wind power; and some studies have established a partially robust unit combination optimization model incorporating frequency constraints by characterizing the uncertainty of new energy sources using fuzzy sets. However, most of these studies only focus on the inertial response after disturbances and primary frequency regulation, neglecting the secondary frequency regulation reserve necessary to cope with continuous wind power fluctuations. Even the few models that consider wind power uncertainty have not unified and coordinated reserve capacity with dynamic frequency security constraints, resulting in scheduling schemes still facing high risks when facing actual fluctuations.

[0028] In the area of ​​coordinated power and heat dispatch, numerous studies have enhanced the operational flexibility of power grids through horizontal energy conversion between electricity and heat. Some studies have established optimized dispatch models for integrated energy systems, targeting the dynamic characteristics of heating networks. Other studies have proposed Flexibility Providing Period (FPP) based on the dynamic characteristics of heating network pipelines. Furthermore, some studies have established virtual thermal storage tank models for heating networks and proposed thermal energy storage state indicators to achieve quantitative control of pipeline thermal storage; some studies have defined a thermal inertia power support model and used it as a flexible reserve. Some studies have proposed a frequency-constrained dispatch method for power-heat microgrids. While these studies have made significant progress in exploring the flexibility of heating networks, there are still shortcomings in applying this flexibility to system frequency support: when CHP units participate in rapid frequency regulation, rapid changes in thermal output can impact safety constraints such as water supply temperature, and existing models do not fully account for the impact of this impact on the safe operation of the heating network.

[0029] To address the shortcomings of the existing technologies, this invention proposes a method for combining electrothermal co-generation units, taking into account both operational risks and frequency safety. It mainly includes: (1) Taking into account various heterogeneous frequency support resources such as thermal power units, CHP units and GFM (Grid-Forming) / GFL wind turbine units, we can deeply characterize the differentiated frequency regulation characteristics of different types of resources and establish a collaborative optimization model.

[0030] (2) Considering the entire process of wind power providing frequency support and the uncertainty of wind power output, the conditional value at risk theory is used to quantify the risks of wind curtailment and power shortage, and incorporate them into the objective function to establish a two-stage robust optimization model.

[0031] (3) Under the framework of electrothermal synergy, the dynamic process of the heating network providing frequency support is described in detail, and the impact of the safety constraints of the heating network operation on its ability to provide frequency support is analyzed in depth, so as to realize the safe synergy of the electrothermal system.

[0032] Example 1 This embodiment provides a method for combining electric and thermal co-generation units that takes into account operational risks and frequency safety, such as... Figure 1 As shown, it includes: Considering the differentiated frequency regulation characteristics of thermal power units, CHP units, GFM wind turbine units, and GFL wind turbine units, a full-process frequency safety constraint including inertial response, primary frequency regulation, and secondary frequency regulation is established. The polyhedral uncertainty set is used to characterize the fluctuation range of wind power output. Conditional risk value is introduced to quantify the wind curtailment risk and power shortage risk caused by wind power output exceeding the limit. The operation risk cost is composed of the wind curtailment risk penalty cost and the power shortage risk penalty cost. The first-stage optimization objective is to minimize the sum of start-up and shutdown costs, power generation costs, reserve costs of primary and secondary frequency regulation, and operational risk costs. The second-stage optimization objective is to minimize the operational risk costs under the worst-case scenario characterized by the polyhedral uncertainty set. Combining the frequency security constraints of the entire process, a two-stage optimization model is constructed to solve for the optimal scheduling scheme for unit start-up and shutdown, electrical and thermal output, and frequency regulation reserve.

[0033] The method of this embodiment will be described in detail below.

[0034] When the system experiences an active power shortage, its frequency dynamic response process is as follows: Figure 2 As shown. Represents the rated frequency. The lowest frequency point, It is the quasi-steady-state frequency. This indicates the corresponding frequency deviation; and These represent the time it takes for the frequency to drop to its lowest point and for it to enter a quasi-steady-state frequency, respectively.

[0035] After the system experiences an active power shortage, the frequency dynamic response is divided into two stages: In the initial stage of the frequency response, the frequency drop is mitigated by the rotational inertia, and the magnitude of the rate of change of frequency (RoCoF) mainly depends on the total inertia of the system; subsequently, the unit participates in the primary frequency response (PFR), and the frequency gradually recovers to the quasi-steady state.

[0036] Based on this dynamic process and its corresponding frequency oscillation differential equation, RoCoF, frequency nadir (FN) constraint, and quasi-steady-state frequency (QSSF) constraint can be derived.

[0037] In the modeling of frequency security constraints, the virtual inertia and primary frequency response reserve capacity provided by the wind farm are considered. The system frequency deviation model after power disturbance can be described by the frequency deviation dynamic swing equation, as shown in equation (1).

[0038] (1); In the formula: For system inertia; This is the load damping coefficient; yes Frequency deviation over time period; , , thermal power units Wind turbine CHP unit exist Adjustment power provided during the time period; , , This refers to the number of thermal power units, wind power units, and CHP units.

[0039] ; (2); In the formula: E is the load damping ratio; For time period t The system load; This refers to the frequency dead zone of the speed controller; For power disturbances exceeding the frequency dead zone; In order to be in tAccording to the N-1 safety criterion for power systems, the system's emergency reserve capacity is generally 5% to 10% of the maximum load to cope with power deficits caused by typical accidents such as the tripping of a single largest generating unit. Therefore, this embodiment uses 10% of the active load as the classic value for the anticipated disturbance.

[0040] Power regulation of thermal power units, wind power units and CHP units Described by a piecewise linear model: (3); In the formula: This includes thermal power units, wind power units, and CHP units; Indicates that unit e is in t The primary frequency regulation reserve capacity provided during the time period; This refers to the frequency dead time when droop control is used. This indicates the response time for releasing all the standby capacity of unit e.

[0041] Unit e in t The primary frequency regulation reserve capacity provided during the time period is: (4); in, , , For thermal power units Wind turbine CHP unit exist The primary frequency regulation reserve capacity provided during the time period.

[0042] Therefore, by considering the differentiated frequency regulation characteristics of thermal power units, CHP units, GFM wind turbine units, and GFL wind turbine units, a full-process frequency safety constraint is established, including inertial response, primary frequency regulation, and secondary frequency regulation; specifically including: (1) Frequency change rate constraint.

[0043] (5); (6); In the formula: This is the limit for the rate of change of frequency; , , These are thermal power units, CHP units, and wind power units during the time period. Provided inertia; , , thermal power units CHP unit Wind turbine During the period The inertia time constant; For thermal power units The installed capacity; For thermal power units During the period The running state is a 0-1 variable; For wind turbines The installed capacity; For wind turbines During the period standby status; For CHP units The installed capacity; For CHP units During the period The running status; It is the system's rated frequency.

[0044] Considering that GFL wind turbines cannot provide instantaneous inertia support in the early stages of disturbances due to phase-locked loop measurement delays, the RoCoF constraint is modified as follows: (7).

[0045] Among them, the total inertia of the system Defined as: (8); In the formula: The inertia constant of a grid-type wind turbine; The number of grid-connected wind turbine units.

[0046] (2) Minimum frequency constraint.

[0047] GFM wind turbines can participate in the entire frequency support process, while GFL wind turbines, due to response delays, can only participate in the latter two stages of frequency support.

[0048] Frequency deviation Satisfying the maximum frequency deviation .

[0049] (9); in, Response time to release full reserve capacity; This is the frequency dead zone of the speed controller.

[0050] when The lowest frequency point in time period t Reaching the minimum limit value ,make Reaching the minimum value can be represented as: (10); in Equation (10) can be used as a constant for calculation, hence: (11).

[0051] (3) Quasi-steady-state frequency constraint.

[0052] Quasi-steady-state frequency deviation It should be within the allowable deviation.

[0053] (12); In the formula: This represents the maximum permissible quasi-steady-state frequency deviation.

[0054] (4) SFR constraints.

[0055] After a power disturbance occurs in the system, the remaining unbalanced power after the primary frequency regulation response is compensated by the SFR reserve: (13); In the formula: The SFR reserve capacity is reserved for thermal power units, CHP units, and wind power units respectively; This refers to the quasi-steady-state frequency deviation. and This is the equivalent primary frequency modulation droop coefficient of the system.

[0056] The SFR reserve capacity of each unit is limited by its ramp rate: (14); in, For thermal power units Maximum uphill climbing rate; The response time for a thermal power unit to release all its reserve capacity; For thermal power units The active power output at time t; For thermal power units The maximum effective output.

[0057] The SFR reserve capacity of a wind turbine is determined by its load shedding capacity: (15); In the formula: For wind turbines During the period Wind farm load reduction rate; For wind turbines During the period Maximum power point tracking output power.

[0058] (16); In the formula: , , These are the secondary standby cost coefficients for thermal power units, CHP units, and wind power units, respectively. This represents the total cost of secondary backup.

[0059] In this embodiment, a polyhedral uncertainty set is used to represent the fluctuation range of wind power output. Conditional value of risk is introduced to quantify the risks of wind curtailment and power shortage caused by exceeding wind power output limits. The operational risk cost consists of the penalty cost for wind curtailment risk and the penalty cost for power shortage risk. Specifically, it includes the following: The fluctuation range of wind power output is described using a polyhedral uncertainty set: (17); In the formula: For wind turbines The output value; and Wind turbines for dispatching decisions exist Wind power output and wind power forecast for the specified time period; and Wind turbine exist Upward and downward adjustment margins for different time periods; and Wind turbine exist The upward and downward adjustment factors for each time period are 0 / 1 variables; and These are the spatial uncertainty parameter and the time uncertainty parameter, respectively.

[0060] Economic losses incurred by the system during wind power integration due to actual output exceeding a preset safety threshold are defined as integration risk. Figure 3 As shown. The Admissible Region of Wind Power (ARWP) for this node is... , and These represent the upper and lower bounds of the acceptable range for wind power, respectively. The risks of wind curtailment and power shortages can be measured using conditional value at risk. (18); (19); In the formula: and These are the risks of wind curtailment and power shortages, respectively. This is the upper limit of the wind power disturbance range at this node; For wind power random disturbances, which are random variables; Let it be the expected function; Let be the probability density function of random disturbances in wind power.

[0061] The operational risk cost is: (20); In the formula: To cover operational risk costs; , These are the unit wind curtailment penalty cost and the unit power shortage penalty cost, respectively.

[0062] In this embodiment, a collaborative scheduling strategy for an electrothermal system that takes into account dynamic safety constraints based on frequency is proposed, which includes the following three stages.

[0063] 1. Cooperative operation in the ground state scenario.

[0064] In the base state, thermal power units, CHP units, and wind power units jointly meet the electrical load demand, and the power balance constraint is: (twenty one); In the formula: , , thermal power units Wind turbine and CHP unit During the period The plan has been successful and the efforts have been made; For the system in time period The electrical load demand.

[0065] 2. Frequency response and flexible supply of heating network under disturbance scenarios.

[0066] After a power disturbance occurs, the system enters the flexibility provisioning process (FPP).

[0067] The output of the CHP unit is: (twenty two); (twenty three); In the formula: This represents the actual heating power under disturbance. This represents the heating power in the ground state. , Upward and downward reserve capacity provided for CHP units; , For the upward and downward changes in heat output; Thermoelectric ratio; For FPP period.

[0068] A heating network can be considered equivalent to a virtual heat storage tank, satisfying the following constraints: (twenty four); In the formula: , All variables are 0–1, representing the heat storage and heat release states of the heating network.

[0069] The flexibility supply constraint of the heat source node is: (25); In the formula: , These represent the maximum upward adjustable capacity and the maximum downward adjustable capacity provided by the heating network, respectively. To account for the water supply pipe outlet temperature after heat transfer delay; and These are the lower and upper limits of the outlet water temperature of the water supply pipeline, respectively. For the unit k Exit time t hot water flow rate; This is the specific heat capacity of hot water.

[0070] To ensure the safe operation of the thermal system, during the FPP period providing frequency response, the actual water supply temperature of the CHP unit is... It must always be maintained within the safe threshold range: (26).

[0071] 3. Restoration of the flexibility of the heating network after frequency response.

[0072] After weathering the disturbance and entering a quasi-steady state, the heating network needs to return to its planned state, thus entering the Flexibility Recovery Period (FRP). This is achieved by controlling the supply water temperature of the CHP units to return to the scheduled setpoint. (27); In the formula: This refers to the actual recovery temperature after the disturbance occurred; This is the optimal planned water supply temperature. This is for the flexibility recovery cycle.

[0073] In this embodiment, the first-stage optimization objective is to minimize the sum of the start-up and shutdown costs of thermal power units, the power generation costs of thermal power units and CHP units, the primary frequency regulation reserve costs, the secondary frequency regulation reserve costs, and the operational risk costs.

[0074] (28); In the formula: , , These are start-up and shutdown costs, power generation costs, and primary frequency regulation reserve costs; The start-up cost of thermal power units is considered, while the shutdown cost is negligible. The power generation cost of thermal power units; The power generation cost of the CHP unit; , and These are the primary frequency regulation standby costs for thermal power units, CHP units, and wind power units, respectively. This is for backup costs for secondary frequency regulation.

[0075] The costs are shown below: (29); Where: T is the total number of unit combination time periods; , For thermal power units Cost coefficient; For thermal power units exist Efforts during a specific time period; , , This is the cost coefficient for the CHP unit; For thermal power units Startup costs; For thermal power units exist Start / stop status during a given time period; For thermal power units Start / stop status during time period t+1; , , thermal power units CHP unit Wind turbine In time The primary frequency regulation reserve capacity within; , , These are the primary frequency regulation cost coefficients for thermal power units, CHP units, and wind power units, respectively. For CHP units During the period The plan has been successful and the efforts have been made; For CHP units During the period The heating power in the ground state.

[0076] Constraints are mainly divided into four categories: power network constraints, thermal network constraints, risk constraints, and frequency security constraints. Specifically, they include the following: 1. Power network constraints include thermal power unit output constraints, thermal power unit start-up and shutdown time constraints, thermal power unit ramping constraints, node power balance constraints, and line capacity constraints.

[0077] (1) Output constraints of thermal power units.

[0078] (30); In the formula: For thermal power units During the period The minimum active power output value; For thermal power units During the period The maximum active power output value.

[0079] (2) Start-up and shutdown time constraints of thermal power units.

[0080] (31); In the formula: and thermal power units The required minimum continuous operating time and minimum continuous downtime; and thermal power units During the period The duration of continuous operation and the duration of continuous shutdown; For thermal power units Start-stop status during time period t-1.

[0081] (3) Slope constraints of thermal power units.

[0082] (32); In the formula: Indicates thermal power unit The maximum achievable uphill climbing rate; Indicates thermal power unit The maximum achievable downhill climbing rate; For thermal power units exist Efforts during a specific time period; For thermal power units Output during time period t-1; For thermal power units The minimum active power output.

[0083] (4) Node power balance constraints.

[0084] (33); In the formula: Total load for The power of the load d during the time period; and They are respectively Time period node z to node and nodes The power transmitted to node z; and They are nodes The set of starting nodes and nodes This is the set of terminating nodes.

[0085] (5) Line capacity constraints.

[0086] (34); In the formula: For node z to node The upper limit of transmission power; For node z to node Admittance; , , They are respectively Time-balanced nodes, node z and node The phase angle; Let be the phase angle of node i.

[0087] 2. Thermal network constraints include CHP unit constraints, heat exchange station constraints, and thermal network constraints.

[0088] (1) CHP unit constraints.

[0089] The electrothermal output of the CHP unit satisfies the following relationship: ; (35); In the formula: , CHP units During the period Electrical and thermal power output; , and These are the units Exit time The hot water flow rate, supply water temperature, and return water temperature.

[0090] The temperature at the outlet of the water supply pipe should be maintained within the specified range: (36); in, and These are the upper and lower limits of the temperature at the outlet of the water supply pipeline.

[0091] (2) Constraints of heat exchange station.

[0092] The heat load constraint can be expressed as: (37); In the formula: For heat exchange stations of the heating network exist The heat load demand at any given time; , and They are heat exchange stations Hot water flow rate, supply water temperature, and return water temperature at the inlet.

[0093] The temperature at the inlet of the heat exchange station must also meet the limit requirements: (38); In the formula: and They are heat exchange stations The upper and lower limits of the return water temperature at the inlet.

[0094] (3) Thermal network constraints.

[0095] At the junction of the pipeline network, the mixing temperature of all inflow pipes must be equal to the mixing temperature of all outflow pipes, that is: (39); In the formula: and Representing nodes respectively Pipes for terminating and starting nodes; and At time respectively Water supply pipe node and return water pipe node The mixing temperature; For a moment water supply pipeline inlet temperature; For a moment Return water pipe inlet temperature; For a moment water supply pipeline The outlet temperature; For a moment Return water pipe The outlet temperature; For a moment hot water pipes The working fluid flow rate.

[0096] 3. Risk constraints.

[0097] (40); In the formula: This is the risk threshold value; , Wind turbine exist Upper and lower bounds of effort output over a given time period; To maximize the output of the wind farm; This is a wind power forecast.

[0098] 4. Frequency security constraints are formulas (7), (9), (12)-(15).

[0099] In this embodiment, the second-stage optimization objective is to minimize the operational risk cost under the worst-case scenario characterized by the polyhedral uncertainty set.

[0100] (41); In the formula: and These are the cost coefficients for the second phase of power shortage and wind curtailment at wind farms, respectively. For the second phase Time period The power shortage of each load; For the second phase Time period j The amount of wind curtailment from a wind farm; This represents the amount of load.

[0101] The constraints are as follows.

[0102] (1) The node power and power balance constraints are as follows: (42).

[0103] (2) The set of uncertainties in wind power is constrained by formula (17).

[0104] (3) The power shortage constraint is: (43).

[0105] (4) The constraint on the amount of air curtailed is: (44).

[0106] The second stage of constraints also includes thermal power unit output and ramping constraints, nodal power balance constraints, and power line capacity constraints.

[0107] In this embodiment, by constructing and solving a two-stage optimization model, the optimal scheduling scheme for unit start-up and shutdown, electrothermal output, and frequency regulation reserve is obtained. The model solution process is as follows.

[0108] 1. Minimum frequency point constraint linearization.

[0109] The minimum frequency constraint shown in equation (9) contains a product term of both 0-1 variables and continuous variables, exhibiting nonlinear characteristics. Therefore, the Big M method is used to transform this constraint into an equivalent set of linear constraints: (45); In the formula: M The value should be a sufficiently large positive real number, greater than the maximum absolute value that any continuous variable in the constraints can reach, but not too large. Therefore, this paper takes... M =10 5 To ensure large M The validity of the law; , and Synchronous generator units Wind farm and CHP unit During the period Auxiliary variables introduced using the Big M method.

[0110] 2. Piecewise linear approximation of wind power acceptance risk.

[0111] To address the nonlinearity problem caused by the integral term in the wind power operation risk function, this embodiment introduces a piecewise linear approximation strategy to linearly relax this integral part. The detailed derivation is as follows: After addressing wind power integration risk using a piecewise linear approximation method, the expression for CVaR can be written as: (46); (47).

[0112] Similarly, the expected power deficit loss caused by wind power output falling below the lower limit of the acceptable range can be expressed as a linear piecewise function as follows: (48); (49).

[0113] In the formula: , , , These are the coefficients of each segment in the piecewise function for wind power acceptance risk; , A 0-1 variable used to indicate whether the wind power output falls within the [number]th [number]. Within each segmented interval; , Represents wind farm exist The time period is located on the line segment The upper and lower boundaries of the output force; , and , The line segments on the piecewise linear function curve of CVaR are respectively The wind power prediction error corresponding to the left and right endpoints; This is the upper boundary cost coefficient for output. This is the lower boundary cost coefficient for output. , This represents the maximum number of segments.

[0114] 3. Column and constraint generation algorithm.

[0115] The second-stage problem is a typical nested max-min problem, which cannot be directly solved as a single-level programming problem. This paper transforms the inner minimization subproblem into a dual maximization form based on the dual theorem, and then merges it with the outer maximization to obtain a single maximization problem.

[0116] After the linearization and dual transformation described above, the model is transformed into a mixed-integer linear programming problem, which is solved using the column and constraint generation (C&CG) algorithm.

[0117] First, the model is written in the following compact mathematical form: (50); In the formula: For the start-up and shutdown variables of thermal power units; For unit output variables; For wind power output variables; The reserve capacity required for the primary and secondary frequency modulation responses of the system; These are continuous variables related to the operation of the heating network. For the unit output decision variables in the second phase; For the amount of wind curtailment and power shortage A variable vector composed of variables; This is the upward and downward adjustment factor for wind power based on the predicted output value, and it is a 0 / 1 variable; It is a matrix product; the main problem is solved to obtain , , , The optimal solution of the objective function ; a、b , c , d , e , g , h , k , u , w , A , B , C , D , E , F , G , H , J , U This is the corresponding coefficient matrix.

[0118] For a given first-level optimal solution and fixed The inner minimization problem is: (51).

[0119] Introducing dual variables Write down its dual problem: (52).

[0120] By the strong duality theorem, the optimal value of the primal minimization problem is equal to the optimal value of the dual maximization problem. Therefore: (53); In the above formula, the outer layer is The inner layer is Both are maximization problems, and Only subject to set constraint, Subject only to linear inequalities, variables and The constraints are independent of each other, so the outer max and inner max problems can be merged into a single maximization problem: (54).

[0121] At this point, the subproblem has been transformed into a single-level maximization, but the objective function contains bilinear terms. This paper uses the Big M method for linearization.

[0122] remember for The One portion, For the corresponding constant, A matrix with constant coefficients The Okay. Then Each product term is ,in yes A linear function. Then for each component With corresponding linear combination The product is linearized using the Big M method. The specific steps are as follows: An auxiliary variable is introduced. replace And set a sufficiently large positive real number M, in this paper M takes the value of Add the following constraints: (55); Replace all bilinear terms with linear terms: (56); in It is a vector of constant coefficients.

[0123] After linearization using the Big M method described above, the subproblem becomes: (57); in yes A linear function. All constraints and the objective function are linear, and Since the variables are 0-1, this is a mixed integer linear programming problem (MILP). Furthermore, the main problem is also clearly a MILP.

[0124] At this point, the original problem (including the main problem and subproblems) has been transformed into MILP, and the entire two-stage robust optimization model can be solved iteratively using the C&CG algorithm. The algorithm flowchart is as follows. Figure 4 As shown, the solution steps are as follows: Step 1: Parameter initialization, set the number of iterations Convergence threshold Set an upper bound. The lower realm .

[0125] Step 2: Solve the main problem to obtain... and the optimal solution to the main problem Update the Nether .

[0126] Step 3: Solve the subproblems to obtain their optimal solutions. Binary variables for the worst-case scenario of wind power output Update the upper realm. .

[0127] Convergence criterion: If Output the optimal solution and end the iteration.

[0128] Step 4: Otherwise, set Return to step 2.

[0129] Example analysis.

[0130] To verify the effectiveness of the constructed model, two test systems of different sizes, E6-H4 and E118-H20, were selected for case analysis.

[0131] 1. E6-H4 test system example.

[0132] This embodiment uses the improved E6-H4 testing system to verify and analyze the proposed model. Two wind farms (W1 and W2) are used, with W1 modified to be a grid-connected wind farm and W2 modified to be a grid-connected wind farm. The system reference frequency is set to 50 Hz, the governor's frequency dead zone is set to 0.015 Hz, and the maximum error in load prediction and wind power prediction are both set to 10%. The dispatch cycle is 24 hours. The system frequency safety constraints are set as follows: the maximum frequency change rate does not exceed 0.125 Hz / s, and the lowest frequency point after a fault does not fall below 49.2 Hz.

[0133] The following five scenarios are set up for comparison.

[0134] Scenario 1: Unit combination without considering frequency security constraints, only considering frequency security constraints based on reserve capacity ( ).

[0135] Scenario 2: Based on Scenario 1, consider frequency security constraints and only consider frequency support provided by thermal power units.

[0136] Scenario 3: Based on Scenario 2, wind power is considered to provide frequency support, but the traditional method is used without distinguishing between GFL and GFM.

[0137] Scenario 4: Based on Scenario 2, consider wind power providing frequency support and distinguish between GFL and GFM.

[0138] Scenario 5: Building on Scenario 4, consider cogeneration units and provide frequency support through electrothermal synergy.

[0139] (1) Verification of the necessity of frequency security constraints.

[0140] To verify the necessity of frequency safety constraints in the combined electric and thermal power unit model, this paper compares the frequency response characteristics of Scenario 1 and Scenario 2 at different time periods. The results are as follows: Figures 5-7As shown in the diagram, Scenario 1, without considering frequency safety constraints, results in more thermal power units operating during periods of lower wind power output, leading to a rise in the minimum frequency and a decrease in the rate of frequency change. Conversely, during periods of higher wind power output, the proportion of thermal power unit output decreases, weakening the frequency regulation capability, with the minimum frequency dropping to 48.72 Hz and the RoCoF reaching a maximum of 0.158 Hz / s. In contrast, Scenario 2, by introducing frequency safety constraints, ensures that both the RoCoF and the minimum frequency meet safety requirements for all time periods.

[0141] From Table 1 and Figure 8 Analysis shows that in Scenario 1, the total cost is 2.3725 million yuan, with fewer thermal power units operating, resulting in an ARWP of 854.94 MW. In Scenario 2, the total cost rises to 2.4709 million yuan, with a significant increase in the number of thermal power units operating, causing the ARWP to drop to 732.50 MW. Furthermore, compared... Figure 7 It is evident that the total primary frequency regulation reserve capacity in Scenario 1 is generally lower than that in Scenario 2. This is because Scenario 1 does not consider frequency safety constraints, and the system underestimates the demand for frequency regulation resources after actual disturbances, reducing the number of generating units in operation and lowering the reserve level in pursuit of lower economic costs. Scenario 2, on the other hand, introduces frequency safety constraints, enabling a more realistic assessment of the frequency drop risk after disturbances. Therefore, it requires more primary frequency regulation reserve to ensure that the system frequency does not exceed the limits.

[0142] (2) Risk and economic analysis.

[0143] To evaluate the impact of different frequency support strategies on system operating characteristics, a comparative analysis was conducted on the total cost, operating cost, start-up and shutdown cost, backup cost, and risk cost of five scenarios. The results are shown in Table 1.

[0144] Table 1. Results of the operation in different scenarios; .

[0145] From Table 1 and Figure 8 As can be seen, Scenario 3 and Scenario 4 gradually introduce wind power to participate in primary frequency regulation, alleviating the pressure on thermal power unit start-up and improving system economy and wind power acceptance. Because Scenario 4 further distinguishes between GFL and GFM units, the number of thermal power units in operation continues to decrease, with total cost dropping to 2.4255 million yuan and ARWP increasing to 783.61 MW. Compared to Scenario 3, this represents a cost saving of nearly 30,000 yuan and a reduction in risk cost of 4,200 yuan. Scenario 5 further introduces an electrothermal synergy mechanism. Through the heat storage and release characteristics of the heating network, the start-up structure of thermal power units becomes more flexible, improving system economy. Total cost drops to 2.3922 million yuan, and ARWP recovers to 819.66 MW, approaching the unconstrained absorption level of Scenario 1. Risk cost and reserve cost are also significantly lower than in Scenario 2-4.

[0146] Figure 9 The frequency change rates of scenarios 3 and 4 were compared. The results showed that scenario 4 effectively reduced the peak RoCoF after system disturbance by distinguishing the instantaneous inertia support capabilities of different types of wind farms, thus ensuring the safety of the frequency change rate as much as possible. In contrast, scenario 3 did not distinguish the wind farm type and overestimated the inertia response capability of grid-connected wind farms, resulting in higher RoCoF and increased risk of frequency exceeding limits during some periods.

[0147] (3) Analysis of electrothermal synergy and frequency modulation reserve capacity.

[0148] To explore the effect of electrothermal synergy on improving frequency response capability, the frequency response characteristics and frequency modulation reserve capacity allocation of scenario 4 and scenario 5 were compared.

[0149] Depend on Figure 9 As can be seen, the frequency change rate in scenario 4 is within the frequency safety threshold at certain times, while the frequency change rate in scenario 5 is generally lower than that in scenario 4. This is due to the complementarity of wind power and heating network in terms of frequency support; Figure 10 In both scenarios, the lowest frequency points meet the safety threshold requirements.

[0150] Figures 11-12 This further demonstrates the differences between scenario 4 and scenario 5 in the allocation of primary frequency regulation reserve capacity. Figure 13 The data shows that in Scenario 4, frequency regulation backup mainly relies on wind farms, which is significantly insufficient during off-peak wind power periods. Scenario 5 utilizes electrothermal synergy: during peak wind power generation at night, the heating network releases heat, and the CHP units reduce their base load, freeing up space for wind power and releasing its upward frequency regulation capability; during peak daytime load periods, the heating network stores heat, and the CHP units increase their base load, while relying on thermal inertia to maintain the primary frequency regulation response, effectively sharing the frequency regulation pressure of conventional thermal power.

[0151] Figure 13 The curves showing the changes in the heat storage / release power and cumulative heat storage of the heating network under Scenario 5 are presented. During the nighttime period when wind power output is high, the heating network actively releases heat to absorb part of the heat load, resulting in a continuous decrease in the cumulative heat storage. Consequently, the thermal output baseline of the CHP unit decreases, freeing up space for wind power to be connected to the grid. During the daytime peak load period, the heating network switches to heat storage mode, and the cumulative heat storage gradually increases, absorbing the excess heat generated by the peak operation of the CHP unit.

[0152] (4) Analysis of the impact of different ratios of GFL and GFM wind farms on the system.

[0153] To investigate the impact of different configuration ratios in grid-connected and grid-connected wind farms on system frequency security and economy, three schemes were designed: Option 1: Considering frequency security constraints, thermal power units and wind power jointly provide frequency support, and both wind farms are GFLs.

[0154] Option 2: Considering frequency security constraints, thermal power units and wind power jointly provide frequency support, with one wind farm serving as GFL and the other as GFM.

[0155] Option 3: Considering frequency security constraints, thermal power units and wind power jointly provide frequency support, and both wind farms are GFM.

[0156] The results of each scheme are shown in Table 2 and Figure 14 As shown.

[0157] Table 2. Results of different schemes; .

[0158] Depend on Figure 14 As shown in Table 2, since the frequency security constraint is embedded in the model as a hard constraint, the scheduling results can strictly meet the safety limits of RoCoF and the lowest frequency point regardless of the change in the ratio of GFL to GFM. With the increase in the proportion of grid-type wind farms, the system frequency security margin and operating economy improve simultaneously: grid-type wind farms can provide instantaneous inertia support, effectively reducing the peak value of RoCoF; their stronger frequency regulation capability reduces the dependence on thermal power unit backup, reducing system backup costs and operating risk costs.

[0159] Furthermore, the algorithm's solution time remains stable at 9-11 seconds under different wind farm type ratios, effectively handling the differentiated frequency regulation characteristics of GFL / GFM. This indicates that changes in the wind farm type ratio do not affect the algorithm's convergence and solution efficiency. Simultaneously, as the proportion of medium-density grid-type wind farms in future systems continues to increase, the proposed method can adapt to this trend, consistently achieving the most economically optimal scheduling scheme while ensuring frequency security.

[0160] 2. E118-H20 test system example.

[0161] The test system is an integrated electrothermal energy system consisting of an improved IEEE-118-node power system and a 20-node thermal system.

[0162] (1) Convergence test.

[0163] Figure 15 The convergence curves of the proposed two-stage robust optimization method are shown under test systems of different scales. When the spatial uncertainty parameter... and time uncertainty parameter When both are set to 24, the algorithm satisfies the convergence criterion after two iterations (i.e., This verifies that the improved C&CG algorithm used in this paper has good convergence performance.

[0164] (3) Computational efficiency test.

[0165] As can be seen from the test results in Table 3, the proposed method does not generate excessive computational burden despite the exponential growth in the number of system nodes, lines, and unit size. A comparison of computation time shows that when the system size increases by approximately 10-11 times, the computation time only increases by about 8 times. It can be predicted that even if the model size continues to increase, the growth rate of computation time will remain within a controllable range due to the linear decoupling of the nonlinear power flow and dynamic heating network equations.

[0166] Table 3 Comparison of solution computation time in different scale case analysis systems; .

[0167] This paper proposes a robust two-stage electrothermal combined unit combination that takes into account operational risks and frequency safety constraints. Simulations of the E6-H4 and E118-H20 systems yield the following conclusions: (1) Based on the frequency deviation equation, a differentiated frequency regulation constraint is constructed for conventional units, CHP units and GFL / GFM wind turbine units. This distinguishes the inertial response differences between grid-connected and grid-following wind farms, effectively suppressing frequency drops and ensuring system frequency safety.

[0168] (2) The polyhedral uncertainty set is used to characterize the wind power output fluctuation, and CVaR is introduced to quantify the risks of wind curtailment and power shortage. The two-stage robust optimization coordinates the reserve capacity of multiple resources in the day-ahead scheduling, while minimizing the operational risk in the worst-case scenario, effectively reducing the total system cost and risk cost, and improving the wind power consumption level.

[0169] (3) The dynamic characteristics of the heating network under frequency support are precisely characterized. The impact of rapid adjustment of the CHP unit on the safety constraint of the water supply temperature is considered. The heat storage characteristics of the heating network are used to provide flexible frequency regulation backup for the system. At the same time, the model can efficiently solve large-scale systems after linearization.

[0170] Example 2 This embodiment provides a combined electric and thermal power unit system that takes into account operational risks and frequency safety, including: The constraint modeling module is configured to consider the differentiated frequency regulation characteristics of thermal power units, CHP units, GFM wind turbine units, and GFL wind turbine units, and establish full-process frequency safety constraints including inertial response, primary frequency regulation, and secondary frequency regulation. The wind power uncertainty characterization module is configured to use a polyhedral uncertainty set to characterize the wind power output fluctuation range, introduce conditional risk value to quantify the wind curtailment risk and power shortage risk caused by wind power output exceeding the limit, and the operation risk cost is composed of the wind curtailment risk penalty cost and the power shortage risk penalty cost. The two-stage optimization module is configured to minimize the sum of start-up and shutdown costs, power generation costs, reserve costs of primary and secondary frequency regulation, and operational risk costs as the first-stage optimization objective, and minimize the operational risk costs under the worst-case scenario characterized by the polyhedral uncertainty set as the second-stage optimization objective. Combining the frequency security constraints of the entire process, a two-stage optimization model is constructed to solve for the optimal scheduling scheme for unit start-up and shutdown, electrical and thermal output, and frequency regulation reserve.

[0171] It should be noted that the above modules correspond to the steps described in Embodiment 1, and the examples and application scenarios implemented by the above modules and the corresponding steps are the same, but are not limited to the content disclosed in Embodiment 1. It should also be noted that the above modules, as part of the system, can be executed in a computer system such as a set of computer-executable instructions.

[0172] In further embodiments, the following is also provided: An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the method described in Embodiment 1. For brevity, further details are omitted here.

[0173] It should be understood that in this embodiment, the processor can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc.

[0174] Memory may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of memory may also include non-volatile random access memory. For example, memory may also store information about the device type.

[0175] A computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the method described in Embodiment 1.

[0176] The method in Example 1 can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor. The software modules can reside in readily available storage media in the field, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, or registers. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, a detailed description is not provided here.

[0177] A computer program product includes a computer program that, when executed by a processor, implements the method described in Embodiment 1.

[0178] The present invention also provides at least one computer program product tangibly stored on a non-transitory computer-readable storage medium. The computer program product includes computer-executable instructions, such as instructions included in program modules, which execute in a device on a target real or virtual processor to perform the processes / methods described above. Typically, program modules include routines, programs, libraries, objects, classes, components, data structures, etc., that perform specific tasks or implement specific abstract data types. In various embodiments, the functionality of program modules can be combined or divided among program modules as needed. The machine-executable instructions for the program modules can execute within a local or distributed device. In a distributed device, the program modules can reside in both local and remote storage media.

[0179] The computer program code used to implement the methods of the present invention may be written in one or more programming languages. This computer program code may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the computer or other programmable data processing device, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code may be executed entirely on a computer, partially on a computer, as a stand-alone software package, partially on a computer and partially on a remote computer, or entirely on a remote computer or server.

[0180] In the context of this invention, computer program code or related data may be carried by any suitable carrier to enable a device, apparatus, or processor to perform the various processes and operations described above. Examples of carriers include signals, computer-readable media, and the like. Examples of signals may include electrical, optical, radio, sound, or other forms of propagation signals, such as carrier waves, infrared signals, etc.

[0181] Those skilled in the art will recognize that the units and algorithm steps described in connection with the various examples of this embodiment can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this invention.

[0182] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for thermal co-optimization of generation units considering operational risk and frequency security, characterized in that, include: Considering the differentiated frequency regulation characteristics of thermal power units, CHP units, GFM wind turbine units, and GFL wind turbine units, a full-process frequency safety constraint including inertial response, primary frequency regulation, and secondary frequency regulation is established. The polyhedral uncertainty set is used to characterize the fluctuation range of wind power output. Conditional risk value is introduced to quantify the wind curtailment risk and power shortage risk caused by wind power output exceeding the limit. The operation risk cost is composed of the wind curtailment risk penalty cost and the power shortage risk penalty cost. The first-stage optimization objective is to minimize the sum of start-up and shutdown costs, power generation costs, reserve costs of primary and secondary frequency regulation, and operational risk costs. The second-stage optimization objective is to minimize the operational risk costs under the worst-case scenario characterized by the polyhedral uncertainty set. Combining the frequency security constraints of the entire process, a two-stage optimization model is constructed to solve for the optimal scheduling scheme for unit start-up and shutdown, electrical and thermal output, and frequency regulation reserve.

2. The method for thermal unit commitment considering operational risk and frequency security according to claim 1, wherein, The fluctuation range of wind power output is: ； in, For wind turbines The output value; and Wind turbine exist Wind power output and wind power forecast for the specified time period; and Wind turbine exist Upward and downward adjustment margins for different time periods; and Wind turbine exist The upward and downward adjustment factors for each time period are 0 / 1 variables; and These are the spatial uncertainty parameter and the time uncertainty parameter, respectively; denoted as the number of wind turbine units; T represents the total number of time periods.

3. The method for combining electrothermal co-generation units considering operational risks and frequency safety as described in claim 1, characterized in that, The risks of wind curtailment and power shortage are respectively: ； ； in, and These are the upper and lower limits of the acceptable range for wind power, respectively. and These are the risks of wind curtailment and power shortages, respectively. This is the upper limit of the wind power disturbance range at this node; For wind power random disturbances, which are random variables; Let it be the expected function; Let be the probability density function of random disturbances in wind power. Operating risk costs for: ； in, , These are the unit wind curtailment penalty cost and the unit power shortage penalty cost, respectively.

4. The method for combining electrothermal co-generation units considering operational risks and frequency safety as described in claim 1, characterized in that, The optimization objective for the second phase is: ； in, and Wind turbine exist The upward and downward adjustment factors for each time period are 0 / 1 variables; T is the total number of time periods; , For the load and the number of wind turbine units; and These are the cost coefficients for the second phase of power shortage and wind curtailment at wind farms, respectively. For the second phase Time period The power shortage of each load; For the second phase Time period j The amount of wind curtailment from a wind farm.

5. The method for combining electrothermal co-generation units considering operational risks and frequency safety as described in claim 1, characterized in that, In the process of constructing the two-stage optimization model, the power balance constraints that thermal power units, CHP units and wind power units must satisfy when operating in coordination under the ground state scenario, the flexible supply constraints of heat source nodes under the disturbance scenario, and the flexible recovery constraints of the heat network after frequency response are also considered. Among them, the supply constraint of flexibility is ； In the formula: , For the upward and downward changes in heat output; , These represent the maximum upward adjustable capacity and the maximum downward adjustable capacity provided by the heating network, respectively. , All are 0–1 variables, representing the heat storage and heat release states of the heating network; To account for the water supply pipe outlet temperature after heat transfer delay; and These are the lower and upper limits of the outlet water temperature of the water supply pipeline, respectively. For a moment t unit Hot water flow rate at the outlet; For FPP cycle; This is the specific heat capacity of hot water; The heating network flexibility recovery constraint is that during the FPP period of providing frequency response, the actual water supply temperature of the CHP unit is always maintained within the safe threshold range.

6. The method for combining electrothermal co-generation units considering operational risks and frequency safety as described in claim 1, characterized in that, The frequency safety constraints throughout the entire process include frequency change rate constraints, frequency minimum point constraints, quasi-steady-state frequency constraints, and secondary frequency modulation constraints; Specifically: The frequency change rate constraint is: ； in, This represents the total inertia of the system. This is the limit for the rate of change of frequency; This is for frequency deviation; In order to be in t Power disturbances during a given period; The minimum frequency point constraint is: frequency deviation. Satisfying the maximum frequency deviation ; ； in, This includes thermal power units, wind power units, and CHP units; For system inertia; This is the load damping coefficient; For unit e in t The primary frequency regulation reserve capacity provided during the time period; Response time to release full reserve capacity; This refers to the frequency dead zone of the speed controller; For power disturbances exceeding the frequency dead zone; The quasi-steady-state frequency constraint is that the deviation of the quasi-steady-state frequency is within the allowable deviation. The second frequency modulation constraint is: ； in, , , The number of thermal power units, wind power units, and CHP units; In order to be in t Power disturbances during a given period; thermal power units CHP unit Wind turbine During the period Reserved SFR spare capacity; This refers to the quasi-steady-state frequency deviation. and This is the equivalent primary frequency modulation droop coefficient of the system.

7. A combined electric and thermal power unit system that takes into account operational risks and frequency safety, characterized in that, include: The constraint modeling module is configured to consider the differentiated frequency regulation characteristics of thermal power units, CHP units, GFM wind turbine units, and GFL wind turbine units, and establish full-process frequency safety constraints including inertial response, primary frequency regulation, and secondary frequency regulation. The wind power uncertainty characterization module is configured to use a polyhedral uncertainty set to characterize the wind power output fluctuation range, introduce conditional risk value to quantify the wind curtailment risk and power shortage risk caused by wind power output exceeding the limit, and the operation risk cost is composed of the wind curtailment risk penalty cost and the power shortage risk penalty cost. The two-stage optimization module is configured to minimize the sum of start-up and shutdown costs, power generation costs, reserve costs of primary and secondary frequency regulation, and operational risk costs as the first-stage optimization objective, and minimize the operational risk costs under the worst-case scenario characterized by the polyhedral uncertainty set as the second-stage optimization objective. Combining the frequency security constraints of the entire process, a two-stage optimization model is constructed to solve for the optimal scheduling scheme for unit start-up and shutdown, electrical and thermal output, and frequency regulation reserve.

8. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the method according to any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, perform the method described in any one of claims 1-6.

10. A computer program product, characterized in that, Includes a computer program, which, when executed by a processor, implements the method described in any one of claims 1-6.

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