A method for energy storage stochastic programming considering frequency stability constraint and related device

Abstract

This invention belongs to the field of power system planning technology, and particularly relates to a stochastic planning method and related apparatus for energy storage considering frequency stability constraints. The method includes: acquiring the frequency response characteristics of a multi-machine system; constructing an aggregated multi-machine system frequency response model based on these characteristics using a parameter equivalence method; establishing a linearized frequency safety margin calculation model based on the aggregated multi-machine system frequency response model and a preset frequency safety margin; establishing a stochastic planning model for energy storage considering frequency stability constraints using a stochastic optimization method, with the objective function being the minimum sum of the total lifecycle cost of energy storage and the total system operating cost, and with system operating conditions and the linearized frequency safety margin calculation model as constraints; and solving the stochastic planning model to obtain energy storage site selection and capacity configuration schemes. This achieves synergistic optimization of the economic efficiency of energy storage planning and system frequency stability.

Description

Technical Field

[0001] This invention belongs to the field of power system planning technology, and in particular relates to a stochastic planning method and related devices for energy storage that takes into account frequency stability constraints. Background Technology

[0002] With the large-scale integration of new energy sources such as wind power and photovoltaics into the power system, traditional synchronous generator sets are gradually decreasing. New energy units are connected to the grid through power electronic interfaces, lacking the inherent inertial support of traditional synchronous generators. This leads to a decrease in system inertia, making the grid more susceptible to significant frequency shifts when subjected to power disturbances.

[0003] To improve the frequency response capability of a system, energy storage systems are widely used to supplement primary frequency regulation resources due to their rapid adjustment characteristics. In existing technologies, energy storage planning methods typically incorporate the frequency regulation capability of energy storage into the planning model in the form of reserve capacity. However, these methods often rely on static reserve capacity or steady-state frequency deviation constraints, failing to fully reflect important indicators closely related to the dynamic behavior of the power grid, such as the frequency minimum and the rate of frequency change. Furthermore, while some methods consider the constraint of the system's frequency minimum after a disturbance, they often use simplified linearization assumptions to replace the actual primary frequency regulation feedback characteristics, making it difficult to accurately describe the dynamic frequency changes of the power grid during disturbances. On the other hand, with the increasing proportion of renewable energy sources, the randomness and volatility of their output have increased, and the techniques for handling such uncertainties in existing energy storage planning models are generally rather coarse. For example, some models do not consider the role of renewable energy power plants in frequency response, nor do they effectively model typical scenarios of renewable energy output, making it difficult for the planning results to fully reflect the actual operating conditions.

[0004] Therefore, there is an urgent need for a new energy storage planning technology solution that can take into account key dynamic indicators such as the lowest frequency point and the rate of frequency change, coordinate the frequency regulation capabilities of multiple types of power sources, address the uncertainty of new energy output, and solve the problems of energy storage optimization configuration and frequency security under high proportion of new energy access. Summary of the Invention

[0005] The purpose of this invention is to provide a stochastic planning method and related apparatus for energy storage that takes into account frequency stability constraints, so as to solve the technical problems in the prior art, such as the inability to fully reflect the dynamic characteristics of system frequency in high-proportion renewable energy access scenarios, the difficulty in simultaneously considering the randomness of renewable energy output and the coordinated response capability of multiple frequency regulation resources, resulting in insufficient accuracy of energy storage configuration results and inability to effectively meet system frequency stability requirements.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a stochastic programming method for energy storage that takes into account frequency stability constraints, comprising: Obtain the frequency response characteristics of the multi-machine system, and based on the frequency response characteristics of the multi-machine system, construct an aggregated multi-machine system frequency response model through the parameter equivalence method; Based on the frequency response model of the aggregated multi-machine system and the preset frequency safety margin, a linearized frequency safety margin calculation model is established. Using stochastic optimization methods, an energy storage stochastic programming model is established with the objective function of minimizing the sum of the total life cycle cost of energy storage and the total operating cost of the system, and with system operating conditions and a linearized frequency safety margin calculation model as constraints. Solve the energy storage stochastic programming model that takes into account frequency stability constraints to obtain the energy storage site selection and capacity configuration scheme.

[0007] Preferably, the frequency response characteristics of the multi-machine system include: the inertial response and primary frequency regulation characteristics of conventional units, the virtual inertia and droop control response of new energy power fields, and the rapid primary frequency regulation capability of energy storage systems.

[0008] Preferably, the frequency safety margin is the maximum power imbalance allowed when the system's frequency is not lower than a set safety threshold at its lowest point.

[0009] Preferably, the step of establishing a linearized frequency safety margin calculation model based on the frequency response model of the aggregated multi-machine system and a preset frequency safety margin includes: Based on the frequency response model of the aggregated multi-machine system, the transfer function of the equivalent multi-machine system frequency response model is derived. Using frequency safety margin as the quantitative basis for system frequency safety constraints, and based on the transfer function of the equivalent multi-machine system frequency response model, a piecewise linearization method is used to establish a linearized frequency safety margin calculation model.

[0010] Preferably, the total life cycle cost of the energy storage is calculated using the total life cycle cost method and converted into an equivalent daily cost through a capital recovery factor; the total operating cost of the system includes three parts: the operating cost of thermal power units, the cost of abandonment of new energy sources and the cost of load loss, and takes into account the uncertainties of multiple scenarios.

[0011] Preferably, the system operating conditions include node power balance constraints, DC power flow constraints, unit combination constraints, new energy electric field constraints, energy storage participation in frequency regulation constraints, as well as operating constraints and frequency stability constraints.

[0012] A second aspect of the present invention provides an energy storage stochastic planning device that takes into account frequency stability constraints, comprising: The aggregation unit is used to obtain the frequency response characteristics of the multi-machine system. Based on the frequency response characteristics of the multi-machine system, the frequency response model of the aggregated multi-machine system is constructed through the parameter equivalence method. The calculation unit is used to establish a linearized frequency safety margin calculation model based on the frequency response model of the aggregated multi-machine system and the preset frequency safety margin. The planning unit is used to establish a stochastic programming model for energy storage that takes frequency stability constraints into account, with the objective function of minimizing the sum of the total life cycle cost of energy storage and the total operating cost of the system, and with the system operating conditions and the linearized frequency safety margin calculation model as constraints. The solution unit is used to solve the energy storage stochastic programming model that takes into account frequency stability constraints, and obtain the energy storage site selection and capacity configuration scheme.

[0013] Preferably, in the computing unit, a linearized frequency safety margin calculation model is established based on the aggregated multi-machine system frequency response model and a preset frequency safety margin, including: Based on the frequency response model of the aggregated multi-machine system, the transfer function of the equivalent multi-machine system frequency response model is derived. Using frequency safety margin as the quantitative basis for system frequency safety constraints, and based on the transfer function of the equivalent multi-machine system frequency response model, a piecewise linearization method is used to establish a linearized frequency safety margin calculation model.

[0014] In a third aspect, the present invention provides an electronic device, characterized in that it includes a processor and a memory, the processor being configured to execute a computer program stored in the memory to implement the steps of the energy storage stochastic programming method considering frequency stability constraints as described in any one of the preceding claims.

[0015] In a fourth aspect, the present invention provides a computer-readable storage medium, characterized in that the computer-readable storage medium stores at least one instruction, which, when executed by a processor, implements the steps of the energy storage stochastic planning method considering frequency stability constraints as described in any one of the preceding claims.

[0016] Compared with the prior art, the present invention has the following beneficial effects: First, this invention establishes a frequency response model for an aggregated multi-machine system. By using the parameter equivalence method, it integrates various frequency regulation resources, such as conventional generating units, new energy power plants, and energy storage systems, into a unified equivalent response entity. While accurately depicting the dynamic frequency characteristics of the system, it reduces the number of state variables and parameters in the model, thereby reducing the complexity of system modeling and solving.

[0017] Second, this invention proposes a linearization modeling method based on frequency safety margin, which transforms nonlinear constraints involving dynamic indicators such as the lowest frequency point into the maximum power imbalance constraint that the system can withstand, and uses a piecewise linearization method to construct linear frequency safety margin constraints, so that dynamic frequency constraints can be directly embedded into the planning model as linear constraints, thereby improving the solution efficiency and engineering applicability of the model.

[0018] Third, this invention constructs an energy storage stochastic programming model that takes into account frequency stability constraints, integrates the energy regulation capability and frequency support capability of energy storage into the optimization framework, and handles the uncertainty of new energy output through multi-scenario stochastic programming. Under the premise of meeting frequency security requirements, it can obtain an energy storage site selection and capacity configuration scheme that takes into account both safety and economy. Attached Figure Description

[0019] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the frequency response model of a multi-machine system according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the frequency response model of the aggregated multi-machine system according to an embodiment of the present invention; Figure 4 This is a schematic diagram of an improved IEEE-39 node system according to an embodiment of the present invention; Figure 5 This is a schematic diagram of the predicted power output of new energy sources on four typical days according to an embodiment of the present invention; where (a) is a wind farm; and (b) is a photovoltaic farm. Figure 6 This is a schematic diagram illustrating the load demand over four typical days according to an embodiment of the present invention; Figure 7 Flowchart for linearizing the frequency safety margin in this embodiment of the invention; Figure 8 The frequency safety margin constraints are those of the embodiments of the present invention; wherein, (a) is a nonlinear frequency safety margin constraint, and (b) is a linear frequency safety margin constraint. Figure 9 The unit output considering the frequency stability constraint model in this embodiment of the invention; wherein, (a) is typical scenario 1, (b) is typical scenario 2, (c) is typical scenario 3, and (d) is typical scenario 4; Figure 10 The unit output of the embodiment of the present invention is without considering the frequency stability constraint model; wherein, (a) is typical scenario 1, (b) is typical scenario 2, (c) is typical scenario 3, and (d) is typical scenario 4; Figure 11 This is a comparison chart of the system frequency safety margins of two models in an embodiment of the present invention; Figure 12 This is a comparison diagram of the frequency dynamics of two models in an embodiment of the present invention; Figure 13This refers to the total cost and frequency safety margin under different new energy sources in this embodiment of the invention; Figure 14 The frequency safety margins corresponding to different unbalanced power in embodiments of the present invention; Figure 15 This is a block diagram of the device structure according to an embodiment of the present invention; Figure 16 This is a structural block diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0020] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0021] The following detailed description is exemplary and intended to provide further detailed explanation of the invention. Unless otherwise specified, all technical terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. The terminology used in this invention is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention.

[0022] This invention addresses the problem that existing power system energy storage planning studies do not adequately consider frequency stability constraints and the uncertainty of new energy output. It proposes a stochastic planning method for energy storage that takes frequency stability constraints into account, including: S1: Obtain the frequency response characteristics of the multi-machine system, and construct an aggregated multi-machine system frequency response model based on the frequency response characteristics of the multi-machine system through the parameter equivalence method; S2: Based on the frequency response model of the aggregated multi-machine system and the preset frequency safety margin, establish a linearized frequency safety margin calculation model; S3: Using stochastic optimization methods, with the objective function of minimizing the sum of the total life cycle cost of energy storage and the total operating cost of the system, and with the system operating conditions and the linearized frequency safety margin calculation model as constraints, a stochastic programming model for energy storage that takes into account frequency stability constraints is established. S4: Solve the energy storage stochastic programming model that takes into account frequency stability constraints to obtain the energy storage site selection and capacity configuration scheme.

[0023] This invention proposes a stochastic planning method for energy storage that considers frequency stability constraints. This method establishes a frequency response model for an aggregated multi-machine system, introduces a frequency safety margin constraint, and combines stochastic planning to model the uncertainty of renewable energy output, achieving synergistic optimization of energy storage planning economy and system frequency stability. In this embodiment, the above-mentioned stochastic planning method for energy storage considering frequency stability constraints is implemented through the following two points: First, addressing the problem of decreased system inertia and reduced frequency stability under high-proportion renewable energy access, a frequency response model for an aggregated multi-machine system is established, and a frequency safety margin is introduced, transforming the system's dynamic frequency stability constraint into an optimizable power imbalance constraint. A piecewise linearization method is used to achieve a linearized expression of the frequency stability constraint. Second, considering the stochastic fluctuation characteristics of renewable energy output, a stochastic optimization method is used to comprehensively consider energy storage configuration costs, system operating costs, and frequency safety constraints, synergistically optimizing the energy storage site selection, capacity, and operation strategy. Through these two aspects of design, economic optimization of energy storage configuration can be achieved while ensuring system frequency safety margin and operational stability.

[0024] In some embodiments, the frequency response characteristics of the multi-machine system include: the inertial response and primary frequency regulation characteristics of conventional units, the virtual inertia and droop control response of new energy power plants, and the rapid primary frequency regulation capability of energy storage systems. Based on this, a parameter equivalence method is used to aggregate multiple types of power generation units with similar dynamic characteristics to construct an aggregated multi-machine system frequency response model, significantly reducing computational complexity while maintaining the consistency of the system's dynamic frequency characteristics.

[0025] In some embodiments, the frequency safety margin is the maximum power imbalance allowed by the system at the lowest frequency point without falling below a set safety threshold. This serves as the quantitative basis for system frequency safety constraints.

[0026] In some embodiments, establishing a linearized frequency safety margin calculation model based on the aggregated multi-machine system frequency response model and a preset frequency safety margin includes: Based on the frequency response model of the aggregated multi-machine system, the transfer function of the equivalent multi-machine system frequency response model is derived; based on the frequency response model of the aggregated multi-machine system, the expression of the equivalent frequency parameters of the system is derived, and the calculation formulas of key indicators such as the minimum frequency point and frequency deviation rate are obtained.

[0027] Using frequency safety margin as the quantitative basis for system frequency safety constraints, and based on the transfer function of the equivalent multi-machine system frequency response model, a piecewise linearization method is employed to establish a linearized frequency safety margin calculation model. Through equivalent frequency parameters, the complex dynamic frequency behavior is transformed into a statically optimizable power constraint. Using the piecewise linearization method, a set of conservative linear hyperplanes is constructed to approximate the nonlinear constraint function, thereby transforming the nonlinear frequency stability constraint into a set of linear constraints that can be directly embedded into the optimization model, improving the model's solution efficiency.

[0028] In some embodiments, the total life cycle cost of energy storage is calculated using the total life cycle cost method and converted into equivalent daily cost through a capital recovery factor; the total operating cost of the system includes three parts: the operating cost of thermal power units, the cost of abandonment of new energy sources and the cost of load loss, and takes into account uncertainties in multiple scenarios.

[0029] In some embodiments, the system operating conditions include node power balance constraints, DC power flow constraints, unit combination constraints, new energy electric field constraints, energy storage participation in frequency regulation constraints, operating constraints, and frequency stability constraints.

[0030] A planning model for coordinating and optimizing long-term investment and short-term operation of energy storage is constructed. The model's objective function is to minimize the sum of the energy storage's total lifecycle cost and the system's total operating cost. The energy storage configuration cost is calculated using the lifecycle cost method and converted to an equivalent daily cost. The system operating cost comprehensively considers the costs of thermal power unit operation, renewable energy curtailment, and load loss. To characterize the uncertainty of renewable energy output, the model utilizes stochastic programming to handle typical scenarios. Regarding constraints, the model includes not only conventional system operation constraints such as nodal power balance, DC power flow, unit combination, renewable energy fields, and energy storage system operation, but more importantly, it embeds frequency stability constraints, such as linearized frequency safety margin constraints, as hard constraints into the model. This ensures the system's frequency safety under disturbances, achieving a balance between economical configuration and safe operation.

[0031] In some embodiments, the established energy storage stochastic programming model considering frequency stability constraints is solved by calling a commercial optimization solver such as Gurobi. Finally, numerical examples are used to analyze and verify the effectiveness and practicality of the established model.

[0032] In some embodiments, the present invention relates to a stochastic programming method for energy storage that takes into account frequency stability constraints. The method includes the following steps: First, a multi-system frequency response model integrating conventional generating units, renewable energy fields, and energy storage is established. The heterogeneous frequency regulation resources are integrated into a unified equivalent response entity using a parameter equivalence method, simplifying calculations while accurately characterizing the system's dynamic characteristics. Second, using the concept of "frequency safety margin," the complex nonlinear constraint at the lowest frequency point is transformed into the maximum power imbalance constraint that the system can withstand. This constraint is then embedded into the planning model using a piecewise linearization method. The planning model aims to minimize the sum of the energy storage's total lifecycle cost and the system's operating cost, synergistically optimizing long-term investment and short-term operation of energy storage. The stochastic programming model for energy storage that takes into account frequency stability constraints established by this invention can transform complex dynamic frequency constraints into optimizable linear constraints. By handling the uncertainties of renewable energy sources through stochastic optimization methods, it can provide a universally applicable energy storage configuration scheme to achieve economic optimization while ensuring system frequency safety.

[0033] Example 1 A stochastic programming method for energy storage that takes into account frequency stability constraints includes: 1) Establish a frequency response model for the aggregated multi-machine system. To comprehensively reflect the frequency dynamics of a power system with diversified frequency regulation resources, this invention first establishes a multi-machine system frequency response model integrating synchronous generators, new energy power plants, and energy storage systems, such as... Figure 2 As shown. This model models various types of frequency modulation resources respectively: 1. Frequency response of conventional units When a disturbance in the system causes a frequency drop, the frequency support process of a conventional thermal power unit is mainly determined by the governor and turbine dynamics, with the turbine often playing a dominant role in the frequency response. The unit's frequency dynamic process can be expressed as: (1) In the formula: Let be the inertial constant of the unit. For frequency deviation, This refers to the mechanical power output after adjustment by the speed controller. For the unbalanced power of the system, is the damping coefficient.

[0034] The regulating behavior of the speed governor itself can be approximated as a first-order inertial system, with the following transfer function: (2) In the formula: This is the droop coefficient of the speed controller. is the response time constant of the governor-turbine system.

[0035] 2. Frequency response of new energy electric fields New energy power plants, connected to the grid via power electronic converters, lack the physical inertia of traditional synchronous generators. Therefore, virtual synchronous machine technology is typically employed, using control logic to simulate the inertial response and droop characteristics of synchronous generators. In the time domain, the frequency response power of a new energy power plant based on a virtual synchronous control strategy can be expressed as: (3) Meanwhile, in the frequency domain, the response delay of the control system also needs to be considered, and its frequency domain expression can be expressed as: (4) Since the frequency response power depends on load shedding operation, the maximum amount of primary frequency regulation response is limited by the curtailment of renewable energy: (5) In the formula: These are the deviations in the time domain and frequency domain, respectively; This represents the maximum frequency deviation. , These represent the total response power in the time domain and frequency domain, respectively. , , These represent the inertial constant, droop constant, and response time of the new energy electric field, respectively. This is a reserve factor used to adjust the preset power margin of the primary frequency modulation response.

[0036] 3. Frequency response of battery energy storage system Energy storage systems can rapidly activate primary frequency regulation response to provide power support, and their power exchange dynamic characteristics can be represented by a first-order transfer function: (6) In the formula: The frequency response power of the energy storage system in the frequency domain; These are the gain coefficient, droop constant, and response time, respectively.

[0037] 4. Frequency response model of aggregated multi-machine system To simplify calculations while ensuring the accuracy of dynamic characteristics, a parameter aggregation and structural equivalence method is adopted to integrate the multi-heterogeneous frequency response units into a unified equivalent response entity.

[0038] The transfer functions of new energy power plants and energy storage systems are converted into equivalent functions respectively: (7) (8) In the formula: , These are the equivalent droop coefficients for new energy electric fields and energy storage systems, respectively. , These are the equivalent power fractions for new energy power plants and energy storage systems, respectively.

[0039] Assuming the system's base power equals the hourly demand, the damping coefficient remains constant throughout any time interval. Therefore, the equivalent system inertia calculation expression is: (9) In the formula: for Equivalent system inertia at any given moment; For thermal power units The inertial constant; For thermal power units Maximum frequency response capacity; for Time bus Load demand; for thermal power units Whether it participates in frequency modulation; This is the set of indices for the power grid bus.

[0040] Based on this, an equivalent governor speed constant and a comprehensive frequency droop coefficient are constructed by linear superposition, thereby completing a unified model of the response capability of the entire multi-source system under frequency disturbances.

[0041] The newly defined governor speed constant is: (10) Based on this, construct respectively and The linear formula: (11) (12) In the formula: , for The frequency support status of the new energy electric field and energy storage system at all times; This represents the maximum response capacity of the energy storage system.

[0042] The frequency response model of the aggregated multi-machine system is obtained as follows: Figure 3 As shown in the figure , and This is the equivalent frequency parameter.

[0043] 2) Establish linearized frequency safety margin constraints 1. Deriving the equivalent frequency parameters Based on the frequency response model of the aggregated multi-machine system, the transfer function of the equivalent multi-machine system frequency response model is derived: (13) In the formula, the natural oscillation frequency Damping ratio The calculation expression is: (14) In the time domain The parsing expression is: (15) In the formula, the damping frequency is... Sum of coefficients , The calculation expression is: (16) Based on the formula for calculating frequency deviation, its derivative is used to derive the maximum frequency deviation. and the corresponding lowest frequency time : (17) In addition, the rate of change of frequency As an important indicator for measuring the short-term inertial support capacity of a system, it is of great significance in the initial stage of sudden disturbances. The expression for calculating the rate of frequency change is: (18) 2. Define frequency safety margin The frequency safety margin is defined as the maximum power disturbance that the system can withstand while satisfying the minimum frequency constraint. To derive the analytical expression for this margin, the following assumptions are made: (1) To simplify the model, it is assumed that all devices with frequency support capability have the same reheat time constant. .

[0044] (2) Since the droop control gain and damping coefficient are usually adjusted within a strict range, the equivalent damping coefficient of the system can be regarded as a constant.

[0045] Based on the above assumptions, the maximum unbalanced power can be expressed as: (19) Therefore, frequency stability constraints can be equivalently transformed into restrictions on the actual power imbalance of the system: (20) 3. Linearization frequency safety margin constraint Based on the equivalent frequency parameter formula of the aggregation model, the equivalent parameters are determined by setting extreme cases where all units participate in / do not participate in frequency regulation. The range of values ​​for .

[0046] Divide the parameter range into a series of subspaces And generate sampling points in each subspace. The closest function is found by solving the following optimization model. Hyperplane: (twenty one) In the formula: represents the coefficients of the hyperplane.

[0047] Based on the above analysis, the nonlinear frequency stability constraint can be transformed into the following linear frequency stability constraint: (twenty two) 3) Establish a stochastic programming model for energy storage that takes into account frequency stability constraints. 1. Objective function The objective function is to minimize the sum of the total lifecycle cost of energy storage and the total operating cost of the system. (twenty three) In the formula: Cost of configuring energy storage; This refers to the system operating cost.

[0048] Energy storage configuration costs are calculated using the life-cycle cost method and converted to equivalent daily costs using a capital recovery factor. (twenty four) In the formula: This is the capital recovery factor; , These are the initial investment cost and the operation and maintenance cost of the battery energy storage system, respectively. These are binary variables, where a value of 1 indicates that the energy storage system is participating in the construction, and a value of 0 indicates that the energy storage system is not being constructed. This application assumes that all energy storage systems are candidate construction projects, and the construction cost of already constructed energy storage systems is set to 0.

[0049] The expressions for the capital recovery factor, initial investment cost, and operation and maintenance cost are as follows: (25) (26) (27) In the formula: The annual discount rate; For the number of years of operation; Rated power; Rated capacity; , These are the unit power cost and the unit capacity cost, respectively.

[0050] The system operating cost comprehensively considers the costs of thermal power unit operation, renewable energy curtailment, and load loss, and takes into account uncertainties in multiple scenarios: (28) In the formula: The probability of the scenario; Let be the scenario probability set. The expressions for the costs of each component are as follows: (29) (30) (31) In the formula: For time intervals; Fuel consumption cost of thermal power units; The startup cost of thermal power units; For the active power output of thermal power units; This is a binary variable; when the variable is 1, the group is in the started state, and when the variable is 0, it is in the unstarted state. Costs associated with abandoning new energy sources; This refers to the abandoned power of new energy power plants; Cost of load interruption; For load transfer costs; For load power; , These are the load-in power and the load-out power, respectively.

[0051] 2. Constraints Node power balance constraints: (32) In the formula: A set of indices for all generators connected to the bus; This is the set of indices for all transmission lines connected to the busbar. For power flow of transmission lines; For load demand.

[0052] DC power flow constraints: (33) (34) In the formula: , These are the voltage phase angles of the starting bus and the ending bus of the line, respectively. For susceptance; , These are the minimum current and the maximum current, respectively.

[0053] Unit combination constraints: The unit combination constraints include the unit start-stop state logic constraints (35), the unit start-stop action mutual exclusion constraints (36), the unit minimum start-stop time constraints (37)-(38), the unit active power output constraints (39), and the unit up / down ramp rate constraints (40).

[0054] (35) (36) (37) (38) (39) (40) In the formula: This is a binary indicator; a value of 1 indicates that the unit is in a shutdown state, and a value of 0 indicates that it is not in a shutdown state. This is a binary indicator; when the variable is 1, the group is in the powered-on state, and when the variable is 0, it is in the powered-off state. , These are the minimum startup time and the minimum downtime, respectively. , These represent the duration of the machine being powered on and powered off at the start of a typical day, respectively. , These are the minimum output and maximum output, respectively. , These are the maximum climbing power and the maximum descending power, respectively. This represents the duration in hours between adjacent time intervals.

[0055] New energy electric field constraints: To meet the renewable energy mix standard, constraint (41) pre-sets a minimum proportion of new energy in total demand. Constraint (42) also considers the power factor of renewable energy curtailment. Restrictions.

[0056] (41) (42) Constraints and operational constraints of energy storage in frequency regulation: The constraints for the battery energy storage system participating in frequency regulation are shown in equations (43)-(50). Equation (43) gives the calculation expression for the total primary frequency regulation response power of the electric field energy storage system. Equation (44) is the mutual exclusion constraint for charging and discharging states. Equations (45)-(46) respectively specify the range of frequency response power of the battery energy storage system in the discharging and charging states. Equation (47) specifies the range of stored energy after the unified frequency response. Equation (48) clearly gives the relationship between the normal operation of the battery energy storage system and the energy stored after participating in frequency regulation. In the equation, 1-3 refer to the energy change caused by frequency regulation. Part 1 corresponds to the situation where the battery energy storage system is discharging during normal operation, part 2 corresponds to the situation where the battery energy storage system is in the charging state during both normal operation and frequency regulation, and part 3 corresponds to the situation where the battery energy storage system is charging during normal operation but changes to the discharging state after frequency regulation. Equation (49) is the mutual exclusion constraint for the frequency regulation state. Equation (50) is the correlation constraint between the energy storage system's construction state and the frequency regulation state.

[0057] (43) (44) (45) (46) (47) (48) (49) (50) In the formula: This represents the total primary frequency response power; , These are the frequency responses provided to the battery energy storage system during charging and discharging, respectively. This is a binary variable. When the variable is 1, the battery energy storage system is in a discharging state, and when the variable is 0, it is not in a discharging state. This is a binary variable. When the variable is 1, the battery energy storage system is in a charging state; when the variable is 0, it is not in a charging state. , These are the maximum discharge power and the maximum charging power, respectively. , These are the actual discharge power and the actual charging power, respectively. , These represent the stored energy before and after the frequency response of the battery energy storage system. , These represent the minimum and maximum stored energy, respectively. This is the duration of a single frequency modulation response; , These are discharge efficiency and charging efficiency, respectively. This is a binary variable. When the variable is 1, the battery energy storage system is in charging frequency regulation mode; when the variable is 0, it is not in charging frequency regulation mode. This is a binary variable. When the variable is 1, the battery energy storage system is in the discharge frequency regulation state; when the variable is 0, it is not in the discharge frequency regulation state. This is a binary variable. When the variable is 1, the electric field energy storage system participates in frequency regulation; when the variable is 0, it does not participate in frequency regulation.

[0058] The operational constraints of the battery energy storage system are shown in equations (51)-(57). Equation (51) represents the dynamic energy balance constraint of the energy storage system, and equation (52) represents the upper and lower limits of the energy of the energy storage system. Equations (53)-(54) limit the charging power and discharging power of the battery energy storage system, respectively. Equation (55) stipulates that the remaining energy of the electric field energy storage system must remain consistent at the beginning and end of a typical day. Equations (56)-(57) indicate that the battery energy storage system can only be in a charging or discharging state when it is put into operation.

[0059] (51) (52) (53) (54) (55) (56) (57) In the formula: This refers to the charge / discharge time. , These represent the remaining energy of the battery energy storage system at the beginning and end of a typical day, respectively.

[0060] Frequency stability constraints: Equations (58)-(60) pre-set sufficient power margins for new energy power plants, thermal power units, and BESS to ensure primary frequency regulation response. Equation (61) requires the system inertia to meet the frequency change rate limit. The equivalent frequency parameters can be calculated using equations (62)-(64). Equation (65) is the frequency safety margin constraint, used to ensure sufficient frequency safety margin.

[0061] (58) (59) (60) (61) (62) (63) (64) (65) 1) Case Analysis This invention is in Figure 5 A case study analysis was conducted using the improved IEEE-39 node system shown. Programming was performed in the Python 3.9 environment, and optimization was performed using the Gurobi 12.0.1 solver. The system comprises 39 buses, 15 generator units, and 46 lines. The 15 power plants include 10 thermal power plants, 3 wind power plants, and 2 photovoltaic power plants. The corresponding plant numbers and installed capacities are shown in Table 1, and the basic parameters of the thermal power units are shown in Table 2. Table 3 displays the basic parameters of two candidate energy storage models. Nodes with candidate energy storage can choose at most one of the two models.

[0062] Table 1 Basic Information of the Power Plant

[0063] Table 2 Basic Parameters of Thermal Power Units

[0064] Table 3 Candidate Energy Storage Parameters

[0065] To reflect the uncertainty and randomness of renewable energy output, wind and solar power output data from four different typical days are used to illustrate fluctuating renewable energy power. The predicted power output of wind and solar farms on the four typical days is shown below. Figure 5 As shown. The load demand curve is shown below. Figure 6 .

[0066] First, the linearized frequency safety margin constraint proposed in this invention is verified. Figure 7 The flowchart shown linearizes the frequency safety margin. Figure 8 The frequency safety margin constraints of nonlinear and piecewise linearized systems were compared. The results show that the linearized constraint plane effectively approximates the original nonlinear surface overall, always lying below or coinciding with it. This verifies the effectiveness of the conservative approximation strategy employed, ensuring that the linearized model does not overestimate the actual safety margin of the system, thus providing reliable safety assurance for system operation.

[0067] Secondly, the planning results considering frequency stability constraints (Model 1) and not considering frequency stability constraints (Model 2) were compared and analyzed, as shown in Table 4. Assuming the system can withstand a maximum unbalanced power of 165MW, the planning results of the two models show that when frequency stability constraints are introduced, the system's frequency safety margin is 171.21MW, which meets the system's frequency safety requirements. However, the model without frequency stability constraints has a frequency safety margin far below the required level. Therefore, introducing frequency stability constraints into the planning model helps improve the system's frequency stability. From an economic perspective, although the model considering frequency constraints has a slightly higher energy storage configuration cost of 172,800 yuan, an increase of approximately 28.6% compared to the 134,400 yuan of the model without frequency constraints, this increase is mainly due to meeting the system's frequency stability requirements.

[0068] Table 4. Planning results of the two models

[0069] contrast Figure 9 and Figure 10 The unit output results of the two models on different typical days reveal the impact of frequency stability constraints on the functions of various power sources in the system. Without considering frequency stability constraints, system scheduling prioritizes operational economy. Thermal power units assume a baseload role with "high baseline, low fluctuations," energy storage systems primarily operate in a peak-shaving and valley-filling "energy arbitrage" mode, while a passive "maximum absorption" strategy is adopted for renewable energy. Considering frequency security constraints, the basic principle of system resource scheduling shifts from a single economic objective to economic optimization under security constraints. Under this principle, the role of thermal power units changes from baseload power to a flexible adjustment resource that also considers peak shaving; the operating strategy of energy storage systems shifts to a "frequency regulation priority" mode, especially during periods of system disturbance and high fluctuations in renewable energy, prioritizing rapid power support, thereby achieving synergistic optimization of system frequency security and renewable energy absorption levels.

[0070] To verify the role of frequency stability constraints in the model, the maximum unbalanced power disturbance of the system was set to 250MW. The performance of the two models—those with and without frequency stability constraints—was compared and analyzed under typical daily conditions. Figure 11 As shown, the planning scheme that takes frequency constraints into account maintains a frequency safety margin above the safety threshold on all typical days with gentle fluctuations. This indicates that the system achieves good dynamic response capabilities by coordinating frequency regulation resources such as energy storage and thermal power units, effectively coping with sudden changes in new energy output and load. Conversely, the model that does not consider frequency constraints has a significantly lower safety range than required, and the system is highly susceptible to instability under disturbances, highlighting the necessity of introducing frequency safety constraints in the planning process.

[0071] Further analysis of the frequency dynamic characteristics of the system after being subjected to disturbances, such as... Figure 12 As shown in the figure, during a specific period on a typical day, the unconstrained model's frequency rapidly dropped to 49.22 Hz after a disturbance, far exceeding the safety threshold of 49.5 Hz. This indicates that the system's inertia support and primary frequency regulation capability are weak under this configuration, making it difficult to meet frequency stability requirements. In contrast, the model considering frequency constraints can maintain the lowest frequency at 49.54 Hz, remaining within the safe range, and exhibits faster oscillation decay characteristics and recovery capability. The system recovers to a quasi-steady-state level within approximately 20 seconds. Simulation results demonstrate that frequency stability constraints not only optimize the allocation of initial inertia resources but also effectively improve the coordinated frequency regulation response capability of energy storage and synchronous generator units, ensuring that the system can quickly suppress frequency shifts and efficiently recover stability under disturbances.

[0072] To explore the impact of renewable energy penetration rate on planning schemes, different renewable energy proportions ranging from 10% to 60% were analyzed. As shown in Table 5, with the increase in renewable energy penetration rate, the energy storage capacity and investment cost required to ensure the dynamic safety of the system increase significantly. At low penetration rates, the system only needs a small amount of energy storage to meet frequency stability requirements; however, when the penetration rate reaches 60%, the number of energy storage sites and the total investment cost both increase significantly to compensate for the system inertia and frequency regulation capability gap caused by the withdrawal of conventional synchronous generator units.

[0073] Table 5. Energy storage planning results under different proportions of new energy sources

[0074] Figure 13 The study further reveals the changing trends of total system cost and frequency safety margin under different penetration rates. On the one hand, the total system cost decreases with the increase in the proportion of renewable energy, mainly due to the near-zero marginal operating cost of renewable energy generation, which effectively reduces the overall operating expenses of the system. On the other hand, the frequency safety margin shows a significant contraction trend, reflecting that the high proportion of renewable energy integration weakens the system's frequency response capability. Nevertheless, in the proposed planning model, due to the mandatory effect of frequency stability constraints, the frequency safety margin in each scenario remains above the safety threshold of 165MW. This indicates that the model, by reasonably increasing the cost of energy storage configuration, reduces the risk of frequency stability decline caused by the increase in the proportion of renewable energy, thereby improving the system's economics while ensuring its dynamic safety performance.

[0075] Figure 14The hourly system frequency safety margin under different unbalanced power conditions is demonstrated. The maximum unbalanced power requirement that the system can withstand gradually increases from 100 MW to 300 MW, with the frequency safety margin gradually expanding. While the frequency safety margin curves show slight differences on different typical days, the system frequency safety margin meets the frequency safety requirements in all cases. This indicates that the proposed model has sufficient flexibility and adaptability to cope with system frequency fluctuations of different scales, thereby ensuring the safe operation of the system. This result further demonstrates the effectiveness and reliability of the model under different unbalanced power conditions.

[0076] Example 2 like Figure 15 As shown, based on the same inventive concept as the above embodiments, the present invention also provides an energy storage stochastic programming device that takes into account frequency stability constraints, comprising: The aggregation unit is used to obtain the frequency response characteristics of the multi-machine system. Based on the frequency response characteristics of the multi-machine system, the frequency response model of the aggregated multi-machine system is constructed through the parameter equivalence method. The calculation unit is used to establish a linearized frequency safety margin calculation model based on the frequency response model of the aggregated multi-machine system and the preset frequency safety margin. The planning unit is used to establish a stochastic programming model for energy storage that takes frequency stability constraints into account, with the objective function of minimizing the sum of the total life cycle cost of energy storage and the total operating cost of the system, and with the system operating conditions and the linearized frequency safety margin calculation model as constraints. The solution unit is used to solve the energy storage stochastic programming model that takes into account frequency stability constraints, and obtain the energy storage site selection and capacity configuration scheme.

[0077] In some embodiments, the computing unit establishes a linearized frequency safety margin calculation model based on the aggregated multi-machine system frequency response model and a preset frequency safety margin, including: Based on the frequency response model of the aggregated multi-machine system, the transfer function of the equivalent multi-machine system frequency response model is derived. Using frequency safety margin as the quantitative basis for system frequency safety constraints, and based on the transfer function of the equivalent multi-machine system frequency response model, a piecewise linearization method is used to establish a linearized frequency safety margin calculation model.

[0078] Example 3 like Figure 16 As shown, the present invention also provides an electronic device 100 for implementing the steps of an energy storage stochastic planning method that takes into account frequency stability constraints; The electronic device 100 includes a memory 101, at least one processor 102, a computer program 103 stored in the memory 101 and executable on at least one processor 102, and at least one communication bus 104.

[0079] The memory 101 can be used to store the computer program 103. The processor 102 implements the steps of the energy storage stochastic planning method taking into account frequency stability constraints by running or executing the computer program stored in the memory 101 and calling the data stored in the memory 101.

[0080] The memory 101 may primarily include a program storage area and a data storage area. The program storage area may store the operating system, application programs required for at least one function (such as sound playback function, image playback function, etc.), etc.; the data storage area may store data created based on the use of the electronic device 100 (such as audio data), etc. In addition, the memory 101 may include non-volatile memory, such as hard disk, RAM, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one disk storage device, flash memory device, or other non-volatile solid-state storage device.

[0081] At least one processor 102 may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. Processor 102 may be a microprocessor or any conventional processor. Processor 102 is the control center of electronic device 100, connecting various parts of electronic device 100 via various interfaces and lines.

[0082] The memory 101 in the electronic device 100 stores multiple instructions to implement the steps of an energy storage stochastic programming method that takes into account frequency stability constraints, and the processor 102 can execute multiple instructions to implement: Obtain the frequency response characteristics of the multi-machine system, and based on the frequency response characteristics of the multi-machine system, construct an aggregated multi-machine system frequency response model through the parameter equivalence method; Based on the frequency response model of the aggregated multi-machine system and the preset frequency safety margin, a linearized frequency safety margin calculation model is established. Using stochastic optimization methods, an energy storage stochastic programming model is established with the objective function of minimizing the sum of the total life cycle cost of energy storage and the total operating cost of the system, and with system operating conditions and a linearized frequency safety margin calculation model as constraints. Solve the energy storage stochastic programming model that takes into account frequency stability constraints to obtain the energy storage site selection and capacity configuration scheme. Example 4 If the modules / units integrated in the electronic device 100 are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, and read-only memory (ROM).

[0083] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0084] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0085] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0086] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0087] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0088] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A stochastic programming method for energy storage considering frequency stability constraints, characterized in that, include: Obtain the frequency response characteristics of the multi-machine system, and based on the frequency response characteristics of the multi-machine system, construct an aggregated multi-machine system frequency response model through the parameter equivalence method; Based on the frequency response model of the aggregated multi-machine system and the preset frequency safety margin, a linearized frequency safety margin calculation model is established, including: Based on the frequency response model of the aggregated multi-machine system, the transfer function of the equivalent multi-machine system frequency response model is derived. Using frequency safety margin as the quantitative basis for system frequency safety constraints, and based on the transfer function of the equivalent multi-machine system frequency response model, a piecewise linearization method is used to establish a linearized frequency safety margin calculation model, specifically including: The maximum unbalanced power is expressed as: Therefore, frequency stability constraints can be equivalently transformed into restrictions on the actual power imbalance of the system: Construct an optimization model to find the closest function hyperplane; Based on the above analysis, the nonlinear frequency stability constraint is transformed into the following linear frequency stability constraint: ； Using stochastic optimization methods, an energy storage stochastic programming model is established with the objective function of minimizing the sum of the total life cycle cost of energy storage and the total operating cost of the system, and with system operating conditions and a linearized frequency safety margin calculation model as constraints. Solve the energy storage stochastic programming model that takes into account frequency stability constraints to obtain the energy storage site selection and capacity configuration scheme.

2. The energy storage stochastic programming method considering frequency stability constraints according to claim 1, characterized in that, The frequency response characteristics of the multi-machine system include: the inertial response and primary frequency regulation characteristics of conventional units, the virtual inertia and droop control response of new energy power plants, and the rapid primary frequency regulation capability of energy storage systems.

3. The energy storage stochastic programming method considering frequency stability constraints according to claim 1, characterized in that, The frequency safety margin is the maximum power imbalance allowed when the system's frequency is not lower than a set safety threshold at its lowest point.

4. The energy storage stochastic programming method considering frequency stability constraints according to claim 1, characterized in that, The energy storage full life cycle cost is calculated using the full life cycle cost method and converted into equivalent daily cost through the capital recovery factor; the total system operating cost includes three parts: thermal power unit operation, new energy curtailment and load loss, and takes into account uncertainties in multiple scenarios.

5. The energy storage stochastic programming method considering frequency stability constraints according to claim 1, characterized in that, The system operating conditions include node power balance constraints, DC power flow constraints, unit combination constraints, new energy electric field constraints, energy storage participation in frequency regulation constraints, as well as operation constraints and frequency stability constraints.

6. A stochastic programming device for energy storage considering frequency stability constraints, characterized in that, The energy storage stochastic programming method considering frequency stability constraints as described in any one of claims 1 to 5 includes: The aggregation unit is used to obtain the frequency response characteristics of the multi-machine system. Based on the frequency response characteristics of the multi-machine system, the frequency response model of the aggregated multi-machine system is constructed through the parameter equivalence method. The calculation unit is used to establish a linearized frequency safety margin calculation model based on the frequency response model of the aggregated multi-machine system and the preset frequency safety margin. The planning unit is used to establish a stochastic programming model for energy storage that takes into account frequency stability constraints, with the objective function of minimizing the sum of the total life cycle cost of energy storage and the total operating cost of the system, and with the system operating conditions and the linearized frequency safety margin calculation model as constraints. The solution unit is used to solve the energy storage stochastic programming model that takes into account frequency stability constraints, and obtain the energy storage site selection and capacity configuration scheme.

7. The energy storage stochastic programming device considering frequency stability constraints according to claim 6, characterized in that, In the computing unit, a linearized frequency safety margin calculation model is established based on the frequency response model of the aggregated multi-machine system and a preset frequency safety margin, including: Based on the frequency response model of the aggregated multi-machine system, the transfer function of the equivalent multi-machine system frequency response model is derived. Using frequency safety margin as the quantitative basis for system frequency safety constraints, and based on the transfer function of the equivalent multi-machine system frequency response model, a piecewise linearization method is used to establish a linearized frequency safety margin calculation model.

8. An electronic device, characterized in that, It includes a processor and a memory, the processor being configured to execute a computer program stored in the memory to implement the steps of the energy storage stochastic programming method taking into account frequency stability constraints as described in any one of claims 1 to 5.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores at least one instruction, which, when executed by a processor, implements the steps of the energy storage stochastic planning method taking into account frequency stability constraints as described in any one of claims 1 to 5.

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