Economic frequency control methods, systems, and equipment for systems considering vibration zone constraints
By constructing a dynamic power model and an economic optimization model for vibration avoidance of variable-speed pumped storage units, and combining distributed algorithms to handle vibration zone constraints, the problems of power system frequency stability and economy were solved, safe and economical frequency control was achieved, regulation costs were reduced, and equipment lifespan was extended.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HOHAI UNIV
- Filing Date
- 2026-03-18
- Publication Date
- 2026-05-26
AI Technical Summary
With the integration of large-scale renewable energy into the grid, existing technologies pose challenges to the frequency stability and economy of the power system. In particular, the vibration safety hazards of variable speed pumped storage units have not been fully considered, and traditional control modes have failed to effectively utilize the most economical power generation resources, resulting in high regulation costs and the risk of shortened equipment lifespan.
A dynamic power model containing variable speed pumped storage units is constructed, an economic optimization model for vibration avoidance is established, a distributed primal-dual solution algorithm is adopted, and vibration zone constraints are handled by Lagrangian functions and forward projection operators. An economical AGC for vibration avoidance is designed and embedded into the existing AGC structure to achieve frequency stability and economic dispatch.
It significantly shortens the unit's residence time in the vibration zone, reduces the total system regulation cost, provides a safe and economical control scheme, has excellent engineering practicality and compatibility, is easy to integrate and deploy, and avoids the defects of black-box intelligent algorithms.
Smart Images
Figure CN121863393B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of automatic generation control and frequency stabilization technology in power systems, and particularly to a system, system, and device for economical frequency control that takes into account vibration zone constraints. Background Technology
[0002] With the large-scale integration of renewable energy into the grid, the net load volatility of the power system is becoming increasingly prominent, characterized by larger fluctuations and faster rates of change. This trend not only poses a severe challenge to frequency stability but also leads to decreased operational economics due to increased pressure on generating units. More importantly, the large-scale grid connection of renewable energy is squeezing out traditional synchronous generators, resulting in a continuous decrease in system inertia and damping levels. Against this backdrop, energy storage technology has become a key means of balancing power and enhancing grid resilience. To mitigate the fluctuations caused by renewable energy, it is necessary not only to enhance the existing regulation capacity of the grid but also to configure additional energy storage power sources.
[0003] With the rapid development of power electronic converters and advanced control algorithms, doubly-fed variable-speed pumped storage technology, characterized by its fast response and excellent power regulation capabilities, has received widespread attention globally. Current research on the participation of variable-speed pumped storage units in frequency regulation largely focuses on the design of unit-level control strategies and grid-level stability analysis, without fully considering the hydraulic-mechanical-electrical coupling vibration problems faced by the units in actual operation. This results in vibration safety hazards in practical applications for many studies. Without effective mitigation strategies, this will not only restrict the full utilization of their regulation capabilities but also shorten equipment lifespan. Furthermore, traditional automatic generation control modes prioritize regional power balance and frequency restoration, lacking comprehensive consideration of cross-regional resource coordination and economic dispatch. In the increasingly complex and volatile operating environment of modern power systems, traditional methods fail to fully utilize the most economical generation resources, resulting in high regulation costs.
[0004] The information disclosed in this background section is intended only to enhance the understanding of the general background of the invention and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention
[0005] This invention provides a system, device, and method for economical frequency control that considers vibration zone constraints, thereby effectively solving the problems in the background art.
[0006] To achieve the above objectives, the technical solution adopted by this invention is: a system economic frequency control method considering vibration zone constraints, comprising the following steps:
[0007] A power dynamic model containing a variable speed pumped storage unit (VSPS) is constructed. The power dynamic model includes at least: a synchronous generator mechanical power deviation model, a VSPS unit converter control dynamic model, a transmission line power flow dynamic model and a node frequency dynamic model, and a traditional automatic generation control (AGC) area control error generation and power adjustment command dynamic model.
[0008] An economic optimization model for vibration avoidance is established. The economic optimization model aims to minimize the total system regulation cost. It adopts a quadratic regulation cost representation and introduces the VSPS unit vibration zone inequality constraint and the auxiliary variable γ for relaxing the power balance constraint to adapt to instantaneous power imbalance.
[0009] For the aforementioned economic optimization model, a Lagrangian function is constructed and a distributed primal-dual solution algorithm is designed. The algorithm uses an adjustable positive step size parameter and utilizes a forward projection operator to ensure the non-negativity of the dual variable, and iteratively solves for the primal and dual variables.
[0010] By matching the power dynamic model with the steady-state conditions of the algorithm, a vibration-damping economical AGC that can be directly embedded into existing AGC structures is derived, implemented, and applied.
[0011] Furthermore, the synchronous generator mechanical power deviation model is a simplified first-order governor deviation model;
[0012] The VSPS unit converter control dynamic model includes virtual inertia and damping terms, and is expressed by dynamic equations;
[0013] The power flow dynamic model of the transmission line is described by a first-order dynamic equation under the assumption of small angle difference, and the power flow deviation is... The changes are caused by the node phase angle and line parameters This is determined and used as the information exchange quantity between adjacent nodes in distributed algorithms;
[0014] The node frequency dynamic model is represented by the oscillation equation;
[0015] The traditional automatic generation control (AGC) area control error generation and power adjustment command dynamic model includes:
[0016] For a specific node The mathematical definition of its regional control error; based on this error signal, the power adjustment command is calculated. The dynamic equation.
[0017] Furthermore, the inequality constraints of the VSPS unit vibration zone are represented by lower and upper bounds, and are explicitly introduced in the form of inequality constraints in the economic optimization model to limit the VSPS output power from falling into the vibration hazard zone.
[0018] Furthermore, the auxiliary variable γ is introduced to relax the power balance constraint of the entire network, and the relaxation term is used as a penalized or constrained variable in the optimization.
[0019] Furthermore, the distributed primal-dual solution algorithm includes:
[0020] The distributed primal-dual gradient algorithm includes alternating or parallel iterative updates of primal and dual variables. The primal variables include governor control deviation, line power flow deviation, variable speed pumped storage unit power deviation, and frequency deviation. The dual variables are Lagrange multipliers defined according to the constructed optimization problem.
[0021] Both the original and dual variables have positive step sizes during the iteration process, and the projection operator is used to apply non-negative constraints to the corresponding dual variables.
[0022] Furthermore, the projection operator For: when or Time output Otherwise, output 0.
[0023] Furthermore, the vibration damping economic AGC is:
[0024] By substituting the system frequency dynamics, power flow dynamics, and traditional AGC dynamics into the steady-state equation of the gradient algorithm, and pairing them up item by item at each node, the feasible controller parameter setting expression is obtained.
[0025] The present invention also includes a system economic frequency control system considering vibration zone constraints, using the method described above, wherein the system comprises:
[0026] The power dynamic model unit is used to construct a power dynamic model containing a variable speed pumped storage unit (VSPS). The power dynamic model includes at least: a synchronous generator mechanical power deviation model, a VSPS unit converter control dynamic model, a transmission line power flow dynamic model and a node frequency dynamic model, and a traditional automatic generation control (AGC) area control error generation and power adjustment command dynamic model.
[0027] The economic optimization model unit is used to establish an economic optimization model for vibration avoidance. The economic optimization model aims to minimize the total system regulation cost, adopts a quadratic regulation cost representation, and introduces VSPS unit vibration zone inequality constraints and auxiliary variable γ for relaxing power balance constraints to adapt to instantaneous power imbalance.
[0028] The algorithm unit is used to construct a Lagrangian function and design a distributed primal-dual solution algorithm for the economic optimization model. The algorithm uses an adjustable positive step size parameter and a forward projection operator to ensure the non-negativity of the dual variables, and iteratively solves for the primal and dual variables.
[0029] The vibration-damping economic AGC unit is used to derive and implement a vibration-damping economic AGC that can be directly embedded into existing AGC structures by matching the power dynamic model with the steady-state conditions of the algorithm, and then apply it.
[0030] The present invention also includes a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the method as described above.
[0031] The present invention also includes a storage medium having a computer program stored thereon, which, when executed by a processor, implements the method as described above.
[0032] The beneficial effects of this invention are as follows: By explicitly embedding vibration zone constraints into the optimization model, online dynamic avoidance is achieved, greatly shortening the time the unit spends in the vibration zone; simultaneously, global economic optimization is achieved while ensuring safety, the proposed model aims to minimize regulation costs, and coordinates the output of each unit through a distributed algorithm, significantly reducing the total system regulation cost; furthermore, it has excellent engineering practicality and compatibility, the proposed control method only requires local improvements to the traditional automatic generation control structure, making it easy to integrate and deploy; finally, it provides a systematic design paradigm with clear physical interpretation, which can prove the convergence of the gradient optimization-based distributed algorithm, avoiding the drawbacks of black-box intelligent algorithms lacking theoretical support, and providing a reliable control scheme for the safe and economical operation of complex power systems. Attached Figure Description
[0033] 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 some embodiments recorded in the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0034] Figure 1 This is a flowchart of the method in Example 1;
[0035] Figure 2 This is a schematic diagram of the system structure in Example 1;
[0036] Figure 3 This is an additional frequency control module for the VSPS in Example 2.
[0037] Figure 4 This is the four-area interconnection system in Example 2.
[0038] Figures 5 to 7 The frequency deviation of the three strategies in scenario 1 of Example 2.
[0039] Figures 8 to 10 The unit power is the power of the three strategies in scenario 1 of Example 2.
[0040] Figures 11 to 13 The frequency deviation of the three strategies in scenario 2 of Example 2.
[0041] Figure 14 The VSPS unit power of the three strategies in scenario 2 of Example 2
[0042] Figure 15 This is a schematic diagram of the structure of the computer device of the present invention. Detailed Implementation
[0043] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.
[0044] Example 1:
[0045] like Figure 1 As shown: An economical frequency control method for a system considering vibration zone constraints, comprising the following steps:
[0046] Construct a power dynamic model containing a variable speed pumped storage unit (VSPS). The power dynamic model includes at least: a synchronous generator mechanical power deviation model, a VSPS unit converter control dynamic model, a transmission line power flow dynamic model and a node frequency dynamic model, and a traditional automatic generation control (AGC) area control error generation and power adjustment command dynamic model.
[0047] An economic optimization model for vibration avoidance is established. The economic optimization model aims to minimize the total system regulation cost. It adopts a quadratic regulation cost representation and introduces the VSPS unit vibration zone inequality constraint and the auxiliary variable γ for relaxing the power balance constraint to adapt to instantaneous power imbalance.
[0048] For the economic optimization model, a Lagrangian function is constructed and a distributed primal-dual solution algorithm is designed. The algorithm uses an adjustable positive step size parameter and a forward projection operator to ensure the non-negativity of the dual variable, and iteratively solves for the primal and dual variables.
[0049] By matching the power dynamics model with the steady-state conditions of the algorithm, a vibration-damping economical AGC that can be directly embedded into existing AGC structures is derived, implemented, and applied.
[0050] By explicitly embedding vibration zone constraints into the optimization model, online dynamic avoidance is achieved, significantly shortening the time the unit spends in the vibration zone. Simultaneously, global economic optimization is achieved while ensuring safety. The proposed model aims to minimize regulation costs and coordinates the output of each unit through a distributed algorithm, significantly reducing the total system regulation cost. Furthermore, it exhibits excellent engineering practicality and compatibility; the proposed control method only requires local modifications to the traditional automatic generation control structure, making it easy to integrate and deploy. Finally, a systematic design paradigm with clear physical interpretation is provided, proving the convergence of the gradient-optimized distributed algorithm and avoiding the drawbacks of black-box intelligent algorithms lacking theoretical support. This provides a reliable control scheme for the safe and economical operation of complex power systems.
[0051] In this embodiment, the synchronous generator mechanical power deviation model is a simplified first-order governor deviation model;
[0052] The dynamic model for converter control of VSPS units includes virtual inertia and damping terms, and is expressed by dynamic equations.
[0053] The power flow dynamic model of a transmission line, under the assumption of small angle difference, is described by a first-order dynamic equation, and the power flow deviation... The changes are caused by the node phase angle and line parameters This is determined and used as the information exchange quantity between adjacent nodes in distributed algorithms;
[0054] The node frequency dynamic model is represented by the oscillation equation;
[0055] The traditional automatic generation control (AGC) area control error generation and power adjustment command dynamic model includes:
[0056] For a specific node The mathematical definition of its regional control error; based on this error signal, the power adjustment command is calculated. The dynamic equation.
[0057] Among them, the vibration zone inequality constraint of VSPS unit is represented by lower and upper bounds, and is explicitly introduced in the form of inequality constraint in the economic optimization model to limit the VSPS output power from falling into the vibration hazard zone.
[0058] As a preferred embodiment of the above, the auxiliary variable γ is introduced to relax the power balance constraint of the entire network, and the relaxation term is used as a penalized or constrained variable in the optimization.
[0059] Distributed primal-dual solution algorithms include:
[0060] The distributed primal-dual gradient algorithm involves alternating or parallel iterative updates of primal and dual variables. The primal variables include governor control deviation, line power flow deviation, variable speed pumped storage unit power deviation, and frequency deviation. The dual variables are Lagrange multipliers defined according to the constructed optimization problem.
[0061] Both the original and dual variables have positive step sizes during the iteration process, and the projection operator is used to apply non-negative constraints to the corresponding dual variables.
[0062] Among them, the projection operator For: when or Time output Otherwise, output 0.
[0063] In this embodiment, the vibration damping economic AGC is:
[0064] By substituting the system frequency dynamics, power flow dynamics, and traditional AGC dynamics into the steady-state equation of the gradient algorithm, and pairing them up item by item at each node, the feasible controller parameter setting expression is obtained.
[0065] like Figure 2 As shown, this embodiment also includes a system economic frequency control system that considers vibration zone constraints. Using the method described above, the system includes:
[0066] The power dynamic model unit is used to construct a power dynamic model containing a variable speed pumped storage unit (VSPS). The power dynamic model includes at least: a synchronous generator mechanical power deviation model, a VSPS unit converter control dynamic model, a transmission line power flow dynamic model and a node frequency dynamic model, and a traditional automatic generation control (AGC) area control error generation and power adjustment command dynamic model.
[0067] The economic optimization model unit is used to establish an economic optimization model for vibration avoidance. The economic optimization model aims to minimize the total system regulation cost, adopts a quadratic regulation cost representation, and introduces the VSPS unit vibration zone inequality constraint and the auxiliary variable γ for relaxing the power balance constraint to adapt to instantaneous power imbalance.
[0068] The algorithm unit is used to construct the Lagrangian function and design a distributed primal-dual solution algorithm for the economic optimization model. The algorithm uses an adjustable positive step size parameter and uses a forward projection operator to ensure the non-negativity of the dual variable, and iteratively solves the primal and dual variables.
[0069] The vibration-damping economic AGC unit is used to derive and implement a vibration-damping economic AGC that can be directly embedded into existing AGC structures and applied by matching the power dynamic model with the steady-state conditions of the algorithm.
[0070] Example 2:
[0071] like Figure 3 As shown, this embodiment provides a system economic frequency control method considering the vibration zone constraints of a variable-speed pumped-storage unit. The method includes:
[0072] (1) Constructing a dynamic model of a power system including VSPS: Based on the traditional governor control model, power network flow equation and regional control error mechanism, key variables such as synchronous generator mechanical power deviation, VSPS unit active power output deviation and line flow deviation are defined, and a comprehensive dynamic model of the power system including synchronous generator dynamics, VSPS unit converter control dynamics, line flow dynamics and system frequency dynamics is established.
[0073] Model the power transmission network as a directed connected graph. . It is a bus set (representing a converged bus or control area). It is a transmission line set. The graph is arbitrarily assigned a direction, such that if ,but For the bus ,symbol refer to busbar The set, similarly, Indicates that bus set For ease of analysis, all variables below are defined as deviations from their nominal values.
[0074] 1) Synchronous generator control:
[0075] In traditional governor and turbine control models, valves adjust based on speed deviations or power variations. Since the time constant of the governor is much smaller than that of the turbine, this control structure can be simplified to a single-state variable, represented as: :
[0076] (1)
[0077] in, The time constant of the speed controller, This is the unit's adjustment coefficient.
[0078] 2) VSPS unit converter control:
[0079] Variable-speed pumped-storage units employ power converters that decouple rotor speed from grid frequency, enabling efficient operation over a wide speed range. However, this decoupling also prevents the rotor's kinetic energy from rapidly responding to frequency changes and converting into active power, resulting in a net reduction in system inertia and necessitating the addition of an auxiliary frequency control module. Therefore, virtual inertia control is applied in the converter control of variable-speed pumped-storage units.
[0080] (2)
[0081] in, This indicates the power deviation of the variable-speed pumped storage unit at busbar j. This represents the time constant of the converter. The proportional gain representing the controller. is the differential coefficient.
[0082] 3) Line power flow dynamics:
[0083] Assuming each node If the frequency deviation is small enough, then the line power flow deviation... This can be described by a set of dynamic equations:
[0084] (3)
[0085] Among them, parameters Determined by the nominal node voltage and line reactance, it is a fixed value and plays a key role in this dynamic process; This represents the voltage at bus j; Representative node The nominal value of the voltage phase angle.
[0086] 4) Frequency dynamics:
[0087] For each node ,set up This indicates its frequency deviation. Indicates the deviation from total load demand. Node The frequency dynamics are represented by the oscillation equation:
[0088] (4)
[0089] in, Indicates the generator's inertia. For nodes The damping constant.
[0090] 5) Traditional AGC control:
[0091] In traditional AGC control systems, power adjustment commands are used... To reduce the regional control error ACE to zero. For a specific node. The mathematical definition of its regional control error is: In the formula, This is the frequency deviation coefficient. Based on this error signal, the power adjustment command... The dynamic equation is:
[0092] (5)
[0093] in, This is the automatic generation control gain, which determines the response speed and amplitude of power adjustment commands generated by regional control errors. This process ensures that power generation matches load demand, thereby maintaining system frequency stability.
[0094] (2) Establish an economic optimization model for vibration avoidance: Based on the analysis of the dynamic equilibrium point and its corresponding optimization problem of the traditional automatic power generation control system, the vibration zone constraint of the variable speed pumped storage unit is defined, and the auxiliary variable γ is introduced to relax the power balance constraint to adapt to the power imbalance, and an economic optimization model for vibration avoidance is established.
[0095] The dynamic model of a power system can be summarized as follows:
[0096] (6)
[0097] (7)
[0098] (8)
[0099] (9)
[0100] (10)
[0101] Finding its equilibrium point can be transformed into finding the solution to the following traditional optimization problem:
[0102] (11)
[0103] (12)
[0104] (13)
[0105] (14)
[0106] For ease of derivation and expression, this paper uses a quadratic function to represent the adjustment cost:
[0107] (15)
[0108] From the perspective of optimization theory, equation (13) shows that traditional automatic power generation control relies solely on local units for regulation. Furthermore, the economic allocation coefficient of traditional automatic power generation control is a fixed value, making real-time optimization impossible, and it often neglects the vibration zone limitations of variable-speed pumped storage units. Therefore, this paper proposes a novel optimization problem that integrates frequency stability, economic operation, and equipment safety, called the vibration avoidance economic optimization model, as follows:
[0109] (16)
[0110] (17)
[0111] (18)
[0112] (19)
[0113] (20)
[0114] The vibration zone constraint is described by equation (19). and The defined safe operating range ensures the avoidance of vibration in variable-speed pumped-storage units. This range can be obtained by consulting the equipment manual or based on operating experience. By explicitly embedding the vibration zone constraint into the optimization model, online dynamic avoidance is achieved, greatly shortening the unit's dwell time in the vibration zone. Considering the vibration zone constraint of the variable-speed pumped-storage unit, the proposed vibration avoidance economic optimization problem introduces the relaxation power balance constraint equation (18), and uses auxiliary variables... To address power imbalances, the optimal solution to this problem represents the most economical operating point for the entire network. The proposed model aims to minimize regulation costs and significantly reduces the total system regulation cost by coordinating the output of each unit through a distributed algorithm. These key improvements will transform traditional automatic generation control from local regulation to system-level coordination, enabling global economic dispatch of inter-regional interconnections.
[0115] (3) Design a distributed gradient solution algorithm: Construct the Lagrangian function corresponding to the vibration avoidance economic optimization model, set a set of adjustable positive step size parameters, and use the forward projection operator to ensure that the dual variables satisfy the non-negativity constraint, so as to effectively handle the vibration zone inequality constraint in the dynamic iteration process and iteratively solve the original variables and dual variables.
[0116] Based on the novel optimization problem constructed, the Lagrange multiplier is defined. , , and The corresponding Lagrange function is constructed as follows:
[0117] (twenty one)
[0118] Based on the constructed Lagrangian function, the partial primal-dual gradient algorithms for solving the vibration avoidance economic optimization problem are summarized as follows:
[0119] (twenty two)
[0120] (twenty three)
[0121] (twenty four)
[0122] (25)
[0123] (26)
[0124] (27)
[0125] (28)
[0126] (29)
[0127] (30)
[0128] in, , , , , , , and All are positive step sizes; their values should be appropriately selected to ensure the stability and convergence of the algorithm. Operators Indicates forward projection operation: when or Time output Otherwise, output 0. This operator is used to apply nonnegativity constraints to the corresponding dual variables, thereby ensuring during the iteration of part of the primal-dual gradient algorithm. The aforementioned distributed gradient provides a convergent sequence of primal and dual variables and a steady-state matching condition for the subsequent derivation of the vibration avoidance economic AGC.
[0129] (4) Vibration-avoidance economic AGC: By matching the dynamic system model with the steady-state conditions of the original-dual gradient algorithm, the step size and intermediate variables are designed, and the mathematical equivalence relationship between the offline optimization problem and the online closed-loop control is established, thereby designing an economic automatic power generation control system that integrates vibration zone constraints and has a distributed structure.
[0130] By matching the steady-state conditions of the dynamic system and the gradient algorithm, the improved AGC is derived. By comparing and confirming equations (3) and (23), and (4) and (26) respectively, we can obtain:
[0131] (31)
[0132] (32)
[0133] Combining equation (1) and equation (24), we get:
[0134] (33)
[0135] Differentiating both sides of the equation with respect to time yields:
[0136] (34)
[0137] remember:
[0138] (35)
[0139] (36)
[0140] Substituting equations (1), (4), (5), and (27) into equation (34), we get:
[0141] (37)
[0142] In formula (37) Since the coefficient before is 0, we can obtain:
[0143] (38)
[0144] Again The coefficient before is 0:
[0145] (39)
[0146] By combining equations (38) and (39), we can derive... The expression:
[0147] (40)
[0148] Will Setting the coefficient before to 0 and substituting it into equation (39), we get:
[0149] (41)
[0150] Re- Substituting the expression back into equation (33), we get The expression:
[0151] (42)
[0152] Similarly, combining equation (2) and equation (25), we get:
[0153] (43)
[0154] Following the same steps, we can solve for... , , The expression:
[0155] (44)
[0156] (45)
[0157] (46)
[0158] Substituting the above results into equations (22)-(30), we get:
[0159] (47)
[0160] (48)
[0161] (49)
[0162] (50)
[0163] (51)
[0164] (52)
[0165] (53)
[0166] (54)
[0167] Vibration-avoidance economic AGC possesses excellent engineering practicality and compatibility, requiring only localized modifications to traditional automatic generation control structures, making it easy to integrate and deploy. By combining the vibration avoidance economic optimization model with the power system dynamic model, and matching the steady-state conditions of the gradient algorithm with the system dynamic equations, an improved control method that can be directly embedded into existing AGC structures is obtained. This provides a systematic design paradigm with clear physical interpretation, and proves the convergence of the gradient-optimized distributed algorithm, avoiding the drawbacks of black-box intelligent algorithms lacking theoretical support. It achieves the unification of frequency stability, vibration zone avoidance, and economic dispatch, providing a clear and implementable mathematical expression for real-time system control.
[0168] Example explanation:
[0169] To verify the effectiveness of the proposed vibration-avoidance economic AGC, we conducted a case study on a four-region interconnected power system. For example... Figure 4 As shown, areas 1-3 contain only traditional thermal power generating units, while area 4 contains one thermal power generating unit and one variable-speed pumped-storage unit. When At that time, the load in region 4 underwent a step change ( ).
[0170] In this example, the vibration zone of the variable-speed pumped-storage unit is defined as the power output range between 0.5 pu and 0.65 pu. Operation within this range is considered undesirable due to the risk of mechanical vibration. To evaluate the performance of the control strategy under different initial conditions, we designed two typical simulation scenarios:
[0171] Scenario 1 (S1): The variable speed pumped storage unit initially operates at 0.4 pu, which is below the lower boundary of the vibration zone.
[0172] Scenario 2 (S2): The variable speed pumped storage unit initially operates at 0.7 pu, which is higher than the upper boundary of the vibration zone.
[0173] In each scenario, this example will compare three control strategies:
[0174] Traditional automatic power generation control: standard control strategy;
[0175] Vibration-damping automatic power generation control: Based on the standard strategy, vibration zone constraints are taken into account;
[0176] Vibration-avoidance economic automatic power generation control: This paper proposes a control strategy that simultaneously considers vibration zone constraints and overall economic efficiency.
[0177] Table 1 Performance comparison of the three strategies in different scenarios
[0178]
[0179] Figures 5 to 7 The middle part represents the frequency deviation of the three strategies in scenario 1. Figures 5 to 7 These correspond to traditional automatic power generation control, vibration-damping automatic power generation control, and vibration-damping economical automatic power generation control, respectively. Figures 8 to 10 The unit power for the three strategies in scenario 1 ( Figures 8 to 10 These correspond to traditional automatic power generation control, vibration-damping automatic power generation control, and vibration-damping economical automatic power generation control, respectively. Figures 11 to 13 The frequency deviation of the three strategies in scenario 2 ( Figures 11 to 13 These correspond to traditional automatic power generation control, vibration-damping automatic power generation control, and vibration-damping economical automatic power generation control, respectively. Figure 14 VSPS unit power for three strategies in scenario 2 ( Figure 14 (A through C correspond to traditional automatic power generation control, vibration-avoidance automatic power generation control, and vibration-avoidance economic automatic power generation control, respectively). Table 1 compares and summarizes the key indicators of the three strategies under different scenarios. Regarding safety: In scenario 1, the vibration-avoidance economic automatic power generation control strategy reduces the residence time in the vibration zone of the variable-speed pumped storage unit to only 1.78 seconds, a reduction of 97.1% and 71.0% compared to the traditional strategy (58.56 seconds) and the vibration avoidance strategy (5.48 seconds), respectively. In scenario 2, the residence time is only 0.14 seconds, a reduction of 99.8% and 95.9% compared to the traditional strategy and the vibration avoidance strategy, respectively. Regarding economy: The vibration-avoidance economic automatic power generation control strategy achieves the lowest adjustment cost in both scenarios, reducing it by 57.33% compared to the traditional strategy. The data in the table show that the proposed vibration-avoidance economic automatic power generation control strategy exhibits optimal performance in both scenarios.
[0180] Please see Figure 15 The diagram shows a structural schematic of a computer device provided in an embodiment of this application. An embodiment of this application provides a computer device 400, including a processor 410 and a memory 420. The memory 420 stores a computer program executable by the processor 410. When the computer program is executed by the processor 410, it performs the method described above.
[0181] This application embodiment also provides a storage medium 430, on which a computer program is stored, and the computer program is executed by a processor 410 to perform the above method.
[0182] The storage medium 430 can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read Only Memory (EPROM), Programmable Red-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk.
[0183] In the description of this invention, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. "A plurality of" means two or more, unless otherwise explicitly specified.
[0184] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.
[0185] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," 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 present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.
[0186] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing a particular logical function or process, and the scope of the preferred embodiments of the invention includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as will be understood by those skilled in the art to which embodiments of the invention pertain.
[0187] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.
[0188] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.
[0189] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.
[0190] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.
Claims
1. A system economic frequency control method considering vibration region constraints, characterized in that, Includes the following steps: A power dynamic model containing a variable speed pumped storage unit (VSPS) is constructed. The power dynamic model includes at least: a synchronous generator mechanical power deviation model, a VSPS unit converter control dynamic model, a transmission line power flow dynamic model and a node frequency dynamic model, and a traditional automatic generation control (AGC) area control error generation and power adjustment command dynamic model. An economic optimization model for vibration avoidance is established. The economic optimization model aims to minimize the total system regulation cost. It adopts a quadratic regulation cost representation and introduces the VSPS unit vibration zone inequality constraint and the auxiliary variable γ for relaxing the power balance constraint to adapt to instantaneous power imbalance. For the aforementioned economic optimization model, a Lagrangian function is constructed and a distributed primal-dual solution algorithm is designed. The algorithm uses an adjustable positive step size parameter and utilizes a forward projection operator to ensure the non-negativity of the dual variable, and iteratively solves for the primal and dual variables. By matching the power dynamic model with the steady-state conditions of the algorithm, a vibration-damping economical AGC that can be directly embedded into existing AGC structures is derived, implemented, and applied.
2. The method of claim 1, wherein, The synchronous generator mechanical power deviation model is a simplified first-order governor deviation model. The VSPS unit converter control dynamic model includes virtual inertia and damping terms, and is expressed by dynamic equations; The power flow dynamic model of the transmission line is described by a first-order dynamic equation under the assumption of small angle difference, and the power flow deviation is... The changes are caused by the node phase angle and line parameters This is determined and used as the information exchange quantity between adjacent nodes in distributed algorithms; The node frequency dynamic model is represented by the oscillation equation; The traditional automatic generation control (AGC) area control error generation and power adjustment command dynamic model includes: For a specific node The mathematical definition of its regional control error; based on this error signal, the power adjustment command is calculated. The dynamic equation.
3. The system economic frequency control method considering vibration zone constraints according to claim 1, characterized in that, The vibration zone inequality constraints of the VSPS unit are represented by lower and upper bounds, and are explicitly introduced in the form of inequality constraints in the economic optimization model to limit the VSPS output power from falling into the vibration hazard zone.
4. The system economic frequency control method considering vibration zone constraints according to claim 1, characterized in that, The auxiliary variable γ is introduced to relax the power balance constraint of the entire network. The relaxation term is used as a penalized or constrained variable in the optimization.
5. The system economic frequency control method considering vibration zone constraints according to claim 2, characterized in that, The distributed primal-dual solution algorithm includes: The distributed primal-dual gradient algorithm includes alternating or parallel iterative updates of primal and dual variables. The primal variables include governor control deviation, line power flow deviation, variable speed pumped storage unit power deviation, and frequency deviation. The dual variables are Lagrange multipliers defined according to the constructed optimization problem. Both the original and dual variables have positive step sizes during the iteration process, and the projection operator is used to apply non-negative constraints to the corresponding dual variables.
6. The system economic frequency control method considering vibration zone constraints according to claim 5, characterized in that, The projection operator For: when or Time output Otherwise, output 0.
7. The system economic frequency control method considering vibration zone constraints according to claim 1, characterized in that, The vibration damping economic AGC is: By substituting the system frequency dynamics, power flow dynamics, and traditional AGC dynamics into the steady-state equation of the gradient algorithm, and pairing them up item by item at each node, the feasible controller parameter setting expression is obtained.
8. A system-economic frequency control system considering vibration zone constraints, characterized in that, Using the method of any one of claims 1 to 7, the system comprises: The power dynamic model unit is used to construct a power dynamic model containing a variable speed pumped storage unit (VSPS). The power dynamic model includes at least: a synchronous generator mechanical power deviation model, a VSPS unit converter control dynamic model, a transmission line power flow dynamic model and a node frequency dynamic model, and a traditional automatic generation control (AGC) area control error generation and power adjustment command dynamic model. The economic optimization model unit is used to establish an economic optimization model for vibration avoidance. The economic optimization model aims to minimize the total system regulation cost, adopts a quadratic regulation cost representation, and introduces VSPS unit vibration zone inequality constraints and auxiliary variable γ for relaxing power balance constraints to adapt to instantaneous power imbalance. The algorithm unit is used to construct a Lagrangian function and design a distributed primal-dual solution algorithm for the economic optimization model. The algorithm uses an adjustable positive step size parameter and a forward projection operator to ensure the non-negativity of the dual variables, and iteratively solves for the primal and dual variables. The vibration-damping economic AGC unit is used to derive and implement a vibration-damping economic AGC that can be directly embedded into existing AGC structures by matching the power dynamic model with the steady-state conditions of the algorithm, and then apply it.
9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1-7.
10. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method as described in any one of claims 1-7.