Parameter optimization methods and equipment for improving the dynamic reactive power characteristics of static synchronous condensers.
By constructing a dynamic reactive power model of a static synchronous condenser and a simulated excitation system, and using artificial intelligence algorithms to optimize parameters, the problem of insufficient adaptability of the static synchronous condenser to the power grid was solved, and its reactive power support capability during power grid faults was improved.
Patent Information
- Application Number
- CN202510013954.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-06
- Publication Date
- 2025-10-28
- Estimated Expiration
- 2045-01-06
AI Technical Summary
The dynamic reactive power characteristics of existing static synchronous condensers are not fully adapted to the actual power grid operation. Traditional parameter optimization methods fail to effectively consider the coupling effect between parameters, resulting in insufficient reactive power support capacity during power grid faults.
A dynamic reactive power model of a static synchronous condenser and a simulated excitation system is constructed. By using evaluation indicators that characterize reactive power regulation performance, a key parameter identification model is established. Artificial intelligence algorithms are used to optimize the parameters, determine the optimization range, and improve the matching degree between the synchronous condenser and the power grid.
It reduces the difficulty of parameter optimization, improves the dynamic reactive power support capability of static synchronous condensers during grid faults, and enhances voltage stability.
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Figure CN119921347B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of power technology, and specifically relates to a parameter optimization method and device for improving the dynamic reactive power characteristics of a static synchronous condenser. Background Technology
[0002] With the continuous advancement of the "dual carbon" target and the in-depth construction of new power systems, the installed capacity of new energy has expanded rapidly, gradually becoming one of the main power sources in some regions. However, large-scale new energy power transmission systems often exhibit the characteristics of "strong DC and weak AC," with weak local power grid structures and severely compressed generation space for synchronous generators. Voltage stability problems caused by weak reactive power support during grid faults are becoming increasingly prominent. New synchronous condensers have strong dynamic reactive power support capabilities and can provide necessary voltage support during system faults. However, traditional synchronous condensers are rotating devices, resulting in high operating losses, high maintenance costs, and slower response speeds than static var compensators (SGMCs). Therefore, some scholars have proposed static synchronous condensers based on SVG structures. These SGMCs add supercapacitors to the DC side of the traditional SVG structure, effectively creating a large-capacity energy storage system. Then, they employ grid-based control to make their external characteristics similar to synchronous condensers, but with lower costs and all components being static parts, resulting in lower losses and easier operation and maintenance.
[0003] However, the dynamic reactive power characteristics of static synchronous condensers are closely related to their simulated electromagnetic parameters and simulated excitation parameters. Their factory model parameters are not fully compatible with the actual power grid operation. It is urgent to carry out parameter optimization methods for static synchronous condensers to comprehensively improve their active support capability for the power grid. Reference [1] identifies the key parameters affecting the reactive power characteristics of the condenser based on the simplified model of the condenser and optimizes the parameters based on experimental analysis. References [2-4] analyze the influence of different parameters such as the d-axis subtransient reactance, open circuit and short circuit time constant, excitation multiple, excitation reactance, excitation resistance and damping resistance of the condenser on the dynamic reactive power characteristics. However, most of the above studies are carried out for traditional condensers and do not consider the coupling effect between many parameters.
[0004] References:
[0005] Pan Xueping, Xu Yi, Zhao Tianqi, et al. Joint optimization of excitation parameters of synchronous condenser and step-up transformer considering system stability boundary [J]. Power System Protection and Control, 2024, 52(08):45-54. DOI:10.19783 / j.cnki.pspc.231472.
[0006] Yuan Bin, Li Hui, Xiang Xueyi, et al. Staged excitation control optimization strategy considering the saturation parameters of the synchronous condenser [J]. Power System Protection and Control, 2023, 51(15):42-54. DOI:10.19783 / j.cnki.pspc.221732.
[0007] Sun Shuangkui, Shi Junjun, Zhang Cunchao, et al. Adaptive optimization of dynamic performance parameters of a novel distributed synchronous condenser [J]. Power Grid and Clean Energy, 2023, 39(04):91-98.
[0008] Fu Min, Cui Cancan, Wang Luyao, et al. Research on parameter optimization model of distributed synchronous condenser excitation system [J]. Journal of Electrical Machines and Control, 2022, 26(02):102-110. DOI:10.15938 / j.emc.2022.02.011. Summary of the Invention
[0009] The purpose of this invention is to provide a parameter optimization method and device for improving the dynamic reactive power characteristics of a static synchronous condenser, which can identify and optimize key parameters affecting the dynamic reactive power characteristics of the condenser, thereby reducing the difficulty of parameter optimization.
[0010] To achieve the above objectives, the solution of the present invention is:
[0011] A parameter optimization method for improving the dynamic reactive power characteristics of a static synchronous condenser includes the following steps:
[0012] Step 1: Construct a dynamic reactive power model of the static synchronous condenser and the simulated excitation system, and determine all parameters;
[0013] Step 2 proposes evaluation indicators to characterize the reactive power regulation performance of static synchronous condensers, providing direction for the optimization of static synchronous condenser parameters;
[0014] Step 3: Establish key parameter identification models for static synchronous condensers at different time scales, determine the parameters affecting the reactive power characteristics of static synchronous condensers in different application scenarios, and reduce the time for parameter optimization.
[0015] Step 4: Determine the optimization range of key parameters based on the system stability boundary;
[0016] Step 5: Use artificial intelligence algorithms to optimize the parameters so that the static synchronous condenser has the highest matching degree with the current power grid.
[0017] In step 1 above, the transient mathematical model of the electromagnetic part of the static synchronous condenser is characterized by the following equation:
[0018]
[0019] Where, X′ d and X′ d ′ represents the d-axis simulated transient reactance and d-axis simulated subtransient reactance of the synchronous modulator, respectively; T d ′0 and T d"0" represents the d-axis simulated transient time constant and the d-axis simulated subtransient time constant, respectively; E′ q and E′ q ′ represents the simulated transient potential along the q-axis and the simulated subtransient potential along the q-axis of the synchronous condenser, respectively; T q "0 is the simulated subtransient time constant of the q-axis of the synchronous condenser; E′" d ′ represents the simulated subtransient potential along the d-axis of the synchronous camera; i d and i q These are the d-axis current and q-axis current of the synchronous condenser, respectively.
[0020] The analog excitation system in a static synchronous condenser comprises three key components: an analog voltage regulator, an analog excitation winding transfer function, and an analog negative feedback circuit. Their models are as follows:
[0021] The analog voltage regulator model is as follows:
[0022]
[0023] Among them, T a K represents the time constant of the analog voltage regulator. a U is the amplification constant of the analog voltage regulator; ref U PSS U R Given the system's guide voltage, additional control voltage, and system output voltage;
[0024] The simulated excitation winding transfer function model is as follows.
[0025]
[0026] Among them, E f To simulate the excitation electromotive force; T e To simulate the time constant of the excitation winding; K e To simulate the amplification factor of the excitation winding;
[0027] The model for simulating a negative feedback loop is as follows:
[0028]
[0029] Among them, T f The time constant for simulating a negative feedback loop; K f To simulate the amplification factor of the negative feedback loop; U F This is to simulate negative feedback voltage.
[0030] In step 2 above, the dynamic reactive current gain coefficient K is proposed. iQ The reactive power support capability of a static synchronous condenser is characterized by the following expression:
[0031]
[0032] Where, Δi d , ΔU R These are the changes in current and voltage of a stationary synchronous condenser, respectively.
[0033] According to Δi d and ΔU R The functional relationship between them
[0034] Δi d =f(d-axis parameter and q-axis parameter; T) a ,T e ,T f ,K a ,K e ,K f |ΔU R )
[0035] Among them, T a T e T f K a K e K f To simulate the parameters to be identified in the excitation system;
[0036] Therefore,
[0037]
[0038] K iQ The larger the value, the stronger the dynamic reactive power support capability of the static synchronous condenser.
[0039] In step 3 above, the expression for the key parameter identification model of the static synchronous condenser is:
[0040]
[0041] in, For the sensitivity of dynamic reactive current gain coefficient, K iQ T is the dynamic reactive current gain coefficient. a T e T f K a K e K f To simulate the parameters to be identified in the excitation system;
[0042] If the parameter θ satisfies the following formula, then the parameter is a critical parameter.
[0043]
[0044] in, This is the sensitivity threshold value for the dynamic reactive current gain coefficient.
[0045] In step 4 above, according to the following formula,
[0046] i d =A·U R
[0047] Among them, i d The current of the synchronous condenser is the d-axis current; A is the key matrix containing d-axis parameters, q-axis parameters, and parameters to be identified in the simulated excitation system; U R This refers to the system output voltage.
[0048] Let the real part of the eigenvalue of A be λ, then,
[0049] λ = Re(lambda(A))
[0050] If a parameter in the key matrix A is adjusted so that λ is exactly 0, then the corresponding value of that parameter is its upper limit.
[0051] In step 5 above, the objective function for parameter optimization is,
[0052]
[0053] Among them, K iQ θ is the dynamic reactive current gain coefficient; 关键参数 For the key parameters of the stationary synchronous camera, ΔU R The voltage change of the stationary synchronous condenser;
[0054] Artificial intelligence algorithms are used to solve the problem and obtain the final optimized parameters.
[0055] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor; when the processor executes the computer program, it implements the steps of the parameter optimization method for improving the dynamic reactive power characteristics of a static synchronous condenser as described above.
[0056] A computer-readable storage medium storing a computer program; when executed by a processor, the computer program implements the steps of the parameter optimization method for improving the dynamic reactive power characteristics of a static synchronous condenser as described above.
[0057] Following the above approach, this invention first constructs a dynamic reactive power model of the static synchronous condenser and the excitation system (simulation) to determine all parameters. Then, it proposes evaluation indicators characterizing the reactive power regulation performance of the static synchronous condenser, providing direction for parameter optimization. Next, it establishes key parameter identification models for the static synchronous condenser at different time scales to determine the parameters affecting its reactive power characteristics in different application scenarios, reducing the time required for parameter optimization. Then, it determines the optimization range of key parameters based on the system stability boundary. Finally, it uses artificial intelligence algorithms to optimize the parameters, maximizing the matching degree of the static synchronous condenser to the current power grid. This method identifies and optimizes key parameters affecting the dynamic reactive power characteristics of the synchronous condenser, reducing the difficulty of parameter optimization. Attached Figure Description
[0058] Figure 1 This is a flowchart of the present invention. Detailed Implementation
[0059] The technical solution and beneficial effects of the present invention will be described in detail below with reference to the accompanying drawings.
[0060] like Figure 1 As shown, this invention provides a parameter optimization method for improving the dynamic reactive power characteristics of a static synchronous condenser, comprising the following steps:
[0061] S1. Construct a dynamic reactive power model of the static synchronous condenser and excitation system (simulation) to determine all parameters;
[0062] S101, the transient mathematical model of the electromagnetic part of the static synchronous condenser can be characterized by the following differential equation.
[0063]
[0064] In the formula: X′ d and X′ d ′ represents the d-axis simulated transient reactance and d-axis simulated subtransient reactance of the synchronous modulator, respectively; T d ′0 and T d "0" represents the d-axis simulated transient time constant and the d-axis simulated subtransient time constant, respectively; E′ q and E′ q ′ represents the simulated transient potential along the q-axis and the simulated subtransient potential along the q-axis of the synchronous condenser, respectively; T q "0 is the simulated subtransient time constant of the q-axis of the synchronous condenser; E′" d ′ represents the simulated subtransient potential along the d-axis of the synchronous camera; i d and i q These are the d-axis current and q-axis current of the synchronous condenser, respectively.
[0065] As can be seen from equation (1), the parameters of a stationary synchronous condenser mainly include d-axis parameters and q-axis parameters.
[0066] S102, the static synchronous condenser also includes an analog excitation system, which comprises three key components: an analog voltage regulator, an analog excitation winding transfer function, and an analog negative feedback circuit. Their models are as follows:
[0067] Analog voltage regulator model
[0068]
[0069] In the formula: T a K represents the time constant of the analog voltage regulator. a U is the amplification constant of the analog voltage regulator; ref U PSS U R Given the system's guide voltage, additional control voltage, and system output voltage.
[0070] Simulated excitation winding transfer function model
[0071]
[0072] Where: E f To simulate the excitation electromotive force; T e To simulate the time constant of the excitation winding; K e This is the amplification factor for simulating the excitation winding.
[0073] Simulated negative feedback loop model
[0074]
[0075] In the formula: T f The time constant for simulating a negative feedback loop; K f To simulate the amplification factor of the negative feedback loop; U F This is to simulate negative feedback voltage.
[0076] The parameters that need to be identified are the time constant and amplification factor of three key components: T a T e T f K a K e K f .
[0077] S2. An evaluation index is proposed to characterize the reactive power regulation performance of synchronous condensers, providing direction for the optimization of synchronous condenser parameters;
[0078] The dynamic reactive current gain coefficient K is proposed. iQThe reactive power support capability of a static synchronous condenser can be expressed as:
[0079]
[0080] In the formula, Δi d , ΔU R These represent the changes in current and voltage for a stationary synchronous condenser, respectively.
[0081] By combining equations (1) to (5), we can see that Δi d and ΔU R There is a functional relationship between them, and the parameters of the synchronous phase adjuster mainly include d-axis parameters, q-axis parameters, and the parameter T to be identified in the simulated excitation system. a T e T f K a K e K f ,
[0082] Δi d =f(d-axis parameter and q-axis parameter; T) a ,T e ,T f ,K a ,K e ,K f |ΔU R (6) Substituting into equation (5), the dynamic reactive current gain coefficient can be obtained as:
[0083]
[0084] K iQ The larger the value, the stronger the dynamic reactive power support capability of the static synchronous condenser.
[0085] S3. Establish key parameter identification models for static synchronous condensers at different time scales, determine the parameters affecting the reactive power characteristics of synchronous condensers in different application scenarios, and reduce the time for parameter optimization.
[0086] The parameters in a static synchronous condenser include the amplification factor and time constant of three key components: d-axis parameters, q-axis parameters, and the analog excitation system. However, not all parameters play a crucial role in the reactive power characteristics of the condenser. When optimizing parameters, only the key parameters need to be optimized, while the remaining parameters can be taken as standard values.
[0087] Since equation (7) characterizes the reactive power support capability of a stationary synchronous condenser, changes in the parameters to be optimized will lead to changes in the dynamic reactive current gain coefficient K shown in equation (7). iQ The significant changes indicate that this parameter is critical. Therefore, a key parameter identification index based on the sensitivity of the dynamic reactive current gain coefficient is proposed:
[0088]
[0089] If a parameter θ satisfies equation (9), then the parameter is a key parameter.
[0090]
[0091] In the formula, The sensitivity threshold value of the dynamic reactive current gain coefficient can be determined comprehensively based on the specific power network and the actual identification accuracy.
[0092] S4. Determine the optimization range of key parameters based on the system stability boundary;
[0093] To further improve the efficiency of parameter optimization, the optimization range of the parameters is first determined. This embodiment proposes a method for determining the upper limit of key parameters based on the system stability boundary. According to stability theory, the system loses stability when the real part of the system characteristic equation is greater than 0. Connecting equations (1) to (5), we can obtain...
[0094] i d =A·U R (10)
[0095] A represents the included d-axis parameters, q-axis parameters, and excitation system parameters T to be identified. a T e T f K a K e K f Key matrix.
[0096] Without loss of generality, let the real part of the eigenvalue of A be λ, then:
[0097] λ=Re(lamda(A)) (11)
[0098] Adjusting the parameter θ so that λ is exactly 0, the corresponding value of θ is its upper limit.
[0099] S5. The parameters are optimized using artificial intelligence algorithms to ensure the highest degree of matching between the static synchronous condenser and the current power grid.
[0100] Since equation (7) characterizes the reactive power support capability of the static synchronous condenser, K iQ The larger the value, the stronger the dynamic reactive power support capability of the synchronous condenser. The objective function for parameter optimization is:
[0101]
[0102] The above model is solved using artificial intelligence algorithms to obtain the final optimized parameters.
[0103] This invention also provides a computer device, including a processor and a memory configured to store a computer program capable of running on the processor; wherein, when the processor is configured to run the computer program, it executes the method steps described in the foregoing embodiments.
[0104] In practical applications, the aforementioned processor includes a Field-Programmable Gate Array (FPGA), and the processor can be a Central Processing Unit (CPU) or a Digital Signal Processor (DSP). It is understood that for different devices, the electronic devices used to implement the functions of the aforementioned processor can also be other types, and this embodiment of the invention does not impose specific limitations.
[0105] The aforementioned memory can be volatile memory, such as random-access memory (RAM); or non-volatile memory, such as read-only memory (ROM), flash memory, hard disk drive (HDD), or solid-state drive (SSD); or a combination of the above types of memory, and provides instructions and data to the processor.
[0106] In an exemplary embodiment, the present invention also provides a computer-readable storage medium for storing a computer program.
[0107] Optionally, the computer-readable storage medium can be applied to any of the methods in the embodiments of the present invention, and the computer program causes the computer to execute the corresponding processes implemented by the processor in the various methods of the embodiments of the present invention. For the sake of brevity, these will not be described in detail here.
[0108] In the several embodiments provided by this invention, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.
[0109] 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 implemented 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. The solutions in the embodiments of the present invention can be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.
[0110] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts 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, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts 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.
[0111] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0112] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.
[0113] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.
[0114] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.
Claims
1. A parameter optimization method for improving the dynamic reactive power characteristics of a stationary synchronous condenser, characterized in that... Includes the following steps: Step 1: Construct a dynamic reactive power model of the static synchronous condenser and the simulated excitation system, and determine all parameters; Step 2 proposes evaluation indicators to characterize the reactive power regulation performance of static synchronous condensers, providing direction for the optimization of static synchronous condenser parameters; Step 3: Establish key parameter identification models for static synchronous condensers at different time scales, determine the parameters affecting the reactive power characteristics of static synchronous condensers in different application scenarios, and reduce the time for parameter optimization. Step 4: Determine the optimization range of key parameters based on the system stability boundary; Step 5: Use artificial intelligence algorithms to optimize the parameters to maximize the matching degree of the static synchronous condenser with the current power grid. In step 2, the dynamic reactive current gain coefficient K is proposed. iQ The reactive power support capability of a static synchronous condenser is characterized by the following expression: Where, Δi d ΔU R These are the changes in current and voltage of a stationary synchronous condenser, respectively. According to Δi d and ΔU R The functional relationship between them Δi d =f(d-axis parameter and q-axis parameter; T) a ,T e ,T f ,K a ,K e ,K f |ΔU R ) Among them, T a T e T f , K a , K e , K f To simulate the parameters to be identified in the excitation system; Therefore, K iQ The larger the value, the stronger the dynamic reactive power support capability of the static synchronous condenser. In step 3, the expression for the key parameter identification model of the static synchronous conversion camera is: in, For the sensitivity of dynamic reactive current gain coefficient, K iQ T is the dynamic reactive current gain coefficient. a T e T f K a K e K f To simulate the parameters to be identified in the excitation system; If the parameter θ satisfies the following formula, then the parameter is a critical parameter. in, This is the sensitivity threshold value for the dynamic reactive current gain coefficient.
2. The method as described in claim 1, characterized in that: In step 1, the transient mathematical model of the electromagnetic part of the static synchronous condenser is characterized by the following equation: Where, X′ d and X″ d These are the d-axis simulated transient reactance and d-axis simulated subtransient reactance of the synchronous condenser, respectively; T′ d0 and T″ d0 These are the d-axis simulated transient time constant and the d-axis simulated subtransient time constant of the synchronous condenser, respectively; E′ q and E″ q These represent the simulated transient potential along the q-axis and the simulated subtransient potential along the q-axis of the synchronous condenser, respectively; T″ q0 E″ is the simulated subtransient time constant for the q-axis of the synchronous condenser. d To simulate the subtransient potential of the d-axis of the synchronous camera; i d and i q These are the d-axis current and q-axis current of the synchronous condenser, respectively. The analog excitation system in a static synchronous condenser comprises three key components: an analog voltage regulator, an analog excitation winding transfer function, and an analog negative feedback circuit. Their models are as follows: The analog voltage regulator model is as follows: Among them, T a K represents the time constant of the analog voltage regulator. a U is the amplification constant of the analog voltage regulator; ref U PSS U R Given the system's guide voltage, additional control voltage, and system output voltage; The simulated excitation winding transfer function model is as follows. Among them, E f To simulate the excitation electromotive force; T e To simulate the time constant of the excitation winding; K e To simulate the amplification factor of the excitation winding; The model for simulating a negative feedback loop is as follows: Among them, T f The time constant for simulating a negative feedback loop; K f To simulate the amplification factor of the negative feedback loop; U F This is to simulate negative feedback voltage.
3. The method as described in claim 1, characterized in that: In step 4, according to the following formula, i d =A·U R Among them, i d The current of the synchronous condenser is the d-axis current; A is the key matrix containing d-axis parameters, q-axis parameters, and parameters to be identified in the simulated excitation system; U R This refers to the system output voltage. Let the real part of the eigenvalue of A be λ, then, λ = Re(lambda(A)) If a parameter in the key matrix A is adjusted so that λ is exactly 0, then the corresponding value of that parameter is its upper limit.
4. The method as described in claim 1, characterized in that: In step 5, the objective function for parameter optimization is, Among them, K iQ θ is the dynamic reactive current gain coefficient; 关键参数 For the key parameters of the stationary synchronous camera, ΔU R The voltage change of the stationary synchronous condenser; Artificial intelligence algorithms are used to solve the problem and obtain the final optimized parameters.
5. 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 steps of the parameter optimization method for improving the dynamic reactive power characteristics of a static synchronous condenser as described in any one of claims 1 to 4.
6. A computer-readable storage medium storing a computer program; characterized in that: When the computer program is executed by the processor, it implements the steps of the parameter optimization method for improving the dynamic reactive power characteristics of a static synchronous condenser as described in any one of claims 1 to 4.
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