A method for calculating the capacity requirement of a static frequency converter for starting a phase modifier

Abstract

The present disclosure provides a method for calculating the capacity requirement of a static frequency converter for starting a phase modifier, which utilizes the known parameters provided by the phase modifier manufacturer, such as the rotor wind friction loss, bearing friction loss and electrical loss at the rated speed, and combines the inertia of the unit to construct an accurate relationship model between the total loss and the speed during the starting process. Then, based on the energy balance equation, the static frequency converter capacity is quantitatively associated with the starting time through integral operation, and the minimum capacity configuration that meets the preset starting time requirement is found through iterative calculation. This method realizes the scientific and quantitative calculation of the capacity of the static frequency converter, fundamentally avoids the problem of overdesign or insufficient capacity caused by relying on experience estimation in traditional engineering design, ensures the reliability and timeliness of the starting process, and effectively optimizes the equipment selection and engineering cost.

Description

Technical Field

[0001] This invention relates to the field of synchronous motor technology, and in particular to a method for calculating the capacity requirements of a static frequency converter suitable for starting a synchronous condenser. Background Technology

[0002] As a type of grid-connected synchronous motor, the synchronous condenser plays a crucial role in supporting transient reactive power / voltage and rotational inertia in the power system. However, since it does not have the drive of a prime mover, it needs to be driven and started by a coaxial motor or by a frequency converter to achieve variable frequency starting.

[0003] The Static Variable Frequency (SFC) starter is a current-source inverter. It typically uses semi-controlled devices such as thyristors to convert mains AC power into continuously adjustable AC power. The inverter's output is connected to the stator windings of the synchronous condenser, forming a rotating stator magnetic field. This, combined with the DC excitation current in the rotor windings, achieves coordinated control, gradually increasing the output AC frequency from rest to start the synchronous condenser. The SFC offers advantages such as stepless speed regulation, smooth starting, and fast response during the starting process of synchronous condensers. It significantly reduces the inrush current during startup and has become the primary starting method for large-capacity synchronous condensers. Summary of the Invention

[0004] A first aspect of this disclosure provides a method for calculating the capacity requirement of a static frequency converter suitable for starting a synchronous condenser, comprising: Obtain the input parameters of the synchronous condenser, including the rated speed and the rotor-air friction loss at the rated speed. Friction loss of thrust bearing and main bearing at rated speed Electrical losses of a synchronous condenser at rated speed And the moment of inertia of the camera; Based on the input parameters, the relationship between the total loss and the rotational speed during the startup process of the synchronous condenser is calculated. The total loss includes rotor-air friction loss, bearing friction loss and electrical loss. Set the initial capacity of the static inverter; Using the relationship between total loss and rotational speed, the starting time required for the synchronous condenser to accelerate from standstill to rated speed under the capacity of the static inverter is calculated by integral calculation. The startup time is compared with the preset startup time requirement. If the startup time does not meet the requirement, the capacity of the static inverter is increased, and the integration calculation and comparison steps are repeated until the startup time meets the requirement.

[0005] In conjunction with the first aspect, , and Based on rated speed The loss was obtained by fitting the following data, specifically: , , , in, Indicates the rated speed Friction loss between the lower rotor and air. Indicates the rated speed Lower bearing friction loss, Indicates the rated speed Lower electrical losses This is the actual rotational speed.

[0006] In conjunction with the first aspect, the relationship between the total loss and the rotational speed is calculated using the following formula: .

[0007] In conjunction with the first aspect, the integral operation is based on the following formula: , in, Start-up time To adjust the camera to the rated speed required for startup, To provide starting electromagnetic torque for the camera, To overcome the resistance torque during the start-up process of the synchronous condenser, This refers to the output power of the static frequency converter. For rotational inertia, ω is the angular acceleration of the rotor.

[0008] In conjunction with the first aspect, the output power of the static inverter With rotational speed Proportional, satisfying: , in, This refers to the capacity of the static inverter.

[0009] In conjunction with the first aspect, the rotor's angular acceleration is calculated using the following formula: .

[0010] In conjunction with the first aspect, the integration operation is implemented through a numerical integration method, including any one of the trapezoidal rule, Simpson's rule, or Romberg's rule.

[0011] In conjunction with the first aspect, the method includes implementation in simulation software by establishing a mathematical model.

[0012] A second aspect of this disclosure provides an electronic device, comprising: One or more processors; A storage unit is used to store one or more programs that, when executed by one or more processors, enable the one or more processors to implement the method for calculating the capacity requirement of a static inverter suitable for starting a synchronous condenser.

[0013] A third aspect of this disclosure provides a computer-readable storage medium having a computer program stored thereon, characterized in that, when the computer program is executed by a processor, it can implement the method for calculating the capacity requirement of a static frequency converter suitable for starting a synchronous condenser.

[0014] Beneficial Effects: This disclosure provides a method for calculating the capacity requirements of static frequency converters (SFDs) suitable for starting synchronous condensers. By utilizing known parameters such as rotor windage loss, bearing friction loss, and electrical loss at rated speed provided by the synchronous condenser manufacturer, combined with the unit's moment of inertia, a precise relationship model between total loss and speed during startup is constructed. Furthermore, based on the energy balance equation, the SFD capacity is quantitatively correlated with startup time through integral calculations, and the minimum capacity configuration that meets the preset startup time requirement is found through iterative calculations. This method achieves scientific and quantitative calculation of SFD capacity, fundamentally avoiding the problem of over- or under-capacity design caused by relying on experience-based estimations in traditional engineering design. It ensures both the reliability and timeliness of the startup process and effectively optimizes equipment selection and engineering costs. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating a method for calculating the capacity requirement of a static inverter suitable for starting a synchronous condenser, according to an embodiment of this disclosure. Figure 2 An electronic device as described in the disclosed embodiments. Detailed Implementation

[0016] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with those disclosed herein.

[0017] The terminology used in this disclosure is for the purpose of describing particular embodiments only and is not intended to be limiting of the present disclosure. The singular forms “a,” “the,” and “the” as used in this disclosure and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any and all possible combinations of one or more of the associated listed items.

[0018] Figure 1 This disclosure provides a method for calculating the capacity requirement of a static inverter suitable for starting a synchronous condenser, comprising the following steps: S1: Obtain the input parameters of the synchronous condenser, including the rated speed and the rotor-air friction loss at the rated speed. Friction loss of thrust bearing and main bearing at rated speed Electrical losses of a synchronous condenser at rated speed And the moment of inertia of the camera; S2: Based on the input parameters, calculate the relationship between the total loss and the rotational speed during the startup process of the synchronous condenser. The total loss includes rotor-air friction loss, bearing friction loss and electrical loss. S3: Set the initial capacity of the static inverter, and use the relationship between the total loss and the speed; calculate the start-up time required for the synchronous condenser to accelerate from standstill to the rated speed under the capacity of the static inverter through integral calculation; S4: Compare the start-up time with the preset start-up time requirement. If the start-up time does not meet the requirement, increase the capacity of the static inverter and repeat the integral calculation and comparison steps until the start-up time meets the requirement.

[0019] This disclosure provides a method for calculating the capacity requirement of a static inverter suitable for starting a synchronous condenser, the implementation process of which is shown in the attached figure. Figure 1 As shown. The method first systematically obtains the key input parameters of the synchronous condenser required for calculation in step S1. These parameters form the basis for subsequent calculations and specifically include the rated operating speed of the synchronous condenser, as well as various typical losses obtained at the rated speed through testing or manufacturer data: windage loss caused by rotor-air friction, mechanical friction loss during the operation of the thrust bearing and main bearing, and electrical losses during the start-up process of the synchronous condenser. Furthermore, the moment of inertia, characterizing the ease of rotor acceleration, is also a core input parameter.

[0020] In step S2, based on the obtained rated parameters, a dynamic relationship model between the total loss and speed of the synchronous condenser during the entire startup process is established. This total loss is a function of the speed and is composed of the superposition of the aforementioned rotor wind-wear loss, bearing mechanical friction loss, and electrical loss. By introducing a proportional relationship between loss and speed (e.g., wind-wear loss is proportional to the cube of the speed, mechanical loss is proportional to the square of the speed, etc.), the known loss value under rated operating conditions can be extrapolated to the entire speed range, thereby accurately describing the total resistance loss characteristics at any speed point from zero speed to rated speed.

[0021] Step S3 is the core of the calculation. In this step, an initial capacity value needs to be set for the stationary inverter. Then, the total loss-speed relationship model established in step S2 is substituted into the integral formula derived based on energy conservation and kinematic equations for calculation. This integral calculation comprehensively considers the balance between the acceleration power provided by the inverter and the power to overcome the total system losses, as well as the influence of rotational inertia on acceleration, and finally calculates the theoretical start-up time required for the synchronous condenser rotor to accelerate from a completely stationary state to the rated speed under this specific inverter capacity configuration.

[0022] Finally, in step S4, the calculated start-up time is compared with the preset start-up time required by the actual project. This step constitutes an iterative optimization loop: if the calculated start-up time fails to meet the preset time requirement, it indicates that the currently set inverter capacity is insufficient and the capacity value needs to be increased; subsequently, the system will return to step S3 with the new capacity value, recalculate the integral of the start-up time, and compare it again. This iterative process will continue until the calculated start-up time is equal to or shorter than the preset requirement. At this point, the corresponding static inverter capacity is the minimum and sufficient capacity configuration to meet the start-up performance requirements, thereby achieving optimal equipment capacity design while ensuring start-up efficiency.

[0023] Furthermore, , and Based on rated speed The loss was obtained by fitting the following data, specifically: , , , in, Indicates the rated speed Friction loss between the lower rotor and air. Indicates the rated speed Lower bearing friction loss, Indicates the rated speed Lower electrical losses This is the actual rotational speed.

[0024] The frictional loss P1 between the rotor and the air varies with rotational speed according to fluid dynamics principles; its value is directly proportional to the cube of the rotational speed. This relationship can be expressed as... ,in Represents the rated speed The rotor air wear loss was measured below. This cubic relationship reflects the characteristic that air wear loss increases sharply with increasing rotational speed.

[0025] Frictional loss of thrust bearing and main bearing It mainly originates from mechanical friction, and its value is proportional to the square of the rotational speed, expressed as: ,in This represents the bearing friction loss at rated speed. This square relationship reflects the typical characteristic of mechanical friction loss varying with rotational speed.

[0026] Electrical losses during the startup process of a synchronous condenser It is also proportional to the square of the rotational speed, that is ,in This represents the electrical losses at rated speed. This relationship takes into account factors such as iron losses and copper losses that vary with frequency (speed).

[0027] By using the above fitting method, several key loss data under rated operating conditions are transformed into continuous functions covering the entire speed range, laying a theoretical foundation for subsequent accurate calculation of total loss at any speed, thereby ensuring the accuracy and engineering practicality of the capacity calculation model.

[0028] Furthermore, the relationship between the total loss and the rotational speed is calculated using the following formula: .

[0029] This formula characterizes the synchronous condenser at any rotation speed. The total resistance loss that needs to be overcome during operation. Among them, As a composite function of rotational speed, its specific expression is determined by the rotational speed characteristics of each component loss.

[0030] This comprehensive calculation model has a clear physical meaning: it quantifies losses from different mechanisms—including fluid losses related to air friction, mechanical friction losses from bearing contact, and electrical losses from electromagnetic processes—as a function of rotational speed. By linearly superimposing three components that each follow different powers of rotational speed, a total loss model that comprehensively reflects the energy consumption characteristics during the startup of a synchronous condenser is obtained.

[0031] In actual calculations, substituting the specific expressions for each individual loss into the superposition formula yields a clear total loss-speed function relationship. This comprehensive relation will become the core input for subsequent integral calculations, directly determining the accuracy of the start-up time calculation, and also providing a reliable mathematical model basis for optimizing the capacity configuration of static inverters.

[0032] Furthermore, the integration operation is based on the following formula: , in, Start-up time To adjust the camera to the rated speed required for startup, To provide starting electromagnetic torque for the camera, To overcome the resistance torque during the start-up process of the synchronous condenser, This refers to the output power of the static frequency converter. For rotational inertia, ω is the angular acceleration of the rotor.

[0033] This integral formula fully describes the dynamics of the starting process: it integrates the rotor's inertia, the drive power provided by the frequency converter, the total system losses varying with the rotational speed, and the influence of the rotational speed itself on the acceleration process. Through a single definite integral, the precise starting time is calculated. This is the core step in transforming physical principles into a computable mathematical model.

[0034] Furthermore, the output power of the static inverter With rotational speed Proportional, satisfying: , in, This refers to the capacity of the static inverter.

[0035] This modeling is based on the operating characteristics of a static frequency converter (SFC) as a current-source frequency converter. During startup, it controls the output current and voltage to ensure that the output active power increases approximately linearly with frequency (proportional to speed). This model simplifies the complex electrical control process into a single process controlled by key parameters. The determined linear function allows capacity calculations to be performed within a clear mathematical framework. Capacity The physical meaning of is the continuous power that the static inverter can output at its rated speed, which is the core variable to be optimized in the entire calculation process.

[0036] Furthermore, the rotor's angular acceleration is calculated using the following formula: .

[0037] This conversion is a crucial step in bridging commonly used engineering units with the International System of Units (SI). All dynamic formulas based on Newton's laws of motion, including the relationships between torque, power, and moment of inertia, are built upon angular velocity measured in radians per second. Therefore, this formula is a necessary bridge to ensure the rigorous consistency of the entire mathematical model both physically and mathematically, allowing parameters such as moment of inertia and power to be correctly correlated and calculated within the same equation.

[0038] Furthermore, the integration operation is implemented through numerical integration methods, including any one of the trapezoidal rule, Simpson's rule, or Romberg's rule.

[0039] The integration operation requires numerical integration methods. The trapezoidal rule, Simpson's method, and Romberg's method mentioned are all mature numerical integration algorithms in computational mathematics with varying degrees of accuracy. These methods approximate the value of the definite integral by performing discrete sampling and weighted summation within the integration interval. Employing numerical methods greatly enhances the versatility and robustness of this calculation method, enabling it to handle various complex and nonlinear loss-speed characteristics without relying on specific functional forms to obtain analytical solutions.

[0040] Furthermore, the method includes implementation in simulation software by establishing a mathematical model.

[0041] The explained physical principles and mathematical formulas are transformed into computer simulation models, such as by building calculation modules or scripts in professional software environments like MATLAB / Simulink, PSCAD, or PSASP. Through simulation, parameter sensitivity analysis, batch calculations, and visualization of results can be easily performed, greatly improving the efficiency and reliability of this capacity calculation method in engineering applications, transforming it from a theoretical formula into a practical tool for engineering design and verification.

[0042] Electronic device 200 can be a desktop computer, laptop, handheld computer, cloud server, or other electronic device. Electronic device 200 may include, but is not limited to, processor 201 and memory 202. Those skilled in the art will understand that... Figure 2 This is merely an example of electronic device 200 and does not constitute a limitation on electronic device 200. It may include more or fewer components than shown, or combine certain components, or different components. For example, electronic device may also include input / output devices, network access devices, buses, etc.

[0043] The processor 201 can 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. A general-purpose processor can be a microprocessor or any conventional processor.

[0044] The memory 202 can be an internal storage unit of the electronic device 200, such as a hard disk or RAM of the electronic device 200. The memory 202 can also be an external storage device of the electronic device 200, such as a plug-in hard disk, Smart Media Card (SMC), Secure Digital (SD) card, or Flash Card equipped on the electronic device 200. Furthermore, the memory 202 can include both internal and external storage units of the electronic device 200. The memory 202 is used to store the computer program 203 and other programs and data required by the electronic device. The memory 202 can also be used to temporarily store data that has been output or will be output.

[0045] The above embodiments are only used to illustrate the technical solutions of this disclosure, and are not intended to limit it. Although this disclosure has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this disclosure, and should all be included within the protection scope of this disclosure.

Claims

1. A method for calculating the capacity requirement of a static frequency converter suitable for starting a synchronous condenser, characterized in that, Includes the following steps: Obtain the input parameters of the synchronous condenser, including the rated speed and the rotor-air friction loss at the rated speed. Friction loss of thrust bearing and main bearing at rated speed Electrical losses of a synchronous condenser at rated speed And the moment of inertia of the camera; Based on the input parameters, the relationship between the total loss and the rotational speed during the startup process of the synchronous condenser is calculated. The total loss includes rotor-air friction loss, bearing friction loss and electrical loss. Set the initial capacity of the static inverter, and use the relationship between the total loss and the speed to calculate the start-up time required for the synchronous condenser to accelerate from standstill to the rated speed under the capacity of the static inverter through integral calculation. The startup time is compared with the preset startup time requirement. If the startup time does not meet the requirement, the capacity of the static inverter is increased, and the integration calculation and comparison steps are repeated until the startup time meets the requirement.

2. The method according to claim 1, characterized in that, , and Based on rated speed The loss was obtained by fitting the following data, specifically: ， ， ， in, Indicates the rated speed Friction loss between the lower rotor and air. Indicates the rated speed Lower bearing friction loss, Indicates the rated speed Lower electrical losses This is the actual rotational speed.

3. The method according to claim 2, characterized in that, The relationship between total loss and rotational speed is calculated using the following formula: 。 4. The method according to claim 3, characterized in that, Integration is based on the following formula: ， in, Start-up time To adjust the camera to the rated speed required for startup, To provide starting electromagnetic torque for the camera, To overcome the resistance torque during the start-up process of the synchronous condenser, This refers to the output power of the static frequency converter. For rotational inertia, ω is the angular acceleration of the rotor.

5. The method according to claim 4, characterized in that, Output power of static frequency converter With rotational speed Proportional, satisfying: ， in, This refers to the capacity of the static inverter.

6. The method according to claim 5, characterized in that, The angular acceleration of the rotor is calculated using the following formula: 。 7. The method according to claim 4, characterized in that, The integration operation is implemented through numerical integration methods, including any one of the trapezoidal rule, Simpson's rule, or Romberg's rule.

8. The method according to claim 1, characterized in that, The method includes implementing it in simulation software by establishing a mathematical model.

9. An electronic device, characterized in that, include: One or more processors; A storage unit for storing one or more programs, which, when executed by one or more processors, enable the one or more processors to implement the method for calculating the capacity requirement of a static inverter for starting a synchronous condenser according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it can implement the method for calculating the capacity requirement of a static frequency converter suitable for starting a synchronous condenser, as described in any one of claims 1 to 8.

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