Method and apparatus for detecting power system oscillation source

Abstract

The application provides a power system oscillation source detection method and device, and relates to the technical field of power operation and maintenance.The method comprises the following steps: determining a first phase difference of generator power data and rotating speed data based on an oscillation period, and determining whether the power system oscillation source is from a prime mover side of the generator based on the first phase difference; if yes, an alarm is given that the prime mover side has an oscillation source; if no, determining a second phase difference of calculated excitation voltage data and measured excitation voltage data based on the oscillation period, and determining an amplitude difference of the calculated excitation voltage data and the measured excitation voltage data; determining whether the power system oscillation source is from a generator excitation system side based on the second phase difference and the amplitude difference; if yes, an alarm is given that the excitation system side has an oscillation source; if no, an alarm is given that the power grid side has an oscillation source.The application can improve the accuracy, speed and applicability of power system oscillation source detection.

Description

Technical Field

[0001] This invention relates to the field of power operation and maintenance technology, and in particular to a method and apparatus for detecting power system oscillation sources. Background Technology

[0002] In response to the requirement to "build a new power system with new energy as the mainstay" and to fully promote the achievement of "dual carbon" goals, the installed capacity of new energy power generation, represented by wind power and photovoltaics, is increasing daily and gradually becoming the dominant power generation mode of the power grid. Traditional thermal power units will gradually shift to a regulatory power source role, and the power grid will gradually exhibit the "dual high" characteristics of "high proportion of renewable energy" and "high proportion of power electronic equipment." On the one hand, new energy units do not possess the mechanical rotational inertia of synchronous generator rotors, and their large-scale integration will lead to a significant decrease in the system's mechanical rotational inertia. On the other hand, to improve the static stability limit and transient stability of the system, many units have adopted fast excitation systems. While this can improve fault response speed, it also reduces system damping. Therefore, with the widespread application of power electronic equipment and fast excitation systems, low-frequency oscillations in the power system are occurring more frequently, posing a significant challenge to the safe and stable operation of the power system.

[0003] Therefore, low-frequency oscillations in power systems are a common phenomenon widely present in interconnected power systems. They manifest as relative oscillations of 0.1 to 2.5 Hz between the rotor angles of grid-connected generators when the system is disturbed or electrical equipment malfunctions. Based on the different causes of low-frequency oscillations, they can be mainly divided into the following categories: The first category is forced oscillations caused by periodic disturbances in the system due to abnormalities on the prime mover side of the unit, such as power oscillations caused by mechanical power fluctuations due to abnormalities in the turbine control valves and their regulating systems; the second category is low-frequency oscillations caused by abnormal output of the generator excitation system, resulting in low-frequency oscillations under the coupling effect of the regulating control system and the power system; the third category is negatively damped or weakly damped oscillations caused by insufficient damping in the power system. In summary, the oscillation sources of power systems mainly originate from the prime mover side, the excitation system side, or the grid side.

[0004] To promote the safe and stable operation of power systems, it is necessary to detect oscillation sources when related oscillation faults occur in the power system, in order to identify the source of the fault and eliminate it accordingly. There are many existing methods for detecting power system oscillation sources, such as the energy function method, mode estimation method, and damped torque method. However, existing methods for detecting power system oscillation sources have at least the following limitations:

[0005] (1) At least some methods are not accurate in detection. The oscillation source can only be located to the generator in the power system, but it cannot further distinguish whether the oscillation comes from the generator prime mover side or the excitation system side, resulting in low detection accuracy.

[0006] (2) The detection process of at least some methods involves various complex calculations and operations, which are cumbersome and time-consuming, resulting in a slow detection speed.

[0007] (3) At least some of the methods are only applicable to laboratory simulation environments and can only be used to locate a certain type of oscillation source. It is difficult to promote and apply them widely in power engineering sites. Therefore, their applicability is poor.

[0008] In summary, existing technologies suffer from low accuracy, slow speed, and poor applicability in detecting power system oscillation sources, which hinders the improvement of efficiency in power system oscillation source detection. Summary of the Invention

[0009] One object of this invention is to provide a method for detecting power system oscillation sources, addressing the problems of low accuracy, slow speed, and poor applicability in existing power system oscillation source detection technologies, which hinders the improvement of power system oscillation source detection efficiency. Another object of this invention is to provide a device for detecting power system oscillation sources. A further object of this invention is to provide a computer device. A further object of this invention is to provide a readable medium. A still further object of this invention is to provide a computer program product.

[0010] To achieve the above objectives, one aspect of the present invention discloses a method for detecting oscillation sources in a power system, the method comprising:

[0011] Based on the oscillation period of the power system, the first phase difference between the generator power data and the speed data of the power system is determined, and based on the first phase difference, it is determined whether the oscillation source of the power system comes from the generator prime mover side. If it comes from the generator prime mover side, an alarm is issued for the presence of an oscillation source on the prime mover side.

[0012] If the oscillation does not originate from the generator prime mover side, based on the oscillation period, the second phase difference between the calculated excitation voltage data and the measured excitation voltage data of the generator in the power system is determined, and the amplitude difference between the calculated excitation voltage data and the measured excitation voltage data is determined. The calculated excitation voltage data is obtained based on the excitation system model corresponding to the generator in the power system. Based on the second phase difference and the amplitude difference, it is determined whether the oscillation source of the power system originates from the generator excitation system side. If it originates from the generator excitation system side, an alarm is triggered indicating the presence of an oscillation source on the excitation system side.

[0013] If the oscillation does not originate from the generator excitation system, an alarm will be triggered indicating the presence of an oscillation source on the grid side.

[0014] Optionally, it may further include:

[0015] Before determining the first phase difference between generator power data and speed data of the power system based on the oscillation period of the power system.

[0016] Based on the generator power data of the power system, determine the corresponding zero-crossing points of multiple generator power;

[0017] The oscillation period is obtained based on the zero-crossing point of the generator power.

[0018] Optionally, determining the first phase difference between the generator power data and speed data of the power system based on the oscillation period of the power system includes:

[0019] Based on the generator power data, determine multiple corresponding generator power zero-crossing points; and based on the rotational speed data, determine multiple corresponding rotational speed zero-crossing points.

[0020] Based on the generator power zero-crossing point and the speed zero-crossing point corresponding to the generator power zero-crossing point, multiple corresponding power and speed zero-crossing point time differences are obtained.

[0021] The first phase difference is determined based on the oscillation period, the time difference between the power and speed zero crossing points, and the number of first time differences between the power and speed zero crossing points.

[0022] Optionally, determining whether the power system oscillation source originates from the generator prime mover side based on the first phase difference includes:

[0023] Subtract the preset normal lag phase from the first phase difference to obtain the initial prime mover oscillation phase, and take the absolute value of the initial prime mover oscillation phase as the prime mover oscillation phase.

[0024] Determine whether the oscillation phase of the prime mover is greater than a preset first oscillation phase threshold. If so, issue an alarm indicating the presence of an oscillation source on the prime mover side.

[0025] Optionally, it may further include:

[0026] Before determining the second phase difference between the calculated excitation voltage data and the measured excitation voltage data of the generator in the power system based on the oscillation period,

[0027] Based on the generator terminal voltage data, preset given voltage data, generator power data, speed data, and preset excitation system model corresponding to the generator in the power system, the initial calculated excitation voltage data is obtained.

[0028] Based on a preset sampling time period, the initial calculated excitation voltage data is truncated to obtain intermediate calculated excitation voltage data, and the fundamental component data of the intermediate calculated excitation voltage data is used as the calculated excitation voltage data of the generator in the power system.

[0029] Optionally, it may further include:

[0030] Before determining the first phase difference between generator power data and speed data of the power system based on the oscillation period of the power system.

[0031] Based on a preset sampling time period, the original generator terminal voltage data of the generator in the power system is extracted to obtain intermediate generator terminal voltage data, and the fundamental component data of the intermediate generator terminal voltage data is used as the generator terminal voltage data.

[0032] Based on the sampling time period, the original generator power data of the generators in the power system is extracted to obtain intermediate generator power data, and the fundamental component data of the intermediate generator power data is used as the generator power data.

[0033] Based on the sampling time period, the original speed data of the generator in the power system is extracted to obtain intermediate speed data, and the fundamental component data of the intermediate speed data is used as the speed data.

[0034] Based on the sampling time period, the original measured excitation voltage data of the generator in the power system is extracted to obtain intermediate measured excitation voltage data, and the fundamental component data of the intermediate measured excitation voltage data is used as the measured excitation voltage data.

[0035] Optionally, determining the second phase difference between the calculated excitation voltage data and the measured excitation voltage data of the generator in the power system based on the oscillation period includes:

[0036] Based on the calculated excitation voltage data, multiple calculated excitation voltage zero-crossing points are determined; and based on the measured excitation voltage data, multiple measured excitation voltage zero-crossing points are determined.

[0037] Based on the calculated excitation voltage zero-crossing point and the measured excitation voltage zero-crossing point corresponding to the calculated excitation voltage zero-crossing point, multiple corresponding excitation voltage zero-crossing point time differences are obtained;

[0038] The second phase difference is determined based on the oscillation period, the time difference of the excitation voltage zero crossing point, and the number of second time differences of the excitation voltage zero crossing point.

[0039] Optionally, determining the amplitude difference between the calculated excitation voltage data and the measured excitation voltage data includes:

[0040] Based on the calculated excitation voltage data, the amplitude of the calculated excitation voltage data is obtained;

[0041] Based on the measured excitation voltage data, the amplitude of the measured excitation voltage data is obtained;

[0042] The amplitude difference is determined based on the calculated excitation voltage amplitude and the measured excitation voltage amplitude.

[0043] Optionally, determining whether the power system oscillation source originates from the generator excitation system side based on the second phase difference and amplitude difference includes:

[0044] Determine whether the absolute value of the second phase difference is greater than the preset second oscillation phase threshold or the absolute value of the amplitude difference is greater than the preset safe amplitude difference threshold. If so, issue an alarm for the presence of an oscillation source on the excitation system side.

[0045] To achieve the above objectives, another aspect of the present invention discloses a power system oscillation source detection device, the device comprising:

[0046] The first detection module is used to determine the first phase difference between the generator power data and speed data of the power system based on the oscillation period of the power system, and to determine whether the oscillation source of the power system comes from the generator prime mover side based on the first phase difference. If it comes from the generator prime mover side, an alarm is triggered to indicate the presence of an oscillation source on the prime mover side.

[0047] The second detection module is used to determine, based on the oscillation period, the second phase difference between the calculated excitation voltage data and the measured excitation voltage data of the generator in the power system, and the amplitude difference between the calculated excitation voltage data and the measured excitation voltage data, if the oscillation does not originate from the generator prime mover side. The calculated excitation voltage data is obtained based on the excitation system model corresponding to the generator in the power system. Based on the second phase difference and the amplitude difference, it determines whether the oscillation source in the power system originates from the generator excitation system side. If it does, it issues an alarm indicating the presence of an oscillation source on the excitation system side.

[0048] The third detection module is used to issue an alarm for the presence of an oscillation source on the grid side if the oscillation does not originate from the generator excitation system side.

[0049] The present invention also discloses a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described above.

[0050] The present invention also discloses a computer-readable medium having a computer program stored thereon, which, when executed by a processor, implements the method described above.

[0051] The present invention also discloses a computer program product, including a computer program that, when executed by a processor, implements the method described above.

[0052] The power system oscillation source detection method and apparatus provided by the present invention determines the first phase difference between the generator power data and speed data of the power system based on the oscillation period of the power system, and determines whether the power system oscillation source comes from the generator prime mover side based on the first phase difference. If it comes from the generator prime mover side, an alarm is issued for the presence of an oscillation source on the prime mover side. It can fully consider the close relationship between the phase difference of generator power and speed and the change of prime mover mechanical power, as well as the relationship between the change of prime mover mechanical power and whether the prime mover is abnormal, so as to accurately detect whether the oscillation source comes from the prime mover, thereby improving the accuracy of power system oscillation source detection.

[0053] If the oscillation source does not originate from the generator prime mover side, based on the oscillation period, the second phase difference between the calculated excitation voltage data and the measured excitation voltage data of the generator in the power system is determined, and the amplitude difference between the calculated excitation voltage data and the measured excitation voltage data is also determined. The calculated excitation voltage data is obtained based on the excitation system model corresponding to the generator in the power system. Based on the second phase difference and amplitude difference, it is determined whether the oscillation source in the power system originates from the generator excitation system side. If it does, an alarm is triggered indicating the presence of an oscillation source on the excitation system side. This approach fully considers the phase and amplitude differences between the actual excitation voltage and the calculated excitation voltage, characterizing the deviation between the actual and normal operating conditions of the excitation system. Furthermore, determining the calculated excitation voltage based on a model that conforms to the expected characteristics of the excitation system ensures that the obtained calculated excitation voltage is more consistent with the normal operating characteristics of the excitation system. Therefore, the above steps can accurately detect whether the oscillation source originates from the excitation system, thereby improving the accuracy of power system oscillation source detection.

[0054] By issuing an alarm for an oscillation source on the grid side if the oscillation source does not originate from the generator excitation system, the system can fully consider the three main sources of power system oscillation: prime mover, excitation system, or grid. If the oscillation source does not originate from either the prime mover or the excitation system, it is highly likely to originate from the grid side. This allows for accurate detection of whether the oscillation source originates from the grid side of the power system, thereby improving the accuracy of power system oscillation source detection.

[0055] The power system oscillation source detection method and apparatus provided by this invention can specifically locate the corresponding oscillation source of the power system oscillation source, refine the granularity of power system oscillation source detection and improve its detection accuracy, thereby improving the accuracy of power system oscillation source detection; and it does not involve complex calculation and processing processes, the operation is relatively simple, and the overall process takes less time, thereby improving the speed of power system oscillation source detection; in addition, the required input information parameters are easy to obtain from the actual production environment, and the requirements for implementation conditions are not harsh, the required human and material costs are not high, and it can also locate multiple types of oscillation sources, which is applicable to the actual production environment of corresponding power engineering projects, making it easy to promote and apply, thereby improving the applicability of power system oscillation source detection.

[0056] In summary, the power system oscillation source detection method and apparatus provided by the present invention can improve the accuracy, speed and applicability of power system oscillation source detection, thereby improving the efficiency of power system oscillation source detection. Attached Figure Description

[0057] 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 of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0058] Figure 1 A flowchart illustrating a power system oscillation source detection method according to an embodiment of the present invention is shown;

[0059] Figure 2 A schematic diagram illustrating an optional step in determining the first phase difference according to an embodiment of the present invention is shown;

[0060] Figure 3 A schematic diagram illustrating an optional step in an embodiment of the present invention for detecting whether the prime mover side is an oscillation source is shown.

[0061] Figure 4 A schematic diagram illustrating an optional step in determining the second phase difference according to an embodiment of the present invention is shown;

[0062] Figure 5 A schematic diagram illustrating an optional step in an embodiment of the present invention for detecting the presence of an oscillation source on the excitation system side is shown.

[0063] Figure 6 A schematic diagram of a power system oscillation source detection device according to an embodiment of the present invention is shown;

[0064] Figure 7A schematic diagram of a computer device suitable for implementing embodiments of the present invention is shown. Detailed Implementation

[0065] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0066] The terms "first," "second," etc., used in this document are not intended to specifically refer to order or sequence, nor are they intended to limit the invention. They are merely used to distinguish elements or operations described using the same technical terms.

[0067] The terms “include,” “including,” “have,” “contain,” etc., used in this article are all open-ended terms, meaning that they include but are not limited to.

[0068] The term "and / or" as used herein includes any or all of the things mentioned.

[0069] It should be noted that the acquisition, storage, use, and processing of data in the technical solution of this invention all comply with the relevant provisions of national laws and regulations.

[0070] It should be noted that the power system oscillation source detection method and device disclosed in this application can be used in the field of power operation and maintenance technology, or in any field other than the field of power operation and maintenance technology. The application field of the power system oscillation source detection method and device disclosed in this application is not limited.

[0071] This invention discloses a method for generating an oscillation source in a power system, such as... Figure 1 As shown, the method specifically includes the following steps:

[0072] S101: Based on the oscillation period of the power system, determine the first phase difference between the generator power data and the speed data of the power system, and determine whether the oscillation source of the power system comes from the generator prime mover side based on the first phase difference. If it comes from the generator prime mover side, issue an alarm for the presence of an oscillation source on the prime mover side.

[0073] S102: If the oscillation does not originate from the generator prime mover side, based on the oscillation period, determine the second phase difference between the calculated excitation voltage data and the measured excitation voltage data of the generator in the power system, and determine the amplitude difference between the calculated excitation voltage data and the measured excitation voltage data, wherein the calculated excitation voltage data is obtained based on the excitation system model corresponding to the generator in the power system; based on the second phase difference and the amplitude difference, determine whether the oscillation source of the power system originates from the generator excitation system side; if it originates from the generator excitation system side, issue an alarm indicating the presence of an oscillation source on the excitation system side.

[0074] S103: If the source is not from the generator excitation system, an alarm will be triggered indicating the presence of an oscillation source on the grid side.

[0075] For example, the oscillation source in the embodiments of the present invention can be, but is not limited to, a low-frequency oscillation source. It should be noted that the nature of the oscillation source can be determined by those skilled in the art based on the actual situation, and the above description is only an example and does not constitute a limitation.

[0076] For example, the prime mover can be, but is not limited to, the prime mover that drives the generator in the power system (e.g., the prime mover can be, but is not limited to, a steam turbine). It should be noted that the nature and type of the prime mover can be determined by those skilled in the art based on the actual situation, and the above description is only an example and does not constitute a limitation.

[0077] For example, the excitation system can be, but is not limited to, the excitation system of the relevant generator set in the power system. The excitation system includes, but is not limited to, an excitation regulator (AVR), a power system stabilizer (PSS), and an excitation power system. The excitation system is mainly used, but is not limited to, maintaining the stability of the generator terminal voltage and suppressing power oscillations. The excitation regulator is the core component of the excitation system; it processes the input terminal voltage measurements and setpoints to control the excitation power system and thereby regulate the excitation voltage output. The power system stabilizer is an additional control device that can control the synchronous motor excitation system with the help of the excitation regulator to suppress power oscillations in the power system. The inputs to the power system stabilizer include, but are not limited to, single variables such as speed, frequency, and power, or combinations of some or all of these single variables. The relevant signals output by the power system stabilizer, along with the terminal voltage measurements and setpoints, are input to the corresponding excitation regulator. It should be noted that the nature, structure, and operating mode of the excitation system can be determined by those skilled in the art based on actual conditions; the above description is merely illustrative and does not constitute a limitation.

[0078] For example, the alarm indicating the presence of an oscillation source on the prime mover side can be, but is not limited to, displaying or sending alarm information such as "The oscillation source originates from the prime mover side; please have relevant personnel conduct a more in-depth investigation into the cause of the fault and repair it promptly." It should be noted that the specific implementation of the prime mover side oscillation source alarm can be determined by those skilled in the art based on the actual situation; the above description is merely an example and does not constitute a limitation.

[0079] For example, the alarm indicating the presence of an oscillation source on the excitation system side can be, but is not limited to, displaying or sending alarm messages to relevant personnel such as "The oscillation source originates from the excitation system side; please conduct a more in-depth investigation into the cause of the fault on the excitation system side and repair it promptly." It should be noted that the specific implementation of the alarm indicating the presence of an oscillation source on the excitation system side can be determined by those skilled in the art based on the actual situation; the above description is merely an example and does not constitute a limitation.

[0080] For example, the data in the embodiments of the present invention may specifically be, but is not limited to, corresponding signals.

[0081] For example, the alarm for the presence of an oscillation source on the power grid side can be, but is not limited to, displaying or sending alarm messages to relevant personnel such as "The oscillation source originates from the power grid side. Please have relevant personnel conduct a more in-depth investigation into the cause of the fault on the power grid side and repair it promptly." It should be noted that the specific implementation method for the alarm for the presence of an oscillation source on the power grid side can be determined by those skilled in the art based on the actual situation. The above description is merely an example and does not constitute a limitation.

[0082] The power system oscillation source detection method and apparatus provided by the present invention determines the first phase difference between the generator power data and speed data of the power system based on the oscillation period of the power system, and determines whether the power system oscillation source comes from the generator prime mover side based on the first phase difference. If it comes from the generator prime mover side, an alarm is issued for the presence of an oscillation source on the prime mover side. It can fully consider the close relationship between the phase difference of generator power and speed and the change of prime mover mechanical power, as well as the relationship between the change of prime mover mechanical power and whether the prime mover is abnormal, so as to accurately detect whether the oscillation source comes from the prime mover, thereby improving the accuracy of power system oscillation source detection.

[0083] If the oscillation source does not originate from the generator prime mover side, based on the oscillation period, the second phase difference between the calculated excitation voltage data and the measured excitation voltage data of the generator in the power system is determined, and the amplitude difference between the calculated excitation voltage data and the measured excitation voltage data is also determined. The calculated excitation voltage data is obtained based on the excitation system model corresponding to the generator in the power system. Based on the second phase difference and amplitude difference, it is determined whether the oscillation source in the power system originates from the generator excitation system side. If it does, an alarm is triggered indicating the presence of an oscillation source on the excitation system side. This approach fully considers the phase and amplitude differences between the actual excitation voltage and the calculated excitation voltage, characterizing the deviation between the actual and normal operating conditions of the excitation system. Furthermore, determining the calculated excitation voltage based on a model that conforms to the expected characteristics of the excitation system ensures that the obtained calculated excitation voltage is more consistent with the normal operating characteristics of the excitation system. Therefore, the above steps can accurately detect whether the oscillation source originates from the excitation system, thereby improving the accuracy of power system oscillation source detection.

[0084] By issuing an alarm for an oscillation source on the grid side if the oscillation source does not originate from the generator excitation system, the system can fully consider the three main sources of power system oscillations: the prime mover, the excitation system, or the power grid. If the oscillation source does not originate from either the prime mover or the excitation system, it is highly likely to originate from the power grid side. This allows for accurate detection of whether the oscillation source originates from the power grid side of the power system, thereby improving the accuracy of power system oscillation source detection.

[0085] The power system oscillation source detection method and apparatus provided by this invention can specifically locate the corresponding oscillation source of the power system oscillation source, refine the granularity of power system oscillation source detection and improve its detection accuracy, thereby improving the accuracy of power system oscillation source detection; and it does not involve complex calculation and processing processes, the operation is relatively simple, and the overall process takes less time, thereby improving the speed of power system oscillation source detection; in addition, the required input information parameters are easy to obtain from the actual production environment, and the requirements for implementation conditions are not harsh, the required human and material costs are not high, and it can also locate multiple types of oscillation sources, which is applicable to the actual production environment of corresponding power engineering projects, making it easy to promote and apply, thereby improving the applicability of power system oscillation source detection.

[0086] In summary, the power system oscillation source detection method and apparatus provided by the present invention can improve the accuracy, speed and applicability of power system oscillation source detection, thereby improving the efficiency of power system oscillation source detection.

[0087] In an optional implementation, it further includes:

[0088] Before determining the first phase difference between generator power data and speed data of the power system based on the oscillation period of the power system.

[0089] Based on the generator power data of the power system, determine the corresponding zero-crossing points of multiple generator power;

[0090] The oscillation period is obtained based on the zero-crossing point of the generator power.

[0091] For example, determining multiple generator power zero-crossing points based on generator power data of the power system can be, but is not limited to, determining all time points where the corresponding generator power value is 0 as the generator power zero-crossing points based on the generator power data. The generator power data can be in the form of a waveform signal, specifically, but not limited to, a sine wave signal. It should be noted that the specific implementation method for determining multiple generator power zero-crossing points based on generator power data of the power system can be determined by those skilled in the art according to the actual situation; the above description is merely an example and does not constitute a limitation.

[0092] For example, the specific meaning and properties of zero-crossing points in the embodiments of the present invention are common knowledge in the field and will not be repeated here.

[0093] For example, obtaining the oscillation period based on the generator power zero-crossing point can be, but is not limited to, selecting two generator power zero-crossing points from a plurality of generator power zero-crossing points as corresponding sample power zero-crossing points; and dividing the time difference between the two sample power zero-crossing points by the number of generator power zero-crossing points between the two sample power zero-crossing points plus 1 to obtain the oscillation period. For example, selecting the first and third generator power zero-crossing points from a plurality of generator power zero-crossing points (the basis for determining the generator power zero-crossing point as the xth generator power zero-crossing point is the time order of the plurality of generator power zero-crossing points (from early to late)) as corresponding sample power zero-crossing points, the oscillation period can be expressed as, but is not limited to, the following formula:

[0094]

[0095] Where, t′ D1_1 This indicates that the power of the first generator crosses zero, t′. D1_3 This indicates the third generator power zero-crossing point. (3-1) represents the number of generator power zero-crossing points between the first and third generator power zero-crossing points plus 1 (if there is one generator power zero-crossing point between the first and third generator power zero-crossing points, i.e., the second generator power zero-crossing point, then the corresponding value after adding 1 is 2 = 3-1).

[0096] Correspondingly, based on the zero-crossing point of the generator power, the oscillation period is obtained, which can be summarized as, but is not limited to, the following formula:

[0097]

[0098] Among them, t' D1_n1 This indicates the zero-crossing point of the power of the n1th generator (n1 represents the sequential number of the corresponding generator power zero-crossing point), t' D1_n2 This indicates the zero-crossing point of the power of the n2th generator (n2 represents the sequential number of the corresponding generator power zero-crossing point).

[0099] It should be noted that the specific implementation method for obtaining the oscillation period based on the zero-crossing point of the generator power can be determined by those skilled in the art according to the actual situation. The above description is only an example and does not constitute a limitation.

[0100] Preferably, the reciprocal of the oscillation period can be used as the corresponding oscillation frequency, and the oscillation frequency can be sent or displayed to the relevant staff to facilitate relevant analysis work.

[0101] The above steps improve the accuracy and convenience of determining the oscillation period, reduce the amount of data processing involved in determining the oscillation period, and increase the speed of determining the oscillation period, thereby improving the accuracy, speed, and adaptability of the overall power system oscillation source detection.

[0102] In one alternative implementation, such as Figure 2 As shown, determining the first phase difference between generator power data and speed data of the power system based on the oscillation period of the power system includes the following steps:

[0103] S201: Based on the generator power data, determine multiple corresponding generator power zero-crossing points; and based on the speed data, determine multiple corresponding speed zero-crossing points.

[0104] S202: Based on the generator power zero-crossing point and the speed zero-crossing point corresponding to the generator power zero-crossing point, obtain multiple corresponding power and speed zero-crossing point time differences.

[0105] S203: Determine the first phase difference based on the oscillation period, the power speed zero-crossing time difference, and the first time difference quantity of the power speed zero-crossing time difference.

[0106] For example, determining multiple corresponding generator power zero-crossing points based on the generator power data can be, but is not limited to, determining all time points where the corresponding generator power value is 0 as the generator power zero-crossing points based on the generator power data. The generator power data can be in the form of a waveform signal, specifically, but not limited to, a sine wave signal. If the generator power zero-crossing points have already been determined during the process of obtaining the oscillation period, then the process of determining multiple corresponding generator power zero-crossing points based on the generator power data does not need to be repeated here. It should be noted that the specific implementation method for determining multiple corresponding generator power zero-crossing points based on generator power data of the power system can be determined by those skilled in the art according to the actual situation; the above description is merely an example and does not constitute a limitation.

[0107] For example, the specific meaning and properties of zero-crossing points in the embodiments of the present invention are common knowledge in the field and will not be repeated here.

[0108] For example, determining multiple corresponding zero-crossing points based on the rotational speed data can be, but is not limited to, determining all time points where the corresponding rotational speed is 0 as the zero-crossing points. The rotational speed data can be a waveform signal, specifically, but not limited to, a sine wave signal. It should be noted that the specific implementation of determining multiple corresponding zero-crossing points based on the rotational speed data can be determined by those skilled in the art according to the actual situation; the above description is merely an example and does not constitute a limitation.

[0109] For example, the speed zero-crossing point corresponding to the generator power zero-crossing point can be, but is not limited to, the speed zero-crossing point that is the same as the generator power zero-crossing point in time sequence. Specifically, it can be, but is not limited to, the speed zero-crossing point that is the same as the generator power zero-crossing point in corresponding time sequence number (the time sequence number from smallest to largest can correspond to, but is not limited to, the time point from earliest to latest). For example, for the first generator power zero-crossing point, its corresponding speed zero-crossing point is specifically the first speed zero-crossing point within the corresponding sampling range; for the fifth generator power zero-crossing point, its corresponding speed zero-crossing point is specifically the fifth speed zero-crossing point within the corresponding sampling range. It should be noted that the specific correspondence between the generator power zero-crossing point and the speed zero-crossing point can be determined by those skilled in the art based on actual circumstances. The above description is merely an example and does not constitute a limitation.

[0110] For example, step S202 can be, but is not limited to, subtracting the corresponding speed zero-crossing point from the generator power zero-crossing point to obtain the corresponding power-speed zero-crossing point time difference. Here, one power-speed zero-crossing point time difference corresponds to one generator power zero-crossing point and one speed zero-crossing point. It should be noted that the specific implementation of step S202 can be determined by those skilled in the art based on actual circumstances; the above description is merely an example and does not constitute a limitation.

[0111] For example, step S203 can be expressed as, but is not limited to, the following formula:

[0112]

[0113] in, Indicates the first phase difference, (t) p ′ e_i -t′ ω_i The 'n' represents the time difference between power and speed zero crossings, 'i' represents the corresponding time sequence number, 'T' represents the oscillation period, 'n1' represents the number of power and speed zero crossings (the same as the number of generator power zero crossings and speed zero crossings within the corresponding sampling range, i.e., the number of the first time differences), and 't' represents the oscillation period. p ′ e_i This indicates the zero-crossing point of the power of the i-th generator within the corresponding sampling range, t′. ω_i This indicates the i-th rotational speed zero-crossing point within the corresponding sampling range.

[0114] It should be noted that the specific implementation of step S203 can be determined by those skilled in the art based on the actual situation. The above description is only an example and does not constitute a limitation.

[0115] Through the above steps, based on relevant waveform principles and physical principles, the first phase difference between generator power data and speed data of a power system can be accurately, quickly, and conveniently determined through simple calculations and with a small amount of data. This improves the accuracy, speed, and adaptability of overall power system oscillation source detection.

[0116] In one alternative implementation, such as Figure 3 As shown, the step of determining whether the power system oscillation source originates from the generator prime mover side based on the first phase difference includes the following steps:

[0117] S301: Subtract the preset normal lag phase from the first phase difference to obtain the initial prime mover oscillation phase, and use the absolute value of the initial prime mover oscillation phase as the prime mover oscillation phase.

[0118] S302: Determine whether the oscillation phase of the prime mover is greater than the preset first oscillation phase threshold. If so, issue an alarm indicating the presence of an oscillation source on the prime mover side.

[0119] For example, the normal lag phase can be, but is not limited to, 90°. It should be noted that the specific value of the normal lag phase can be determined by those skilled in the art based on the actual situation; the above description is merely an example and does not constitute a limitation.

[0120] For example, the first oscillation phase threshold can be, but is not limited to, a threshold ranging from [0°, 10°] (preferably, in integer form). It should be noted that the first oscillation phase threshold can be determined by those skilled in the art based on actual circumstances; the above description is merely an example and does not constitute a limitation.

[0121] Through the above steps, the relevant phase laws and characteristics between the prime mover power, corresponding speed and generator power of the generator in the power system can be fully considered, and the specific standards for detecting the presence of oscillation sources on the prime mover side can be refined accordingly, thereby improving the accuracy of detecting the presence of oscillation sources on the prime mover side. Moreover, the above judgment and processing process is not complicated, takes less time and is easy to apply, thus improving the speed and applicability of detecting the presence of oscillation sources on the prime mover side, and further improving the accuracy, speed and adaptability of oscillation source detection in the overall power system.

[0122] The following illustrates the relevant principle for detecting the presence of an oscillation source on the prime mover side:

[0123] When mechanical damping is neglected, the equation of motion for the synchronous generator rotor can be simplified to the following relationship:

[0124]

[0125] Where M is the moment of inertia of the generator, ω is the generator speed, and P m P is the mechanical power of the prime mover. e This refers to the electromagnetic power of the generator (also known as, but not limited to, generator power, generator output power, generator active power, generator electrical power, or electrical power, etc.).

[0126] When the prime mover mechanical power of the generator remains constant (ΔP) m =0), the phase lag of the speed signal Δω behind the negative value of the power signal (-ΔP) e The phase of ) is 90°; when the mechanical power of the generator prime mover changes significantly (ΔP) m (≠0), the phase lag of the speed signal Δω is the difference between the mechanical power and electrical power signals (ΔP). m -ΔP eThe phase of the speed signal Δω is 90°, therefore, the phase of the speed signal Δω lags behind the negative value of the power signal (-ΔP). e The phase of ) is no longer equal to 90°.

[0127] Oscillation caused by a fault on the prime mover side leads to ΔP m Since the value is not zero, this rule can be used to determine whether power system oscillations are caused by a fault on the prime mover side. However, in practical applications, even if the oscillation source does not originate from the prime mover side, the change in the prime mover's mechanical power ΔP... m It is also difficult for it to be exactly 0. Therefore, a first oscillation phase threshold needs to be introduced as a standard value for detecting whether there is an oscillation source on the prime mover side, instead of directly alarming when the prime mover oscillation phase is greater than 0 (to reduce false alarms).

[0128] Based on the synchronous generator rotor motion equation and the above-mentioned laws, the rationality of steps S201 to S203 and steps S301 to S302 can be deduced.

[0129] It should be noted that the relevant principles for detecting whether there is an oscillation source on the prime mover side can be determined by those skilled in the art based on the actual situation, and the embodiments of the present invention do not impose any limitations on this.

[0130] In an optional implementation, it further includes:

[0131] Before determining the second phase difference between the calculated excitation voltage data and the measured excitation voltage data of the generator in the power system based on the oscillation period,

[0132] Based on the generator terminal voltage data, preset given voltage data, generator power data, speed data, and preset excitation system model corresponding to the generator in the power system, the initial calculated excitation voltage data is obtained.

[0133] Based on a preset sampling time period, the initial calculated excitation voltage data is truncated to obtain intermediate calculated excitation voltage data, and the fundamental component data of the intermediate calculated excitation voltage data is used as the calculated excitation voltage data of the generator in the power system.

[0134] For example, the given voltage data can be, but is not limited to, a given voltage signal with a default value of 1 p.u. It should be noted that the given voltage data can be determined by those skilled in the art based on the actual situation; the above description is merely an example and does not constitute a limitation.

[0135] For example, obtaining the initial calculated excitation voltage data based on the generator terminal voltage data, preset given voltage data, generator power data, speed data, and a preset excitation system model corresponding to the generator in the power system can be, but is not limited to, inputting the generator terminal voltage data, given voltage data, generator power data, and speed data into the excitation system model for calculation and processing to obtain the initial calculated excitation voltage data output by the excitation system model (whose properties can be, but are not limited to, the corresponding theoretical calculated value). The given voltage data can also be provided directly by the corresponding model without additional input. Specifically, the above steps can be, but are not limited to, inputting the generator terminal voltage data and given voltage data into the excitation regulator model (AVR model) in the excitation system model for processing, and inputting the generator power data and speed data into the power system stabilizer model (PSS model) in the excitation system model for processing, finally obtaining the initial calculated excitation voltage data output by the corresponding excitation power system model in the excitation system model. The power system stabilizer model can output a first model internal signal U. PSS The excitation regulator model serves as its input, and the excitation regulator model can output a second model internal signal U. c The excitation power system model is used as its input. It should be noted that the specific implementation method for obtaining the initial calculated excitation voltage data based on the generator terminal voltage data, preset given voltage data, generator power data, speed data, and the preset excitation system model corresponding to the generator in the power system can be determined by those skilled in the art according to the actual situation. The above description is only an example and does not constitute a limitation.

[0136] For example, the excitation system model can be obtained by modeling the actual excitation system of the generator in the power system using relevant modeling tools, and the specific operation of modeling is a conventional technical means in the field, which will not be described in detail here.

[0137] For example, the step of truncating the initial calculated excitation voltage data based on a preset sampling time period to obtain intermediate calculated excitation voltage data can be, but is not limited to, truncating a data segment from the initial calculated excitation voltage data that corresponds to the sampling time period to obtain intermediate calculated excitation voltage data. Specifically, the initial calculated excitation voltage data can be in the form of a waveform signal; in this case, the truncating operation involves truncating the waveform of the calculated excitation voltage data corresponding to the sampling time period to obtain intermediate calculated excitation voltage data. It should be noted that the specific implementation method for truncating the initial calculated excitation voltage data based on a preset sampling time period to obtain intermediate calculated excitation voltage data can be determined by those skilled in the art based on actual conditions. The above description is merely an example and does not constitute a limitation.

[0138] For example, the fundamental component data of the intermediate calculated excitation voltage data can be obtained by, but is not limited to, performing Fourier analysis (Fourier decomposition) on the intermediate calculated excitation voltage data. During the Fourier analysis, other harmonic components in the intermediate calculated excitation voltage data are removed. It should be noted that the specific method for obtaining the fundamental component data of the intermediate calculated excitation voltage data can be determined by those skilled in the art based on the actual situation. The above description is merely an example and does not constitute a limitation.

[0139] Through the above steps, based on the correct use of the excitation system model and the obtaining of accurate excitation voltage prediction results, the time range of excitation voltage data to be used subsequently is specifically defined. The fundamental component that mainly characterizes the calculated excitation voltage is then selected for subsequent use. This not only effectively reduces the amount of data and improves sampling efficiency, but also significantly reduces noise interference and interference from poorly correlated information in the calculated excitation voltage data. As a result, the determined calculated excitation voltage data for subsequent use has strong typicality and accuracy, thereby improving the accuracy and adaptability of the overall power system oscillation source detection.

[0140] In an optional implementation, it further includes:

[0141] Before determining the first phase difference between generator power data and speed data of the power system based on the oscillation period of the power system.

[0142] Based on a preset sampling time period, the original generator terminal voltage data of the generator in the power system is extracted to obtain intermediate generator terminal voltage data, and the fundamental component data of the intermediate generator terminal voltage data is used as the generator terminal voltage data.

[0143] Based on the sampling time period, the original generator power data of the generators in the power system is extracted to obtain intermediate generator power data, and the fundamental component data of the intermediate generator power data is used as the generator power data.

[0144] Based on the sampling time period, the original speed data of the generator in the power system is extracted to obtain intermediate speed data, and the fundamental component data of the intermediate speed data is used as the speed data.

[0145] Based on the sampling time period, the original measured excitation voltage data of the generator in the power system is extracted to obtain intermediate measured excitation voltage data, and the fundamental component data of the intermediate measured excitation voltage data is used as the measured excitation voltage data.

[0146] For example, the sampling time period can be determined by those skilled in the art based on actual circumstances, and this embodiment of the invention does not impose any limitations on it. However, the sampling time period is preferably included within the time range covered by the collected power system data.

[0147] For example, the raw generator terminal voltage data, raw generator power data, raw speed data, and raw measured excitation voltage data can be acquired from the corresponding generator in the power system through, but not limited to, corresponding PMU devices (Phasor Measurement Units), and then the data in the PMU devices can be exported. The PMU device is a phasor measurement unit that uses the second pulse of the Global Positioning System (GPS) as a synchronization clock. It can be used in the fields of dynamic monitoring, system protection, system analysis, and prediction of power systems, and is one of the important devices for ensuring the safe operation of the power grid. The specific data format of the raw generator terminal voltage data, raw generator power data, raw speed data, and raw measured excitation voltage data can be the corresponding waveform signals. Furthermore, the raw generator power data and raw speed data can be obtained or determined after processing by, but not limited to, the DC blocking link corresponding to the actual power system stabilizer of the actual excitation system of the generator in the power system, and then acquired accordingly. It should be noted that the data format, specific source, and transfer process in the power system of the original generator terminal voltage data, original generator power data, original speed data, and original measured excitation voltage data can be determined by those skilled in the art based on the actual situation. The above description is only an example and does not constitute a limitation.

[0148] For example, the raw rotational speed data may be, but is not limited to, the rotational speed data of the corresponding generator in the power system; the raw terminal voltage data may be, but is not limited to, the terminal voltage data of the corresponding generator in the power system; the raw generator power data may be, but is not limited to, the active power data or electrical power data of the corresponding generator in the power system; and the raw measured excitation voltage data may be, but is not limited to, the measured excitation voltage data of the corresponding excitation system in the power system. It should be noted that the specific nature of the raw terminal voltage data, raw generator power data, raw rotational speed data, and raw measured excitation voltage data can be determined by those skilled in the art based on the actual situation. The above description is merely an example and does not constitute a limitation.

[0149] For example, the step of extracting intermediate terminal voltage data from the original generator terminal voltage data in a power system based on a preset sampling time period can be, but is not limited to, extracting data segments from the original terminal voltage data that correspond to the sampling time period. The original terminal voltage data can be in the form of a waveform signal; in this case, the extraction operation involves extracting the waveform corresponding to the sampling time period from the original terminal voltage data to obtain the intermediate terminal voltage data. It should be noted that the specific implementation of extracting intermediate terminal voltage data from the original generator terminal voltage data in a power system based on a preset sampling time period can be determined by those skilled in the art based on actual conditions. The above description is merely an example and does not constitute a limitation.

[0150] For example, the fundamental component data of the intermediate terminal voltage data can be obtained by, but is not limited to, performing Fourier analysis (Fourier decomposition) on the intermediate terminal voltage data. During the Fourier analysis, other harmonic components in the intermediate terminal voltage data are removed. It should be noted that the specific method for obtaining the fundamental component data of the intermediate terminal voltage data can be determined by those skilled in the art based on the actual situation. The above description is merely an example and does not constitute a limitation.

[0151] For example, the step of extracting intermediate generator power data from the original generator power data of the power system based on the sampling time period can be, but is not limited to, extracting data segments from the original generator power data that correspond to the sampling time period. Specifically, the original generator power data can be in the form of a waveform signal; in this case, the extraction operation involves extracting the waveform corresponding to the sampling time period from the original generator power data to obtain the intermediate generator power data. It should be noted that the specific implementation method for extracting intermediate generator power data from the original generator power data of the power system based on the sampling time period can be determined by those skilled in the art according to the actual situation. The above description is merely an example and does not constitute a limitation.

[0152] For example, the fundamental component data of the intermediate generator power data can be obtained by, but is not limited to, performing Fourier analysis (Fourier decomposition) on the intermediate generator power data. During the Fourier analysis, other harmonic components in the intermediate generator power data are removed. It should be noted that the specific method for obtaining the fundamental component data of the intermediate generator power data can be determined by those skilled in the art based on the actual situation. The above description is merely an example and does not constitute a limitation.

[0153] For example, the step of extracting intermediate speed data from the original generator speed data in the power system based on the sampling time period can be, but is not limited to, extracting data segments from the original speed data corresponding to the sampling time period. The original speed data can be in the form of a waveform signal, and the corresponding extraction operation is to extract the waveform corresponding to the sampling time period from the original speed data to obtain the intermediate speed data. It should be noted that the specific implementation of extracting intermediate speed data from the original generator speed data in the power system based on the sampling time period can be determined by those skilled in the art according to the actual situation. The above description is merely an example and does not constitute a limitation.

[0154] For example, the fundamental component data of the intermediate speed data can be obtained by, but is not limited to, performing Fourier analysis (Fourier decomposition) on the intermediate speed data. During the Fourier analysis, other harmonic components in the intermediate speed data are removed. It should be noted that the specific method for obtaining the fundamental component data of the intermediate speed data can be determined by those skilled in the art based on the actual situation. The above description is merely an example and does not constitute a limitation.

[0155] For example, the step of extracting intermediate measured excitation voltage data from the original measured excitation voltage data of the generator in the power system based on the sampling time period can be, but is not limited to, extracting data segments from the original measured excitation voltage data that correspond to the sampling time period. Specifically, the original measured excitation voltage data can be in the form of a waveform signal; in this case, the extraction operation involves extracting the waveform corresponding to the sampling time period from the original measured excitation voltage data to obtain the intermediate measured excitation voltage data. It should be noted that the specific implementation of extracting intermediate measured excitation voltage data from the original measured excitation voltage data of the generator in the power system based on the sampling time period can be determined by those skilled in the art based on actual conditions. The above description is merely an example and does not constitute a limitation.

[0156] For example, the fundamental component data of the intermediate measured excitation voltage data can be obtained by, but is not limited to, performing Fourier analysis (Fourier decomposition) on the intermediate measured excitation voltage data. During the Fourier analysis, other harmonic components in the intermediate measured excitation voltage data are removed. It should be noted that the specific method for obtaining the fundamental component data of the intermediate measured excitation voltage data can be determined by those skilled in the art based on the actual situation. The above description is merely an example and does not constitute a limitation.

[0157] Through the above steps, the time range of the generator terminal voltage data, generator power data, speed data, and measured excitation voltage data to be used subsequently can be specifically defined. The fundamental component that mainly characterizes the relevant data can be screened out for subsequent use. This not only effectively reduces the amount of data and improves sampling efficiency, but also significantly reduces noise interference and interference from poorly correlated information in the relevant data. This makes the determined generator terminal voltage data, generator power data, speed data, and measured excitation voltage data to be used subsequently highly typical and accurate, thereby improving the accuracy and adaptability of the overall power system oscillation source detection.

[0158] In one alternative implementation, such as Figure 4 As shown, determining the second phase difference between the calculated excitation voltage data and the measured excitation voltage data of the generator in the power system based on the oscillation period includes the following steps:

[0159] S401: Based on the calculated excitation voltage data, determine the corresponding multiple calculated excitation voltage zero-crossing points; and based on the measured excitation voltage data, determine the corresponding multiple measured excitation voltage zero-crossing points.

[0160] S402: Based on the calculated excitation voltage zero-crossing point and the measured excitation voltage zero-crossing point corresponding to the calculated excitation voltage zero-crossing point, multiple corresponding excitation voltage zero-crossing point time differences are obtained.

[0161] S403: Determine the second phase difference based on the oscillation period, the time difference of the excitation voltage zero crossing point, and the number of second time differences of the excitation voltage zero crossing point.

[0162] For example, determining multiple zero-crossing points of the calculated excitation voltage based on the calculated excitation voltage data can be, but is not limited to, determining all time points where the calculated excitation voltage is 0 as the zero-crossing points. The calculated excitation voltage data can be in the form of a waveform signal. It should be noted that the specific implementation of determining multiple zero-crossing points of the calculated excitation voltage based on the calculated excitation voltage data can be determined by those skilled in the art according to the actual situation; the above description is merely an example and does not constitute a limitation.

[0163] For example, determining multiple zero-crossing points of the measured excitation voltage based on the measured excitation voltage data can be, but is not limited to, determining all time points where the measured excitation voltage is 0 as the zero-crossing points. The measured excitation voltage data can be in the form of a waveform signal. It should be noted that the specific implementation of determining multiple zero-crossing points of the measured excitation voltage based on the measured excitation voltage data can be determined by those skilled in the art according to the actual situation; the above description is merely an example and does not constitute a limitation.

[0164] For example, the measured zero-crossing point of the excitation voltage corresponding to the calculated zero-crossing point can be, but is not limited to, the measured zero-crossing point of the excitation voltage that is in the same time sequence as the calculated zero-crossing point. Specifically, it can be, but is not limited to, the measured zero-crossing point of the excitation voltage that is the same as the calculated zero-crossing point in the corresponding time sequence number (the time sequence number from smallest to largest can correspond to, but is not limited to, the time point from earliest to latest). For example, for the first calculated zero-crossing point of the excitation voltage, its corresponding measured zero-crossing point of the excitation voltage is specifically the first measured zero-crossing point of the excitation voltage within the corresponding sampling range; for the fifth calculated zero-crossing point of the excitation voltage, its corresponding measured zero-crossing point of the excitation voltage is specifically the fifth measured zero-crossing point of the excitation voltage within the corresponding sampling range. It should be noted that the specific correspondence between the calculated and measured zero-crossing points of the excitation voltage can be determined by those skilled in the art based on the actual situation. The above description is merely an example and does not constitute a limitation.

[0165] For example, step S402 can be, but is not limited to, using the time difference between the calculated excitation voltage zero-crossing point and the measured excitation voltage zero-crossing point corresponding to the calculated excitation voltage zero-crossing point as the corresponding excitation voltage zero-crossing point time difference. Here, one excitation voltage zero-crossing point time difference corresponds to one calculated excitation voltage zero-crossing point and one measured excitation voltage zero-crossing point. It should be noted that the specific implementation of step S402 can be determined by those skilled in the art based on actual circumstances; the above description is merely an example and does not constitute a limitation.

[0166] For example, step S403 can be expressed as, but is not limited to, the following formula:

[0167]

[0168] in, Indicates the second phase difference. This represents the time difference between the zero-crossing points of the excitation voltage, where i represents the corresponding time sequence number, T represents the oscillation period, and n2 represents the number of time differences between the zero-crossing points of the excitation voltage (the same as the number of calculated and measured zero-crossing points of the excitation voltage within the corresponding sampling range, i.e., the number of second time differences). This indicates the zero-crossing point of the i-th measured excitation voltage within the corresponding sampling range. This indicates the i-th calculated excitation voltage zero-crossing point within the corresponding sampling range.

[0169] It should be noted that the specific implementation of step S403 can be determined by those skilled in the art based on the actual situation. The above description is only an example and does not constitute a limitation.

[0170] Through the above steps, based on relevant waveform principles and physical principles, the second phase difference between the calculated excitation voltage data and the measured excitation voltage data of the generator in the power system can be accurately, quickly and conveniently determined through simple calculations and with a small amount of data. This improves the accuracy, speed and adaptability of the overall power system oscillation source detection.

[0171] In an optional implementation, determining the amplitude difference between the calculated excitation voltage data and the measured excitation voltage data includes:

[0172] Based on the calculated excitation voltage data, the amplitude of the calculated excitation voltage data is obtained;

[0173] Based on the measured excitation voltage data, the amplitude of the measured excitation voltage data is obtained;

[0174] The amplitude difference is determined based on the calculated excitation voltage amplitude and the measured excitation voltage amplitude.

[0175] For example, obtaining the calculated excitation voltage amplitude based on the calculated excitation voltage data can be, but is not limited to, performing Fourier decomposition on the calculated excitation voltage data to obtain the corresponding calculated excitation voltage amplitude. It should be noted that the specific implementation method for obtaining the calculated excitation voltage amplitude based on the calculated excitation voltage data can be determined by those skilled in the art according to the actual situation; the above description is merely an example and does not constitute a limitation.

[0176] For example, obtaining the amplitude of the measured excitation voltage data based on the measured excitation voltage data can be, but is not limited to, performing Fourier decomposition on the measured excitation voltage data to obtain the corresponding amplitude of the measured excitation voltage data. It should be noted that the specific implementation method for obtaining the amplitude of the measured excitation voltage data based on the measured excitation voltage data can be determined by those skilled in the art according to the actual situation; the above description is merely an example and does not constitute a limitation.

[0177] For example, determining the amplitude difference based on the calculated excitation voltage data amplitude and the measured excitation voltage data amplitude can be, but is not limited to, subtracting the measured excitation voltage data amplitude from the calculated excitation voltage data amplitude. It should be noted that the specific implementation of determining the amplitude difference based on the calculated excitation voltage data amplitude and the measured excitation voltage data amplitude can be determined by those skilled in the art according to the actual situation; the above description is merely an example and does not constitute a limitation.

[0178] For example, the calculated excitation voltage data can be, but is not limited to, the theoretical value of the excitation voltage of a generator in a corresponding power system under normal operating conditions, obtained through model calculation. It should be noted that the nature of the calculated excitation voltage data can be determined by those skilled in the art based on actual circumstances; the above description is merely illustrative and does not constitute a limitation.

[0179] Through the above steps, more detailed simple decomposition and calculation can be performed, improving the accuracy and speed of determining the amplitude difference, thereby improving the accuracy, speed and adaptability of the overall power system oscillation source detection.

[0180] In one alternative implementation, such as Figure 5 As shown, determining whether the power system oscillation source originates from the generator excitation system side based on the second phase difference and amplitude difference includes the following steps:

[0181] S501: Determine whether the absolute value of the second phase difference is greater than the preset second oscillation phase threshold or the absolute value of the amplitude difference is greater than the preset safe amplitude difference threshold. If so, issue an alarm for the presence of an oscillation source on the excitation system side.

[0182] For example, the second oscillation phase threshold can be, but is not limited to, a threshold ranging from [0°, 10°] (preferably, in integer form). It should be noted that the second oscillation phase threshold can be determined by those skilled in the art based on actual circumstances; the above description is merely illustrative and does not constitute a limitation.

[0183] For example, the safety amplitude difference threshold can be, but is not limited to, a threshold ranging from [0, 0.05]. It should be noted that the safety amplitude difference threshold can be determined by those skilled in the art based on actual circumstances; the above description is merely an example and does not constitute a limitation.

[0184] Through the above steps, the relevant phase laws and amplitude characteristics of the excitation system of the generator in the power system can be fully considered, and the specific standards for detecting whether the oscillation originates from the generator excitation system side can be refined accordingly. This improves the accuracy of detecting whether there is an oscillation on the excitation system side. Moreover, the above judgment and processing process is not complicated, takes less time, and is easy to apply. Therefore, it also improves the speed and applicability of detecting whether there is an oscillation source on the excitation system side, thereby improving the accuracy, speed, and adaptability of the overall power system oscillation source detection.

[0185] The following illustrates the relevant principle for detecting the presence of an oscillation source on the excitation system side:

[0186] Theoretically, if the excitation system output is normal, the generator terminal voltage, speed, and active power signals collected by the PMU should be input into the corresponding model of the generator excitation system (including PSS, AVR, and power system). The calculated excitation voltage should have the same phase and amplitude as the measured excitation voltage from the power system. If the excitation system malfunctions, there should be a significant difference in amplitude or phase between the calculated and measured excitation voltages. However, in practical applications, even if the excitation system is relatively normal, there will still be a corresponding phase and amplitude difference (small difference) between the calculated and measured excitation voltages. Therefore, it is difficult to achieve a phase and amplitude difference of exactly zero. Thus, a second oscillation phase threshold and a safe amplitude difference threshold are needed as reference information to detect the presence of an oscillation source on the excitation system side.

[0187] Based on relevant physical principles, power system principles, and the aforementioned laws, the rationality of steps S401 to S403 and step S501 can be deduced.

[0188] It should be noted that the relevant principles for detecting the presence of an oscillation source on the excitation system side can be determined by those skilled in the art based on the actual situation, and the embodiments of the present invention do not impose any limitations on this.

[0189] Based on the same principle, this invention discloses a power system oscillation source detection device 600, such as... Figure 6 As shown, the power system oscillation source detection device 600 includes:

[0190] The first detection module 601 is used to determine the first phase difference between the generator power data and speed data of the power system based on the oscillation period of the power system, and to determine whether the oscillation source of the power system comes from the generator prime mover side based on the first phase difference. If it comes from the generator prime mover side, an alarm is triggered to indicate the presence of an oscillation source on the prime mover side.

[0191] The second detection module 602 is used to determine, based on the oscillation period, a second phase difference between the calculated excitation voltage data and the measured excitation voltage data of the generator in the power system, and to determine the amplitude difference between the calculated excitation voltage data and the measured excitation voltage data, if the oscillation does not originate from the generator prime mover side. The calculated excitation voltage data is obtained based on the excitation system model corresponding to the generator in the power system. Based on the second phase difference and the amplitude difference, it determines whether the oscillation source in the power system originates from the generator excitation system side. If it does, it issues an alarm indicating the presence of an oscillation source on the excitation system side.

[0192] The third detection module 603 is used to issue an alarm for the presence of an oscillation source on the grid side if the oscillation does not originate from the generator excitation system side.

[0193] In an optional implementation, the system further includes an oscillation period determination module, used for:

[0194] Before determining the first phase difference between generator power data and speed data of the power system based on the oscillation period of the power system.

[0195] Based on the generator power data of the power system, determine the corresponding zero-crossing points of multiple generator power;

[0196] The oscillation period is obtained based on the zero-crossing point of the generator power.

[0197] In an optional implementation, the first detection module 601 is configured to:

[0198] Based on the generator power data, determine multiple corresponding generator power zero-crossing points; and based on the rotational speed data, determine multiple corresponding rotational speed zero-crossing points.

[0199] Based on the generator power zero-crossing point and the speed zero-crossing point corresponding to the generator power zero-crossing point, multiple corresponding power and speed zero-crossing point time differences are obtained.

[0200] The first phase difference is determined based on the oscillation period, the time difference between the power and speed zero crossing points, and the number of first time differences between the power and speed zero crossing points.

[0201] In an optional implementation, the first detection module 601 is configured to:

[0202] Subtract the preset normal lag phase from the first phase difference to obtain the initial prime mover oscillation phase, and take the absolute value of the initial prime mover oscillation phase as the prime mover oscillation phase.

[0203] Determine whether the oscillation phase of the prime mover is greater than a preset first oscillation phase threshold. If so, issue an alarm indicating the presence of an oscillation source on the prime mover side.

[0204] In an optional implementation, a model computation module is further included, for:

[0205] Before determining the second phase difference between the calculated excitation voltage data and the measured excitation voltage data of the generator in the power system based on the oscillation period,

[0206] Based on the generator terminal voltage data, preset given voltage data, generator power data, speed data, and preset excitation system model corresponding to the generator in the power system, the initial calculated excitation voltage data is obtained.

[0207] Based on a preset sampling time period, the initial calculated excitation voltage data is truncated to obtain intermediate calculated excitation voltage data, and the fundamental component data of the intermediate calculated excitation voltage data is used as the calculated excitation voltage data of the generator in the power system.

[0208] In an optional implementation, a further preprocessing module is used for:

[0209] Before determining the first phase difference between generator power data and speed data of the power system based on the oscillation period of the power system.

[0210] Based on a preset sampling time period, the original generator terminal voltage data of the generator in the power system is extracted to obtain intermediate generator terminal voltage data, and the fundamental component data of the intermediate generator terminal voltage data is used as the generator terminal voltage data.

[0211] Based on the sampling time period, the original generator power data of the generators in the power system is extracted to obtain intermediate generator power data, and the fundamental component data of the intermediate generator power data is used as the generator power data.

[0212] Based on the sampling time period, the original speed data of the generator in the power system is extracted to obtain intermediate speed data, and the fundamental component data of the intermediate speed data is used as the speed data.

[0213] Based on the sampling time period, the original measured excitation voltage data of the generator in the power system is extracted to obtain intermediate measured excitation voltage data, and the fundamental component data of the intermediate measured excitation voltage data is used as the measured excitation voltage data.

[0214] In an optional implementation, the second detection module 602 is used for:

[0215] Based on the calculated excitation voltage data, multiple calculated excitation voltage zero-crossing points are determined; and based on the measured excitation voltage data, multiple measured excitation voltage zero-crossing points are determined.

[0216] Based on the calculated excitation voltage zero-crossing point and the measured excitation voltage zero-crossing point corresponding to the calculated excitation voltage zero-crossing point, multiple corresponding excitation voltage zero-crossing point time differences are obtained;

[0217] The second phase difference is determined based on the oscillation period, the time difference of the excitation voltage zero crossing point, and the number of second time differences of the excitation voltage zero crossing point.

[0218] In an optional implementation, the second detection module 602 is used for:

[0219] Based on the calculated excitation voltage data, the amplitude of the calculated excitation voltage data is obtained;

[0220] Based on the measured excitation voltage data, the amplitude of the measured excitation voltage data is obtained;

[0221] The amplitude difference is determined based on the calculated excitation voltage amplitude and the measured excitation voltage amplitude.

[0222] In an optional implementation, the third detection module 603 is used for:

[0223] Determine whether the absolute value of the second phase difference is greater than the preset second oscillation phase threshold or the absolute value of the amplitude difference is greater than the preset safe amplitude difference threshold. If so, issue an alarm for the presence of an oscillation source on the excitation system side.

[0224] Since the principle of the power system oscillation source detection device 600 in solving the problem is similar to the above method, the implementation of this power system oscillation source detection device 600 can refer to the implementation of the above method, and will not be repeated here.

[0225] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer device, specifically, a computer device can be, for example, a personal computer, a laptop computer, a cellular phone, a camera phone, a smartphone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or any combination of these devices.

[0226] In a typical example, a computer device specifically includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method described above.

[0227] The following is for reference. Figure 7 It shows a schematic diagram of the structure of a computer device 700 suitable for implementing the embodiments of this application.

[0228] like Figure 7 As shown, the computer device 700 includes a central processing unit (CPU) 701, which can perform various appropriate tasks and processes based on programs stored in read-only memory (ROM) 702 or programs loaded from storage section 708 into random access memory (RAM) 703. The RAM 703 also stores various programs and data required for the operation of the system 700. The CPU 701, ROM 702, and RAM 703 are interconnected via a bus 704. An input / output (I / O) interface 705 is also connected to the bus 704.

[0229] The following components are connected to the I / O interface 705: an input section 706 including a keyboard, mouse, etc.; an output section 707 including a cathode ray tube (CRT), liquid crystal feedback (LCD), etc., and speakers, etc.; a storage section 708 including a hard disk, etc.; and a communication section 709 including a network interface card such as a LAN card, modem, etc. The communication section 709 performs communication processing via a network such as the Internet. A drive 710 is also connected to the I / O interface 705 as needed. A removable medium 711, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on the drive 710 as needed so that computer programs read from it can be installed in the storage section 708 as needed.

[0230] In particular, according to embodiments of the present invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of the present invention include a computer program product comprising a computer program tangibly embodied on a machine-readable medium, the computer program including program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via communication section 709, and / or installed from removable medium 711.

[0231] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0232] For ease of description, the above devices are described separately by function as various units. Of course, in implementing this application, the functions of each unit can be implemented in one or more software and / or hardware.

[0233] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0234] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0235] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0236] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0237] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0238] This application can be described in the general context of computer-executable instructions, such as program modules, that are executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform a specific task or implement a specific abstract data type. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0239] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments.

[0240] The above description is merely an embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for detecting oscillation sources in a power system, characterized in that, include: Based on the oscillation period of the power system, the first phase difference between the generator power data and the speed data of the power system is determined, and based on the first phase difference, it is determined whether the oscillation source of the power system comes from the generator prime mover side. If it comes from the generator prime mover side, an alarm is issued for the presence of an oscillation source on the prime mover side. If the oscillation does not originate from the generator prime mover side, based on the oscillation period, the second phase difference between the calculated excitation voltage data and the measured excitation voltage data of the generator in the power system is determined, and the amplitude difference between the calculated excitation voltage data and the measured excitation voltage data is determined. The calculated excitation voltage data is obtained based on the excitation system model corresponding to the generator in the power system. Based on the second phase difference and the amplitude difference, it is determined whether the oscillation source of the power system originates from the generator excitation system side. If it originates from the generator excitation system side, an alarm is triggered indicating the presence of an oscillation source on the excitation system side. If the oscillation source does not originate from the generator excitation system side, an alarm will be triggered indicating the presence of an oscillation source on the grid side. The calculated excitation voltage data is obtained based on the excitation system model corresponding to the generator in the power system, including: Before determining the second phase difference between the calculated excitation voltage data and the measured excitation voltage data of the generator in the power system based on the oscillation period, Based on the generator terminal voltage data, preset given voltage data, generator power data, speed data, and preset excitation system model corresponding to the generator in the power system, the initial calculated excitation voltage data is obtained. Based on a preset sampling time period, the initial calculated excitation voltage data is truncated to obtain intermediate calculated excitation voltage data, and the fundamental component data of the intermediate calculated excitation voltage data is used as the calculated excitation voltage data of the generator in the power system.

2. The method according to claim 1, characterized in that, Further includes: Before determining the first phase difference between generator power data and speed data of the power system based on the oscillation period of the power system. Based on the generator power data of the power system, determine the corresponding zero-crossing points of multiple generator power; The oscillation period is obtained based on the zero-crossing point of the generator power.

3. The method according to claim 1, characterized in that, The determination of the first phase difference between generator power data and speed data of the power system based on the oscillation period of the power system includes: Based on the generator power data, determine multiple corresponding generator power zero-crossing points; and based on the rotational speed data, determine multiple corresponding rotational speed zero-crossing points. Based on the generator power zero-crossing point and the speed zero-crossing point corresponding to the generator power zero-crossing point, multiple corresponding power and speed zero-crossing point time differences are obtained. The first phase difference is determined based on the oscillation period, the time difference between the power and speed zero crossing points, and the number of first time differences between the power and speed zero crossing points.

4. The method according to claim 1, characterized in that, The step of determining whether the power system oscillation source originates from the generator prime mover side based on the first phase difference includes: Subtract the preset normal lag phase from the first phase difference to obtain the initial prime mover oscillation phase, and take the absolute value of the initial prime mover oscillation phase as the prime mover oscillation phase. Determine whether the oscillation phase of the prime mover is greater than a preset first oscillation phase threshold. If so, issue an alarm indicating the presence of an oscillation source on the prime mover side.

5. The method according to claim 1, characterized in that, Further includes: Before determining the first phase difference between generator power data and speed data of the power system based on the oscillation period of the power system. Based on a preset sampling time period, the original generator terminal voltage data of the generator in the power system is extracted to obtain intermediate generator terminal voltage data, and the fundamental component data of the intermediate generator terminal voltage data is used as the generator terminal voltage data. Based on the sampling time period, the original generator power data of the generators in the power system is extracted to obtain intermediate generator power data, and the fundamental component data of the intermediate generator power data is used as the generator power data. Based on the sampling time period, the original speed data of the generator in the power system is extracted to obtain intermediate speed data, and the fundamental component data of the intermediate speed data is used as the speed data. Based on the sampling time period, the original measured excitation voltage data of the generator in the power system is extracted to obtain intermediate measured excitation voltage data, and the fundamental component data of the intermediate measured excitation voltage data is used as the measured excitation voltage data.

6. The method according to claim 1, characterized in that, The determination of the second phase difference between the calculated excitation voltage data and the measured excitation voltage data of the generator in the power system based on the oscillation period includes: Based on the calculated excitation voltage data, multiple calculated excitation voltage zero-crossing points are determined; and based on the measured excitation voltage data, multiple measured excitation voltage zero-crossing points are determined. Based on the calculated excitation voltage zero-crossing point and the measured excitation voltage zero-crossing point corresponding to the calculated excitation voltage zero-crossing point, multiple corresponding excitation voltage zero-crossing point time differences are obtained; The second phase difference is determined based on the oscillation period, the time difference of the excitation voltage zero crossing point, and the number of second time differences of the excitation voltage zero crossing point.

7. The method according to claim 1, characterized in that, Determining the amplitude difference between the calculated excitation voltage data and the measured excitation voltage data includes: Based on the calculated excitation voltage data, the amplitude of the calculated excitation voltage data is obtained; Based on the measured excitation voltage data, the amplitude of the measured excitation voltage data is obtained; The amplitude difference is determined based on the calculated excitation voltage amplitude and the measured excitation voltage amplitude.

8. The method according to claim 1, characterized in that, The step of determining whether the power system oscillation source originates from the generator excitation system side based on the second phase difference and amplitude difference includes: Determine whether the absolute value of the second phase difference is greater than the preset second oscillation phase threshold or the absolute value of the amplitude difference is greater than the preset safe amplitude difference threshold. If so, issue an alarm for the presence of an oscillation source on the excitation system side.

9. A power system oscillation source detection device, characterized in that, include: The first detection module is used to determine the first phase difference between the generator power data and speed data of the power system based on the oscillation period of the power system, and to determine whether the oscillation source of the power system comes from the generator prime mover side based on the first phase difference. If it comes from the generator prime mover side, an alarm is triggered to indicate the presence of an oscillation source on the prime mover side. The second detection module is used to determine, based on the oscillation period, the second phase difference between the calculated excitation voltage data and the measured excitation voltage data of the generator in the power system, and the amplitude difference between the calculated excitation voltage data and the measured excitation voltage data, if the oscillation does not originate from the generator prime mover side. The calculated excitation voltage data is obtained based on the excitation system model corresponding to the generator in the power system. Based on the second phase difference and the amplitude difference, it determines whether the oscillation source in the power system originates from the generator excitation system side. If it does, it issues an alarm indicating the presence of an oscillation source on the excitation system side. The third detection module is used to alarm the presence of an oscillation source on the grid side if the oscillation source does not originate from the generator excitation system side. The calculated excitation voltage data is obtained based on the excitation system model corresponding to the generator in the power system, including: Before determining the second phase difference between the calculated excitation voltage data and the measured excitation voltage data of the generator in the power system based on the oscillation period, Based on the generator terminal voltage data, preset given voltage data, generator power data, speed data, and preset excitation system model corresponding to the generator in the power system, the initial calculated excitation voltage data is obtained. Based on a preset sampling time period, the initial calculated excitation voltage data is truncated to obtain intermediate calculated excitation voltage data, and the fundamental component data of the intermediate calculated excitation voltage data is used as the calculated excitation voltage data of the generator in the power system.

10. 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 program, it implements the method as described in any one of claims 1-8.

11. A computer-readable medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1-8.

12. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the method of any one of claims 1-8.

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