Power system forced oscillation source equipment-level tracing method based on CPSD

Abstract

The invention discloses a CPSD-based power system forced oscillation source equipment level tracing method, and relates to the technical field of power system forced oscillation disturbance source equipment level positioning, and the method comprises the steps: collecting and calculating the active power, reactive power, frequency and voltage amplitude measurement data of a generator node during a forced oscillation period; obtaining a dynamic component of the relative steady-state value; calculating a frequency domain dissipation energy spectrum, and confirming a forced oscillation dominant oscillation frequency and a forced oscillation source; respectively calculating the frequency domain cross-power spectral density of the speed regulation system and the excitation system during the forced oscillation period; calculating amplitude spectrums and phase spectrums of each generator speed regulation system and excitation system at the forced oscillation frequency, and cooperatively positioning forced oscillation disturbance equipment by the amplitude spectrums and the phase spectrums; and calculating the energy contribution rate of each generator speed regulation system and excitation system, and determining the dominant forced oscillation disturbance equipment. Therefore, by adopting the method, the control system where the disturbance source is located can be accurately positioned, and forced oscillation equipment-level positioning is realized.

Description

Technical Field

[0001] This invention relates to the field of device-level location technology for forced oscillation disturbance sources in power systems, and in particular to a device-level tracing method for forced oscillation sources in power systems based on CPSD. Background Technology

[0002] Forced oscillation (FO) in power systems is a power oscillation phenomenon caused by continuous periodic disturbances. When the frequency of forced oscillation in the power grid approaches the system's natural oscillation frequency, it will lead to significant power oscillations in the grid, resulting in serious safety and stability incidents. Existing research shows that there are many types of disturbance sources in the power grid that can induce forced oscillations. In addition to traditional excitation system faults, improper settings of power system stabilizer parameters, and abnormal throttle movements of prime movers, the highly random access of new energy sources such as wind power and photovoltaic power can also induce forced oscillations. Because forced oscillations are characterized by rapid onset and rapid subsidence after the oscillation source is removed, the common measure used in practical engineering to suppress forced oscillations in the power grid is to quickly locate and isolate the oscillation source. Therefore, quickly and accurately locating the forced oscillation source is the primary task in suppressing forced oscillations in the power grid.

[0003] For forced oscillations dominated by synchronous generator units, compared to directly cutting off the disturbing generator unit after locating the source of the forced oscillation, accurately locating the control system where the disturbance is located and taking targeted suppression measures, such as adjusting control parameters or shutting down the control system where the disturbance is located, can effectively reduce the scope of the accident's impact and has important research significance.

[0004] Currently, some studies have located forced oscillation sources in the prime mover system by comparing the analytical relationship between the generator's active power transfer function and its power spectral density. However, this method cannot locate disturbance sources in the excitation system. To address this issue, some studies have identified disturbance devices in the excitation and prime mover systems by comparing the degree of agreement between the predicted and actual power spectral density values ​​of the model response. Other studies have used the frequency domain response characteristics of the transfer function matrix to locate forced oscillation sources in the prime mover and excitation systems, respectively. Still other studies have combined dynamic state estimation with DEF to locate forced oscillation sources and defined mechanical power energy and excitation voltage energy to identify disturbance control systems. However, the mechanical power of actual systems is usually not easily obtained directly.

[0005] Therefore, in response to the difficulty of intuitively and accurately locating the control equipment where the forced oscillation source is located by existing methods, this invention proposes a device-level tracing method for forced oscillation sources in power systems based on CPSD, which further locates the forced oscillation source to the generator's speed regulation system and excitation system, while accurately assessing the oscillation contribution of each control equipment during the oscillation. Summary of the Invention

[0006] The purpose of this invention is to provide a device-level tracing method for forced oscillation sources in power systems based on CPSD. This method defines the cross-power spectral density of the generator speed control system and the excitation system based on measurement information, provides a device-level cooperative positioning criterion for the disturbance source, and achieves accurate device-level positioning of the forced oscillation source.

[0007] To achieve the above objectives, this invention provides a device-level tracing method for forced oscillation sources in power systems based on CPSD, comprising:

[0008] S1. Collect and calculate the active power, reactive power, frequency and voltage amplitude measurement data of the generator node during forced oscillation, and obtain the dynamic components of each measurement data relative to the steady-state value.

[0009] S2. By performing Fourier transform on the dynamic components, the time-domain dissipated energy flow into the system from the motor node is converted into the frequency-domain dissipated energy spectrum, thus confirming the dominant oscillation frequency and the source of the forced oscillation.

[0010] S3. Based on the time-domain dissipated energy flow structure, define the frequency domain cross power spectral density of the speed regulation system and excitation system during forced oscillation, and calculate the amplitude spectrum and phase spectrum of each generator speed regulation system and excitation system at the forced oscillation frequency according to the dominant oscillation frequency. The forced oscillation disturbance equipment is located by the amplitude spectrum and phase spectrum in concert.

[0011] S4. Based on the dominant oscillation frequency band energy, calculate the energy contribution rate of each generator speed control system and excitation system, and determine the dominant forced oscillation disturbance equipment.

[0012] Furthermore, in S2, the peak value of the frequency domain dissipative energy spectrum corresponds to the dominant oscillation frequency of the system, and the positive and negative characteristics correspond to different forced oscillation sources.

[0013] Furthermore, the expression for the frequency domain dissipation energy spectrum is as follows:

[0014]

[0015] In the formula, E D The frequency domain dissipation energy spectrum is represented by *, where * indicates conjugate; ΔP(F), Δf(F), ΔQ(F), and ΔlnV(F) represent the dynamic components of the natural logarithm of active power, frequency, reactive power, and voltage amplitude in the frequency domain relative to their steady-state values, respectively.

[0016] Furthermore, in S3, the frequency domain cross-power spectral density of the speed control system and the excitation system during forced oscillation is expressed as follows:

[0017]

[0018] In the formula, H gov (F), H exc(F) represent the frequency domain cross power spectral density of the speed governor and the excitation system, respectively;

[0019] The amplitude spectrum and phase spectrum of each generator speed control system and excitation system at the forced oscillation frequency are expressed as follows:

[0020]

[0021]

[0022] In the formula, M gov (F FO M exc (F FO The numbers ) represent the speed control system and the excitation system at the dominant oscillation frequency F, respectively. FO The amplitude spectrum below, θ gov (F FO ), θ exc (F FO The speed control system and the excitation system are respectively located at the dominant oscillation frequency F. FO The phase spectrum, where Im represents the imaginary part, Re represents the real part, and sgn represents the sign function.

[0023] Furthermore, in S3, the forced oscillation disturbance device, which is located by the coordinated use of amplitude and phase spectra, includes:

[0024] Based on amplitude spectrum location of forced oscillation disturbance equipment: when the amplitude spectrum of the generator control equipment at the forced oscillation frequency is negative, it is determined to be a forced oscillation disturbance equipment; when the amplitude spectrum of the generator control equipment at the forced oscillation frequency is positive, it is determined to be a forced oscillation energy dissipation equipment.

[0025] Based on phase spectrum identification of forced oscillation disturbance equipment: when the generator control equipment has a significant phase deviation from other equipment at the forced oscillation frequency, it is a forced oscillation disturbance equipment; when the phase spectrum of the generator control equipment is consistent at the forced oscillation frequency, it is a device without forced oscillation disturbance; when the phase spectrum of the generator control equipment at the forced oscillation frequency shows multiple disordered distributions, it indicates the presence of natural oscillation.

[0026] Furthermore, S4 includes defining the energy contribution rate based on frequency band energy, expressed as follows:

[0027]

[0028] in,

[0029] ψ i =∫ ΔF H i,FO (F FO )dF;

[0030] In the formula, I represents the total number of speed governors and excitation systems in the system, and ξ i Let ψ be the energy contribution rate of the i-th generator control device. i H represents the frequency band energy of the i-th generator control device. i,FO (F FO ) represents the frequency domain cross-power spectral density of the i-th control device within the dominant oscillation frequency band.

[0031] Therefore, the present invention employs the above-mentioned device-level tracing method for forced oscillation sources in power systems based on CPSD, and has the following technical advantages:

[0032] (1) This invention derives the cross power spectral density of the speed regulation system and the excitation system based on the measurement data, proposes two equipment-level positioning criteria for forced oscillation disturbance sources based on the cross power spectral density, and defines the oscillation contribution evaluation index of the disturbance equipment, so as to accurately locate the control system where the forced oscillation disturbance source is located, and has strong adaptability.

[0033] (2) This invention proposes an oscillation contribution evaluation index, which can evaluate the degree of oscillation participation of each control system in a multi-disturbance source scenario and obtain the dominant disturbance device of the system.

[0034] (3) This invention can provide a more complete and sufficient theoretical positioning system for power system operation and dispatch personnel, and at the same time provide technical support and data support for the dynamic stability supervision and control of the power system.

[0035] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0036] Figure 1 This is a flowchart of a device-level tracing method for forced oscillation sources in power systems based on CPSD;

[0037] Figure 2 This is a schematic diagram of the cross-power spectral density of the forced oscillation signal in an embodiment of a device-level tracing method for forced oscillation sources in a power system based on CPSD.

[0038] Figure 3 This is an example of a device-level tracing method for forced oscillation sources in a power system based on CPSD, showing the dissipated energy spectrum of each generator in scenario one.

[0039] Figure 4 This is the amplitude spectrum of the speed controller and excitation system in scenario one of the embodiments of the CPSD-based power system forced oscillation source device-level tracing method.

[0040] Figure 5This is a device-level tracing method for forced oscillation sources in a power system based on CPSD. In scenario one, the phase spectra of each generator speed governor and excitation system are shown, where (a) is the phase spectrum of each generator speed governor and (b) is the phase spectrum of each generator excitation system.

[0041] Figure 6 This is a device-level tracing method for forced oscillation sources in power systems based on CPSD, and the dissipated energy spectrum of each generator in scenario two of the embodiments.

[0042] Figure 7 This is the amplitude spectrum of the speed controller and excitation system in scenario two of the embodiment of a CPSD-based device-level tracing method for forced oscillation sources in power systems.

[0043] Figure 8 This is a phase spectrum of the speed regulation and excitation system of each generator in scenario two of the embodiment of the CPSD-based power system forced oscillation source device-level tracing method, where (a) is the phase spectrum of each generator speed regulator and (b) is the phase spectrum of each generator excitation system. Detailed Implementation

[0044] The present invention will be explained in more detail through the following embodiments. The purpose of disclosing the present invention is to protect all changes and modifications within the scope of the present invention. The present invention is not limited to the following embodiments.

[0045] Example 1

[0046] like Figure 1 As shown, this invention provides a device-level tracing method for forced oscillation sources in power systems based on CPSD, with the following specific steps:

[0047] S1 and PMU collect and calculate the active power, reactive power, frequency and voltage of the generator node during forced oscillation, and calculate the dynamic components of its relative steady-state value.

[0048] S2. Calculate the dissipation energy spectrum to confirm the dominant oscillation frequency and the source of the forced oscillation.

[0049] S3. Calculate the mutual power spectral density of the speed control system and the excitation system respectively.

[0050] S4. Calculate the amplitude spectrum of each generator speed control system and excitation system at the forced oscillation frequency, and locate the forced oscillation disturbance equipment by amplitude spectrum criterion.

[0051] S5. Calculate the phase spectrum at the forced oscillation frequency of each generator speed control system and excitation system, and use the phase spectrum criterion to locate the equipment causing the forced oscillation disturbance.

[0052] S6. Calculate the energy contribution rate of each generator speed control system and excitation system, and determine the dominant forced oscillation disturbance equipment.

[0053] This embodiment, through the above steps combined with cross power spectral density (CPSD), can accurately locate the control system where the disturbance source is located, and achieve forced oscillation device-level positioning.

[0054] Example 2

[0055] This invention provides a device-level tracing method for forced oscillation sources in power systems based on CPSD, and the specific steps and formulas involved are as follows:

[0056] S1 and PMU collect measurement data of active power, reactive power, frequency, and voltage amplitude, and effectively extract key data x(t) and y(t) reflecting the forced oscillation (FO) state of the power grid to obtain the cross-power spectral density S. xy (ω).

[0057] The signal models x(t) and y(t) of any two electrical quantities can be expressed as:

[0058]

[0059] In the formula, A FO B FO φ represents the amplitude of the corresponding signal FO component. FO , n represents the phase of the corresponding signal FO component. x (t), n y (t) represents random noise with a mean of zero. In this embodiment, x(t) and y(t) represent measurements of active power and frequency, or measurements of reactive power and voltage amplitude.

[0060] Considering only the positive spectrum, the Fourier transform (FT) of x(t) and y(t) can be expressed as:

[0061]

[0062] In the formula, N x (F), N y (F) represents the noise spectrum, and δ is the Dirac function.

[0063] Based on the above equation, the cross power spectral density (CPSD) of x(t) and y(t) can be further obtained, expressed as:

[0064]

[0065] In the formula, * indicates conjugate.

[0066] Due to noise component N x (F), Ny The expectation of (F) is zero, and their Fourier transforms are very small at the forced oscillation frequency, and are usually ignored. Therefore, the cross-power spectral density is mainly determined by the sinusoidal components of the signal, and at the forced oscillation frequency, it can be further simplified to:

[0067]

[0068] In the formula, S xy (F FO The expression denoted by represents the CPSD of signals x(t) and y(t) in the frequency domain, used to characterize the correlation between signals and the strength of their interaction at a specific frequency. For example... Figure 2 As shown, the peak value corresponding to the cross-power spectral density of the two signals represents the significant energy interaction between the two signals at that frequency, which is the dominant forced oscillation frequency.

[0069] S2. Calculate the dissipated energy spectrum using the measurement data, and then determine the dominant oscillation frequency and the source of forced oscillation based on the energy emitted or consumed by the component.

[0070] The dissipated energy flow from the generator node into the system can be expressed as:

[0071] W D =∫(2πΔP(t)Δf(t)dt+ΔQ(t)d(ΔlnV(t)));

[0072] When the internal energy flow within the control system is ignored, the first term of this formula can be approximated as the energy flowing into the system through the speed governor, while the second term can be approximated as the energy flowing into the system from the excitation system; ΔP(t), Δf(t), ΔQ(t), and ΔlnV(t) represent the dynamic components of the natural logarithm of active power, frequency, reactive power, and voltage amplitude relative to their steady-state values, respectively. Each parameter is obtained by inverse Fourier transform, and the expression is:

[0073]

[0074] Where ΔP(F), Δf(F), ΔQ(F), and ΔlnV(F) are the Fourier transforms of ΔP(t), Δf(t), ΔQ(t), and ΔlnV(t), respectively.

[0075] Taking the complex conjugates of Δf(t) and ΔlnV(t), we can obtain:

[0076]

[0077] By using the integral formula of the complex exponential function to eliminate the time integral term, it can be simplified to the frequency domain form of the dissipated energy flow:

[0078]

[0079] For each electrical parameter at the same FO frequency, if F = F' and the Dirac function integral is 1, then the above equation can be further simplified to:

[0080]

[0081] At this point, the time-domain dissipated energy flow is transformed into the frequency-domain dissipated energy spectrum, where the energy in both domains is equal. The peak value of the energy in the frequency domain can determine the dominant FO frequency of the system, and its positive or negative characteristic can determine the FO source.

[0082] S3. Referencing the time-domain dissipated energy flow structure, define the frequency domain cross-power spectral density of the speed regulation system and excitation system during forced oscillation, and use the amplitude spectrum criterion of CPSD to locate the control equipment where the forced oscillation source is located.

[0083] Referring to the form of time-domain dissipated energy flow, the frequency-domain dissipated energy spectrum of the speed governor and excitation system can be expressed as:

[0084]

[0085] In the formula, E gov E exc These represent the frequency domain dissipation energy spectra of the speed controller and the excitation system, respectively.

[0086] To further analyze the energy dissipation of the control device in the frequency domain, the integral term in the above equation is processed, and the CPSD of the speed governor and excitation system is defined as follows:

[0087]

[0088] In the formula, H gov (F), H exc (F) represents the frequency domain CPSD of the speed controller and the excitation system, respectively.

[0089] Once the FO frequency of the system is determined by S2, the amplitude spectrum of the speed governor and excitation system at the FO frequency can be defined as:

[0090]

[0091] In the formula, M gov (F FO M exc (F FO ) represent the amplitude spectra of the speed governor and excitation system at the FO frequency, respectively; Im represents the imaginary part; sgn represents the sign function, defined as:

[0092]

[0093] The amplitude spectrum characterizes the strength of the energy dissipation of the speed control system and excitation system at a given frequency, and its sign indicates the direction of energy flow; a positive value corresponds to energy dissipation, and a negative value corresponds to energy injection. This relationship stems from the equivalence between time-domain dissipated energy flow and frequency-domain CPSD. Therefore, the criterion for locating forced oscillation disturbance devices based on the amplitude spectrum is as follows: if the amplitude spectrum of the generator control device at the forced oscillation frequency is negative, it indicates that it continuously injects oscillation energy into the system, and is therefore a forced oscillation disturbance device; if the amplitude spectrum of the generator control device at the forced oscillation frequency is positive, it indicates that it continuously absorbs oscillation energy from the system, and is therefore a forced oscillation energy dissipation device.

[0094] The amplitude spectrum essentially represents the intensity of energy dissipated by the speed regulation and excitation system at the oscillation frequency, reflecting its degree of participation in the oscillation; the higher the amplitude, the deeper the participation. However, when forced oscillation resonates with a weakly damped natural oscillation mode, during the oscillation, in addition to the disturbing equipment, other generator control equipment may also inject oscillation energy into the system. Therefore, from the perspective of the amplitude spectrum alone, it is impossible to accurately reflect whether the generator control system actively participates in the oscillation due to an internal disturbance source or participates in the resonance due to external disturbances. Considering that the measurement information of the control equipment where the forced oscillation disturbance is located is affected by the oscillation time delay characteristics and propagation path, the phase of the cross power spectral density at the forced oscillation frequency will be significantly different from that of the non-disturbed equipment. Therefore, the phase spectrum of the cross power spectral density can be used for discrimination, i.e.:

[0095]

[0096] In the formula, θ gov (F FO ), θ exc (F FO ( ) are the phase spectra of the speed controller and the excitation system at the FO frequency, respectively, and Re represents the real part.

[0097] The phase spectrum reveals the phase difference between measurements of the generator control system in the frequency domain. In the case of FO, oscillatory behavior propagates along a defined path from the source to the sink, resulting in time delays in measurements obtained at different locations. These time delays manifest in the frequency domain, with the phase spectrum of the interfering device showing a significant deviation compared to other control devices. In contrast, natural oscillations typically occur without a significant source of interference. Therefore, the phase spectrum of the control device is randomly distributed in the complex plane, indicating relative oscillations between various coherent groups.

[0098] In summary, the criteria for identifying FO interference control devices based on phase spectrum are as follows: If the generator control device exhibits a significant phase deviation from other devices at the FO frequency, the interfering device is located within that control device. Conversely, if the phase spectrum of the generator control device is consistent, the corresponding device does not have a FO interference source. Furthermore, if the phase spectrum displays multiple disordered distributions, it indicates the presence of natural oscillations.

[0099] Based on the above, the phase spectrum at the forced oscillation frequency of each generator speed control system and excitation system can be calculated, and the forced oscillation disturbance device can be located collaboratively by the phase spectrum criterion.

[0100] S4. Calculate the energy contribution rate of each generator speed control system and excitation system, determine the dominant forced oscillation disturbance device, and use the energy contribution rate (ECR) as a quantitative indicator to evaluate the contribution of each generator control device to the oscillation energy.

[0101] In scenarios with multiple disturbing devices, prioritizing oscillation suppression measures on the main disturbing devices with high oscillation energy participation can effectively suppress oscillations while avoiding the introduction of new impacts to the system by simultaneously and repeatedly removing disturbing devices. Therefore, after identifying the devices causing forced oscillation disturbances, to further quantitatively measure the oscillation energy contribution of each device during forced oscillation, the frequency band energy of the i-th control device within the FO frequency band is defined as follows:

[0102] ψ i =∫ ΔF H i,FO (F FO )dF;

[0103] In the formula, H i,FO (F FO ) represents the CPSD of the i-th control device within the FO frequency band, and ΔF represents the range of the FO frequency band.

[0104] Energy contribution rate can be defined as:

[0105]

[0106] In the formula, I is the total number of speed governors and excitation systems in the system.

[0107] Through the above steps, rapid and accurate location of forced oscillation disturbance sources in power systems based on CPSD is achieved at the device level.

[0108] Example 3

[0109] This invention provides a device-level source tracing method for forced oscillation sources in power systems based on CPSD, applied to the WECC-179 node system, and verified through simulation analysis. In the WECC-179 node system, all 29 generators are simulated using classical second-order systems with positive damping coefficients, and all loads are constant power loads.

[0110] The disturbance in scenario one is set to continuously inject a 0.37Hz sine wave into the speed control system of generator G77 and resonate with the 0.37Hz inter-regional oscillation mode that exists in the system.

[0111] First, the active power, reactive power, and frequency of each generator are calculated using voltage and current measurement data. Then, the dynamic components of the active power, reactive power, frequency, and voltage amplitude relative to the steady-state value are calculated. Further, FFT is performed on the dynamic components of each electrical quantity, and the dissipation energy spectrum of each generator is calculated, such as... Figure 3 As shown. By Figure 3 It can be seen that the dissipation energy spectrum of each generator has an extreme value at 0.375Hz, indicating that the identified forced oscillation frequency is 0.375Hz. At this frequency, the dissipation energy spectrum of generator G77 is negative, indicating it is a forced oscillation source, while the dissipation energy spectra of the other generators are positive, indicating they are all non-forced oscillation sources. The identified forced oscillation source is consistent with the disturbance setting, verifying the accuracy of the proposed method.

[0112] To further locate the disturbing equipment, the cross-power spectral density of each generator speed control system and excitation system at a frequency of 0.375Hz was calculated, and their amplitude spectrum at the forced oscillation frequency was also calculated. Figure 4 As shown. By Figure 4 It can be seen that the amplitude spectrum of the G77 speed control system of the generator has the highest negative amplitude, indicating that the G77 speed control system is highly involved in the interaction of oscillation energy at the forced oscillation frequency, and is a device for forced oscillation disturbance. In addition, the amplitude spectra of G35, G65, and G79 have relatively high positive amplitudes, and are the main devices for dissipating oscillation energy. It should be noted that some generator excitation systems have relatively weak negative amplitudes due to the influence of system resonance, which also inject oscillation energy into the system, but are much smaller than the amplitude of the G77 speed control system and can be ignored. Figure 5 The phase spectra of each generator speed control system and excitation system at the forced oscillation frequency are further given. Figure 5 As shown in (a), the phase spectrum of the G77 speed control system has a significant phase difference from that of the other generators, indicating that the G77 speed control system is affected by a forced disturbance signal. The phase relationship between the frequency and active power measurement data at the forced oscillation frequency is significantly different from that of the other generators, indicating that the G77 speed control system is a forced oscillation disturbance device; and Figure 5 The phase spectra of the excitation systems of each generator shown in (b) are basically consistent, indicating that there are no forced oscillation disturbance devices in the excitation system.

[0113] Finally, the forced oscillation frequency band energy and energy contribution rate of each device were calculated, and the results are shown in Table 1. Table 1 shows that the generator G77 speed control system mainly participated in the forced oscillation, contributing 49.58% of the network oscillation energy. The above results demonstrate that the method of this invention can accurately locate the disturbance source to the speed control system.

[0114] Table 1 Energy contribution rate of each generator speed regulation and excitation system in Case FM-3 scenario

[0115]

[0116] The disturbance in scenario two is set to continuously inject a 0.43Hz sine wave into the excitation system of generators G70 and G118.

[0117] Perform FFT on the dynamic components of each electrical quantity and calculate the dissipated energy spectrum of each generator, such as... Figure 6 As shown. By Figure 6 It can be seen that the method of this invention identifies the forced oscillation frequency as 0.425Hz, which is basically consistent with the injected disturbance frequency. At this frequency, the dissipated energy spectra of generators G70 and G118 are negative, indicating they are forced oscillation sources, while the remaining generators are non-forced oscillation sources. This positioning result is consistent with the simulation disturbance settings. Then, the cross-power spectral density of the speed control system and excitation system of each generator at the forced oscillation frequency is calculated, and its amplitude spectrum is calculated, such as... Figure 7 As shown. By Figure 7 It can be seen that at the forced oscillation frequency, the excitation system amplitude spectrum of generators G70 and G118 is negative and has a high amplitude, mainly participating in the interaction of oscillation energy and acting as forced oscillation disturbance devices. The speed regulation system amplitude spectrum of G65 is positive, acting as the main oscillation energy dissipation device.

[0118] Figure 8 The calculated phase spectra of the speed control system and excitation system of each generator at the forced oscillation frequency are presented. Among them, the phase spectra of the speed control systems of each generator are basically consistent, while the phase spectra of the excitation systems of G70 and G118 have significant phase differences from the other generators, indicating that they are forced oscillation disturbance devices.

[0119] Table 2 further calculates the energy contribution rate of each generator unit. The excitation systems of generators G70 and G118 mainly participated in forced oscillation, contributing 6.30% and 57.53% of the network oscillation energy, respectively. The above analysis results demonstrate that the method of this invention can effectively and accurately locate the disturbance source in the excitation system.

[0120] Table 2 Energy contribution rate of each generator speed regulation and excitation system in Case F-7-2 scenario.

[0121]

[0122] Therefore, this invention adopts the above-mentioned CPSD-based device-level tracing method for forced oscillation sources in power systems. By using the amplitude and phase spectra of the speed regulation system and the excitation system at the forced oscillation frequency, it provides a device-level collaborative positioning criterion for the disturbance source. At the same time, it proposes an oscillation contribution index based on frequency band energy to evaluate the dominant disturbance device in the forced oscillation, thereby achieving accurate device-level positioning of the forced oscillation source.

[0123] Finally, it should be noted that, unless otherwise specified, the model numbers of the devices in this embodiment of the invention are not limited; any device capable of performing the above functions is acceptable. Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of a preferred embodiment, and the above embodiment numbers are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments. The above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions should not cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A device-level tracing method for forced oscillation sources in power systems based on CPSD, characterized in that, Includes the following steps: S1. Collect and calculate the active power, reactive power, frequency and voltage amplitude measurement data of the generator node during forced oscillation, and obtain the dynamic components of each measurement data relative to the steady-state value. S2. By performing Fourier transform on the dynamic components, the time-domain dissipated energy flow into the system from the motor node is converted into the frequency-domain dissipated energy spectrum, thus confirming the dominant oscillation frequency and the source of the forced oscillation. S3. Based on the time-domain dissipated energy flow structure, define the frequency domain cross power spectral density of the speed regulation system and excitation system during forced oscillation, and calculate the amplitude spectrum and phase spectrum of each generator speed regulation system and excitation system at the forced oscillation frequency according to the dominant oscillation frequency. The forced oscillation disturbance equipment is located by the amplitude spectrum and phase spectrum in concert. S4. Based on the dominant oscillation frequency band energy, calculate the energy contribution rate of each generator speed control system and excitation system, and determine the dominant forced oscillation disturbance equipment.

2. The device-level tracing method for forced oscillation sources in power systems based on CPSD according to claim 1, characterized in that, In S2, the peak value of the frequency domain dissipation energy spectrum corresponds to the dominant oscillation frequency of the system, and the positive and negative characteristics correspond to different forced oscillation sources.

3. The device-level tracing method for forced oscillation sources in power systems based on CPSD according to claim 1, characterized in that, The expression for the frequency domain dissipative energy spectrum is as follows: In the formula, E D The frequency domain dissipation energy spectrum is represented by *, where * indicates conjugate; ΔP(F), Δf(F), ΔQ(F), and ΔlnV(F) represent the dynamic components of the natural logarithm of active power, frequency, reactive power, and voltage amplitude in the frequency domain relative to their steady-state values, respectively.

4. The device-level tracing method for forced oscillation sources in power systems based on CPSD according to claim 1, characterized in that, In S3, the frequency domain cross-power spectral density of the speed regulation system and the excitation system during forced oscillation is expressed as follows: In the formula, H gov (F), H exc (F) represent the frequency domain cross power spectral density of the speed governor and the excitation system, respectively; The amplitude spectrum and phase spectrum of each generator speed control system and excitation system at the forced oscillation frequency are expressed as follows: In the formula, M gov (F FO M exc (F FO The numbers ) represent the speed control system and the excitation system at the dominant oscillation frequency F, respectively. FO The amplitude spectrum below, θ gov (F FO ), θ exc (F FO The speed control system and the excitation system are respectively located at the dominant oscillation frequency F. FO The phase spectrum, where Im represents the imaginary part, Re represents the real part, and sgn represents the sign function.

5. The device-level tracing method for forced oscillation sources in power systems based on CPSD according to claim 1, characterized in that, In S3, the forced oscillation disturbance device, which is located by the combined use of amplitude spectrum and phase spectrum, includes: Based on amplitude spectrum location of forced oscillation disturbance equipment: when the amplitude spectrum of the generator control equipment at the forced oscillation frequency is negative, it is determined to be a forced oscillation disturbance equipment; when the amplitude spectrum of the generator control equipment at the forced oscillation frequency is positive, it is determined to be a forced oscillation energy dissipation equipment. Based on phase spectrum identification of forced oscillation disturbance equipment: when the generator control equipment has a significant phase deviation from other equipment at the forced oscillation frequency, it is a forced oscillation disturbance equipment; when the phase spectrum of the generator control equipment is consistent at the forced oscillation frequency, it is a device without forced oscillation disturbance; when the phase spectrum of the generator control equipment at the forced oscillation frequency shows multiple disordered distributions, it indicates the presence of natural oscillation.

6. The device-level tracing method for forced oscillation sources in power systems based on CPSD according to claim 1, characterized in that, S4 includes defining the energy contribution rate based on frequency band energy, as shown in the following expression: in, ψ i =∫ ΔF H i,FO (F FO )dF; In the formula, I represents the total number of speed governors and excitation systems in the system, and ξ i Let ψ be the energy contribution rate of the i-th generator control device. i H represents the frequency band energy of the i-th generator control device. i,FO (F FO ) represents the frequency domain cross-power spectral density of the i-th control device within the dominant oscillation frequency band.

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