Forced oscillation suppression method combining phase shift compensation and active damping

Abstract

The invention discloses a forced oscillation suppression method combining phase shift compensation and active damping, and belongs to the technical field of stable operation analysis of a power system. According to the forced oscillation suppression method combining phase shift compensation and active damping, most inter-harmonic disturbance sources are suppressed through direct-current voltage phase shift compensation, system damping is improved in a small-amplitude mode by combining active damping control, and the forced oscillation amplitude is suppressed under the condition that system performance is not affected. The mechanism that the inter-harmonic disturbance source triggers forced oscillation of the forced system is elaborated by using an equivalent disturbance equation, the influence of the amplitude of the inter-harmonic disturbance source and the damping of the forced system on the amplitude of forced oscillation is considered, and a forced oscillation suppression strategy of phase shift compensation and active damping is combined. The amplitude of an inter-harmonic disturbance source is suppressed through phase shift compensation, and the weak damping state of a forced system is improved through active damping, so that the amplitude of forced oscillation is suppressed.

Description

Technical Field

[0001] This invention belongs to the field of power system stability operation analysis technology. Background Technology

[0002] Currently, most large-scale photovoltaic (PV) transmission systems utilize centralized PV power plant connections, with capacities often reaching hundreds of megawatts. However, the widespread application of power electronics technology and the volatility and randomness of PV output have introduced severe harmonic problems into the power grid, significantly impacting system stability. In particular, maximum power point tracking (MPPT) control in PV systems can lead to a large number of interharmonics output by the PV inverter. In large-scale PV power plant grid-connected environments, these interharmonic current components can accumulate to very high amplitudes, potentially causing forced power oscillations in other PV power generation systems at the junction. Excessively high oscillation amplitudes can trigger widespread blackouts or even system collapse.

[0003] Therefore, it is necessary to analyze the mechanism of forced power oscillation caused by photovoltaic interharmonics and take corresponding suppression measures to suppress the amplitude of forced power oscillation to a reasonable range, so as to ensure the safe and stable operation of the power system. Summary of the Invention

[0004] The purpose of this invention is to suppress most interharmonic disturbance sources by using DC voltage phase-shift compensation and combining it with active damping control to slightly increase system damping, thereby suppressing the forced oscillation amplitude without affecting system performance.

[0005] The steps of this invention are: S1. The relationship between the disturbance source and the forced system can be expressed as a second-order nonhomogeneous differential equation: (5) In the equation: the left side represents the equivalent equation of the forced photovoltaic system, and the right side represents the interharmonic disturbance source emitted by the photovoltaic power station; Δx is the state variable of the forced system; P0 and ω h These represent the amplitude and angular frequency of the interharmonic disturbance source, respectively; ω n ζ and ζ represent the natural frequency and damping ratio of the forced system, respectively; The oscillation amplitude B is: (7) Based on the above equation, we can derive three conditions for interharmonic disturbance sources to induce forced oscillations in the system: Condition 1: The output interharmonic frequency of the photovoltaic system is close to the natural frequency of the forced system; Condition 2: The forced system has weak damping at its natural frequency; Condition 3: Interharmonic disturbances must reach a certain amplitude; S2. Based on the stable oscillation characteristics of DC voltage, the basic principle of phase-shift compensation control is divided into three stages: Phase 1: The MPPT control of the two photovoltaic power generation modules works independently, and the system operates at the maximum power point; during this phase, the DC voltage oscillation amplitude of the photovoltaic power generation system is superimposed, resulting in a relatively large interharmonic current output. Phase Two: When the DC reference voltage of photovoltaic module 1 completes three consecutive three-point periodic oscillations, the system is considered to have stably tracked the maximum power point. At this time, the MPPT control of module 2 is stopped, and the phase angle φ of the DC reference voltage of module 1 at this moment is obtained. pv1 ; Phase 3: After a certain delay, the MPPT control of the two modules reaches synchronization. The delay time is determined by the sampling period and the serial communication delay. S3. After differentiating the DC voltage to obtain the DC current, feed it back to the outer loop of the DC voltage. The expression for the outer loop of the DC voltage is then: (18) In the formula, k p1 k i1 k represents the proportional-integral parameter of the voltage outer loop. d For feedback coefficient, This is the reference value for the inner current loop after feedback.

[0006] In this invention, the interharmonic current caused by the photovoltaic MPPT (Multi-Pulse Test) flows through the line impedance and generates an interharmonic disturbance voltage at the collector, causing the forced system to generate disturbance power. When the frequency of the disturbance source is close to the weakly damped natural frequency of the forced system, the system will experience forced oscillation, and the amplitude of the interharmonic disturbance source is proportional to the amplitude of the forced oscillation. Therefore, this invention suppresses the amplitude of the interharmonic disturbance source through phase-shift compensation and improves the weakly damped state of the forced system through active damping, thereby suppressing the amplitude of the forced oscillation. Attached Figure Description

[0007] Figure 1 This is a schematic diagram of a typical structure of a large-scale photovoltaic power plant system; Figure 2 This is a schematic diagram of a typical photovoltaic power generation unit; Figure 3 This is a schematic diagram of a typical phase-locked loop control structure; Figure 4 This is a schematic diagram of the DC reference voltage oscillation of a photovoltaic system. Figure 5 This is a schematic diagram of the eigenvalue distribution of a forced photovoltaic system. Figure 6 A schematic diagram of the root locus for key eigenvalues ​​of a forced system; Figure 7 This is a schematic diagram of the phase-shift compensation strategy. Figure 8 This is the block diagram of the control structure of module 2 after phase shift compensation; Figure 9 This is a block diagram of an active damping control system. Figure 10 This is a schematic diagram of harmonic spectrum analysis between photovoltaic power generation units; Figure 11 The output power waveforms of the forced system under two different operating conditions are shown. Figure 12 The diagram shows the simulation results of the two photovoltaic power generation modules after phase shift compensation; where (a) is the DC side voltage, (b) is the grid-connected A-phase current of the two modules, and (c) is the FFT spectrum analysis. Figure 13 The output power waveforms of the forced system before and after compensation; Figure 14 This is a schematic diagram showing the distribution of key characteristic values ​​before and after the increase in damping; Figure 15 The output power waveforms of the forced system before and after the damping is increased are shown. Detailed Implementation

[0008] This invention first establishes a typical model of a large-scale photovoltaic power plant and photovoltaic power generation unit, and analyzes the mechanism of interharmonic disturbance source generation by MPPT control. Then, based on the analysis of the inherent modes of the forced system, the mechanism of forced oscillation of the forced system caused by the interharmonic disturbance source is explained using the equivalent disturbance equation. Next, considering the influence of the amplitude of the interharmonic disturbance source and the damping of the forced system on the amplitude of the forced oscillation, a forced oscillation suppression strategy combining phase shift compensation and active damping is proposed. Finally, simulation analysis verifies the effectiveness of the proposed suppression strategy in reducing the oscillation amplitude.

[0009] To achieve the above objectives, the specific technical solution of the present invention, "a forced oscillation suppression method combining phase-shift compensation and active damping," is as follows: First, a typical structure for a large-scale photovoltaic power plant system is established, comprising a photovoltaic power plant, a 35 / 220kV step-up transformer, and transmission lines. The large-scale photovoltaic power plant consists of multiple 500kW photovoltaic power generation units that converge to a 35kV bus, and after being stepped up by the 35 / 220kV transformer, are fed into the AC main grid. Each photovoltaic power generation unit consists of a photovoltaic array, a photovoltaic inverter, an LC filter, and a 0.48 / 35kV on-site step-up transformer. The control system includes photovoltaic MPPT control and dual closed-loop control of inverter voltage and current. To achieve phase synchronization between the control system and the grid, a phase-locked loop structure based on a synchronization reference coordinate system is adopted to provide the grid voltage vector orientation angle θ.

[0010] Next, the forced oscillation mechanism of a large-scale photovoltaic power plant system is analyzed. The amplitude of the forced oscillation is closely related to the disturbance source and the weak damping characteristics of the forced system. The following analysis is made regarding the generation mechanism of the interharmonic disturbance source and the weak damping characteristics of the forced system.

[0011] Regarding the generation mechanism of interharmonics in photovoltaic systems, random fluctuations in DC voltage are the fundamental cause of output interharmonics. The automatic optimization function of MPPT control continuously adjusts the DC-side voltage reference value, leading to constant fluctuations in the DC-side voltage. After modulation by the inverter, this results in output interharmonic components. Currently, MPPT control based on the disturbance observation method is widely used. In steady state, the disturbance step size ΔU and the sampling frequency f... MPPT Once determined, the DC voltage reference value will exhibit a three-point periodic oscillation pattern.

[0012] The premise for analyzing the weak damping characteristics of a forced photovoltaic system is to establish a small-signal state model of the forced photovoltaic system in the dq coordinate system, calculate the eigenvalues ​​of the forced photovoltaic system, and obtain the inherent weak damping modes of the forced photovoltaic system.

[0013] A typical structure of a large-scale photovoltaic power plant system is as follows: Figure 1 As shown, the system comprises a photovoltaic power station, a 35 / 220kV step-up transformer, and transmission lines. The large-scale photovoltaic power station consists of multiple 500kW photovoltaic power generation units that converge to a 35kV busbar, and after being stepped up by the 35 / 220kV transformer, are fed into the AC main grid. (R in the diagram...) s L s These represent the equivalent resistance and inductance of the transmission line, respectively.

[0014] A typical structure of a photovoltaic power generation unit and its control system is as follows: Figure 2 As shown, L, C, and R constitute a filter, and C dc For DC voltage regulation capacitor, i pv For the output current of the photovoltaic array, u dc and i dc These represent the DC side voltage and current, u abc and i abc These are the filter output voltage and inverter output current, respectively. MPPT control uses u dc and i pv As input, after selecting an appropriate perturbation step size and sampling frequency, the output is... The inverter control system employs a dual closed-loop control system, using voltage and current as the DC reference voltage for the outer voltage loop. and The input reference value for the inner current loop, u td and u tq i cd and i cqThese represent the filter output voltage and the inverter output current, respectively, where ω0 is the system angular frequency. and These are the reference values ​​for the inverter output voltage.

[0015] To achieve phase synchronization between the control system and the power grid, the following is adopted: Figure 3 The phase-locked loop control structure based on the synchronous reference coordinate system shown provides the grid voltage vector orientation angle θ, where k ppll and k ipll These are the PI control parameters for the phase-locked loop.

[0016] When the system is in steady state, the disturbance step size ΔU and the sampling frequency f MPPT Once determined, the DC voltage reference value will exhibit a three-point periodic oscillation pattern, such as... Figure 4 As shown. Among them. The expression and its Fourier expansion are as follows: (1) (2) In the formula: U MPP T represents the voltage at the maximum power point. MPPT Indicates the sampling period. U n This represents the amplitude of the frequency component of the DC voltage. This represents the phase angle of the frequency component of the DC voltage.

[0017] The d-axis component of the inverter output current in the dq rotating coordinate system is: (3) In the formula: i d0 Represents the d-axis current component, i dn Indicates the amplitude of the current frequency component. This represents the phase angle of the current frequency component.

[0018] The expression for abc in stationary coordinates obtained by the inverse Parkian transformation is: (4) In the formula: i a / b / c Let φ represent the three-phase currents a / b / c, φ0 represent the grid phase angle, and m take values ​​of 0, -1, and 1, respectively. Under the same disturbance step size and sampling frequency parameters, the photovoltaic inverter will generate interharmonic currents with the same amplitude but different phases, and the angular frequencies are distributed as ω0+nω and ω0-nω. It is easy to see that when the external environment such as illumination and temperature changes, only the amplitude of the interharmonic current changes, and the phase does not change.

[0019] A small-signal state model of the forced photovoltaic system in the dq coordinate system was established, and the eigenvalues ​​of the forced photovoltaic system were calculated. The results are shown in Table 1. Figure 5 This is a complex plane distribution diagram of the eigenvalues ​​of a forced system.

[0020] Table 1. Characteristic values ​​of forced photovoltaic systems

[0021] The analysis results show that the system contains a total of 4 oscillation modes, of which λ 5.6 The mode is a low-frequency oscillation with weak damping, and its frequency is close to the frequency of the interharmonic current dq coordinate system of the photovoltaic MPPT control output, which is a key characteristic value that is easy to induce forced oscillation.

[0022] For pattern λ 5.6 Participation factor analysis reveals that this oscillation mode is dominated by the proportional-integral parameters of the system's phase-locked loop. When k ppll k ipll When λ changes, 5.6 The root locus diagram is as follows Figure 6 As shown, we can know that k ppll It mainly affects damping, and has little effect on frequency, k ipll It affects both damping and frequency.

[0023] The relationship between the disturbance source and the forced system can be expressed in the form of a second-order nonhomogeneous differential equation: (5) In the formula: the left side of the equation represents the equivalent equation of the forced photovoltaic system, the right side of the equation represents the interharmonic disturbance source emitted by the photovoltaic power station, Δx represents the state variable of the forced system, and P0 represents the amplitude of the interharmonic disturbance source; ω h ω represents the angular frequency of the interharmonic disturbance source. n ζ represents the natural frequency of the forced system, and ζ represents the damping ratio of the forced system.

[0024] Solving the above equation, the particular solution represents the forced oscillation component, and its expression is: (6) In the formula: B represents the amplitude of the forced oscillation.

[0025] The forced oscillation amplitude B is: (7).

[0026] Based on the above equation, we can derive three conditions for interharmonic disturbance sources to induce forced oscillations in the system: Condition 1: The interharmonic frequency of the photovoltaic system output is close to the natural frequency of the forced system, i.e., ω h= ω nThe oscillation amplitude is at its maximum at this time. Here, the interharmonic disturbance corresponds to the component in the dq coordinate system, and the corresponding frequency in the abc coordinate system is (ω0±ω). h )Hz; Condition 2: The forced system has weak damping at its natural frequency. ζ is inversely proportional to B; the smaller ζ is, the larger B is. Condition 3: Interharmonic disturbances must reach a certain amplitude. P0 is directly proportional to B; the larger the amplitude of P0, the larger the forced oscillation amplitude.

[0027] For ease of analysis, it is assumed that the bus voltage contains only a pair of interharmonics caused by a single disturbance, and the forced system output current contains only the fundamental component, which are defined as follows: (8) (9) In the formula: U h θ represents the amplitude of the interharmonic voltage component. h1 θ h2 Let θ be the initial phase of the interharmonic voltage component. h1 +θ h2 =2φ0,θ h1 -θ h2 =2φ dn I represents the amplitude of the forced system output current, and φ represents the initial phase of the forced system output current.

[0028] The instantaneous interharmonic disturbance power of the inverter output is: (10).

[0029] When the frequency ω of the periodic component of the interharmonic disturbance power h When the frequency is close to the weakly damped natural frequency of the system, it is easy to induce forced oscillations in the photovoltaic forced system.

[0030] Based on the above mechanism analysis, the larger the amplitude of the interharmonic disturbance and the smaller the forced system damping, the larger the amplitude of the resulting oscillation. Therefore, the power oscillation caused by interharmonics can be suppressed by reducing the amplitude of the disturbance source and increasing the system damping. The photovoltaic power station is reconfigured into multiple modules, each maintaining an equal capacity of photovoltaic units. The DC reference voltage phase of module 1 is selected as the reference signal source, and phase-shift compensation control is implemented on the DC reference voltage in module 2. This ultimately makes the DC voltages of the two modules exhibit anti-phase characteristics, outputting interharmonic components with equal amplitude but opposite magnitudes. This effectively suppresses the interharmonic amplitude output by an even number of modules. For forced oscillations caused by uncompensated photovoltaic power generation units, an active damping control strategy is used for suppression.

[0031] A phase-shift compensation suppression strategy for two photovoltaic power generation modules is analyzed and studied. Ignoring the influence of system parameters and MPPT sampling period, the amplitude of the interharmonic current is only related to the MPPT disturbance step size. First, the principle of phase-shift compensation control is analyzed. Based on the stable oscillation characteristics of DC voltage, the basic principle of phase-shift compensation control is as follows: Figure 7 As shown, it can be divided into three stages: Phase 1: The MPPT control of the two photovoltaic power generation modules operates independently, and the system operates at its maximum power point. During this phase, the DC voltage oscillation amplitudes of the photovoltaic power generation system are superimposed, resulting in a relatively large interharmonic current output. Phase Two: When the DC reference voltage of photovoltaic module 1 completes three consecutive three-point periodic oscillations, the system is considered to have stably tracked the maximum power point. At this time, the MPPT control of module 2 is stopped, and the phase angle φ of the DC reference voltage of module 1 at this moment is obtained. pv1 ; Phase 3: After a certain delay, the MPPT control of the two modules reaches synchronization. The delay time is determined by the sampling period and the serial communication delay.

[0032] The DC voltage reference value is decomposed using the Sliding Discrete Fourier Transform (SDFT) algorithm, and its recursive formula is as follows: (11) In the formula: U pv (x+1), U pv (x) represents the frequency components of the (x+1)th and xth Fourier transforms. This represents the latest sampled reference voltage. This represents the reference voltage recorded N sampling periods ago.

[0033] At this time, the phase angle of the DC reference voltage is: (12).

[0034] After the system meets the conditions for three cycles of steady-state operation, the phase angle φ of module 1 will be obtained. pv1 The signal is transmitted to module 2 via a serial communication system. Considering the time delay in the serial communication between the two modules, the phase received by module 2 can be compensated using the signal transmission time; in this case, the phase φ of module 2... pv2 for: (13) In the formula: t YS This represents the serial communication delay, where the delay time of module 2 is t. delay =(φ pv2 -φ pv1 4T MPPT / 2π. The control system of module 2 after adopting this strategy is as follows: Figure 8As shown.

[0035] After adopting the phase-shift compensation suppression strategy, the DC reference voltage disturbances of the two power generation modules can be mutually compensated. Taking phase A as an example, the interharmonic currents output by module 1 and module 2 are respectively: (14) (15) In the formula: M represents the number of photovoltaic power generation units in the photovoltaic power generation module. At this time, the amplitude of the total interharmonic current output after the two power generation modules are connected in parallel is 0, which theoretically completely suppresses the forced oscillation caused by the interharmonic disturbance source.

[0036] However, in practice, due to various factors such as the distribution of photovoltaic units and the intensity of sunlight in a photovoltaic power plant, the DC-side disturbance step size parameters of the photovoltaic modules are not the same, and the phase-shift compensation strategy used only applies to an even number of power generation modules. In this case, it is necessary to suppress the oscillations caused by the small number of uncompensated interharmonic disturbances.

[0037] The smaller the damping of the natural frequency of the forced system, the larger the amplitude of the forced oscillation. Therefore, an active damping control strategy can be used to increase the damping of the weakly damped natural frequency and suppress the forced oscillation caused by interharmonic disturbances. The expression for the inverter output power is: (16) In the formula: P out P in —Inverter output power and input power, W.

[0038] Under the small-signal model, the above equation can be simplified to: (17).

[0039] As shown in the above equation, under interharmonic disturbances, the oscillation amplitude of the inverter output power is proportional to the DC capacitor current. Therefore, the DC capacitor current can be used as a feedback variable to suppress the output power oscillations caused by interharmonic disturbances. The DC current is obtained by differentiating the DC voltage and fed back to the outer loop of the DC voltage. The corresponding control structure is as follows: Figure 9 As shown, where k d For feedback coefficient, This is the reference value for the inner current loop after feedback.

[0040] With active damped feedback, the small-signal model of the DC voltage loop becomes: (18) In the formula: k p1 k i1 k represents the proportional-integral parameter of the voltage outer loop.d For feedback coefficient, This is the feedback-received inner loop current reference value. When power oscillations cause DC voltage fluctuations, the active damping control adds a reverse disturbance to the DC voltage command value. The two disturbances cancel each other out, thus suppressing output power oscillations.

[0041] To verify the effectiveness of the above mechanism and suppression strategy, a large-scale photovoltaic grid-connected system simulation model was built in MATLAB / Simulink. The system includes a 100MW photovoltaic forced system and a 500MW photovoltaic interharmonic disturbance source, both of which are equivalently aggregated from 500kW photovoltaic power generation units. The system reference frequency is 50Hz.

[0042] The generation mechanism of interharmonics was verified using a photovoltaic power generation unit simulation. The MPPT employed the perturbation-observation method, with a perturbation step size ΔU = 10V and a sampling period T. MPPT =0.1s, simulation results are as follows Figure 10 As shown in the figure. Simulation results show that the DC-side voltage exhibits a regular three-point periodic oscillation mode. FFT analysis reveals that the DC-side voltage contains disturbance components with frequencies of 2.5, 7.5, 12.5, and 17.5 Hz. The AC-side output current contains a series of interharmonic components symmetrical about 50 Hz, with frequencies of 47.5 / 52.5 Hz, 42.5 / 57.5 Hz, 37.5 / 62.5 Hz, and 32.5 / 67.5 Hz. The frequency of the d-axis interharmonic component of the AC-side output current is the same as the frequency component of the DC-side disturbance component, consistent with theoretical analysis. Therefore, when a photovoltaic inverter uses the MPPT control method, it will output complex interharmonic components. When the dq-axis component frequency of the interharmonics is close to the frequency of the weakly damped natural oscillation and both reach a certain amplitude, forced oscillation is easily triggered.

[0043] Adjust the phase-locked loop parameters of the forced photovoltaic system to k ppll =6、k ipll =100, at this point the characteristic value of the inherent oscillation mode of the forced system is -1.0±j52.92, that is, the system contains a near-zero damped oscillation mode with an oscillation frequency of 8.42Hz. The interharmonic disturbance source module is composed of 100 photovoltaic power generation units, with a capacity of 50MW. The disturbance step size of the photovoltaic MPPT of the system is adjusted to 15V, and the sampling period is 0.145s. To verify the influence of the interharmonic disturbance source amplitude on the forced oscillation amplitude, different photovoltaic power generation modules are connected in parallel to the system, and the influence of the interharmonic disturbance source amplitude on the output power oscillation amplitude of the forced system is analyzed. In case one, 10 photovoltaic power generation modules are connected to the grid; in case two, 6 photovoltaic power generation modules are connected to the grid. The simulation results of the active power of the forced system are as follows: Figure 11As shown in the figure. Simulation results show that after the power oscillation reaches a constant amplitude, FFT analysis of the output power reveals that the forced oscillation amplitude at 8.42Hz is 3.2MW for the forced system in condition one and 1.53MW for the forced system in condition two. This indicates that the larger the amplitude of the interharmonic disturbance source, the larger the amplitude of the forced oscillation it induces; therefore, suppressing the disturbance source amplitude can reduce the forced oscillation amplitude.

[0044] Phase-shift compensation measures were applied to the two photovoltaic power generation modules, and the simulation results are as follows: Figure 13 As shown. At 2.03s, the DC-side voltage has undergone three stable oscillation cycles. At this point, the suppression strategy is activated, the MPPT control of module 2 stops working, and it acquires the phase information of module 1 at this time. After a delay of two sampling cycles, the acquired phase of module 1 is synchronized to module 2. For example... Figure 12 As shown in (a), after adopting the suppression strategy, the DC-side voltage phases of the two modules achieve reverse compensation operation. Figure 12 As shown in (b), the waveform distortion of the phase A current of the two-module grid-connected system is significantly improved after adopting the compensation strategy. The results of FFT analysis of the phase A current are as follows: Figure 12 As shown in (c), the amplitude of the interharmonic components is significantly reduced, and the amplitudes of the 41.38 Hz and 58.62 Hz components that cause forced oscillations are reduced to 0.0425 A and 0.1003 A, respectively.

[0045] The simulation results of the active power of the forced system after grid connection of 10 photovoltaic power generation modules under the first operating condition, before and after adopting the suppression strategy, are as follows: Figure 13 As shown. FFT analysis of the simulation results shows that the forced oscillation amplitude of the forced system at 8.42Hz is 0.109MW. After adopting the phase-shift compensation suppression strategy, the influence of the interharmonic disturbance source on the forced system oscillation can be basically eliminated.

[0046] To verify the effectiveness of the active damping strategy in suppressing forced oscillations caused by a small number of disturbance sources, a feedback coefficient k was set. d =0.5, the changes in key eigenvalues ​​of the forced system are as follows Figure 14 As shown in the figure. The analysis shows that after adopting the active damping control strategy, the damping of the original weakly damped system was improved and the frequency did not change significantly.

[0047] When three photovoltaic power generation modules are connected to the power grid, the simulation results of forced system power oscillation before and after the implementation of active damping control are as follows: Figure 15As shown, without active damping control, the forced oscillation amplitude of the forced system at 8.42Hz is 0.645MW; with active damping control, the forced oscillation amplitude is 0.184MW, which is within the allowable range. Therefore, after implementing the phase-shift compensation strategy, a slight increase in system damping can limit the forced oscillation amplitude to within the allowable range.

Claims

1. A method for suppressing forced oscillations combining phase-shift compensation and active damping, characterized in that: S1. The relationship between the disturbance source and the forced system can be expressed as a second-order nonhomogeneous differential equation: （5） In the equation: the left side represents the equivalent equation of the forced photovoltaic system, and the right side represents the interharmonic disturbance source emitted by the photovoltaic power station; Δx is the state variable of the forced system; P0 and ω h These represent the amplitude and angular frequency of the interharmonic disturbance source, respectively; ω n ζ and ζ represent the natural frequency and damping ratio of the forced system, respectively; The oscillation amplitude B is: （7） Based on the above equation, we can derive three conditions for interharmonic disturbance sources to induce forced oscillations in the system: Condition 1: The output interharmonic frequency of the photovoltaic system is close to the natural frequency of the forced system; Condition 2: The forced system has weak damping at its natural frequency; Condition 3: Interharmonic disturbances must reach a certain amplitude; S2. Based on the stable oscillation characteristics of DC voltage, the basic principle of phase-shift compensation control is divided into three stages: Phase 1: The MPPT control of the two photovoltaic power generation modules works independently, and the system operates at the maximum power point; during this phase, the DC voltage oscillation amplitude of the photovoltaic power generation system is superimposed, resulting in a relatively large interharmonic current output. Phase Two: When the DC reference voltage of photovoltaic module 1 completes three consecutive three-point periodic oscillations, the system is considered to have stably tracked the maximum power point. At this time, the MPPT control of module 2 is stopped, and the phase angle φ of the DC reference voltage of module 1 at this moment is obtained. pv1 ; Phase 3: After a certain delay, the MPPT control of the two modules reaches synchronization. The delay time is determined by the sampling period and the serial communication delay. S3. After differentiating the DC voltage to obtain the DC current, feed it back to the outer loop of the DC voltage. The expression for the outer loop of the DC voltage is then: （18） In the formula, k p1 k i1 k represents the proportional-integral parameter of the voltage outer loop. d For feedback coefficient, This is the reference value for the inner current loop after feedback.

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