Cooperative control method for grid-connected microgrid with optical storage based on modal feedforward and virtual inertia adaptation

Abstract

The application discloses a network type photovoltaic and energy storage micro-grid cooperative control method based on modal feedforward and virtual inertia self-adaption, and belongs to the field of micro-grid stability control. The method establishes a small signal model of a photovoltaic Boost and energy storage bidirectional DC / DC converter, and establishes a conductance matrix model of positive and negative sequence decoupling of the network type inverter through harmonic linearization. According to the state of charge imbalance degree of the energy storage, a droop coefficient is dynamically adjusted to balance power and compensate bus voltage, power instructions are subjected to spectral decomposition to distribute power between the battery and the super capacitor, virtual inertia and damping coefficients are adaptively adjusted according to frequency deviation and its change rate, and active current and reactive voltage compensation are introduced. Modal analysis is conducted on the node conductance matrix of the multi-machine system, resonance modes are extracted, and an oscillation source is located according to a participation factor, modal information is used as a feedforward amount, and virtual inertia of each unit is dynamically adjusted through a multi-agent consistency protocol. The application improves the system frequency stability and wide frequency oscillation suppression capability.

Description

Technical Field

[0001] This invention relates to the field of photovoltaic-storage DC microgrid modeling and stability analysis, specifically to a collaborative control method for grid-type photovoltaic-storage microgrids based on modal feedforward and virtual inertia adaptive control. Background Technology

[0002] Photovoltaic-storage microgrids, as highly efficient power generation and distribution systems integrating distributed photovoltaic (PV) and energy storage technologies, can effectively mitigate the intermittency and volatility of renewable energy and have become an important component in building new power systems. However, with the large-scale integration of high-proportion PV and energy storage power electronic converters, the system is gradually exhibiting low inertia and weak damping operation characteristics, posing severe challenges to the frequency stability and power quality of photovoltaic-storage microgrids. Specifically, existing technologies still have the following shortcomings in three aspects: DC-side energy storage management, AC-side single-unit frequency regulation, and multi-unit system-level oscillation suppression.

[0003] First, it is difficult to balance the State of Charge (SOC) of multiple energy storage units on the DC side with the stability of the bus voltage. Due to differences in manufacturing process, initial capacity and aging degree, the SOC of each energy storage unit operating in parallel is prone to imbalance, resulting in overcharging and over-discharging of some batteries and accelerating the deterioration of the energy storage system. Although traditional droop control can achieve autonomous power allocation, there is an inherent problem that current sharing accuracy and bus voltage deviation are mutually constrained. Reference [1] discloses a segmented adaptive droop control method for SOC balancing of multiple energy storage units in DC microgrids. It dynamically adjusts the droop coefficient according to the SOC deviation of the energy storage units to accelerate the balancing speed, and uses the bus voltage deviation to output the common voltage compensation amount through the PI regulator to restore the bus voltage. However, this method is only for the single energy storage medium of the battery and does not consider the power spectrum distribution problem between the hybrid energy storage system composed of the battery and the supercapacitor. Moreover, the segmented adjustment method is prone to sudden changes in control quantity when the operating conditions are frequently switched. The balancing speed and voltage recovery performance still need to be improved.

[0004] Secondly, the dynamic adaptability of the virtual synchronous generator (VSG) control with fixed parameters of AC-side grid-connected inverters is insufficient. Traditional VSG control provides inertia and damping support to the system by simulating the rotor motion equation of the synchronous generator. However, its virtual inertia and damping coefficient are usually fixed values. Under the conditions of photovoltaic power output fluctuation and load change, the frequency overshoot and recovery time cannot be optimized at the same time, and the adaptability in weak grid environment is poor. Reference [2] discloses an adaptive control method for virtual inertia and virtual damping coefficient of virtual synchronous generator. It applies the improved particle swarm algorithm to the active-frequency control link and realizes the real-time adaptive adjustment of virtual inertia and damping coefficient with the goal of minimizing frequency deviation and system stability. However, this type of adjustment method based on intelligent optimization algorithm relies on iterative calculation, which limits the real-time performance and engineering feasibility. Moreover, it does not combine active current compensation and reactive voltage compensation links, and the dynamic response speed and grid connection point voltage support capability under grid disturbance are still insufficient.

[0005] Third, there is a lack of system-level oscillation source tracing and active suppression methods when multi-grid inverters are running in parallel. In the scenario of multi-machine parallel operation, the inertia parameters of each grid-type unit are easily coupled due to the mismatch of line impedance and the inertia parameters, which can cause subsynchronous oscillations. At the same time, the interaction between the inverter output impedance and the grid impedance may also induce broadband resonance, which seriously threatens the safe operation of the system. Reference [3] discloses a high-frequency oscillation suppression method and system for grid-type converters. It determines the influencing factors that cause high-frequency oscillations in the converter by constructing a high-frequency impedance model of the wind farm and the converter station and performing equivalent transformation, and then formulates a suppression strategy. However, this method is only for high-frequency oscillations and belongs to passive suppression at the single-machine level. It does not involve modal analysis and oscillation source localization of multi-machine systems, nor does it use modal information to coordinate the control parameters of each unit. It is difficult to fundamentally suppress the subsynchronous oscillations and broadband resonances caused by multi-machine coupling.

[0006] In addition, reference [4] discloses a photovoltaic-storage microgrid collaborative control method to deal with the uncertainty of photovoltaic output. It uses the droop control and PQ control of the energy storage module's state of charge switching to maximize the absorption of photovoltaic power and ensure the continuous power supply of the load. However, this type of method focuses on the control mode switching at the energy management level and does not involve the frequency support and broadband oscillation suppression problem under the grid-type control.

[0007] In summary, existing research often treats DC-side energy management, AC-side single-unit frequency regulation, and multi-unit system stability analysis in a fragmented manner, failing to form an integrated hierarchical collaborative control architecture. Furthermore, it lacks active damping strategies that use modal analysis results as feedforward information to dynamically guide virtual inertia adjustment. Therefore, there is an urgent need to establish a complete theoretical system encompassing impedance modeling, modal analysis, and adaptive collaborative regulation to improve the frequency stability and broadband oscillation suppression capabilities of photovoltaic-storage microgrids under various operating conditions.

[0008] References: Reference [1]: Chinese Invention Patent Application CN112600188A, “A Segmented Adaptive Droop Control Method for Equalization of Multiple Energy Storage SOCs in DC Microgrids”, Applicant: Inner Mongolia University of Technology, Publication Date: April 2, 2021 (Authorization Announcement No. CN112600188B).

[0009] Reference [2]: Chinese invention patent application CN109256801A, “Adaptive control method for virtual inertia and virtual damping coefficient of virtual synchronous generator”, applicant: Northeastern University, application date: September 28, 2018, publication date: January 22, 2019 (authorization announcement number CN109256801B).

[0010] Reference [3]: Chinese invention patent application CN119209623A, “A method and system for suppressing high frequency oscillations of a grid-type converter”, applicant: Guangdong Power Grid Co., Ltd., Guangdong Power Grid Co., Ltd. Power Dispatch and Control Center, application date: November 15, 2024, publication date: December 27, 2024.

[0011] Reference [4]: ​​Chinese invention patent application CN118889542A, “A method for coordinated control of photovoltaic and energy storage microgrids to cope with the uncertainty of photovoltaic output”, applicants: State Grid Sichuan Electric Power Research Institute and Southwest Jiaotong University, application date: September 3, 2024, publication date: November 1, 2024. Summary of the Invention

[0012] This invention addresses the technical challenges in existing grid-connected photovoltaic-storage microgrids, including the difficulty in simultaneously achieving DC-side energy storage SOC balance and bus voltage stability, insufficient dynamic adaptability of fixed-parameter VSGs, and the lack of system-level active suppression measures for subsynchronous oscillations and broadband resonances in multi-machine parallel operation. It proposes a collaborative control method for grid-connected photovoltaic-storage microgrids based on modal feedforward and virtual inertia adaptation. This method establishes a complete small-signal impedance model encompassing the photovoltaic boost converter, the energy storage bidirectional DC / DC converter, and the grid-connected inverter. Combined with improved droop control based on SOC unbalance, an adaptive virtual inertia algorithm dynamically adjusted according to frequency deviation and rate of change, and a multi-agent consensus collaborative adjustment strategy using the modal participation factor as the feedforward quantity, it achieves integrated hierarchical control from impedance modeling and modal analysis to adaptive collaborative regulation. This significantly improves the energy storage balance speed, frequency stability, and broadband oscillation suppression capability of photovoltaic-storage microgrids with high-proportion renewable energy access, providing reliable technical support for the safe and stable operation of grid-connected photovoltaic-storage systems.

[0013] The technical solution adopted in this invention is as follows: A collaborative control method for grid-connected photovoltaic-storage microgrids based on modal feedforward and virtual inertia adaptive control includes the following steps: S1: Establish a small-signal model of the photovoltaic Boost converter and the energy storage bidirectional DC / DC converter, and use the harmonic linearization method to establish the admittance matrix model of the grid-type inverter with positive and negative sequence decoupling; S2: Dynamically adjust the droop coefficient according to the imbalance of the state of charge of each energy storage unit to balance the output power of each energy storage unit and compensate the DC bus voltage; perform spectrum decomposition on the power command and distribute power between the battery and the supercapacitor. S3: Based on the frequency deviation and its rate of change of the grid-type inverter, the virtual inertia and damping coefficient are adaptively adjusted, and active current compensation and reactive voltage compensation are introduced to improve the frequency regulation capability and power quality of a single grid-type unit. S4: Perform modal analysis on the node admittance matrix of the multi-machine system, extract key resonant modes, and locate the oscillation source based on the participation factors of each node for the key resonant modes; use the modal information as feedforward quantity, dynamically adjust the virtual inertia of each unit through a multi-agent consensus protocol, and realize multi-machine parallel collaborative control.

[0014] In step S1, a small-signal model of the photovoltaic Boost converter is established, including: 1.1: Based on the circuit topology of the photovoltaic Boost converter, establish its state-space equations: ; ; ; in, This refers to the inductance value of the photovoltaic converter. This refers to the inductor current of the photovoltaic converter. For time; This refers to the output voltage of the photovoltaic array. This refers to the photovoltaic duty cycle. This is the DC bus voltage; For filtering capacitors on the photovoltaic array side; Output current for the photovoltaic array; For bus capacitors; For the output current of the photovoltaic converter; 1.2: The state-space equation is linearized using small-signal processing and transformed to the frequency domain to obtain the frequency-domain small-signal expression: ; ; ; in, It is a complex frequency variable; For small-signal variables; , , They are respectively , , The steady-state value; 1.3: Based on the aforementioned frequency domain small-signal expression, derive the open-loop output impedance of the photovoltaic Boost converter without considering the control loop: ; in, This refers to the open-loop output impedance of the photovoltaic Boost converter; 1.4: Based on the open-loop output impedance, the duty cycle disturbance introduced by the control loop is taken into account to obtain the closed-loop output impedance of the photovoltaic Boost converter: ; in, The closed-loop output impedance of the photovoltaic Boost converter; The transfer function from a small duty cycle disturbance to a small disturbance in the converter output bus voltage; The transfer function is given by the small perturbation of the converter output bus current to the small perturbation of the photovoltaic array output voltage. The transfer function from a small duty cycle perturbation to a small perturbation in the output voltage of the photovoltaic array; This is the transfer function for the photovoltaic-side controller.

[0015] In step S1, a small-signal model of the energy storage bidirectional DC / DC converter is established, including: 1.5: Establish the state-space equations for the energy storage bidirectional DC / DC converter circuit: ; ; in, Inductor for energy storage converter; Output current for energy storage; For time; This is the energy storage output voltage; This refers to the duty cycle of the energy storage converter. This is the DC bus voltage; For bus capacitors; This is the output current of the energy storage converter; 1.6: By superimposing small signals onto the above state-space equations and eliminating steady-state quantities, we obtain the frequency-domain small-signal expression: ; ; in, It is a complex frequency variable; For small-signal variables; , , They are respectively , , The steady-state value; 1.7: Based on the above frequency domain small-signal expression, derive the open-loop output impedance of the energy storage bidirectional DC / DC converter without considering the control loop: ; in, This refers to the open-loop output impedance of the energy storage bidirectional DC / DC converter. 1.8: Based on the open-loop output impedance and incorporating the control loop, the closed-loop output impedance of the energy storage bidirectional DC / DC converter is obtained: ; in, The closed-loop output impedance of the energy storage bidirectional DC / DC converter; Transfer function for the energy storage side current controller; The transfer function is given by the small perturbation of the converter output current to the small perturbation of the energy storage output current. The transfer function from a small duty cycle disturbance to a small disturbance in the converter output bus voltage; The transfer function from a small duty cycle disturbance to a small disturbance in the energy storage output current; This is the transfer function for the energy storage side voltage controller.

[0016] In S1, the admittance matrix model for the positive and negative sequence decoupling of the grid-type inverter is established, including: 1.9: Based on the characteristics of grid-type inverters, where the DC side is a voltage-stabilized energy storage device, no bus voltage outer loop is required, and AC / DC frequency coupling is weak, the positive and negative sequence decoupling output admittance equations are established: ; ; in, , These are the positive-sequence and negative-sequence current disturbance frequency domain components at the common connection point, respectively. , These are the positive-sequence and negative-sequence voltage perturbation frequency domain components at the common connection point, respectively. It is a positive-order admittance; It is a negative-order admittance; It is a complex frequency variable; 1.10: Using the harmonic linearization method, derive the expressions for the positive-sequence admittance and the negative-sequence admittance: ; ; in, Transfer function for the inner loop PI controller of the grid-connected inverter; Transfer function for the outer loop PI controller of the grid-connected inverter; The imaginary unit; The fundamental angular frequency; For filtering capacitors in grid-type inverters; This is the filter inductor for a grid-type inverter.

[0017] In step S2, balancing the output power of each energy storage unit and compensating for the DC bus voltage includes: S2.1: Calculate the state of charge of each battery energy storage unit: ; in, for The state of charge of the battery energy storage unit at all times; This represents the initial state of charge of the battery energy storage unit. The total capacity of the battery energy storage unit; For time; This refers to the charging and discharging current of the battery energy storage unit. For integration variables; S2.2: Calculation The average state of charge (SOC) of the parallel-connected battery energy storage units is used to determine the SOC imbalance of each battery energy storage unit. ; ; in, This represents the average state of charge of the battery energy storage unit. The number of parallel battery energy storage units; This refers to the serial number of the battery energy storage unit; For the first The state of charge of the battery energy storage unit; For the first Imbalance in the state of charge of the battery energy storage unit; S2.3: Dynamically adjust the droop coefficient of each battery energy storage unit according to the aforementioned imbalance, and determine the output voltage of each battery energy storage unit converter by combining the bus voltage compensation and equalization speed adjustment function: ; ; in, For the first The droop coefficient of the battery energy storage unit; This is the equilibrium droop coefficient when all battery energy storage units have the same state of charge. For the first The output voltage of the battery energy storage unit converter; This is the reference value for the converter output voltage; This is the function for bus voltage compensation and equalization speed regulation. For the first The output current of the battery energy storage unit converter; S2.4: Construct the adjustment function in the following form to determine the dynamic characteristics of the bus voltage compensation and equalization speed: ; in, This is the voltage compensation amplitude control coefficient; This refers to the state of charge of the battery energy storage unit. This is a control coefficient for the degree of nonlinearity in the equilibrium speed; It is a natural constant; S2.5: Establish a small-signal model for the dynamic adjustment process of the droop coefficient, and use the system characteristic equation. Verify the stability of the system, among which, , , , These are system parameters determined by circuit parameters and control parameters. It is a complex frequency variable.

[0018] In step S2, the power command is spectrally decomposed, and power is allocated between the battery and the supercapacitor, including: S2.6: The spectral characteristics of the power command are extracted in real time using the sliding discrete Fourier transform. The difference equation is as follows: ; in, For the first The sampling time of the first sampling moment The spectral values ​​of each frequency component; The frequency component number; The sampling time sequence number; It is a natural constant; The imaginary unit; Pi; The length of the sliding window; For the first Power command input signal at each sampling time; S2.7: Dynamically adjust the time constant of the low-pass filter based on the extracted spectral characteristics, and determine the smoothing factor of the discrete low-pass filter: ; in, It is a smoothing factor; This represents the time constant of the low-pass filter. The sampling period; S2.8: Based on the smoothing factor, perform discrete low-pass filtering on the power command, allocate the filtered low-frequency power component to the battery, and allocate the high-frequency power component to the supercapacitor. ; in, For the first The filter output value at each sampling time.

[0019] In S3, the adaptive adjustment of virtual inertia and damping coefficient includes: S3.1: Establish the oscillation equation of the virtual synchronous generator: ; in, This is a virtual moment of inertia; The output angular frequency of the virtual synchronous generator; For time; This is a reference value for active power. This is the rated angular frequency; The active power-frequency droop factor; This represents the actual output value of active power. The damping coefficient; The measured angular frequency at the grid connection point; S3.2: Define frequency deviation: Using the sign of the product of the frequency deviation and its rate of change as the adjustment criterion, an adaptive adjustment law for virtual inertia and active power-frequency droop coefficient is constructed: when hour, ; when hour, ; when hour, ; when hour, ; in, The rate of change of the output angular frequency of the virtual synchronous generator; This serves as the baseline value for virtual inertia. This is the adjustment coefficient for virtual inertia; This is the baseline value for the active power-frequency droop factor; S3.3: After determining the virtual inertia and the active-frequency droop coefficient, the damping coefficient is coordinated and tuned according to the optimal damping ratio. ; in, The optimal damping ratio; The virtual internal potential amplitude of the virtual synchronous generator; This refers to the voltage amplitude at the grid connection point. This is the virtual impedance value.

[0020] In S3, active current compensation and reactive voltage compensation are introduced, including: S3.4: When the grid frequency changes abruptly, the active power reference current compensation is calculated based on the active power deviation and added to the original active power reference value. ; ; in, This is the active power reference current compensation amount; This is the proportionality coefficient; This is a reference value for active power. This refers to the actual active power output of the inverter. This is the active power deviation compensation value; Inverter output voltage Axial components; This is the original active current reference value; This is the reference value for the compensated active current; S3.5: When the grid voltage drops or the line impedance is mismatched, calculate the reactive voltage compensation amount based on the reactive power reference value, and construct a virtual negative impedance to offset the line voltage drop and maintain the stability of the voltage amplitude at the grid connection point. ; ; in, This is the reactive voltage compensation amount; The equivalent reactance of the line; This is a reference value for reactive power. This is the measured voltage at the grid connection point; This is the reactive power compensation coefficient; This is a virtual negative impedance value; This is a virtual negative resistance component; It is a complex frequency variable; The baseline virtual inductance value; This is the reactive power regulation coefficient.

[0021] In step S4, modal analysis is performed on the nodal admittance matrix and the oscillation source is located, including: S4.1: Aggregate the admittance models of each unit and network element to generate a model containing... A photovoltaic-storage microgrid with individual nodes at a frequency The nodal admittance matrix at the location This ensures that the node voltage and the node injected current satisfy the following conditions: ; in, This refers to the number of nodes in a photovoltaic-storage microgrid. For frequency; For frequency The nodal admittance matrix at the location; The node voltage matrix; Inject a current matrix into the node; S4.2: Perform eigenvalue decomposition on the node admittance matrix: ; And define the modal voltage With modal current Then the modal voltage and modal current satisfy: ; in, The left eigenvector matrix; It is a diagonal matrix of eigenvalues; The right eigenvector matrix; This is the modal voltage matrix; This is the modal current matrix; S4.3: When an eigenvalue in the eigenvalue diagonal matrix approaches zero, the corresponding mode is determined to be a critical resonant mode, and the nodes are calculated. For key resonant modes The participation factor is used to identify the node with the largest participation factor as the oscillation source. ; in, For nodes For key resonant modes Participating factors; The node number; The resonant mode number; The left eigenvector matrix is ​​the first... Line number Column elements; The right eigenvector matrix is ​​the first... Line number Column elements.

[0022] In S4, the virtual inertia of each unit is dynamically adjusted through a multi-agent consensus protocol, including: S4.4: Establishing a system containing In a multi-machine system with virtual synchronous generators, the first Rotor motion equations of the tandem generator set: ; ; in, The number of virtual synchronous generators; Unit serial number; For the first The actual angular frequency of the virtual synchronous generator; For time; For the first Reference value of active power of virtual synchronous generator; This is the rated angular frequency; For the first The actual active power of the virtual synchronous generator; For the first Damping coefficient of the virtual synchronous generator; For the first The power angle of a virtual synchronous generator; S4.5: Using the modal information obtained from modal analysis as the feedforward quantity, and based on the angular frequency information of neighboring units, construct the first... The adaptive virtual inertia model of the rig: ; in, For the first The virtual inertia of a virtual synchronous generator; For the first The reference inertia of the virtual synchronous generator; This is the inertia compensation coefficient; The serial number of the neighboring unit; For the first The set of neighboring units of a virtual synchronous generator; For the first The actual angular frequency of the neighboring unit; S4.6: An improved active-frequency control law is adopted, which uses real-time active power and the angular frequency of neighboring units as inputs to directly output the angular frequency reference value, in order to avoid measurement noise introduced by frequency differentiation. ; in, The active-frequency regulation function is determined by the slip frequency and the remaining power; , The first Taiwan, No. The slip frequency of the virtual synchronous generator; This represents the remaining power.

[0023] This invention discloses a collaborative control method for a grid-connected photovoltaic-storage microgrid based on modal feedforward and virtual inertia adaptive control, with the following technical advantages: 1) Achieved a synergistic improvement in DC-side energy storage SOC balancing speed and bus voltage stability: This invention addresses the problems in existing technologies where multiple energy storage units suffer from uneven state of charge (SOC) due to manufacturing process and aging differences, and where traditional droop control struggles to balance current sharing accuracy with bus voltage deviation. The invention dynamically adjusts the droop coefficient based on the SOC imbalance of each energy storage unit. Through an adjustment function, it accelerates battery equalization while compensating for DC bus voltage. This avoids overcharging and over-discharging of some batteries, delays energy storage system degradation, and keeps bus voltage deviation within acceptable limits, fundamentally resolving the contradiction between SOC equalization and voltage stability.

[0024] 2) It achieves a reasonable spectrum allocation of power in the hybrid energy storage system, extending the battery's lifespan: To address the issue that a single energy storage medium cannot simultaneously meet both energy-intensive and power-intensive requirements, this invention performs real-time spectrum decomposition of power commands and dynamically adjusts filtering parameters. Low-frequency, smooth power components are allocated to the battery, while high-frequency, abrupt power components are allocated to the supercapacitor. This fully leverages the complementary advantages of the two energy storage media, reduces the number of battery charge / discharge cycles and current surges, and provides continuous and stable DC bus voltage support for grid-connected inverters.

[0025] 3) Significantly improved the frequency dynamic response capability and adaptability to weak power grids of a single grid-connected unit under all operating conditions: This invention addresses the challenge of simultaneously optimizing frequency overshoot and recovery time in fixed-parameter virtual synchronous generator control under conditions of photovoltaic fluctuations and sudden load changes. It uses the sign of the product of frequency deviation and its rate of change as the criterion, increasing the virtual inertia during the frequency deviation phase to enhance disturbance rejection, and reverting to the reference value during the frequency recovery phase to accelerate response speed. Furthermore, it coordinates the tuning of the damping coefficient and introduces active current compensation and reactive voltage compensation. This approach accelerates power point tracking while maintaining stable voltage amplitude at the grid connection point, thus balancing frequency stability and power quality.

[0026] 4) Achieved precise positioning of the oscillation source and active suppression of subsynchronous oscillation and wideband resonance in multi-machine parallel systems: To address the problem of subsynchronous oscillations easily caused by inertia parameter mismatch and line impedance differences during parallel operation of multi-grid inverters, and the lack of system-level oscillation source tracing methods, this invention extracts key resonant modes through modal analysis of the admittance matrices of multi-machine system nodes and uses participation factors to quantitatively characterize the degree of participation of each node in the resonance, achieving precise location of the oscillation source. Furthermore, using modal information as feedforward and dynamically adjusting the virtual inertia of each unit through a multi-agent consensus protocol, the traditional passive stability analysis is transformed into active damping injection, effectively suppressing subsynchronous oscillations caused by multi-machine coupling and broadband resonances induced by inverter-grid impedance interaction. Moreover, the improved control law adopted avoids measurement noise introduced by frequency differentiation, enhancing the engineering feasibility of the control.

[0027] 5) An integrated hierarchical collaborative control architecture was constructed, providing complete technical support for the safe operation of grid-type photovoltaic-storage systems with a high proportion of new energy access. To address the problem that existing research treats DC-side energy management, AC-side single-unit frequency regulation, and multi-unit system stability analysis in a fragmented manner, failing to establish an integrated control system, this invention establishes a complete small-signal impedance model covering photovoltaic boost converters, energy storage bidirectional DC / DC converters, and grid-type inverters. It establishes a complete technical chain from impedance modeling, DC-side equalization distribution, single-unit adaptive frequency regulation to system-level modal feedforward collaborative control. The control at each level is interconnected, and information is transmitted layer by layer, systematically improving the frequency stability and broadband oscillation suppression capability of the photovoltaic-storage microgrid under multiple operating conditions. This provides a reliable theoretical basis and technical means for the planning, design, parameter tuning, and safe operation of grid-type photovoltaic-storage systems. Attached Figure Description

[0028] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 This is a circuit topology diagram of the photovoltaic Boost converter in an embodiment of the present invention.

[0029] Figure 2 This is a discharge characteristic curve of the battery in an embodiment of the present invention.

[0030] Figure 3 The above are system frequency response waveforms of a grid-type photovoltaic-storage microgrid under different virtual inertia values ​​in embodiments of the present invention.

[0031] Figure 4 This is a comparison chart of the theoretical calculation curve and the frequency scan simulation value of the output admittance of the grid-type inverter in this embodiment of the invention.

[0032] Figure 5(a) is a waveform diagram of the active power response of the grid-type inverter after the DC bus voltage is disturbed in an embodiment of the present invention. Figure 5(b) is a waveform diagram of the reactive power response of the grid inverter after the DC bus voltage is disturbed in the embodiment of the present invention.

[0033] Figure 6 This is a waveform diagram of the system frequency response of a grid-type photovoltaic-storage microgrid under communication delay conditions in an embodiment of the present invention. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0035] Example 1: This embodiment provides a collaborative control method for a grid-type photovoltaic-storage microgrid based on modal feedforward and virtual inertia adaptation. The overall concept of this method is as follows: First, a complete small-signal impedance model covering the photovoltaic Boost converter, the energy storage bidirectional DC / DC converter, and the grid-type inverter is established to lay the mathematical foundation for the system frequency domain characteristic analysis and multi-machine node admittance matrix aggregation. Second, for the DC side, self-balancing among multiple battery energy storage units is achieved through improved droop control based on SOC imbalance, and an adaptive filtering algorithm based on sliding discrete Fourier transform is introduced to complete the interaction between the batteries and the supercapacitor. Power spectrum decomposition provides a stable DC bus voltage for grid-connected inverters. Next, for the AC side, an adaptive algorithm dynamically adjusts virtual inertia and damping coefficients with frequency deviation and rate of change, supplemented by active current compensation and reactive voltage compensation, to improve the frequency dynamic response and power quality of a single virtual synchronous generator. Finally, the single-generator model is extended to a multi-generator parallel scenario. Modal analysis of the node admittance matrix extracts key resonant modes and participation factors to accurately locate the oscillation source. This modal information is then used as a feedforward to construct a multi-agent consensus protocol, enabling coordinated adjustment of the virtual inertia of each unit.

[0036] The aforementioned three-layer progressive control architecture—"DC-side energy balancing - AC-side single-unit frequency modulation - system-level oscillation suppression"—overcomes the shortcomings of existing technologies that separate DC-side energy management, AC-side single-unit frequency modulation, and multi-unit system stability analysis, achieving a complete technical closed loop from impedance modeling and modal analysis to adaptive collaborative control. Specifically, it includes the following steps: Step S1: Establish the time-domain small-signal model of the photovoltaic Boost converter and the energy storage bidirectional DC / DC converter, and use the harmonic linearization method to establish the admittance matrix model of the positive and negative sequence decoupling of the grid-type inverter: Photovoltaic-storage microgrids contain numerous power electronic converters. The impedance interactions between converters and between converters and the grid are the root cause of broadband oscillations. Therefore, accurately establishing impedance models for each converter over a wide frequency range is the primary prerequisite for conducting system stability analysis and collaborative control design. This step establishes time-domain small-signal models for the DC-side photovoltaic Boost converter and the energy storage bidirectional DC / DC converter, and establishes a positive- and negative-sequence decoupled second-order admittance matrix model for the AC-side grid-type inverter.

[0037] (1) Closed-loop impedance modeling of photovoltaic Boost converter: The photovoltaic array has a low output voltage and needs to be boosted by a Boost converter before it can be connected to the grid. Its circuit topology is as follows: Figure 1 As shown. This converter contains one inductor and two capacitors, and is a typical third-order circuit. According to Figure 1 The state-space equations for the inductor volt-second balance and capacitor charge balance in the topology shown can be expressed as follows: (1); (2); (3); in, This refers to the inductance value of the photovoltaic converter. This refers to the inductor current of the photovoltaic converter. For time; This refers to the output voltage of the photovoltaic array. This refers to the photovoltaic duty cycle. This is the DC bus voltage; For filtering capacitors on the photovoltaic array side; Output current for the photovoltaic array; For photovoltaic side bus capacitors; This is the output current of the photovoltaic converter.

[0038] Because the switching characteristics of the Boost converter make it essentially a nonlinear time-varying system, in order to obtain a linearized model that can be used for frequency domain impedance analysis, small-signal perturbations are superimposed on each state variable near the steady-state operating point, and higher-order infinitesimal terms are ignored. That is, the state-space equations are subjected to small-signal linearization and transformed to the frequency domain, resulting in the frequency domain small-signal expression: (4); (5); (6); in, It is a complex frequency variable; For small-signal variables; , , They are respectively , , The steady-state value.

[0039] Without considering the control loop, setting the duty cycle disturbance to zero, and eliminating internal variables by simultaneously solving the above frequency domain small-signal expressions, the open-loop output impedance of the photovoltaic Boost converter can be derived: (7); in, This represents the open-loop output impedance of the photovoltaic Boost converter.

[0040] However, in actual operation, the converter operates in a closed-loop control state, and the duty cycle disturbance introduced by the control loop will significantly change the converter's impedance characteristics in the mid-to-low frequency range. Considering the duty cycle disturbance of the switching transistors introduced by the control loop, the closed-loop output impedance of the photovoltaic Boost converter is obtained through small-signal modeling as follows: (8); in, The closed-loop output impedance of the photovoltaic Boost converter; The transfer function from a small duty cycle disturbance to a small disturbance in the converter output bus voltage; The transfer function is given by the small perturbation of the converter output bus current to the small perturbation of the photovoltaic array output voltage. The transfer function from a small duty cycle perturbation to a small perturbation in the output voltage of the photovoltaic array; The transfer function of the photovoltaic-side controller is given. In a preferred embodiment, the photovoltaic-side controller employs a proportional-integral controller, and its transfer function is: (9); in, The proportional gain of the photovoltaic-side controller. The integral coefficient of the photovoltaic-side controller is denoted as . The physical meaning of the closed-loop impedance model is that the control loop is equivalent to connecting an equivalent admittance branch determined by the controller in parallel with the open-loop impedance, thereby causing the output impedance presented by the converter to change with the controller parameters. This is the theoretical basis for subsequently improving the system impedance characteristics through control parameter optimization.

[0041] (2) Closed-loop impedance modeling of the energy storage bidirectional DC / DC converter: The energy storage unit is connected to the DC bus via a bidirectional DC / DC converter, undertaking the function of smoothing power fluctuations and maintaining bus voltage stability. The state-space equation of its conversion circuit can be expressed as: (10); (11); in, Inductor for energy storage converter; For energy storage output current; For time; This is the energy storage output voltage; This refers to the duty cycle of the energy storage converter. This is the DC bus voltage; For the energy storage side bus capacitor; This is the output current of the energy storage converter.

[0042] Consistent with the modeling approach of photovoltaic Boost converters, by superimposing small signals onto the above state-space equations and eliminating steady-state quantities, the frequency-domain small-signal expression is obtained: (12); (13); in, It is a complex frequency variable; For small-signal variables; , , They are respectively , , The steady-state value.

[0043] Without considering the control loop, the open-loop output impedance of the energy storage bidirectional DC / DC converter can be expressed as: (14); in, This is the open-loop output impedance of the energy storage bidirectional DC / DC converter.

[0044] After incorporating the control loop, the closed-loop output impedance of the energy storage bidirectional DC / DC converter is obtained through small-signal modeling as follows: (15); in, The closed-loop output impedance of the energy storage bidirectional DC / DC converter; Transfer function for the energy storage side current controller; The transfer function is given by the small perturbation of the converter output current to the small perturbation of the energy storage output current. The transfer function from a small duty cycle disturbance to a small disturbance in the converter output bus voltage; The transfer function from a small duty cycle disturbance to a small disturbance in the energy storage output current; This is the transfer function for the energy storage side voltage controller.

[0045] In a preferred embodiment, both the current controller and voltage controller on the energy storage side employ proportional-integral controllers, with transfer functions respectively. and ,in, , These are the proportional and integral coefficients of the energy storage side current controller, respectively. , These are the proportional and integral coefficients of the energy storage side voltage controller, respectively.

[0046] (3) Modeling of the second-order admittance matrix of the grid-type inverter: Impedance modeling of grid-connected inverters typically falls into two categories: state-space methods based on the dq coordinate system and harmonic linearization methods based on the phasor domain. The former involves a complex modeling process and has a high order; the latter directly describes the frequency coupling relationship of voltage and current disturbances in the phasor domain, resulting in a lower model order and clearer physical meaning. This invention employs a harmonic linearization method: a small-signal disturbance of a single frequency is superimposed at the steady-state operating point, ignoring the higher-order harmonic components generated by the disturbance excitation, and retaining only the dominant components near the fundamental frequency, thereby equating the nonlinear switching element to a linear frequency domain element.

[0047] For grid-connected inverters, since their DC side is a voltage-stabilized energy storage device, no bus voltage outer loop is required, and AC / DC frequency coupling is weak. Positive-sequence disturbances only excite the positive-sequence response, and negative-sequence disturbances only excite the negative-sequence response. Therefore, their output admittance matrix exhibits a second-order diagonal form with positive and negative sequence decoupling, i.e.: (16); (17); in, , These are the positive-sequence and negative-sequence voltage perturbation frequency domain components at the common connection point, respectively. , These are the positive-sequence and negative-sequence current disturbance frequency domain components at the common connection point, respectively. It is a positive-order admittance; It is a negative-order admittance; For complex frequency variables. The positive and negative order decoupling characteristics simplify the coupling impedance problem, which originally required a fourth-order matrix, into two independent scalar admittance problems, significantly reducing the computational complexity of subsequent node admittance matrix aggregation and modal analysis in multi-machine systems.

[0048] Using the harmonic linearization method, the expressions for the positive-sequence admittance and the negative-sequence admittance can be derived as follows: (18); (19); in, The transfer function for the proportional-integral controller of the inner current loop of a grid-type inverter; For the voltage outer loop proportional-integral controller transfer function of the grid-type inverter; The imaginary unit; The fundamental angular frequency; For filtering capacitors in grid-type inverters; This is the filter inductor for a grid-type inverter. It should be noted that the frequency shift term in the positive-sequence expression... With the frequency shift term in the negative order expression This demonstrates the mirror symmetry relationship between the positive and negative sequence components in the phasor domain with respect to the fundamental frequency, which is key to characterizing the frequency characteristics of the sequence components using the harmonic linearization method.

[0049] Step S2: Improved droop control and hybrid energy storage power spectrum allocation based on SOC imbalance: Based on the mathematical model of the bidirectional DC / DC converter established in step S1, the energy storage system is further concretized as a hybrid energy storage system composed of batteries and supercapacitors. The DC side faces two levels of problems: First, when multiple battery energy storage units operate in parallel, due to differences in manufacturing processes, initial capacity, and aging levels, the state of charge of each unit is prone to imbalance. Without intervention, some batteries will deteriorate rapidly due to overcharging and over-discharging, and may even cease operation. Second, a single energy storage medium cannot simultaneously meet the energy demand for smoothing slow power fluctuations and the power demand for smoothing rapid power surges. This step designs control strategies for both of these levels.

[0050] (1) Improved droop control based on SOC imbalance: Battery discharge characteristic curve as shown Figure 2 As shown, its optimal operating state is typically between 20% and 90% state of charge; exceeding this range will significantly accelerate battery aging. Its state of charge can be expressed as: (20); in, for The state of charge of the battery energy storage unit at all times; This represents the initial state of charge of the battery energy storage unit. The total capacity of the battery energy storage unit; For time; This refers to the charging and discharging current of the battery energy storage unit. It is the integral variable.

[0051] Traditional droop control distributes the output power of each energy storage unit according to a fixed droop coefficient. Although it can achieve autonomous power distribution without communication, it has inherent drawbacks: the larger the droop coefficient, the higher the current distribution accuracy, but the greater the DC bus voltage deviation. Current sharing accuracy and voltage quality are mutually restrictive and cannot be simultaneously achieved. To address this, this invention introduces state-of-charge imbalance to correct the droop coefficient online. The average state of charge (SOC) of the parallel-connected battery energy storage units and the SOC imbalance of each unit can be expressed as: (twenty one); (twenty two); in, This represents the average state of charge of the battery energy storage unit. The number of parallel battery energy storage units; This refers to the serial number of the battery energy storage unit; For the first The state of charge of the battery energy storage unit; For the first The imbalance of the state of charge of the battery energy storage unit.

[0052] Improved droop control dynamically adjusts the droop coefficient of each battery energy storage unit by adjusting the state-of-charge imbalance. This allows the output voltage of each unit to adaptively adjust according to its state of charge, which can be expressed as: (twenty three); (twenty four); in, For the first The droop coefficient of the battery energy storage unit; This is the equilibrium droop coefficient when all battery energy storage units have the same state of charge. For the first The output voltage of the battery energy storage unit converter; This is the reference value for the converter output voltage; This is the function for bus voltage compensation and equalization speed regulation. For the first The output current of the battery energy storage unit converter.

[0053] The working principle of the above control is as follows: when the state of charge of a certain battery energy storage unit is higher than the average value, that is... When, its droop coefficient As the charge level decreases, the output voltage increases, and the unit automatically takes on more discharge power; conversely, the droop factor of units with a state of charge below the average increases, and the discharge power decreases. Therefore, the output power of each unit is distributed on demand according to its state of charge, driving the state of charge of each unit to converge towards the average value, achieving self-balancing without a centralized controller. Simultaneously, the adjustment function... It compensates for the inherent bus voltage drop in droop control, thereby breaking the deadlock between current sharing accuracy and voltage quality.

[0054] The form of the adjustment function determines the dynamic characteristics of the bus voltage compensation and equalization speed, and can be expressed as: (25); in, This is the voltage compensation amplitude control coefficient; This refers to the state of charge of the battery energy storage unit. This is a control coefficient for the degree of nonlinearity in the equilibrium speed; It is a natural constant. This function increases monotonically with the state of charge and has nonlinear amplification characteristics: the higher the state of charge, the greater the compensation, the stronger the discharge tendency of the high-charge-state cell, and the equalization speed adaptively increases with the increase of the imbalance.

[0055] As a preferred implementation method, The value of the setting is limited to ensuring that the bus voltage deviation does not exceed ±5% of the rated voltage; The larger the value, the faster the convergence speed in the later stage of equilibrium, but excessively large values... This may cause voltage overshoot. In engineering practice, a value between 1 and 3 can be used and verified through simulation.

[0056] A small-signal model of the improved droop control is established, and its system characteristic equation can be expressed as: (26); in, , , , These are system parameters determined by circuit parameters and control parameters; For complex frequency variables. As a preferred implementation, the Routh criterion can be used to check the stability of the above characteristic equation: when all coefficients of the characteristic equation have the same sign and all elements in the first column of the Routh array are positive, the improved droop control system is stable. Based on this, it can be determined that... , , The feasible range of values ​​is determined to ensure that the parameter tuning process has clear stability constraints.

[0057] 2) Hybrid energy storage power spectrum allocation based on sliding discrete Fourier transform: Based on state-of-charge equilibrium, a supercapacitor is further introduced to form a hybrid energy storage system. Batteries have high energy density and are suitable for handling low-frequency, high-power components, but their slow power response and frequent charging / discharging shorten their lifespan. Supercapacitors, on the other hand, have high power density, fast response, and long cycle life, making them suitable for handling high-frequency, low-energy components. The two have naturally complementary power spectrum characteristics. Traditional low-pass filter allocation methods with fixed time constants cannot adapt to changes in the power command spectrum under varying operating conditions. Therefore, this invention uses a sliding discrete Fourier transform to extract the spectral characteristics of the power command in real time and dynamically adjusts the time constant of the low-pass filter, achieving complementary advantages between the two energy storage media. The difference equation of the sliding discrete Fourier transform network can be expressed as: (27); in, For the first The sampling time of the first sampling moment The spectral values ​​of each frequency component; The frequency component number; The sampling time sequence number; It is a natural constant; The imaginary unit; Pi; The length of the sliding window; For the first The power command input signal at each sampling time. This recursive structure can complete the spectrum update by entering a new sampling point and exiting an old sampling point. Only one complex number operation is required at each sampling time, and the amount of computation is much less than that of a complete Fourier transform, which is convenient for real-time implementation in digital controllers.

[0058] In a preferred embodiment, the sliding window length is taken as ,in, Sampling frequency, The fundamental frequency is used to ensure that the spectral resolution reaches the level of the fundamental frequency.

[0059] The relationship between the smoothing factor of a low-pass filter and the time constant can be expressed as: (28); in, It is a smoothing factor; This represents the time constant of the low-pass filter. The sampling period.

[0060] The difference equation for a discrete low-pass filter can be expressed as: (29); in, For the first The filter output value at each sampling time. The low-frequency power component obtained from the filter is allocated to the battery, and the difference between the power command and the low-frequency component is the high-frequency power component, which is allocated to the supercapacitor. The adaptive adjustment rule is: when the sliding discrete Fourier transform detects an increase in the proportion of the high-frequency component of the power command, the time constant is decreased. Raising the filter cutoff frequency allows more fluctuating power to be smoothed by the supercapacitor, preventing the battery from being subjected to high-frequency charging and discharging shocks; conversely, when the power command is dominated by low-frequency components, increasing the filter cutoff frequency allows more power to be delivered to the supercapacitor for smoothing, thus preventing the battery from being subjected to high-frequency charging and discharging shocks. This fully utilizes the energy capacity of the storage battery and reduces the energy consumption of the supercapacitor. This allows for online adaptive adjustment of the filter parameters according to the power spectrum characteristics.

[0061] Step S3: Adaptive adjustment of virtual inertia and damping coefficient, and active current compensation and reactive voltage compensation: After achieving bus voltage stability on the DC side through state-of-charge balancing and hybrid energy storage power distribution, the AC side needs to further address the system inertia deficiency caused by the high penetration rate of new energy sources in the grid. Traditional power systems rely on the rotor inertia of synchronous generators to suppress frequency fluctuations. However, power electronic converters have no physical rotor, and after large-scale replacement of synchronous power sources, the system exhibits low inertia and weak damping characteristics, resulting in a significant decrease in frequency disturbance rejection capability. Virtual synchronous generator control, by simulating the rotor motion equation of a synchronous generator, enables the grid-connected inverter to exhibit inertia and damping characteristics, which is an effective way to solve the above problems. Its oscillation equation can be expressed as: (30); in, This is virtual inertia; The output angular frequency of the virtual synchronous generator; For time; This is a reference value for active power. This is the rated angular frequency; The active power-frequency droop factor; This represents the actual output value of active power. The damping coefficient; The measured angular frequency at the grid connection point.

[0062] However, the fixed values ​​for virtual inertia and damping coefficient in traditional virtual synchronous generator control present an inherent performance contradiction: while a large virtual inertia can suppress the rate of frequency change and reduce the frequency offset depth during disturbances, it slows down the frequency recovery speed; conversely, a small value has the opposite effect. Fixed parameters cannot simultaneously address the opposing needs of disturbance suppression and rapid recovery. Therefore, this invention defines frequency deviation... and the frequency deviation is compared with its rate of change. The sign of the product is used as the adjustment criterion, the rate of change This represents the rate of change of the output angular frequency of the virtual synchronous generator over time. The physical meaning of this adjustment criterion is: when... When the absolute value of the frequency deviation is increasing, the system is in the frequency deviation stage. At this time, increasing the virtual inertia can enhance the anti-disturbance capability and suppress rapid frequency shift; when At this time, the absolute value of the frequency deviation is decreasing, and the system is in the frequency recovery phase. Restoring the reference inertia at this stage can accelerate the recovery speed and shorten the adjustment time. Based on this, an adaptive adjustment law for virtual inertia and active power-frequency droop coefficient is constructed: when hour, ; when hour, ; when hour, ; when hour, ; in, This serves as the baseline value for virtual inertia. This is the adjustment coefficient for virtual inertia; This is the baseline value for the active power-frequency droop factor; This is the adjustment coefficient for the active-frequency droop coefficient. This adjustment law does not rely on iterative calculations using intelligent optimization algorithms; it provides parameter adjustments in real time based solely on locally measurable frequency signals. It is simple to calculate, responds quickly, and is highly feasible for engineering applications. For ease of implementation, Table 1 presents the adjustment strategies for virtual inertia and the active-frequency droop coefficient under different frequency deviation quadrants:

[0063] exist and Once determined, to suppress frequency oscillations, the damping coefficients are coordinated and tuned based on the optimal damping ratio, which can be expressed as: (31); in, The optimal damping ratio; The virtual internal potential amplitude of the virtual synchronous generator; This refers to the voltage amplitude at the grid connection point. This represents the virtual impedance value. According to classical second-order system theory, a damping ratio of 0.707 achieves an optimal trade-off between overshoot and settling time; therefore, it is chosen as a preferred implementation method. This tuning formula establishes an analytical relationship between the damping coefficient and the virtual inertia, enabling the damping coefficient to adjust accordingly as the virtual inertia changes adaptively, thus avoiding frequency oscillations caused by mismatch between the two.

[0064] Based on adaptive inertia damping adjustment, active power reference current compensation and reactive power voltage compensation are introduced to improve the dynamic response speed and power quality under grid disturbances. When the grid frequency changes abruptly, the active power reference current compensation is calculated based on the power deviation to accelerate power point tracking, which can be expressed as: (32); (33); in, This is the active power reference current compensation amount; This is the proportionality coefficient; This is a reference value for active power. This refers to the actual active power output of the inverter. This is the active power deviation compensation value; Inverter output voltage Axial components; This is the original active current reference value; This is the compensated active current reference value. This compensation circuit directly feeds the active power deviation forward to the inner current loop reference value, bypassing the adjustment delay of the outer power loop, enabling the active power to quickly track the reference value in the early stages of the disturbance.

[0065] When the grid voltage drops or the line impedance is mismatched, the voltage drop at the grid connection point is offset by virtual negative impedance matching and reactive power compensation to maintain a stable voltage amplitude. This can be expressed as: (34); (35); in, This is the reactive voltage compensation amount; The equivalent reactance of the line; This is a reference value for reactive power. This is the measured voltage at the grid connection point; This is the reactive power compensation coefficient; This is a virtual negative impedance value; This is a virtual negative resistance component; It is a complex frequency variable; The baseline virtual inductance value; This is the reactive power regulation coefficient. The virtual negative resistance component is used to offset the voltage drop across the line resistance, while the virtual inductance component, which is adjusted according to the reactive power reference value, is used to dynamically compensate for the voltage drop across the line reactance. Together, they ensure that the voltage at the grid connection point remains stable when the grid voltage drops or the impedance changes.

[0066] Figure 3 For different virtual inertia The system frequency response waveform is given by Figure 3It is evident that increasing the virtual inertia can reduce the frequency change rate and suppress the frequency offset depth, while an excessively large virtual inertia will prolong the frequency recovery time. This phenomenon experimentally confirms the necessity of the present invention to adopt adaptive adjustment rather than a fixed value.

[0067] Step S4: Multi-machine system modal analysis and virtual inertia cooperative adjustment based on multi-agent consensus protocol: In multi-unit parallel operation scenarios, the interaction and coupling between different grid-type units may trigger subsynchronous oscillations. Locating the oscillation source and coordinating its suppression are crucial for stable system operation. Existing oscillation suppression methods are mostly passive suppression at the single-unit level, which cannot answer the question of where the oscillation source is located, nor can they coordinate the units to jointly suppress oscillations. This step first achieves system-level oscillation source tracing through modal analysis, and then uses modal information as a feedforward to achieve coordinated damping injection across multiple units.

[0068] The parallel resonance of a photovoltaic-storage microgrid manifests as a singular term in the node admittance matrix. Specifically, when a certain eigenvalue of the node admittance matrix approaches zero, the corresponding eigenvalue of its inverse matrix approaches infinity. Injecting a small current into this node can then induce a high voltage, thereby triggering parallel resonance. Assuming... A photovoltaic-storage microgrid system with multiple nodes at a frequency Parallel resonance occurs at a certain point, at which time the node voltage and node injected current of the system satisfy: (36); in, This refers to the number of nodes in a photovoltaic-storage microgrid. For frequency; For frequency The node admittance matrix at the location is generated by aggregating the impedance models of each converter and the parameters of network elements established in step S1. The node voltage matrix; Inject a current matrix into the node. Eigenvalue decomposition can be represented as: (37); in, The left eigenvector matrix; It is a diagonal matrix of eigenvalues; This is the right eigenvector matrix. Modal voltages are defined. With modal current The relationship between modal voltage and modal current is as follows: (38); After the above transformation, the originally coupled voltage and current relationships of the nodes are decoupled into independent mode domain equations: each eigenvalue corresponds to an independent mode; the closer the eigenvalue is to zero, the easier the corresponding mode is to be excited, and the higher the risk of resonance. By analyzing the key modes and their left and right eigenvectors, the specific location of the resonance, the severity of the resonance, and the degree of participation of each node in the resonance can be determined. To locate the oscillation source, nodes are defined. For key resonant modes Participating factors , can be represented as: (39); in, The node number; The resonant mode number; The left eigenvector matrix is ​​the first... Line number Column elements; The right eigenvector matrix is ​​the first... Line number The participation factor integrates information from corresponding nodes in the left and right eigenvectors, quantitatively characterizing the controllability and observability of each node for the key resonant mode. The larger the participation factor, the more likely the oscillation source is located at that node. Based on this, the node with the largest participation factor is identified as the oscillation source, and the modal information, such as the key resonant mode frequency, damping level, and participation factors of each node, is output as feedforward quantities to the cooperative control layer.

[0069] After locating the oscillation source through modal analysis, a multi-agent consensus protocol is employed to dynamically adjust the virtual inertia of each unit. The basic idea of ​​the multi-agent consensus protocol is that each unit only exchanges state information with its neighboring units in the communication topology, achieving global state convergence through local interaction. This eliminates the need for a centralized controller, reduces communication burden, and provides good scalability. For units containing... A multi-machine system with virtual synchronous generators, the first The rotor motion equation of the virtual synchronous generator can be expressed as: (40); (41); in, This refers to the virtual synchronous generator serial number; For the first The actual angular frequency of the virtual synchronous generator; For time; For the first Reference value of active power of virtual synchronous generator; This is the rated angular frequency; For the first The actual active power of the virtual synchronous generator; For the first Damping coefficient of the virtual synchronous generator; For the first The power angle of a virtual synchronous generator.

[0070] Each virtual synchronous generator exchanges angular frequency information through a sparse communication network to construct an adaptive virtual inertia mathematical model, which can be expressed as: (42); in, For the first The virtual inertia of a virtual synchronous generator; For the first The reference inertia of the virtual synchronous generator; This is the inertia compensation coefficient; The serial number of the neighboring unit; For the first The set of neighboring units of a virtual synchronous generator; For the first The actual angular frequency of the neighboring units. The physical meaning of this regulation law is: when the angular frequency of this unit deviates from that of the neighboring units and the deviation trend intensifies, it indicates that there is relative oscillation between the units. At this time, the virtual inertia of this unit is increased to inject damping into the system and suppress relative oscillation; when the angular frequencies of all units tend to be consistent and reach consistency convergence, the correction term automatically returns to zero, and the inertia of each unit returns to the reference value, thereby realizing on-demand inertia supply and coordinated damping injection after oscillation smoothing. Modal feedforward information is used to determine the inertia compensation coefficient. Allocation: Nodes with larger participation factors are assigned larger inertia compensation coefficients to their corresponding units, ensuring that inertia adjustment is precisely applied to the oscillation source and avoiding indiscriminate adjustment that would waste inertia. As a preferred implementation, the topology of the sparse communication network satisfies the connectivity condition, meaning that the Laplace matrix corresponding to the communication topology contains only one zero eigenvalue, to guarantee the convergence of the multi-agent consensus protocol.

[0071] To avoid measurement noise introduced by frequency differentiation, an improved active-frequency control law is further adopted, which can be expressed as: (43); in, The active-frequency regulation function is determined by the slip frequency and the remaining power; , The first Taiwan, No. The slip frequency of the virtual synchronous generator; The remaining power is used as input. The control law takes the real-time active power and the angular frequency of the neighboring unit as inputs, and directly outputs the angular frequency reference value through the integral stage, avoiding the frequency derivative term. This effectively suppresses the amplification effect of differential operations on measurement noise and improves the robustness of the control strategy in noisy engineering environments.

[0072] Step S5: Experimental simulation and hardware-in-the-loop testing verification: To fully verify the above modeling method and control strategy, a simulation model of a photovoltaic-storage DC microgrid including a photovoltaic array, a hybrid energy storage system, and a grid-type inverter was built. The sequence impedance model, state-of-charge adaptive droop control, and mode feedforward collaborative control strategy proposed in this invention were applied to evaluate system frequency stability and broadband oscillation suppression. Typical operating conditions were set, and state variables such as DC bus voltage, energy storage state of charge, grid connection point frequency, and inverter output power were collected. The control effects of traditional fixed-parameter virtual synchronous generator control, collaborative control without mode feedforward, and the method of this invention were compared. The main parameters of the simulation model can be selected according to Table 2.

[0073] Furthermore, a hardware-in-the-loop test platform was built based on a real-time digital simulator and a physical controller: the main circuit model of the photovoltaic-storage microgrid was run in the real-time simulator, and the cooperative control algorithm of this invention was downloaded to the actual controller. The two were connected in a closed loop through physical input / output interfaces, thereby verifying the effectiveness and transient robustness of the proposed modeling, power sharing, frequency regulation, and multi-machine cooperative strategies under conditions close to real control hardware. Simulation and frequency sweep verification show that the sequence impedance model established in this invention can accurately reveal the broadband interaction mechanism between the DC and AC sides of the photovoltaic-storage system, and the adaptive virtual inertia adjustment significantly improves the frequency response speed and stability, providing reliable technical support for the planning and safe operation of grid-type photovoltaic-storage microgrids with high proportion of new energy access.

[0074] The information transmission relationships between the various control levels of this invention are explained from a system architecture perspective: The small-signal impedance models of each converter established in step S1 are aggregated to form the node admittance matrix of the multi-machine system, which serves as the input for the modal analysis in step S4. The DC-side equalization and power distribution control in step S2 stabilizes the DC bus voltage, providing constant DC-side boundary conditions for the single-machine virtual synchronous generator control in step S3. The single-machine adaptive frequency regulation results in step S3 determine the inertia reference level of each unit, serving as the initial value for the coordinated adjustment in step S4. The modal analysis results in step S4 are fed forward to each unit to correct its virtual inertia setting, thus forming a closed-loop hierarchical control architecture that connects modeling, equalization, frequency regulation, and coordination step by step, transforming passive stability analysis into active damping injection. In this architecture, the output of the previous level serves as the input or boundary condition of the next level, and each level can be implemented independently or combined to form a complete coordinated control system.

[0075] Example 2: This embodiment verifies the effectiveness of the present invention, and the verification results are as follows: Figure 4 Figure 5(a), Figure 5(b) Figure 6 As shown.

[0076] To verify the accuracy of the constructed output admittance equivalent model, a grid-type inverter simulation system including a three-phase LC filter was built in the PSCAD environment, and the frequency scanning method was used for verification. Since the load impedance connected to the common coupling point will generate voltage and current division effects at the harmonic source, thus causing an inherent deviation in the admittance measurement value, the load branch was disconnected in the simulation to eliminate interference. Figure 4 The verification curve for the inverter output admittance model is provided by... Figure 4 It can be seen that, within a relatively wide frequency range, the amplitude-frequency and phase response curves obtained by theoretical calculation are basically consistent with the measured values ​​obtained by frequency sweep simulation, proving the reliability and effectiveness of the established impedance model.

[0077] To verify the control method proposed in this invention, assuming the DC bus voltage is already in a steady state, a preset random sinusoidal disturbance is applied at 2 seconds during the stable operation of the distribution network under rated load. The response characteristics on the grid side are observed, as shown in Figures 5(a) and 5(b). Affected by this power disturbance, the active power output of the inverter in Figure 5(a) drops from 21kW to 15kW, while the reactive power in Figure 5(b) jumps to 13kVar. Compared with the traditional virtual synchronous generator control strategy, the control strategy proposed in this invention has advantages in suppressing the active power drop and supporting the dynamic response of reactive power.

[0078] To verify the robustness of the proposed cooperative control method under communication delay conditions, a communication delay is set in the controller and the communication link. Figure 6The waveform of the system frequency response under this operating condition is presented. Experimental results show that even with communication delay, the proposed control strategy can still maintain the maximum frequency deviation of the system at a small level, fully demonstrating that the method has good frequency maintenance capability under delay conditions and can effectively reduce the adverse effects of frequency fluctuations on power grid operation.

Claims

1. A collaborative control method for grid-type photovoltaic-storage microgrids based on modal feedforward and virtual inertia adaptive control, characterized in that... Includes the following steps: S1: Establish a small-signal model of the photovoltaic Boost converter and the energy storage bidirectional DC / DC converter, and use the harmonic linearization method to establish the admittance matrix model of the grid-type inverter with positive and negative sequence decoupling; S2: Dynamically adjust the droop coefficient according to the imbalance of the state of charge of each energy storage unit to balance the output power of each energy storage unit and compensate the DC bus voltage; perform spectrum decomposition on the power command and distribute power between the battery and the supercapacitor. S3: Based on the frequency deviation and its rate of change of the grid-type inverter, the virtual inertia and damping coefficient are adaptively adjusted, and active current compensation and reactive voltage compensation are introduced to improve the frequency regulation capability and power quality of a single grid-type unit. S4: Perform modal analysis on the node admittance matrix of the multi-machine system, extract key resonant modes, and locate the oscillation source based on the participation factor of each node to the key resonant modes; Using modal information as feedforward, the virtual inertia of each unit is dynamically adjusted by multiple agents to achieve multi-machine parallel and collaborative control.

2. The method for coordinated control of a grid-type photovoltaic-storage microgrid based on modal feedforward and virtual inertia adaptation as described in claim 1, characterized in that: In step S1, a small-signal model of the photovoltaic Boost converter is established, including: 1.1: Based on the circuit topology of the photovoltaic Boost converter, establish its state-space equations: ； ； ； in, This refers to the inductance value of the photovoltaic converter. This refers to the inductor current of the photovoltaic converter. For time; This refers to the output voltage of the photovoltaic array. This refers to the photovoltaic duty cycle. This is the DC bus voltage; For filtering capacitors on the photovoltaic array side; Output current for the photovoltaic array; For bus capacitors; For the output current of the photovoltaic converter; 1.2: The state-space equation is linearized using small-signal processing and transformed to the frequency domain to obtain the frequency-domain small-signal expression: ； ； ； in, It is a complex frequency variable; For small-signal variables; , , They are respectively , , The steady-state value; 1.3: Based on the aforementioned frequency domain small-signal expression, derive the open-loop output impedance of the photovoltaic Boost converter without considering the control loop: ； in, This refers to the open-loop output impedance of the photovoltaic Boost converter; 1.4: Based on the open-loop output impedance, the duty cycle disturbance introduced by the control loop is taken into account to obtain the closed-loop output impedance of the photovoltaic Boost converter: ； in, The closed-loop output impedance of the photovoltaic Boost converter; The transfer function from a small duty cycle disturbance to a small disturbance in the converter output bus voltage; The transfer function is given by the small perturbation of the converter output bus current to the small perturbation of the photovoltaic array output voltage. The transfer function from a small duty cycle perturbation to a small perturbation in the output voltage of the photovoltaic array; This is the transfer function for the photovoltaic-side controller.

3. The method for coordinated control of a grid-type photovoltaic-storage microgrid based on modal feedforward and virtual inertia adaptive control according to claim 2, characterized in that: In step S1, a small-signal model of the energy storage bidirectional DC / DC converter is established, including: 1.5: Establish the state-space equations for the energy storage bidirectional DC / DC converter circuit: ； ； in, Inductor for energy storage converter; For energy storage output current; For time; This is the energy storage output voltage; This refers to the duty cycle of the energy storage converter. This is the DC bus voltage; For bus capacitors; This is the output current of the energy storage converter; 1.6: By superimposing small signals onto the above state-space equations and eliminating steady-state quantities, we obtain the frequency-domain small-signal expression: ; ； in, It is a complex frequency variable; For small-signal variables; , , They are respectively , , The steady-state value; 1.7: Based on the above frequency domain small-signal expression, derive the open-loop output impedance of the energy storage bidirectional DC / DC converter without considering the control loop: ； in, This refers to the open-loop output impedance of the energy storage bidirectional DC / DC converter. 1.8: Based on the open-loop output impedance and incorporating the control loop, the closed-loop output impedance of the energy storage bidirectional DC / DC converter is obtained: ； in, The closed-loop output impedance of the energy storage bidirectional DC / DC converter; Transfer function for the energy storage side current controller; The transfer function is given by the small perturbation of the converter output current to the small perturbation of the energy storage output current. The transfer function from a small duty cycle disturbance to a small disturbance in the converter output bus voltage; The transfer function from a small duty cycle disturbance to a small disturbance in the energy storage output current; This is the transfer function for the energy storage side voltage controller.

4. The method for coordinated control of a grid-type photovoltaic-storage microgrid based on modal feedforward and virtual inertia adaptive control according to claim 3, characterized in that: In S1, the admittance matrix model for the positive and negative sequence decoupling of the grid-type inverter is established, including: 1.9: Based on the characteristics of grid-type inverters, where the DC side is a voltage-stabilized energy storage device, no bus voltage outer loop is required, and AC / DC frequency coupling is weak, the positive and negative sequence decoupling output admittance equations are established: ； ； in, , These are the positive-sequence and negative-sequence current disturbance frequency domain components at the common connection point, respectively. , These are the positive-sequence and negative-sequence voltage perturbation frequency domain components at the common connection point, respectively. It is a positive-order admittance; It is a negative-order admittance; It is a complex frequency variable; 1.10: Using the harmonic linearization method, derive the expressions for the positive-sequence admittance and the negative-sequence admittance: ； ； in, Transfer function for the inner loop PI controller of the grid-connected inverter; Transfer function for the outer loop PI controller of the grid-connected inverter; The imaginary unit; The fundamental angular frequency; For filtering capacitors in grid-type inverters; This is the filter inductor for a grid-type inverter.

5. The method for coordinated control of a grid-type photovoltaic-storage microgrid based on modal feedforward and virtual inertia adaptation as described in claim 4, characterized in that: In step S2, balancing the output power of each energy storage unit and compensating for the DC bus voltage includes: S2.1: Calculate the state of charge of each battery energy storage unit: ； in, for The state of charge of the battery energy storage unit at all times; This represents the initial state of charge of the battery energy storage unit. The total capacity of the battery energy storage unit; For time; This refers to the charging and discharging current of the battery energy storage unit. For integration variables; S2.2: Calculation The average state of charge (SOC) of the parallel-connected battery energy storage units is used to determine the SOC imbalance of each battery energy storage unit. ； ； in, This represents the average state of charge of the battery energy storage unit. The number of parallel battery energy storage units; This refers to the serial number of the battery energy storage unit; For the first The state of charge of the battery energy storage unit; For the first Imbalance in the state of charge of the battery energy storage unit; S2.3: Dynamically adjust the droop coefficient of each battery energy storage unit according to the aforementioned imbalance, and determine the output voltage of each battery energy storage unit converter by combining the bus voltage compensation and equalization speed adjustment function: ； ； in, For the first The droop coefficient of the battery energy storage unit; This is the equilibrium droop coefficient when all battery energy storage units have the same state of charge. For the first The output voltage of the battery energy storage unit converter; This is the reference value for the converter output voltage; This is the function for bus voltage compensation and equalization speed regulation. For the first The output current of the battery energy storage unit converter; S2.4: Construct the adjustment function in the following form to determine the dynamic characteristics of the bus voltage compensation and equalization speed: ; in, This is the voltage compensation amplitude control coefficient; This refers to the state of charge of the battery energy storage unit. This is a control coefficient for the degree of nonlinearity in the equilibrium speed; It is a natural constant; S2.5: Establish a small-signal model for the dynamic adjustment process of the droop coefficient, and use the system characteristic equation. Verify the stability of the system, among which, , , , These are system parameters determined by circuit parameters and control parameters. It is a complex frequency variable.

6. The method for coordinated control of a grid-type photovoltaic-storage microgrid based on modal feedforward and virtual inertia adaptation as described in claim 5, characterized in that: In step S2, the power command is spectrally decomposed, and power is allocated between the battery and the supercapacitor, including: S2.6: The spectral characteristics of the power command are extracted in real time using the sliding discrete Fourier transform. The difference equation is as follows: ； in, For the first The sampling time of the first sampling moment The spectral values ​​of each frequency component; The frequency component number; The sampling time sequence number; It is a natural constant; The imaginary unit; Pi; The length of the sliding window; For the first The power command input signal at each sampling time; S2.7: Dynamically adjust the time constant of the low-pass filter based on the extracted spectral characteristics, and determine the smoothing factor of the discrete low-pass filter: ； in, It is a smoothing factor; This represents the time constant of the low-pass filter. The sampling period; S2.8: Based on the smoothing factor, perform discrete low-pass filtering on the power command, allocate the filtered low-frequency power component to the battery, and allocate the high-frequency power component to the supercapacitor. ； in, For the first The filter output value at each sampling time.

7. The method for coordinated control of a grid-type photovoltaic-storage microgrid based on modal feedforward and virtual inertia adaptive control according to claim 6, characterized in that: In S3, the adaptive adjustment of virtual inertia and damping coefficient includes: S3.1: Establish the oscillation equation of the virtual synchronous generator: ； in, This is a virtual moment of inertia; The output angular frequency of the virtual synchronous generator; For time; This is a reference value for active power. This is the rated angular frequency; The active power-frequency droop factor; This represents the actual output value of active power. The damping coefficient; The measured angular frequency at the grid connection point; S3.2: Define frequency deviation: Using the sign of the product of the frequency deviation and its rate of change as the adjustment criterion, an adaptive adjustment law for virtual inertia and active power-frequency droop coefficient is constructed: when hour, ; when hour, ; when hour, ; when hour, ; in, The rate of change of the output angular frequency of the virtual synchronous generator; This serves as the baseline value for virtual inertia. This is the adjustment coefficient for virtual inertia; This is the baseline value for the active power-frequency droop factor; S3.3: After determining the virtual inertia and the active-frequency droop coefficient, the damping coefficient is coordinated and tuned according to the optimal damping ratio. ; in, The optimal damping ratio; The virtual internal potential amplitude of the virtual synchronous generator; This refers to the voltage amplitude at the grid connection point. This is the virtual impedance value.

8. The method for coordinated control of a grid-type photovoltaic-storage microgrid based on modal feedforward and virtual inertia adaptive control according to claim 7, characterized in that: In S3, active current compensation and reactive voltage compensation are introduced, including: S3.4: When the grid frequency changes abruptly, the active power reference current compensation is calculated based on the active power deviation and added to the original active power reference value. ； ； in, This is the active power reference current compensation amount; This is the proportionality coefficient; This is a reference value for active power. This refers to the actual active power output of the inverter. This is the active power deviation compensation value; Inverter output voltage Axial components; This is the original active current reference value; This is the reference value for the compensated active current; S3.5: When the grid voltage drops or the line impedance is mismatched, calculate the reactive voltage compensation amount based on the reactive power reference value, and construct a virtual negative impedance to offset the line voltage drop and maintain the stability of the voltage amplitude at the grid connection point. ； ； in, This is the reactive voltage compensation amount; The equivalent reactance of the line; This is a reference value for reactive power. This is the measured voltage at the grid connection point; This is the reactive power compensation coefficient; This is a virtual negative impedance value; This is a virtual negative resistance component; It is a complex frequency variable; The baseline virtual inductance value; This is the reactive power regulation coefficient.

9. The method for coordinated control of a grid-type photovoltaic-storage microgrid based on modal feedforward and virtual inertia adaptation as described in claim 8, characterized in that: In step S4, modal analysis is performed on the nodal admittance matrix and the oscillation source is located, including: S4.1: Aggregate the admittance models of each unit and network element to generate a model containing... A photovoltaic-storage microgrid with individual nodes at a frequency The nodal admittance matrix at the location This ensures that the node voltage and the node injected current satisfy the following conditions: ； in, This refers to the number of nodes in a photovoltaic-storage microgrid. For frequency; For frequency The nodal admittance matrix at the location; The node voltage matrix; Inject a current matrix into the node; S4.2: Perform eigenvalue decomposition on the node admittance matrix: ； And define the modal voltage With modal current Then the modal voltage and modal current satisfy: ； in, The left eigenvector matrix; It is a diagonal matrix of eigenvalues; The right eigenvector matrix; This is the modal voltage matrix; This is the modal current matrix; S4.3: When an eigenvalue in the eigenvalue diagonal matrix approaches zero, the corresponding mode is determined to be a critical resonant mode, and the nodes are calculated. For key resonant modes The participation factor is used to identify the node with the largest participation factor as the oscillation source. ； in, For nodes For key resonant modes Participating factors; The node number; The resonant mode number; The left eigenvector matrix is ​​the first... Line number Column elements; The right eigenvector matrix is ​​the first... Line number Column elements.

10. The method for coordinated control of a grid-type photovoltaic-storage microgrid based on modal feedforward and virtual inertia adaptation as described in claim 9, characterized in that: In S4, the virtual inertia of each unit is dynamically adjusted through a multi-agent consensus protocol, including: S4.4: Establishing a system containing In a multi-machine system with virtual synchronous generators, the first Rotor motion equations of the tandem generator set: ； ； in, The number of virtual synchronous generators; Unit serial number; For the first The actual angular frequency of the virtual synchronous generator; For time; For the first Reference value of active power of virtual synchronous generator; This is the rated angular frequency; For the first The actual active power of the virtual synchronous generator; For the first Damping coefficient of the virtual synchronous generator; For the first The power angle of a virtual synchronous generator; S4.5: Using the modal information obtained from modal analysis as the feedforward quantity, and based on the angular frequency information of neighboring units, construct the first... The adaptive virtual inertia model of the rig: ； in, For the first The virtual inertia of a virtual synchronous generator; For the first The reference inertia of the virtual synchronous generator; This is the inertia compensation coefficient; The serial number of the neighboring unit; For the first The set of neighboring units of a virtual synchronous generator; For the first The actual angular frequency of the neighboring unit; S4.6: An improved active-frequency control law is adopted, which uses real-time active power and the angular frequency of neighboring units as inputs to directly output the angular frequency reference value, in order to avoid measurement noise introduced by frequency differentiation. ； in, The active-frequency regulation function is determined by the slip frequency and the remaining power; , The first Taiwan, No. The slip frequency of the virtual synchronous generator; This represents the remaining power.

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