Small signal modeling method for module-level power optimizer

Abstract

The invention belongs to the technical field of power electronic control and system stability analysis in a new energy power generation system, and discloses a small signal modeling method for a module-level power optimizer. According to the method, a unified small signal model among a photovoltaic module, a DC / DC power converter, an inductor, a capacitor, a load and a controller is established; determining a transfer function relationship among output voltage disturbance, duty ratio disturbance and a control error signal; packaging a single-module model into a standard negative feedback control structure, and supporting Bode and Nyquist stability analysis; the method can be popularized to a multi-module series or parallel system, and system-level small signal stability evaluation is realized.

Description

Technical Field

[0001] This invention mainly relates to the field of power electronic control and system stability analysis technology in new energy power generation systems, and in particular to a small-signal modeling method for module-level power optimizers. Background Technology

[0002] With the continuous increase in the installed capacity of photovoltaic power generation systems, distributed maximum power point tracking (DMPPT) technology has gradually become an important means to improve the energy utilization efficiency of the system. In this architecture, each photovoltaic module is usually equipped with an independent DC / DC power converter (such as Boost, Buck, or Buck-Boost structures) to achieve maximum power point tracking control at the module level.

[0003] Compared with traditional centralized inverter systems, distributed photovoltaic systems have the following characteristics: (1) a large number of modules and highly dispersed power converters; (2) each module is coupled in series or in parallel through a DC bus; (3) each module contains an independent voltage / current feedback loop and duty cycle control loop.

[0004] However, while the above structure improves energy output efficiency, it also brings difficulties to system stability analysis and control design: (1) multiple DC / DC converters are dynamically coupled through the DC bus; (2) the controller parameters of each module are inconsistent, which can easily lead to low-frequency oscillations or subsynchronous instability; (3) traditional analysis methods based on steady-state power flow cannot reflect the dynamic relationship between duty cycle disturbances, inductor current, capacitor voltage and feedback loop. Existing methods are difficult to provide a clear frequency domain stability basis for controller parameter tuning.

[0005] Therefore, there is an urgent need for a small-signal modeling method that is module-level and can be extended to multi-module systems, in order to systematically characterize the dynamic behavior of distributed photovoltaic systems and support frequency domain stability analysis and controller design. Summary of the Invention

[0006] To address the problems in system stability analysis and control design in existing technologies, this invention provides a small-signal modeling method for module-level power optimizers. This invention establishes a unified small-signal model among photovoltaic modules, DC / DC converters, inductors, capacitors, loads, and controllers; clarifies the transfer function relationships between output voltage disturbances, duty cycle disturbances, and control error signals; encapsulates the single-module model into a standard negative feedback control structure, supporting Bode and Nyquist stability analysis; and can be extended to multi-module series or parallel systems to achieve system-level small-signal stability assessment.

[0007] To achieve the above objectives, the present invention provides a small-signal modeling method for a module-level power optimizer, comprising the following steps: Step 1: Taking the DC / DC power converter corresponding to a single photovoltaic module as the modeling object, the system structure includes the photovoltaic module equivalent voltage source, input-side inductor, output-side filter capacitor, equivalent load, PWM modulation unit, voltage sampling and feedback network, error comparator, and controller module; Step 2: Small-signal perturbation decomposition: Near the steady-state operating point, perform small-signal perturbation decomposition on the system variables, expressed as follows: ,in, For steady-state operating point, steady-state operating point The corresponding small signal perturbation, This refers to the instantaneous output voltage at the output terminal of the module-level power optimizer. This represents the instantaneous duty cycle value of the PWM modulation unit. This represents the instantaneous value of the inductor current in the DC / DC power converter. Step 3: Establish the small-signal transfer function of the power stage: Perform linearization modeling on the DC / DC power converter, and establish the transfer function between the duty cycle disturbance and the output voltage disturbance, expressed as follows: This is used to describe the dynamic response characteristics of a DC / DC power converter to duty cycle disturbances, where... The Laplace transform of the small-signal perturbation of the output voltage. The Laplace transform of a small-signal perturbation with duty cycle; Step 4: Model the controller module and feedback loop, and establish the power stage model: Step 4.1: Let the transfer function of the controller module be... ; Step 4.2: After sampling, compare the output voltage with the reference voltage. By comparison, the error signal is obtained, and its expression is: ,in, To control the error signal, For small-signal disturbances of the reference voltage, For small signal disturbances in the output voltage; Step 4.3: The controller module outputs a duty cycle disturbance based on the error signal, expressed as follows: ; Step 5: Construct a closed-loop small-signal model: Combine the controller module with the power stage model to form a standard negative feedback control system. The open-loop transfer function is... ,in, Pass functions to the controller module. This is the transfer function between the duty cycle disturbance and the output voltage disturbance; Step 6: Small-signal model extension: When multiple module-level power optimizers are connected in series or parallel via a DC bus, each module-level power optimizer uses the same small-signal modeling method. The output impedances of each module-level power optimizer are dynamically coupled through the bus. Finally, the system is represented as a multiple-input multiple-output (MIMO) small-signal state-space model, expressed as follows: It is used to analyze the system stability under the collaborative operation of multiple module-level power optimizers, where A, B, and C are matrices determined by circuit parameters.

[0008] Furthermore, in step 3, the DC / DC power converter is linearized and modeled based on the state-space averaging method.

[0009] Beneficial Effects: This invention provides a small-signal modeling method for module-level power optimizers, which has the following beneficial effects: (1) Realizing the modelability, analysis and determination of the stability of distributed photovoltaic systems: This invention establishes a small-signal model of a module-level DC / DC converter, transforming the duty cycle disturbance, output voltage disturbance and feedback control relationship in the distributed photovoltaic system into an explicit transfer function form, so that the system stability can be quantitatively analyzed by frequency domain methods, avoiding the traditional stability judgment method that relies on experience or experimentation. (2) Effectively solving the system-level instability problem under multi-module coupling conditions: This invention explicitly introduces a DC bus and equivalent load model in the small-signal modeling, and characterizes the dynamic coupling relationship between multiple module-level power optimizers through bus voltage, current and output impedance, so as to identify and analyze the system-level oscillation risk that occurs when a single module is stable but multiple modules are connected in parallel or series. (3) Provide a unified theoretical basis for controller parameter design and system scale expansion: Based on the small signal model of this invention, the controller parameters can be designed and optimized directly using the Bode plot or Nyquist criterion, and the consistency and scalability of the modeling method can be maintained when the number of modules changes, providing reliable theoretical support for the engineering design, debugging and large-scale application of distributed photovoltaic systems. Attached Figure Description

[0010] Figure 1 This is a flowchart of a small-signal modeling method for a module-level power optimizer, which is involved in this invention; Figure 2 This is a Boost small-signal modeling control block diagram constructed based on the present invention; Figure 3 This is a block diagram of the coupled structure of a multi-module Boost control system; Figure 4 This is a schematic diagram illustrating the Nyquist stability analysis of a module-level or multi-module photovoltaic power conversion system based on the present invention. Detailed Implementation

[0011] The preferred mechanisms and implementation methods of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0012] like Figures 1-4 As shown, the present invention provides a small-signal modeling method for a module-level power optimizer. Figure 1 This is a flowchart of a small-signal modeling method for a module-level power optimizer, which is involved in this invention; Figure 2 This is a Boost small-signal modeling control block diagram constructed based on the present invention; Figure 3 This is a block diagram of the coupled structure of a multi-module Boost control system; Figure 4 This is a schematic diagram illustrating the Nyquist stability analysis of a module-level or multi-module photovoltaic power conversion system based on the present invention.

[0013] Example 1: A small-signal modeling method for a module-level power optimizer, comprising the following steps: Step 1: Taking the DC / DC power converter corresponding to a single photovoltaic module as the modeling object, the system structure includes the photovoltaic module equivalent voltage source, input-side inductor, output-side filter capacitor, equivalent load, PWM modulation unit, voltage sampling and feedback network, error comparator, and controller module; Step 2: Small-signal perturbation decomposition: Near the steady-state operating point, perform small-signal perturbation decomposition on the system variables, expressed as follows: ,in, For steady-state operating point, steady-state operating point The corresponding small signal perturbation, This refers to the instantaneous output voltage at the output terminal of the module-level power optimizer. This represents the instantaneous duty cycle value of the PWM modulation unit. This represents the instantaneous value of the inductor current in the DC / DC power converter. Step 3: Establish the small-signal transfer function of the power stage based on the state-space averaging method: Linearize the DC / DC power converter and establish the transfer function between the duty cycle disturbance and the output voltage disturbance, expressed as follows: This is used to describe the dynamic response characteristics of a DC / DC power converter to duty cycle disturbances, where... The Laplace transform of the small-signal perturbation of the output voltage. The Laplace transform of a small-signal perturbation with duty cycle; Step 4: Model the controller module and feedback loop, and establish the power stage model: Step 4.1: Let the transfer function of the controller module be... Common forms are PI (proportional-integral), PID, or more advanced compensators (such as Type II, Type III), which are used to adjust the error, provide sufficient phase lead and gain, and make the system stable and have good dynamic performance. Step 4.2: After sampling, compare the output voltage with the reference voltage. By comparison, the error signal is obtained, and its expression is: ,in, To control the error signal, For small-signal disturbances of the reference voltage, For small signal disturbances in the output voltage; Step 4.3: The controller module outputs a duty cycle disturbance based on the error signal, expressed as follows: ; Step 5: Construct a closed-loop small-signal model: Combine the controller module with the power stage model to form a standard negative feedback control system. The open-loop transfer function is... ,in, Pass functions to the controller module. This is the transfer function between the duty cycle disturbance and the output voltage disturbance; Step 6: Small-signal model extension: When multiple module-level power optimizers are connected in series or parallel via a DC bus, each module-level power optimizer uses the same small-signal modeling method. The output impedances of each module-level power optimizer are dynamically coupled through the bus. Finally, the system is represented as a multiple-input multiple-output (MIMO) small-signal state-space model, expressed as follows: It is used to analyze the system stability under the collaborative operation of multiple module-level power optimizers, where A, B, and C are matrices determined by circuit parameters.

[0014] Example 2: This example is basically the same as Example 1, except that this example is based on module-level small-signal modeling of a Boost converter.

[0015] Taking a Boost DC / DC converter as an example, the inductor current is selected. With output voltage As a state variable, its state-space average model is established: , where the matrix It is determined by circuit parameters and steady-state duty cycle.

[0016] By performing a Laplace transform on the above model, the transfer function from the duty cycle disturbance to the output voltage disturbance can be obtained. Where A, B, and C are matrices determined by the circuit parameters. This model is used for frequency domain transfer function derivation and closed-loop controller design.

[0017] Figure 2The block diagram of Boost small-signal modeling control constructed based on the present invention is shown, which facilitates subsequent frequency domain analysis and bandwidth margin calculation. Figure 2 It shows the reference voltage The data is processed through error comparison, controller module transfer function, and duty cycle perturbation, and then enters the Boost dynamic model. The closed-loop control path. Output voltage disturbance. Feedback then forms a closed loop. This control block diagram shows the control from the reference voltage... To output voltage disturbance The feedback control path includes: Reference voltage System target voltage setting; Error block Σ: Calculation ; Controller module pass function : Adjustment error, output duty cycle disturbance; Power converter; converts duty cycle disturbances into voltage disturbances; Closed-loop feedback: Sample the output voltage and adjust it accordingly.

[0018] Figure 3 This is a block diagram of the coupled structure of a multi-module Boost control system.

[0019] Figure 3 This diagram illustrates a system structure formed by multiple module-level power optimizers coupled via a DC bus, used to analyze the mutual influence between modules. Figure 3 This paper illustrates a series-coupled closed-loop control structure formed by multiple module-level Boost power optimizers in a distributed photovoltaic system. The structure uses "one Boost converter and its independent closed-loop controller for each photovoltaic module" as the basic unit. Multiple units are connected on the DC side via a bus (or series bus), thus forming a strongly coupled multi-module system electrically. Figure 3 The core of this system is that each module is a closed-loop control system, while the modules are dynamically coupled through the voltage, current and equivalent impedance of the DC bus.

[0020] 1. Composition and signal flow of a single module unit Any number Each module unit (denoted as Module-) It should include at least the following parts: (1) Photovoltaic module equivalent source (PVk): The photovoltaic module provides input voltage / current, which can be equivalent to a voltage source near the operating point superimposed with small signal disturbance (or equivalent to Thevenin / Norton small signal model) in small signal modeling, and the output is connected to the input terminal of the Boost converter.

[0021] (2) Boost Power Stage ): Including input inductance Switching transistors and diodes (or synchronous rectifiers), output capacitors The power stage in continuous conduction mode can be modeled using a linearized small-signal model obtained through state-space averaging. In a block diagram, this power stage is typically represented by a transfer function as follows: This indicates duty cycle perturbation. Caused module output voltage disturbance .

[0022] (3) Sampling and error comparison process (Feedback) ): Module output voltage The feedback signal is obtained through sampling (which may include voltage division / filtering / sample and hold), and compared with the reference voltage. Comparison, forming an error signal: .

[0023] (4) Controller The controller transfer function is: The error signal is mapped to a duty cycle perturbation: .

[0024] The controller can be a PI, PID, type II / type III compensator, or a control structure with feedforward.

[0025] Therefore, each module forms a standard negative feedback closed loop, and its open-loop transfer function is: .

[0026] 2. The "coupling points" and "coupling variables" between multiple modules Figure 3 The emphasized coupling does not occur between controllers (which are typically independent), but rather between the outputs of each module and the system DC bus / load network. The main coupling channels include: Bus voltage coupling: The outputs of multiple modules work together to affect the DC bus voltage of the system. When any module When the output voltage or output impedance changes by a small signal, it will cause a disturbance in the bus voltage. This disturbance will act as an external disturbance, "feedback" to affect the output voltage and error signal of other modules, thus creating cross-coupling.

[0027] This can be understood as: Module- of → Change

[0028] → Affecting the Module via Bus and Load Networks of ( ).

[0029] (2) Bus current coupling: Each module injects current into the bus. When the output current of a certain module is disturbed... When this happens, the bus current distribution and the bus equivalent load will change, resulting in changes in the bus voltage or port conditions of other modules.

[0030] (3) Impedance Coupling: In the small-signal sense, each closed-loop module presents a "port equivalent impedance / admittance" (output impedance) to the outside world. or output admittance When multiple modules are connected through a bus network, these port impedances and load impedances together form a high-order dynamic network.

[0031] When a module controller has a high bandwidth, a negative impedance, or a large phase lag, it is prone to unfavorable impedance matching with other modules or load networks, which can lead to oscillations.

[0032] 3. Figure 3 The "system-level equivalence relation" (used for stability analysis) exist Figure 3 In the structure shown, the system can be abstracted as: Each module consists of a controlled power supply (or a controlled voltage source / controlled current source) + output impedance.

[0033] The bus and load network is a dynamic passive network (including equivalent). Bus capacitors, line inductance / resistance, etc.

[0034] Therefore, the system stability problem can be reduced to: Whether the closed-loop of a single module is stable (by...) Decide); Whether cross-coupling instability occurs after multiple modules are interconnected (this is determined by the combination of "module output impedance + bus / load impedance").

[0035] Common analysis interfaces used in engineering include: Port variables: , , , ; Port model: or ; Network Model: (Including bus capacitance / line impedance, etc.).

[0036] Figure 3 The multi-module coupling structure shown indicates that even if each module is stable within its own closed-loop context, system-level oscillations may still occur when multiple modules are interconnected via a DC bus due to the interaction between bus voltage / current disturbances and output impedance. Therefore, the module-level small-signal modeling method proposed in this invention can not only be used for single-module controller design but also serve as a unified modeling basis for multi-module systems. By establishing module port models and bus network models, system-level frequency domain stability analysis and parameter co-tuning can be achieved.

[0037] Figure 4 This is a schematic diagram illustrating the Nyquist stability analysis of a module-level or multi-module photovoltaic power conversion system based on the present invention.

[0038] Figure 4 This diagram illustrates a Nyquist stability analysis of a module-level or multi-module photovoltaic power conversion system based on the small-signal model established in this invention. The diagram serves to explain how, in a closed-loop control system, the system stability and stability margin can be determined using the frequency domain trajectory of the open-loop transfer function. Figure 4 This diagram illustrates a Nyquist stability analysis of a module-level or multi-module photovoltaic power conversion system based on the small-signal model established in this invention. The diagram serves to explain how, in a closed-loop control system, the system stability and stability margin can be determined using the frequency domain trajectory of the open-loop transfer function.

[0039] 4. Meaning of coordinate axes and trajectory in Nyquist plot: Figure 4 The frequency domain characteristics of the open-loop transfer function are represented using a complex plane coordinate system: the horizontal axis represents the real axis of the complex plane; the vertical axis represents the imaginary axis of the complex plane.

[0040] In this coordinate system, the system open-loop transfer function In the complex frequency domain Response on With frequency The trajectory formed when the value changes from 0 to infinity is called the Nyquist trajectory.

[0041] The trajectory in the figure typically includes: a positive frequency component ( ); Symmetrical negative frequency component ( ), used to form a complete closed curve.

[0042] 5. Definition of open-loop transfer function: In this invention, the open-loop transfer function corresponding to the Nyquist diagram... for: .in: This is the transfer function for the module-level controller, used to convert the error signal into a duty cycle disturbance; This is the small-signal transfer function of the power converter, used to describe the dynamic response of duty cycle disturbances to output voltage disturbances. This open-loop transfer function can be established for a single module or for an equivalent port model in a multi-module system, for system-level stability analysis.

[0043] 6. The physical meaning of the key criterion point "-1": Figure 4 The key decision points on the complex plane are specially marked. That is, the point -1 on the real axis. This point corresponds to the characteristic equation of the closed-loop system: The critical condition is that when the Nyquist trajectory encircles the point −1 in the complex plane, it means that the eigenvalues ​​of the closed-loop system enter the right half-plane, leading to system instability.

[0044] 7. Explanation of the stability criterion: Based on the Nyquist stability criterion, Figure 2 The rules for judging the stability of expressions are as follows: When open-loop transfer function When there are no unstable poles in the right half-plane (i.e., the open-loop system is stable): If the Nyquist trajectory does not enclose the point −1, then the closed-loop system is stable; If the Nyquist trajectory encircles point -1 clockwise Then the closed-loop system exists. An unstable pole indicates system instability.

[0045] When open-loop transfer function When there is an unstable pole in the right half-plane: The number of times the Nyquist trajectory encircles the −1 point needs to be used in conjunction with the number of unstable poles in the open loop to determine the stability of the closed loop.

[0046] In typical application scenarios of this invention, module-level power converters and their controllers are usually designed as open-loop stable systems, so the first scenario is the primary focus.

[0047] The application value of Nyquist diagrams in this invention: through Figure 4 The Nyquist stability analysis method shown can intuitively determine the following issues: whether the controller parameter configuration meets the closed-loop stability requirements; whether the system has sufficient phase margin and gain margin; and whether the cross-influence caused by the coupling of multiple modules leads to the trajectory approaching or surrounding the −1 point, thereby causing system-level instability.

[0048] Especially in distributed photovoltaic systems, even if a single module meets the stability requirements when operating independently, its equivalent open-loop transfer function will change when multiple modules are coupled through a DC bus. Figure 4 The Nyquist analysis shown can be used to assess the impact of this coupling effect on system stability.

[0049] 9. Correspondence with the method of this invention: Figure 4 This intuitively demonstrates the role of the small-signal modeling method proposed in this invention in stability analysis: Obtained through module-level small signal modeling method ; controller model Combined with power stage model to form ; based on Plot the Nyquist trajectory; The stability of the system is determined by the positional relationship of the trajectory relative to the -1 point.

[0050] This demonstrates that the present invention not only provides a modeling method, but also offers a direct and effective engineering analysis tool for the stability analysis and controller design of distributed photovoltaic systems.

[0051] In existing distributed photovoltaic system (DMPPT or MLPE) related technologies, the following technical routes are usually adopted for system modeling and stability analysis: (1) Analysis method based on steady-state power or equivalent circuit: This type of method mainly focuses on the power matching relationship between photovoltaic modules and DC / DC converters under steady-state conditions, ignores the response characteristics of the system under dynamic disturbance conditions, and cannot reflect the dynamic coupling relationship between duty cycle disturbance, inductor current and output voltage. (2) Small-signal modeling method for a single DC / DC converter: Some existing technologies perform small-signal modeling for a single DC / DC module, but usually assume that the load is ideal or fixed, and do not consider the mutual coupling effect generated after multiple modules are connected through the DC bus, which is difficult to extend to multi-module systems. (3) Stability design method based on empirical parameter tuning or experimental verification: In engineering practice, controller parameters are often determined through experience or repeated experiments, lacking a unified modeling and analysis framework, especially when the number of modules changes or the system scale expands, stability is difficult to predict.

[0052] The aforementioned existing technologies generally suffer from the following shortcomings: they cannot quantitatively analyze and determine the system-level stability under multi-module coupling conditions within a unified modeling framework.

[0053] Compared with the prior art, the present invention has essential differences in at least the following key technical features: (1) The modeling level is fundamentally different: the prior art mainly stays at the steady state of the system or the single module level, and lacks description of dynamic coupling between modules; This invention uses a modular DC / DC converter as the basic modeling unit, establishes a transfer function between duty cycle disturbance and output voltage disturbance at the small signal level, and further introduces a DC bus and equivalent load model to achieve unified modeling of multi-module systems.

[0054] This difference is not a parameter replacement, but a fundamental improvement in the modeling level and the object of analysis. (2) Different explicit modeling methods of coupling mechanism: Existing technology: usually implies or ignores the coupling effect between modules through the bus; This invention: explicitly introduces bus voltage, current and module output impedance in the small signal model, reveals the physical mechanism of interaction between modules, and enables the problem of single module stability but system instability to be modeled and analyzed. This technical feature solves the long-standing problem that has not been modeled by the system. (3) Different stability judgment methods: Existing technology: mostly relies on time domain simulation results or empirical judgment, lacking generalizable stability criteria; This invention: by constructing a clear open-loop small signal transfer function, directly introduces the Bode plot and Nyquist criterion to quantitatively judge the system stability. This difference transforms stability analysis from "phenomenal observation" to "theoretical judgment".

[0055] Finally, it should be noted that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. However, any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A small-signal modeling method for a module-level power optimizer, characterized in that, Includes the following steps: Step 1: Taking the DC / DC power converter corresponding to a single photovoltaic module as the modeling object, the system structure includes the photovoltaic module equivalent voltage source, input-side inductor, output-side filter capacitor, equivalent load, PWM modulation unit, voltage sampling and feedback network, error comparator, and controller module; Step 2: Small-signal perturbation decomposition: Near the steady-state operating point, perform small-signal perturbation decomposition on the system variables, expressed as follows: ,in, For steady-state operating point, steady-state operating point The corresponding small signal perturbation, This refers to the instantaneous output voltage at the output terminal of the module-level power optimizer. This represents the instantaneous duty cycle value of the PWM modulation unit. This represents the instantaneous value of the inductor current in the DC / DC power converter. Step 3: Establish the small-signal transfer function of the power stage: Perform linearization modeling on the DC / DC power converter, and establish the transfer function between the duty cycle disturbance and the output voltage disturbance, expressed as follows: This is used to describe the dynamic response characteristics of a DC / DC power converter to duty cycle disturbances, where... The Laplace transform of the small-signal perturbation of the output voltage. The Laplace transform of a small-signal perturbation with duty cycle; Step 4: Model the controller module and feedback loop, and establish the power stage model: Step 4.1: Let the controller module transfer function be... ; Step 4.2: After sampling, compare the output voltage with the reference voltage. By comparison, the error signal is obtained, and its expression is: ,in, To control the error signal, For small-signal disturbances of the reference voltage, For small signal disturbances in the output voltage; Step 4.3: The controller module outputs a duty cycle disturbance based on the error signal, expressed as follows: ; Step 5: Construct a closed-loop small-signal model: Combine the controller module with the power stage model to form a standard negative feedback control system. The open-loop transfer function is: ,in, Pass functions to the controller module. This is the transfer function between the duty cycle disturbance and the output voltage disturbance; Step 6: Small-signal model extension: When multiple module-level power optimizers are connected in series or parallel via a DC bus, each module-level power optimizer uses the same small-signal modeling method. The output impedances of each module-level power optimizer are dynamically coupled through the bus. Finally, the system is represented as a multiple-input multiple-output (MIMO) small-signal state-space model, expressed as follows: It is used to analyze the system stability under the collaborative operation of multiple module-level power optimizers, where A, B, and C are matrices determined by circuit parameters.

2. The small-signal modeling method for a module-level power optimizer according to claim 1, characterized in that, In step 3, the DC / DC power converter is linearized and modeled based on the state-space averaging method.

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