Power grid impedance identification method based on gradient descent method, inverter and storage medium

Abstract

The application relates to the technical field of grid-connected inverter control, in particular to a power grid impedance identification method based on a gradient descent method, an inverter and a storage medium. The power grid impedance identification method comprises the following steps: a first-order dynamic estimation model is established, taking a capacitor voltage and a power grid voltage as inputs and a grid-connected current as output; a grid-connected current estimation value output by the first-order dynamic estimation model is compared with a grid-connected current sample value to obtain an estimation error; a cost function is constructed based on the estimation error, and an updating law of the power grid impedance is obtained by using the gradient descent method; the capacitor voltage, the power grid voltage and the grid-connected current obtained periodically are used to iteratively update the power grid impedance according to the updating law until the estimation error converges, so that the power grid impedance approximating the real value is obtained. The method of the application does not need to actively inject any harmonic or frequency disturbance signal into the power grid, fundamentally eliminating the influence on the grid-connected power quality, and is particularly suitable for a weak power grid environment sensitive to harmonics.

Description

Technical Field

[0001] This application relates to the field of grid-connected inverter control technology, and in particular to a grid impedance identification method based on gradient descent, an inverter, and a storage medium. Background Technology

[0002] With the rapid development of distributed generation technology, grid-connected inverters, as key interface devices between renewable energy systems and the power grid, directly affect the power quality and system stability of the grid. In practical engineering applications, a significant challenge faced by grid-connected inverters is operating in weak grid conditions. A weak grid refers to a grid environment with high impedance and time-varying characteristics. Changes in grid impedance significantly alter the open-loop transfer function of the inverter control system. In particular, when the grid impedance interacts with the inverter output filter, the system's phase margin and gain margin change, potentially leading to current control loop instability, resonance surges, or even system collapse. Therefore, accurately obtaining grid impedance information is crucial for ensuring the stable operation of grid-connected inverters.

[0003] Grid impedance identification is considered an effective way to improve the adaptability of weak grids. By acquiring grid impedance information in real time, the control system can adjust control parameters or adopt active damping strategies to counteract the adverse effects of grid impedance changes. Currently, grid impedance identification technology mainly involves injecting a disturbance signal of a specific frequency into the inverter, detecting the system response, and calculating the grid impedance. This method requires the injection of a disturbance signal, which degrades the grid-connected current quality. Summary of the Invention

[0004] The embodiments of this application aim to provide a grid impedance identification method, inverter and storage medium based on gradient descent method, mainly to solve the problem that the existing grid impedance identification technology requires additional injection of disturbance signals, which leads to a decline in grid-connected power quality.

[0005] To address the aforementioned technical problems, this application provides the following technical solutions: According to a first aspect of this application, a grid impedance identification method based on gradient descent is provided, applied to a single-phase grid-connected inverter, comprising: A first-order dynamic estimation model is established with capacitor voltage and grid voltage as inputs and grid-connected current as output. The parameter to be identified in the first-order dynamic estimation model is grid impedance. The grid-connected current estimate output by the first-order dynamic estimation model is compared with the grid-connected current sample value to obtain the estimation error; A cost function is constructed based on the estimation error, and the update law of the grid impedance is obtained by using the gradient descent method. Using the periodically acquired capacitor voltage, grid voltage, and grid-connected current, the grid impedance is iteratively updated according to the update law until the estimation error converges, thus obtaining the grid impedance that approximates the true value. The first-order dynamic estimation model is as follows:

[0006] in, The grid-connected current estimate is given. The grid voltage is... The capacitor voltage is... The impedance of the power grid is given.

[0007] Optionally, the update rate of the grid impedance is:

[0008] in, For discrete periods, To adjust the step size, For the first k The estimation error of the period, For the first k Estimated grid impedance for +1 cycle For the first k Periodic grid impedance estimates For the first k Periodic capacitor voltage, For the first k Periodic grid voltage.

[0009] Optionally, the cost function is half the square of the estimation error.

[0010] Optionally, the capacitor voltage is acquired by a capacitor voltage sensor.

[0011] Optionally, the single-phase grid-connected inverter includes an LCL filter circuit composed of a filter inductor, a filter capacitor, and grid impedance, wherein the capacitor voltage is reconstructed through the following steps: Based on the phasor equation of the LCL filter circuit at the fundamental frequency, the phasor expression of the capacitor voltage is obtained; The grid-connected current and the inverter arm midpoint voltage are obtained. The grid-connected current and the inverter arm midpoint voltage are multiplied by a cosine signal and a sine signal that are in phase with the grid voltage, respectively, to obtain four product signals. The four product signals are then low-pass filtered to obtain the fundamental phasor of the inverter arm midpoint voltage and the fundamental phasor of the grid-connected current. The magnitude and phase angle of the capacitor voltage phasor are calculated based on the fundamental phasor of the inverter arm midpoint voltage, the fundamental phasor of the grid current, and the phasor expression. Then, the reconstructed instantaneous capacitor voltage is obtained based on the magnitude and phase angle of the capacitor voltage phasor.

[0012] Optionally, the phasor expression for the capacitor voltage is:

[0013] in, , , These are the inverter bridge arm midpoint voltages. capacitor voltage and grid-connected current phasor form, The fundamental angular frequency, For filtering inductors, For filtering capacitors, It is the imaginary unit.

[0014] Optionally, the midpoint voltage of the inverter bridge arm is calculated based on the modulated wave signal output by the current loop.

[0015] According to a second aspect of this application, a single-phase grid-connected inverter is provided, the single-phase grid-connected inverter including a controller, the controller including: at least one processor and a memory communicatively connected to the at least one processor, the memory storing instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the method described in any of the above.

[0016] Optionally, the single-phase grid-connected inverter includes an LCL filter circuit composed of a filter inductor, a filter capacitor, and grid impedance.

[0017] According to a third aspect of this application, a computer-readable storage medium is provided, the computer-readable storage medium storing a computer program, which, when executed by a processor, performs the steps of any of the methods described above.

[0018] The beneficial effects of this application's embodiments are as follows: Unlike existing technologies, this application provides a grid impedance identification method for single-phase grid-connected inverters based on the gradient descent method. First, a first-order dynamic estimation model is established with capacitor voltage and grid voltage as inputs and grid-connected current as output. Then, a cost function is constructed based on the estimation error of the first-order dynamic estimation model, and an update law for the grid impedance is obtained using the gradient descent method. Finally, the grid impedance is iteratively updated according to the update law using periodically acquired capacitor voltage, grid voltage, and grid-connected current to obtain a grid impedance close to the true value. This method fully utilizes the inherent voltage and current information of the system for identification, without actively injecting any harmonic or frequency disturbance signals into the grid, fundamentally eliminating the impact on grid power quality. It is particularly suitable for weak grid environments sensitive to harmonics. The gradient descent method used has low computational complexity and can converge to the true grid impedance value in real time and quickly, effectively tracking the time-varying characteristics of the grid impedance and providing reliable parameter basis for the adaptive control of the inverter. Attached Figure Description

[0019] One or more embodiments are illustrated by way of example with reference numerals in the accompanying drawings. These illustrations do not constitute a limitation on the embodiments. Elements with the same reference numerals in the drawings are denoted as similar elements. Unless otherwise stated, the figures in the drawings are not to be limited by scale.

[0020] Figure 1 This is a schematic diagram of the structure of a single-phase grid-connected inverter provided in an embodiment of this application; Figure 2 This is a schematic diagram of the controller provided in an embodiment of this application; Figure 3 This is a schematic diagram of the grid-connected current control strategy provided in the embodiments of this application; Figure 4 This is a flowchart of a power grid impedance identification method based on gradient descent provided in an embodiment of this application; Figure 5 This is a flowchart of a method for reconstructing capacitor voltage provided in an embodiment of this application; Figure 6 This is a schematic diagram of the entire process of discretization implementation of the grid impedance identification method based on gradient descent provided in the embodiments of this application; Figure 7 This is a diagram showing the identification effect of the grid impedance identification method based on gradient descent provided in the embodiments of this application. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0022] Furthermore, the technical features involved in the various embodiments of this application described below can be combined with each other as long as they do not conflict with each other.

[0023] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0024] Please refer to Figure 1 , Figure 1 This is a schematic diagram of the structure of a single-phase grid-connected inverter provided in an embodiment of this application. For example... Figure 1 As shown, the grid-connected inverter includes an inverter circuit 10 and a controller 20. The inverter circuit 10 includes a DC voltage input source. First switching transistor Second switching transistor Third switching transistor Fourth switching transistor Filter inductor Filter capacitor and grid impedance The grid-connected inverter is connected to the power grid. The inverter bridge arm midpoint voltage is expressed as .

[0025] The switching transistors in controller 20 and inverter circuit 10 ~ The controller connects and controls the switching on and off of each transistor based on a built-in control program. In some embodiments, the controller may be a microcontroller unit (MCU) or a digital signal processing (DSP) controller, etc.

[0026] Please refer to Figure 2 , Figure 2 This is a schematic diagram of the controller provided in an embodiment of this application. Figure 2As shown, the controller 20 includes at least one processor 21 and a memory 22. The memory 22 can be built into the controller 20 or external to the controller 20. The memory 22 can also be a remotely configured memory connected to the controller 20 via a network.

[0027] Memory 22, as a non-volatile computer-readable storage medium, can be used to store non-volatile software programs, non-volatile computer-executable programs, and modules. Memory 22 may include a program storage area and a data storage area, wherein the program storage area may store the operating system and application programs required for at least one function; the data storage area may store data created based on the use of the terminal, etc. Furthermore, memory 22 may include high-speed random access memory and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other non-volatile solid-state storage device. In some embodiments, memory 22 may optionally include memory remotely located relative to processor 21, and these remote memories can be connected to the terminal via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0028] The processor 21 performs various functions of the terminal and processes data by running or executing software programs and / or modules stored in the memory 22 and calling data stored in the memory 22, thereby performing overall monitoring of the terminal, such as implementing the grid impedance identification method based on gradient descent method described in any embodiment of this application.

[0029] Processor 21 can be one or more. Figure 2 The example provided is a processor 21. Processor 21 and memory 22 can be connected via a bus or other means. Processor 21 may include a central processing unit (CPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a controller, a field-programmable gate array (FPGA) device, etc. Processor 21 can also be implemented as a combination of computing devices, such as a combination of a DSP and a microprocessor, multiple microprocessors, one or more microprocessors combined with a DSP core, or any other such configuration.

[0030] Please refer to Figure 3 , Figure 3 This is a schematic diagram of the grid-connected current control strategy provided in an embodiment of this application. For example... Figure 3 As shown, the grid voltage sampling value The phase of the grid voltage is obtained through a PLL (Phase-Locked Loop) circuit. After trigonometric function calculations, it is compared with the set grid-connected current amplitude reference. Multiply to obtain the grid-connected current reference. Grid-connected current reference With grid-connected current sampling value The difference is then fed into the current loop controller. The modulated wave is obtained. Modulated wave The switching transistor is generated through the PWM (Pulse Width Modulation) modulation stage. The drive signal is used to obtain the midpoint voltage of the inverter bridge arm. Inverter bridge arm midpoint voltage With the voltage of the filter capacitor The voltage of the filter inductor is obtained by subtraction. Voltage of the filter inductor inductive reactance of the filter inductor Divide the two to obtain the current of the filter inductor. The current of the filter inductor With grid-connected current The difference is used to obtain the current of the filter capacitor. The current in the filter capacitor capacitive reactance of the filter capacitor Divide the two to obtain the voltage across the filter capacitor. Voltage of the filter capacitor With grid voltage The voltage of the grid impedance is obtained by subtraction. Voltage of the grid impedance With grid inductance Divide to obtain the grid-connected current. .

[0031] Please refer to Figure 4 , Figure 4 This is a flowchart illustrating a grid impedance identification method based on gradient descent, provided in an embodiment of this application. This method is applied to a single-phase grid-connected inverter. The single-phase grid-connected inverter may include inverter circuitry and a controller, among other things. In some embodiments, the single-phase grid-connected inverter can... Figures 1-2 The implementation of the structure is described in detail in the above embodiments and will not be repeated here.

[0032] like Figure 4 As shown, the grid impedance identification method based on gradient descent includes: Step S401: Establish a first-order dynamic estimation model with capacitor voltage and grid voltage as inputs and grid-connected current as output. The parameter to be identified in the first-order dynamic estimation model is grid impedance.

[0033] by Figure 1 Taking the single-phase grid-connected inverter shown as an example, the following system model can be established based on Kirchhoff's voltage and current laws: (1) in, For grid-connected current, For filter capacitors The voltage (i.e., capacitor voltage), This is the grid voltage. This represents the power grid impedance.

[0034] Based on the above system model, the following first-order dynamic estimation model with the same structure as the actual system is established to describe the grid-side current dynamics: (2) in, This is the grid-connected current estimate output by the model. The impedance of the power grid to be identified.

[0035] Step S402: Compare the grid-connected current estimate output by the first-order dynamic estimation model with the grid-connected current sample value to obtain the estimation error.

[0036] Discretizing the first-order dynamic estimation model yields: (3) in, It is a discrete period.

[0037] Based on the discretized first-order dynamic estimation model, the estimation error of the grid-connected current is defined as: (4) in, For the first k The estimation error of the period, For the first k Periodic grid-connected current sampling values, For the first k Estimated grid-connected current for the period.

[0038] Step S403: Construct a cost function based on the estimation error, and use the gradient descent method to obtain the update law of the grid impedance.

[0039] Gradient descent is a simple and intuitive optimization method. For a first-order system, under continuous excitation, if the cost function is convex, gradient descent guarantees that the parameter estimation converges to a local optimum that minimizes the error. In one implementation, the cost function is half the square of the estimation error, and its calculation formula is: (5) Based on equations (4) and (5), and based on the cost function Treatment of identification parameters By finding the gradient, we can obtain: (6) Based on equation (3), right The partial derivative is: (7) Combining equations (6) and (7), we can obtain right gradient: (8) When using gradient descent, the parameters should be adjusted and updated along the negative gradient direction, that is: (9) in, To adjust the step size.

[0040] Furthermore, substituting equation (8) into equation (9) yields the grid impedance. The renewal law: (10) in, For the first k Estimated grid impedance for +1 cycle For the first k Periodic grid impedance estimates For the first k Periodic capacitor voltage, For the first k Periodic grid voltage.

[0041] Step S404: Using the periodically acquired capacitor voltage, grid voltage, and grid-connected current, the grid impedance is iteratively updated according to the update law until the estimation error converges, thus obtaining a grid impedance that approximates the true value.

[0042] In one implementation, the capacitor voltage, grid voltage, and grid-connected current are all periodically acquired by sensors.

[0043] In other implementations, to reduce costs, grid-connected inverters typically only measure grid voltage and grid current, without installing capacitor voltage sensors, thus failing to obtain capacitor voltage in real time. Based on this, this application proposes a method for reconstructing capacitor voltage. This method utilizes known filter inductors and capacitors, measurable inverter bridge arm midpoint voltage, and grid current to reconstruct the capacitor voltage based on the phasor relationship of the LCL filter circuit at the fundamental frequency.

[0044] Please refer to Figure 5 , Figure 5 This is a flowchart of a method for reconstructing capacitor voltage according to an embodiment of this application, which specifically includes the following steps: Step S501: Based on the phasor equation of the LCL filter circuit at the fundamental frequency, obtain the phasor expression of the capacitor voltage.

[0045] Let the fundamental angular frequency of the power grid be... The phase-locked loop outputs a phase that is in phase with the grid voltage in real time. At the fundamental angular frequency According to Kirchhoff's voltage and current laws, Figure 1 The LCL filter circuit shown satisfies the following phasor equation: (11) (12) in, , , , These are the inverter bridge arm midpoint voltages. capacitor voltage Inductor current Grid-connected current phasor form, For filtering inductors, For filtering capacitors, It is the imaginary unit.

[0046] Combining equations (11) and (12), eliminate The phasor expression for the capacitor voltage can be obtained as follows: (13) Assuming the inverter bridge arm midpoint voltage and grid-connected current They are respectively: (14) (15) in, and These are the inverter bridge arm midpoint voltages. The amplitude and initial phase, and These are the grid-connected currents. The amplitude and initial phase.

[0047] Its phasor form can then be expressed as: (16) (17) Substituting equations (16) and (17) into the molecule of equation (13), the phasor of the molecule in equation (13) is... for: (18) Furthermore, equation (18) can be written as a superposition of the real and imaginary parts: (19) in: (20) (twenty one) The denominator of equation (13) is a real number: (twenty two) According to equations (19) to (22), the capacitor voltage phasor It can be reformulated as: (twenty three) Step S502: Obtain the grid-connected current and the inverter arm midpoint voltage. Multiply the grid-connected current and the inverter arm midpoint voltage by a cosine signal and a sine signal that are in phase with the grid voltage, respectively, to obtain four product signals. Then, after low-pass filtering, the four product signals are used to obtain the fundamental phasor of the inverter arm midpoint voltage and the fundamental phasor of the grid-connected current.

[0048] According to equation (23), to calculate the capacitor voltage phasor, it is necessary to first calculate the... and To calculate and Then you need to get , , and (i.e., the fundamental phasor of the inverter arm midpoint voltage and the fundamental phasor of the grid-connected current).

[0049] Specifically, the grid-connected current and the inverter arm midpoint voltage are first obtained, and then the grid-connected current and the inverter arm midpoint voltage are multiplied by a cosine signal that is in phase with the grid voltage. and sinusoidal signal We obtain four product signals: (twenty four) (25) (26) (27) Furthermore, after low-pass filtering the four product signals, the following can be extracted: , , and This yields the fundamental phasor of the inverter bridge arm midpoint voltage and the fundamental phasor of the grid-connected current.

[0050] Step S503: Calculate the magnitude and phase angle of the capacitor voltage phasor based on the fundamental phasor of the inverter arm midpoint voltage, the fundamental phasor of the grid current, and the phasor expression. Then, based on the magnitude and phase angle of the capacitor voltage phasor, obtain the reconstructed instantaneous capacitor voltage.

[0051] According to the capacitor voltage phasor The rewritten expression (23), capacitor voltage phasor model and phase angle The calculation formula is: (28) (29) According to the extraction in step S502 , , and It can be calculated and Then and Substituting into equations (28) and (29), the magnitude and phase angle of the capacitor voltage phasor are calculated.

[0052] Finally, the instantaneous capacitor voltage is reconstructed based on the calculated magnitude and phase angle. : (30) To simplify the calculation, the inverter arm midpoint voltage can be calculated based on the modulated wave signal output from the current loop. Specifically, the inverter arm midpoint voltage... Modulated wave signal output from the current loop Gain of the PWM modulation stage Multiplication yields: (31) (32) in, The input DC voltage amplitude, This is the preset triangular carrier amplitude.

[0053] Please refer to Figure 6 , Figure 6 This is a schematic diagram illustrating the entire process of the discretized implementation of the grid impedance identification method based on gradient descent provided in this application, including the following steps: Step 601, parameter initialization.

[0054] Specifically, set known parameters , , , , , , and initialization and .

[0055] Step S602, data sampling.

[0056] Specifically, to obtain the first Periodic modulated wave signal Grid voltage Grid current And based on the modulated wave signal Calculate the midpoint voltage of the inverter bridge arm .

[0057] Step S603: Trigonometric function multiplication and low-pass filtering extraction.

[0058] Specifically, the inverter arm midpoint voltage and grid-connected current are respectively compared with a sinusoidal signal. Sum and cosine signals After multiplication and low-pass filtering, the fundamental phasor of the inverter arm midpoint voltage is obtained. and grid-connected current fundamental phasor .

[0059] Step S604: Reconstruct the capacitor voltage.

[0060] Specifically, the capacitor voltage phasor is calculated from equations (19) to (22). The real and imaginary parts are then used to reconstruct the instantaneous value of the capacitor voltage based on the current phase. .

[0061] Step S605: Perform recursive calculations based on the first-order dynamic estimation model.

[0062] Specifically, use the The estimated grid impedance for the period and the first Calculation of grid voltage and capacitor voltage during a cycle Estimated grid-connected current during the period .

[0063] Step S606: Calculate the estimation error.

[0064] Specifically, based on Calculate the first The estimation error between the estimated grid-connected current and the sampled grid-connected current during the period.

[0065] Step S607: Update parameters.

[0066] Specifically, the grid impedance estimate is updated along the negative gradient direction of the cost function according to equation (10). .

[0067] Step S608: Determine whether the estimation error has converged. If not, return to step S602; if yes, proceed to step S609.

[0068] In one implementation, the estimation error is considered convergent when the absolute value of the estimation error is less than a preset small threshold for multiple consecutive periods. It is understood that when the estimation error... hour, It tends towards the true value. The convergence speed is adjusted by the learning rate and step size. Decide, The larger the value, the faster the convergence, but excessively large values ​​can lead to oscillations or even divergence. If it is too small, the convergence will be slow.

[0069] Step S609: Output the final grid impedance.

[0070] Please refer to Figure 7 , Figure 7 This is a diagram illustrating the identification effect of the grid impedance identification method based on gradient descent provided in this application. Figure 7 It is known that, according to the identification method provided in this application, it can converge to the vicinity of the true value of the power grid impedance within 300ms and has high identification accuracy.

[0071] The grid impedance identification method for single-phase grid-connected inverters provided in this application allows for the acquisition of capacitor voltage through a reconstruction algorithm, thus eliminating the need for expensive capacitor voltage sensors. Identification can be completed using only the existing voltage and current sampling of the system. Even when sensors are used, only conventional sampling is required. The algorithm itself is simple and easy to implement in real time in an embedded controller.

[0072] This application also provides a non-volatile computer-readable storage medium storing computer-executable instructions that are executed by one or more processors, for example, to perform the method steps described above.

[0073] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and not to limit them; under the concept of this application, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of this application as described above, which are not provided in detail for the sake of brevity; although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A grid impedance identification method based on gradient descent, applied to a single-phase grid-connected inverter, characterized in that, include: A first-order dynamic estimation model is established with capacitor voltage and grid voltage as inputs and grid-connected current as output. The parameter to be identified in the first-order dynamic estimation model is grid impedance. The grid-connected current estimate output by the first-order dynamic estimation model is compared with the grid-connected current sample value to obtain the estimation error; A cost function is constructed based on the estimation error, and the update law of the grid impedance is obtained by using the gradient descent method. Using the periodically acquired capacitor voltage, grid voltage, and grid-connected current, the grid impedance is iteratively updated according to the update law until the estimation error converges, thus obtaining the grid impedance that approximates the true value. The first-order dynamic estimation model is as follows: in, The grid-connected current estimate is given. The grid voltage is... The capacitor voltage is... The power grid impedance; The single-phase grid-connected inverter includes an LCL filter circuit composed of a filter inductor, a filter capacitor, and grid impedance. The capacitor voltage is reconstructed through the following steps: Based on the phasor equation of the LCL filter circuit at the fundamental frequency, the phasor expression of the capacitor voltage is obtained; The grid-connected current and the inverter arm midpoint voltage are obtained. The grid-connected current and the inverter arm midpoint voltage are multiplied by a cosine signal and a sine signal that are in phase with the grid voltage, respectively, to obtain four product signals. The four product signals are then low-pass filtered to obtain the fundamental phasor of the inverter arm midpoint voltage and the fundamental phasor of the grid-connected current. The magnitude and phase angle of the capacitor voltage phasor are calculated based on the fundamental phasor of the inverter arm midpoint voltage, the fundamental phasor of the grid current, and the phasor expression. Then, the reconstructed instantaneous capacitor voltage is obtained based on the magnitude and phase angle of the capacitor voltage phasor.

2. The method according to claim 1, characterized in that, The update rate of the power grid impedance is: in, For discrete periods, To adjust the step size, For the first k The estimation error of the period, For the first k Estimated grid impedance for +1 cycle For the first k Periodic grid impedance estimates For the first k Periodic capacitor voltage, For the first k Periodic grid voltage.

3. The method according to claim 1, characterized in that, The cost function is half the square of the estimation error.

4. The method according to any one of claims 1 to 3, characterized in that, The capacitor voltage is acquired by a capacitor voltage sensor.

5. The method according to any one of claims 1 to 3, characterized in that, The phasor expression for the capacitor voltage is: in, , , These are the inverter bridge arm midpoint voltages. capacitor voltage and grid-connected current phasor form, The fundamental angular frequency, For filtering inductors, For filtering capacitors, It is the imaginary unit.

6. The method according to any one of claims 1 to 3, characterized in that, The voltage at the midpoint of the inverter arm is calculated based on the modulated wave signal output from the current loop.

7. A single-phase grid-connected inverter, characterized in that, The single-phase grid-connected inverter includes a controller, the controller comprising: at least one processor and a memory communicatively connected to the at least one processor, the memory storing instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the method according to any one of claims 1 to 6.

8. The single-phase grid-connected inverter according to claim 7, characterized in that, The single-phase grid-connected inverter includes an LCL filter circuit consisting of a filter inductor, a filter capacitor, and grid impedance.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of the method as described in any one of claims 1 to 6.

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