A method and system for a single-phase lcl grid-connected inverter considering phase-locked loop

Abstract

A modeling method of single-phase LCL grid-connected inverter considering phase-locked loop, comprising: establishing a single-phase LCL grid-connected inverter system circuit; the circuit comprises: an inverter composed of four switching tubes, a set of LCL type filter, a constant voltage source parallel DC side capacitor on the DC side, and an ideal AC voltage source series grid side impedance on the grid side; based on the single-phase LCL grid-connected inverter system circuit, the control strategy of current control based on PI regulator in the stationary coordinate system is selected, and the simplified control block diagram of the single-phase LCL grid-connected inverter system circuit is obtained; according to the simplified control block diagram, the impedance analysis method is used to obtain the output impedance expression of the grid-connected inverter; for the second-order generalized integrator phase-locked loop, the output impedance model of the phase-locked loop is obtained through small signal analysis; according to the output impedance expression of the grid-connected inverter and the output impedance model of the phase-locked loop, the impedance model of the single-phase LCL grid-connected inverter considering the phase-locked loop is obtained, which is used for stability analysis.

Description

Technical Field

[0001] This invention belongs to the field of single-phase grid-connected inverter modeling, and more specifically, relates to a modeling method and system for a single-phase LCL type grid-connected inverter that considers a phase-locked loop. Background Technology

[0002] With the advancement of the carbon neutrality strategy, the penetration rate of distributed power sources such as photovoltaics and wind power will increase for a considerable period of time. Simultaneously, the proportion of synchronous generator capacity in the system will continue to decrease, and the system will develop towards lower inertia and lower damping, posing severe challenges to system operation and control. Energy storage, with its multiple functions of rapid response, power regulation, and energy transfer, can facilitate the integration of renewable energy generation into the DC side of traditional grid-connected inverters. It can also assist the distribution network in peak shaving, voltage support, and demand response, effectively improving power quality and reliability. However, since the direct output of energy storage is mostly in the form of DC, it needs to be inverted to AC for normal grid connection. Furthermore, if the harmonic content in the inverter's input current cannot be effectively suppressed, it will significantly impact the stability of the grid-connected inverter system, potentially causing system oscillations and jeopardizing its safe operation. To effectively study system stability, a mathematical model of the grid-connected inverter needs to be established to theoretically explain the mathematical principles underlying stability. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention aims to propose a modeling method for single-phase LCL grid-connected inverters based on impedance stability analysis and considering phase-locked loops (PLLs). The method involves a detailed analysis of the grid-connected inverter and PLL architectures using impedance analysis, yielding their respective impedance models. These models are then combined to obtain a comprehensive impedance model. Furthermore, this invention points out that considering the PLL mathematical model reduces the amplitude of the overall inverter output impedance model's amplitude-frequency characteristic curve and lowers the intersection frequency with the grid impedance Bode curve. This results in a reduced phase margin in the impedance ratio, negatively impacting system stability.

[0004] The present invention adopts the following technical solution.

[0005] A modeling method for a single-phase LCL grid-connected inverter considering a phase-locked loop (PLL) includes the following steps:

[0006] Step 1: Establish a single-phase LCL grid-connected inverter system circuit; the circuit includes: an inverter composed of four switching transistors, a set of LCL filters, a constant voltage source on the DC side connected in parallel with a DC-side capacitor, and an ideal AC voltage source on the grid side connected in series with the grid-side impedance.

[0007] Step 2: Based on the single-phase LCL grid-connected inverter system circuit, select the current control strategy based on the PI regulator in the stationary coordinate system to obtain a simplified control block diagram of the single-phase LCL grid-connected inverter system circuit.

[0008] Step 3: Based on the simplified control block diagram, the output impedance expression of the grid-connected inverter is obtained using impedance analysis.

[0009] Step 4: For the second-order generalized integrator phase-locked loop, obtain the output impedance model of the phase-locked loop through small-signal analysis;

[0010] Step 5: Based on the output impedance expression of the grid-connected inverter and the output impedance model of the phase-locked loop, obtain the impedance model of the single-phase LCL grid-connected inverter considering the phase-locked loop for stability analysis.

[0011] Furthermore, the control strategy includes: multiplying the output current of the LCL filter and the cosine of the phase-locked loop angle, subtracting it from the set current, and transmitting the result to the PI controller. This result is then superimposed with the grid voltage to obtain a modulated wave signal, which is then modulated by SPWM to generate a drive signal that is transmitted to the switching transistor.

[0012] Furthermore, step 3 specifically includes:

[0013] Step 31: Perform a stability analysis on the grid-connected inverter system to determine whether the grid-connected inverter system is stable;

[0014] Step 32: If the grid-connected inverter system is stable, calculate the output impedance expression of the grid-connected inverter based on the simplified control block diagram.

[0015] Furthermore, step 31 specifically includes:

[0016] Step 311: Divide the inverter grid-connected system into a power supply subsystem and a load subsystem; wherein, the power supply subsystem uses a voltage source U s and resistance Z s In series representation, the load subsystem is represented by resistor Z1;

[0017] Step 312, determine Z s If the Nyquist criterion is satisfied, the grid-connected inverter system is determined to be stable, where s is the Laplace operator.

[0018] Furthermore, the expression for the output impedance of the grid-connected inverter is:

[0019]

[0020] Where L1, C, and L2 are interface filters, i g U is the grid input current, u0 is the grid voltage at the grid connection point, and R is the input current. dK is the grid-side resistance. pwm Here, is the amplification gain of the inverter bridge arm output voltage to the duty cycle signal, s is the Laplace operator, and H is... i (s) is the transfer function of the current regulator, Z inv (s) is the output impedance in the s-domain.

[0021] Furthermore, step 4 specifically includes:

[0022] Calculate the error signal ε, output angular frequency ω0, and output phase angle θ respectively. v With the instantaneous given value i of the grid-connected current ref :

[0023] ε=-V α sinω0t+V β cosω0t

[0024] ω0=(K p +K i ∫)ε

[0025] θ v =∫ω0dt

[0026] i ref =I m ×cosθ v

[0027]

[0028] Among them, V α =V s cosθ, V β =V s sinθ, t is time; ∫ represents the integrator's integral over the error signal ε, K p K is the proportional gain of the PI controller. i I represents the integral coefficient of the PI controller. m The magnitude of the grid current; and V α V β , ε, ω0, θ v i ref The amount of disturbance;

[0029] Based on the above formula, the output impedance model of the phase-locked loop is obtained as follows:

[0030]

[0031] Among them, U m Let be the grid voltage amplitude, s be the Laplace operator, and j be the imaginary unit.

[0032] Furthermore, step 5 specifically includes:

[0033] Step 51: Calculate the output impedance model of the grid-connected inverter system based on the output impedance expression of the grid-connected inverter.

[0034] Step 52: Based on the output impedance model of the grid-connected inverter system and the output impedance model of the phase-locked loop, obtain the impedance model of the single-phase LCL grid-connected inverter considering the phase-locked loop, and use it for stability analysis.

[0035] Furthermore, step 51 specifically includes: the output impedance model of the grid-connected inverter system is:

[0036]

[0037]

[0038] Where s is the Laplace operator, j is the imaginary unit, ω0 is the output angular frequency, and K p K is the proportional gain of the PI controller. i U is the integral coefficient of the PI controller. m i represents the grid voltage amplitude. g It is the grid connection current, H i (s) is the transfer function of the current regulator, K pwm This represents the amplification gain of the inverter bridge arm output voltage on the duty cycle signal. L1, C, and L2 are interface filters, and R... d It is the grid-side resistance, and u0 is the grid voltage at the grid connection point.

[0039] Furthermore, considering the phase-locked loop, the impedance model of a single-phase LCL grid-connected inverter is as follows:

[0040]

[0041] in, u0(s) is the grid voltage at the grid connection point in the s-domain, i g Z is the grid current at the grid connection point in the s-domain. inv (s) is the output impedance in the s-domain without considering the phase-locked loop, Z′ inv (s) is the output impedance of the phase-locked loop in the s-domain.

[0042] A modeling system for a single-phase LCL grid-connected inverter considering a phase-locked loop includes: a single-phase LCL grid-connected inverter system circuit, a circuit simplification module, and a calculation module;

[0043] The single-phase LCL grid-connected inverter system circuit includes: an inverter composed of four switching transistors, a set of LCL filters, a constant voltage source on the DC side connected in parallel with a DC-side capacitor, and an ideal AC voltage source on the grid side connected in series with the grid-side impedance.

[0044] The circuit simplification module is used to obtain a simplified control block diagram;

[0045] The calculation module is used to obtain the output impedance expression of the grid-connected inverter, the output impedance model of the phase-locked loop, and the impedance model of the single-phase LCL grid-connected inverter considering the phase-locked loop.

[0046] The beneficial effects of the present invention are as follows: Compared with the prior art, the present invention has the following advantages:

[0047] (1) This invention establishes that the grid-connected inverter system for control current can be equivalent to the parallel connection of an ideal current source and the output impedance. Taking the impedance model of a single-phase LCL grid-connected inverter without considering the phase-locked loop as an example, it is convenient to perform impedance analysis on the grid-connected inverter with current source when studying system stability.

[0048] (2) The present invention uses the harmonic small signal injection method to establish the impedance model mathematical model of the second-order generalized integrator phase-locked loop, which helps to study the influence of the phase-locked loop on the system stability.

[0049] (3) This invention establishes an impedance model for a single-phase LCL grid-connected inverter considering a phase-locked loop (PLL). The inverter output impedance model is compared with that without considering the PLL, demonstrating that the parallel equivalent resistance caused by the PLL reduces the amplitude-frequency characteristic curve of the output impedance and decreases the system phase margin. This provides a direction for further research on the impact of the PLL on system stability. Attached Figure Description

[0050] Figure 1 This is a structural diagram of a single-phase LCL type grid-connected inverter system.

[0051] Figure 2 This is a structural diagram of a single-phase grid-connected inverter control system based on a PI regulator.

[0052] Figure 3 This is a simplified control block diagram of the single-phase LCL grid-connected inverter system described in this invention.

[0053] Figure 4 This is the small-signal equivalent circuit diagram of a voltage source system.

[0054] Figure 5 This is a block diagram of a closed-loop negative feedback control system.

[0055] Figure 6 This is the small-signal equivalent circuit of the grid-connected inverter system described in this invention.

[0056] Figure 7 This is a block diagram of a phase-locked loop (PLL).

[0057] Figure 8 This is a schematic diagram of a phase-locked loop.

[0058] Figure 9 This is a block diagram of a second-order generalized integrator.

[0059] Figure 10 This is a simplified control block diagram of a single-phase LCL grid-connected inverter system considering the phase-locked loop, as described in this invention.

[0060] Figure 11 This invention presents the Bode plot of the output impedance of the grid-connected inverter before and after the phase-locked loop.

[0061] Figure 12 This is a flowchart of a modeling method for a single-phase LCL grid-connected inverter that considers a phase-locked loop according to the present invention. Detailed Implementation

[0062] The present application will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention, and should not be construed as limiting the scope of protection of the present application.

[0063] This invention discloses a modeling method for a single-phase LCL grid-connected inverter based on impedance stability analysis and considering phase-locked loops. It requires the calculation of impedance models for various components, including: the output impedance model of the single-phase LCL grid-connected inverter system, the output impedance model of the second-order generalized integrator phase-locked loop, and the output impedance model of the single-phase LCL grid-connected inverter system with phase-locked loops.

[0064] The output impedance model of a single-phase LCL grid-connected inverter system is a mathematical model calculated using current control based on a PI regulator in a stationary coordinate system for this inverter circuit.

[0065] The output impedance model of a second-order generalized integrator phase-locked loop is obtained by rewriting the input and output signals into a superposition of steady-state and disturbance quantities using small-signal analysis, and then calculating the disturbance quantity after separating it.

[0066] The output impedance model of a single-phase LCL grid-connected inverter system with phase-locked loop is obtained by combining the output impedance model of a single-phase LCL grid-connected inverter system, the output impedance model of a second-order generalized integrator phase-locked loop, and load current feedforward.

[0067] Modeling methods such as Figure 12 As shown, it includes the following steps:

[0068] Step 1: Establish a single-phase LCL grid-connected inverter system circuit, which includes an inverter composed of four switching transistors, a set of LCL filters, and considers the DC side as a constant voltage source with a DC-side capacitor in parallel, and the grid side as an ideal AC voltage source with a grid-side impedance in series.

[0069] Circuits of single-phase LCL type grid-connected inverter systems, such as Figure 1 As shown in the figure. The grid voltage is supplied by an ideal voltage source u. g Represented in series with the grid impedance; R g and L g These represent the grid-side resistance and inductance, respectively; C in Indicates the DC-side capacitor; VT1-VT4 represent the four switching transistors; L1, C f L2 forms an LCL-type filter, i g U is the grid current, and u0 is the voltage at the point of common connection (PCC).

[0070] Step 2: The control strategy for the single-phase LCL grid-connected inverter is selected based on current control using a PI regulator in a stationary coordinate system, resulting in a simplified control block diagram. The control method involves multiplying the output current of the LCL filter by the cosine of the phase-locked loop angle, subtracting this product from the set current, and transmitting the result to the PI controller. This difference is then superimposed with the grid voltage to obtain a modulated wave signal, which is then modulated by SPWM to generate a drive signal that is transmitted to the switching transistor, thereby achieving control of the single-phase grid-connected inverter in a stationary coordinate system.

[0071] The output impedance model of an inverter is not only related to the interface filter structure but also directly related to the inverter control method. This invention focuses on single-phase voltage-source inverters, whose control methods can be divided into two main categories: control in a stationary coordinate system and control in a synchronous rotating coordinate system. For small-to-medium power single-phase grid-connected inverters, a relatively simple single-loop PI regulator control strategy can be adopted, and its system and control structure are as follows: Figure 2 As shown.

[0072] exist Figure 2 In the middle, C dc For DC-side capacitors, L1 and C f L2 is an LCL filter with an interface, i g For grid connection current, u g This is the grid voltage. The given current amplitude is calculated based on the given power, and θ is the output phase angle of the grid voltage after passing through the phase-locked loop. Multiplying the given AC current i by the cosine of the phase angle output of the phase-locked loop (PLL) (cosθ) yields the given AC current i. ref * i ref * With the feedback of the grid-connected current i gThe difference is calculated, and then the current loop output is obtained through a PI regulator. The current loop output is superimposed with the feedforward grid voltage to generate a modulated wave signal, which is then modulated by SPWM to generate a drive signal as the switching signal for the switching transistors, thus realizing the control of the single-phase grid-connected inverter in a stationary coordinate system. The feedforward grid voltage in the control loop can eliminate the influence of voltage disturbances on the inverter output.

[0073] Considering that the main objective of this invention is to establish an output impedance model for a single-phase grid-connected inverter system, and to facilitate the analysis and study of system stability, the following is provided: Figure 1 The single-phase LCL grid-connected inverter system circuit adopts current control based on a PI regulator in stationary coordinates, and a simplified control block diagram of its input and output signals in the s-domain is extracted to obtain... Figure 3 .

[0074] Step 3: For the simplified control block diagram of a single-phase LCL grid-connected inverter, the output impedance expression of the grid-connected inverter is obtained by impedance analysis.

[0075] Step 3 specifically includes:

[0076] Step 31: Perform a stability analysis on the grid-connected inverter system to determine whether the grid-connected inverter system is stable;

[0077] Step 32: If the grid-connected inverter system is stable, calculate the output impedance expression of the grid-connected inverter based on the simplified control block diagram.

[0078] The basic principle of impedance analysis for studying the stability of grid-connected inverter systems is to divide the entire grid-connected inverter system into two subsystems: the power supply and the load. For the power supply subsystem, a voltage source U can be used. s and resistance Z s In series representation, the load subsystem can be represented by resistor Z1, such as... Figure 4 The diagram shown is the small-signal equivalent circuit of the voltage source system.

[0079] from Figure 4 The expression for the current I flowing through the load resistor Z1 can be calculated as follows:

[0080]

[0081] The following prerequisites apply when performing stability analysis on the system: when the system has no load resistor Z1, the voltage source U... s It is stable when the voltage source U s When the power source is ideal, the current I flowing through the load Z1 is stable. In this case, U in equation (1) s (s) and 1 / Z(s) are stable, and the stability of the load current depends on the second term in equation (1), namely:

[0082]

[0083] Therefore, the stability of the system depends on H(s). From equation (2), it can be seen that H(s) is similar to a negative feedback system, such as... Figure 5 As shown, its forward channel gain is 1, and its negative feedback channel gain is Z. s (s) / Z1(s), according to linear control theory, only when Z... s The system is stable only when (s) / Z1(s) satisfies the Nyquist criterion.

[0084] The above stability criterion is based on the fact that the power supply subsystem is a voltage source and that the power supply voltage can remain stable under no-load conditions. For grid-connected inverter systems, the output voltage is controlled by the grid voltage, and the grid-connected inverter controls the grid current when it is working normally, which is a current source. Therefore, the above stability criterion cannot be directly applied to grid-connected inverter systems.

[0085] For systems where the power supply subsystem is a current source, the stability criterion is also based on the small-signal equivalent circuit, such as... Figure 6 As shown, the grid-connected inverter is its power subsystem, which can be equivalent to a current source I. s Its output impedance Z inv In the parallel configuration, the grid voltage is its load subsystem, which can be equivalent to an ideal voltage source U. g With output impedance Z grd The series form.

[0086] Based on the small-signal equivalent circuit for Figure 3 By analyzing the simplified system block diagram, the expression for the output impedance of the grid-connected inverter can be obtained:

[0087]

[0088] Where L1, C, and L2 are interface filters, i g U is the grid input current, u0 is the grid voltage at the grid connection point, and R is the input current. d K is the grid-side resistance. pwm Here, is the amplification gain of the inverter bridge arm output voltage to the duty cycle signal, s is the Laplace operator, and H is... i (s) is the transfer function of the current regulator.

[0089] The stability analysis of this voltage source system and the application of the current source system to stability analysis have the following prerequisites: when the grid impedance Z grd When the voltage is zero, the grid current I is stable. When there is no grid-connected inverter, the grid voltage U... g It is stable. According to linear control theory, it is only stable when Z... grd (s) / Zinv (s) The system can operate stably when the Nyquist criterion is satisfied. The above judgment is based on the assumption that the power grid is operating stably. If the power grid is unstable, the inverter will also be unable to operate stably.

[0090] Step 4: For the second-order generalized integrator phase-locked loop, obtain the output impedance model of the phase-locked loop through small-signal analysis:

[0091] The basic structure of a phase-locked loop (PLL) mainly consists of four parts: a phase detector, a loop filter, a voltage-controlled oscillator (VCO), and a frequency divider. Its main function is to track the phase angle and frequency of AC signals. A block diagram of its main structure is shown below. Figure 7 As shown.

[0092] The phase detector mainly calculates the difference between the phase angle obtained by the frequency divider and the given phase angle, then converts it into an electrical signal and sends it to the loop filter. The loop filter then converts the error electrical signal into a voltage compensation signal. The voltage-controlled oscillator then uses this voltage compensation signal to compensate the output signal, thereby achieving consistency between the phase angle frequency of the input signal and the output signal.

[0093] The block diagram of the phase-locked loop structure studied in this invention is as follows: Figure 8 As shown, the function of this system is to make the output phase angle θ v Tracking input phase angle θ s θ s That is, the input grid phase angle, where [V α V β ] T =[V s cosθ s V s sinθ s ] T V s This refers to the input voltage amplitude. The input voltage V... α V β respectively with sinθ v cosθ v Multiply and then subtract to form the error signal ε = -V α sinθ v +V β cosθ v =-V s sin(θ v -θ s ) performs negative feedback tracking. When (θ v -θ s When the value is very small, sin(θ) can be computationally satisfied. v -θ s )≈(θ v -θ sThe error signal ε passes through the proportional module K. p and Integral Module K i This allows for error-free tracking of the angular frequency ω. v Then, after passing through an integration module, the phase angle θ is output. v .

[0094] The phase-locked loop system follows the phase angle tracking principle as follows: assuming that θ is present during initialization... v <θ s Then we have sin(θ) v -θ s ) < 0, because -π < (θ) v -θ s Since ) < 0, the error signal ε = -V s sin(θ v -θ s ) > 0, after passing through the PI module and an integral module, θ v Increase, when (θ) v -θ s When ) = 0, θ v Stop increasing, at which point we have θ v =θ s The phase-locked loop successfully implemented the phase angle tracking function.

[0095] The aforementioned phase-locked loop input consists of two orthogonal quantities with a 90° phase difference. For a three-phase grid-connected inverter system, this can be achieved by performing a coordinate transformation on the three-phase grid voltage. However, this cannot be directly used for the single-phase grid-connected inverter system described in this invention. Therefore, it is necessary to construct a virtual orthogonal quantity with a 90° phase difference from the grid voltage, based on the grid voltage. To avoid the noise caused by grid frequency fluctuations in the delay method and the noise introduced by the differential method, this invention employs a second-order generalized integral method to construct the orthogonal quantity.

[0096] Figure 9 This is a block diagram of a second-order generalized integrator, where v is the input signal and v′ and qv′ are the output signals. From the block diagram, the closed-loop transfer function of the system can be derived as:

[0097]

[0098] In actual grid-connected inverter control circuits, the main function of the phase-locked loop (PLL) is to track the grid voltage frequency and phase angle. The output of the PLL affects the current input in the current control loop, which in turn affects the inverter output impedance. The small-signal mathematical model of the PLL, i.e., the superposition of steady-state and disturbance quantities in equation (10), is derived below: First, the time-domain equations are written according to the PLL control block diagram. Figure 9 Input voltage V α V β respectively with sinθv cosθ v Multiply and then subtract to form the error signal, i.e.:

[0099] ε=-V α sinω0t+V β cosω0t (5)

[0100] The error signal ε is passed through a PI controller to obtain the output angular frequency, i.e.:

[0101] ω0=(K p +K i ∫)ε (6)

[0102] Where ∫ represents the integrator's integral over the error signal ε, K p K is the proportional gain of the PI controller. i The integral coefficient of the PI controller.

[0103] The output angular frequency is integrated to obtain the output phase angle, i.e.:

[0104] θ v =∫ω0 dt (7)

[0105] The cosine value of the output phase angle and the magnitude of the grid current I m The product serves as the instantaneous given value of the grid-connected current, i.e.:

[0106] i ref =I m ×cosθ v (8)

[0107] The variables in equations (5)-(8) can be written as a superposition of steady-state and disturbance quantities, i.e.:

[0108]

[0109] in, and V α V β , ε, ω0, θ v i ref The amount of disturbance.

[0110] Substitute the variables in equation (9) into equations (5)-(8) respectively, and consider... Separating the disturbance quantity yields:

[0111]

[0112] Among them, U m This is the grid voltage amplitude. Based on this, consider... The phase-locked loop output impedance model can be obtained by taking the Laplace transform of both sides of equation (10) simultaneously, where the phase-locked loop is an orthogonal quantity with a phase difference of 90 degrees.

[0113]

[0114] Among them, K p K i These are the proportional and integral coefficients of the PI controller mentioned above.

[0115] Step 5: Combining the two impedance models from Steps 3 and 4, the control structure of the single-phase LCL grid-connected inverter system considering the phase-locked loop is obtained (i.e., Figure 10 (As shown). In Figure 3 Based on the single-phase LCL inverter structure, the grid voltage sampled at the output end is fed back to the input end through the phase-locked loop system described in step 4 to form a current control loop. The above structure integrates the phase-locked loop structure into the inverter through feedback. The impedance analysis method is used on the above structure as a whole, and the two impedance models in steps 3 and 4 are further analyzed in the s-domain to finally obtain the impedance model of the single-phase LCL grid-connected inverter considering the phase-locked loop, i.e., from equation (15).

[0116] By considering the Bode plots of the grid-connected inverter output impedance before and after the phase-locked loop (PLL), it is concluded that the amplitude of the amplitude-frequency characteristic curve of the inverter output impedance model after considering the PLL is lower, and the intersection frequency with the grid impedance Bode plot is lower. This leads to a decrease in the phase margin of the impedance ratio between the two, which will have an adverse effect on the stability of the system.

[0117] After considering phase-locked loops Figure 1 The simplified control block diagram of a single-phase LCL grid-connected inverter system can be represented as follows: Figure 10 As shown, with Figure 9 In comparison, the simplified control block diagram of the system has an additional parallel loop that feeds back from the PCC to the current control terminal.

[0118] Similarly, using impedance analysis, from Figure 10 The output impedance model expression for a single-phase LCL grid-connected inverter system can be derived as follows:

[0119]

[0120] Substituting equation (3) into equation (12) yields:

[0121]

[0122] in:

[0123]

[0124] After considering the phase-locked loop, the output impedance Z′ of the grid-connected inverter inv have:

[0125]

[0126] in:

[0127]

[0128] As can be seen from equation (15), after considering the phase-locked loop, the equivalent output impedance of the inverter is equivalent to the parallel connection of two equivalent resistors. One is the inverter output impedance without considering the phase-locked loop, and the other is the equivalent impedance in parallel with the inverter output impedance caused by the phase-locked loop.

[0129] An analysis of the output impedance of the grid-connected inverter before and after considering the phase-locked loop yields the following results: Figure 11 The Bode plots of the grid-connected inverter output impedance before and after considering the phase-locked loop (PLL) are shown. The blue curve represents the Bode plot of the grid-connected inverter output impedance without considering the PLL. (Z) inv The green curve represents the Bode plot of the grid-connected inverter output impedance after considering the phase-locked loop, denoted by Z'. inv The red curve represents the Bode plot of the equivalent grid impedance, expressed as Z. g Indicates. From Figure 11 As can be seen, due to the effect of the parallel equivalent resistance caused by the phase-locked loop, the amplitude of the inverter output impedance amplitude-frequency characteristic curve is reduced, the intersection frequency with the grid impedance is changed, and the phase angle difference between the two phase-frequency characteristic curves at the intersection frequency is increased, that is, the system phase margin is reduced, thereby reducing the stability of system operation.

[0130] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0131] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0132] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0133] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0134] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0135] The applicant of this invention has provided a detailed description of the embodiments of the invention in conjunction with the accompanying drawings. However, those skilled in the art should understand that the above embodiments are merely preferred embodiments of the invention. The detailed description is only intended to help readers better understand the spirit of the invention and is not intended to limit the scope of protection of the invention. On the contrary, any improvements or modifications made based on the inventive spirit of the invention should fall within the scope of protection of the invention.

Claims

1. A modeling method for a single-phase LCL-type grid-connected inverter considering a phase-locked loop, characterized in that, Includes the following steps: Step 1: Establish a single-phase LCL grid-connected inverter system circuit; the circuit includes: an inverter composed of four switching transistors, a set of LCL filters, a constant voltage source on the DC side connected in parallel with a DC-side capacitor, and an ideal AC voltage source on the grid side connected in series with a grid-side impedance; the LCL filters include inverter-side inductors. , grid-side inductor and the filter capacitor With passive damping resistor Branches formed by series connection; Step 2: Based on the single-phase LCL grid-connected inverter system circuit, a control strategy based on PI regulator current control in the stationary coordinate system is selected to obtain a simplified control block diagram of the single-phase LCL grid-connected inverter system circuit. The control strategy includes: multiplying the filter output current of the LCL and the angle cosine of the phase-locked loop, subtracting it from the set current, and transmitting it to the PI controller. The modulated wave signal is then superimposed with the grid voltage to obtain a modulated wave signal, which is then modulated by SPWM to generate a drive signal that is transmitted to the switching transistor. Step 3: Perform a stability analysis on the grid-connected inverter system to determine whether the system is stable. If the system is stable, based on the simplified control block diagram, use impedance analysis to obtain the output impedance expression of the grid-connected inverter: in This is the grid-connected current. The grid voltage at the grid connection point. This represents the amplification gain of the inverter bridge arm output voltage relative to the duty cycle signal. For the Laplace operator, For the current regulator transfer function, yes The output impedance of the domain; Step 4: For the second-order generalized integrator phase-locked loop, obtain the output impedance model of the phase-locked loop through small-signal analysis; Step 5: Based on the output impedance expression of the grid-connected inverter and the output impedance model of the phase-locked loop (PLL), the impedance model of the single-phase LCL grid-connected inverter considering the PLL is obtained for stability analysis; the impedance model of the single-phase LCL grid-connected inverter considering the PLL is as follows: in, yes Considering the output impedance of the phase-locked loop in the domain, For the Laplace operator, The imaginary unit, It is the output angular frequency. The proportional gain of the PI controller. The integral coefficient of the PI controller. The voltage amplitude of the power grid. The magnitude of the grid current. It is the transfer function of the current regulator. This refers to the grid voltage at the grid connection point.

2. The modeling method for a single-phase LCL grid-connected inverter considering a phase-locked loop according to claim 1, characterized in that, Step 3 involves performing a stability analysis on the grid-connected inverter system to determine its stability. This includes: The inverter grid-connected system is divided into a power supply subsystem and a load subsystem; the power supply subsystem uses a voltage source. and resistance In series representation, the load subsystem uses resistors. express; judge If the Nyquist criterion is met, the grid-connected inverter system is considered stable. For the Laplace operator.

3. The modeling method for a single-phase LCL grid-connected inverter considering a phase-locked loop according to claim 1, characterized in that, Step 4 specifically includes: Calculate the error signal separately Output angular frequency Output phase angle Instantaneous setpoint of grid-connected current : in, , , It is time; Indicates the integrator's response to the error signal The points, The proportional gain of the PI controller. The integral coefficient of the PI controller; The magnitude of the grid current; , , , , and They are respectively , , , , , The amount of disturbance; Based on the above formula, the output impedance model of the phase-locked loop is obtained as follows: in, The voltage amplitude of the power grid. For the Laplace operator, It is the imaginary unit.

4. The modeling method for a single-phase LCL grid-connected inverter considering a phase-locked loop according to claim 1, characterized in that, Step 5 specifically includes: Step 51: Calculate the output impedance model of the grid-connected inverter system based on the output impedance expression of the grid-connected inverter. Step 52: Based on the output impedance model of the grid-connected inverter system and the output impedance model of the phase-locked loop, obtain the impedance model of the single-phase LCL grid-connected inverter considering the phase-locked loop, and use it for stability analysis.

5. The modeling method for a single-phase LCL grid-connected inverter considering a phase-locked loop according to claim 1, characterized in that, Step 51 specifically includes: The output impedance model of the grid-connected inverter system is as follows: in, For the Laplace operator, The imaginary unit, It is the output angular frequency. The integral coefficient of the PI controller. The voltage amplitude of the power grid. It is the transfer function of the current regulator.

6. A modeling system for a single-phase LCL grid-connected inverter considering a phase-locked loop, used to perform the method according to any one of claims 1-5, characterized in that, The system includes: a single-phase LCL grid-connected inverter system circuit, a circuit simplification module, and a calculation module; The single-phase LCL grid-connected inverter system circuit includes: an inverter composed of four switching transistors, a set of LCL filters, a constant voltage source on the DC side connected in parallel with a DC-side capacitor, and an ideal AC voltage source on the grid side connected in series with the grid-side impedance. The circuit simplification module is used to obtain a simplified control block diagram; The calculation module is used to obtain the output impedance expression of the grid-connected inverter, the output impedance model of the phase-locked loop, and the impedance model of the single-phase LCL grid-connected inverter considering the phase-locked loop.

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