A harmonic linearization-based impedance modeling method for a network-structured MMC photovoltaic grid-connected system

Abstract

The application relates to a kind of network type MMC photovoltaic grid-connected system impedance modeling methods based on harmonic linearization, comprising: step S1, the small signal model of photovoltaic array and Boost converter is established, the output impedance of photovoltaic side is calculated;Step S2, the method for establishing the sequence impedance model of network type MMC photovoltaic system using harmonic linearization;Step S3, the sequence impedance model of network type MMC is processed, and the admittance impedance model of network type MMC photovoltaic system is obtained;Step S4, the output impedance of the photovoltaic side is integrated with the admittance impedance model of network type MMC photovoltaic system, and the complete network type MMC photovoltaic grid-connected system impedance model is obtained and the correctness of the network type MMC photovoltaic grid-connected system impedance model is verified.Compared with prior art, the present application has prior art coverage scene sufficient, high modeling precision, can be stable and accurate evaluation, model verification method is reliable, and engineering practicality is strong.

Description

Technical Field

[0001] This invention relates to the field of power system modeling and analysis technology, and in particular to an impedance modeling method for grid-connected MMC photovoltaic grid-connected systems based on harmonic linearization. Background Technology

[0002] With the increasing prominence of global energy shortages and environmental pollution, promoting the development and utilization of renewable energy has become a global trend. Solar energy, due to its environmentally friendly, clean, and widely distributed advantages, has become a major driving force for the development and utilization of renewable energy, and photovoltaic power generation is widely recognized as the core approach to achieving large-scale development and utilization of solar energy resources. To promote the transmission and consumption of photovoltaic power and strengthen the support capacity of receiving-end power grids, flexible DC transmission technology has significant technical advantages in areas such as renewable energy grid connection, power supply for large cities, and interconnection of coastal islands. Modular multilevel converters, with their high degree of modularity, low loss, and high power quality, are gradually becoming the preferred topology for flexible DC transmission.

[0003] However, with the rapid development of photovoltaic (PV) systems, the proportion of converters connected to the grid has increased while the proportion of grid synchronous machines has decreased. The intermittency and volatility of PV system grid connection can cause grid fluctuations, leading to frequent under-disturbance stability issues in the receiving-end system. Several flexible DC transmission projects have experienced secondary and supersynchronous oscillation accidents, constantly affecting the safe operation of the power system. In particular, a PV grid-connected system refers to connecting a PV system to the power grid.

[0004] Currently, research on impedance modeling for grid-connected MMC photovoltaic systems remains significantly insufficient. Existing studies mainly focus on the impedance characteristics of wind power systems connected to the grid via MMC-HVDC, while research on impedance modeling for photovoltaic power plants connected to the grid via MMC-HVDC is relatively limited. For photovoltaic systems, a system impedance model considering grid-connected MMC has not yet been established, lacking a complete sequence impedance model that accurately describes the overall characteristics of the photovoltaic array, Boost converter, and grid-connected MMC. Traditional modeling methods struggle to effectively handle the nonlinear characteristics of virtual synchronous machine control in grid-connected MMC and the strong nonlinear output characteristics of the photovoltaic array, resulting in insufficient impedance modeling accuracy.

[0005] A search revealed a method for impedance modeling and virtual impedance design of a grid-connected MMC based on virtual synchronous machine control, disclosed in Chinese Patent Publication No. CN120300755A. First, a mathematical model of the grid-connected MMC converter based on virtual synchronous machine control is established through a control strategy, and a harmonic linearization method is used to establish the sequence impedance model of the MMC. Then, virtual impedance control is designed to optimize traditional VSG control, and a sequence impedance model after introducing virtual impedance control is proposed. Finally, the impedance characteristics and grid-connected stability of the MMC converter after introducing virtual impedance control are analyzed. However, this existing patent only performs impedance modeling on the grid-connected MMC converter itself, assuming the DC side is an ideal voltage source, completely ignoring the strong nonlinear IV characteristics of the photovoltaic array and the dynamic influence of the MPPT control of the Boost converter. It cannot reflect the DC link impedance coupling characteristics when the actual photovoltaic array is connected to the MMC via DC / DC converter; furthermore, the output of this existing patent is only the AC port admittance of the MMC, without considering the mapping relationship between the DC side impedance and the overall stability of the grid-connected system.

[0006] Therefore, there is an urgent need to propose a method to accurately establish the impedance model of a grid-connected MMC photovoltaic system. This method involves establishing the output impedance model of the photovoltaic side and the sequence impedance model of the grid-connected MMC system separately using harmonic linearization technology, integrating them to form a complete system sequence impedance model, and verifying the correctness of the model using a frequency sweep verification method. This provides an accurate model basis for subsequent system stability analysis and parameter optimization. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the existing technology and provide an impedance modeling method for grid-connected MMC photovoltaic systems based on harmonic linearization.

[0008] The objective of this invention can be achieved through the following technical solutions: An impedance modeling method for grid-connected MMC photovoltaic systems based on harmonic linearization includes: Step S1: Establish a small-signal model of the photovoltaic array and the Boost converter, and calculate the output impedance on the photovoltaic side; Step S2: Use the harmonic linearization method to establish the sequence impedance model of the grid-type MMC photovoltaic system; Step S3: Process the sequence impedance model of the grid-type MMC to obtain the admittance impedance model of the grid-type MMC photovoltaic system. Step S4: Integrate the output impedance of the photovoltaic side with the admittance impedance model of the grid-connected MMC photovoltaic system to obtain a complete impedance model of the grid-connected MMC photovoltaic system and verify the correctness of the impedance model.

[0009] As a preferred technical solution, step S1 specifically includes: Step S101: Construct a photovoltaic array; Step S102: Construct the external characteristic mathematical model of the photovoltaic array, and linearize the external characteristic mathematical model to obtain the small signal model of the photovoltaic array; Step S103: Based on the maximum power output characteristics of the photovoltaic array, derive the small-signal model of the voltage and current at the maximum power point of the photovoltaic array; Step S104: Establish the time-domain average model of the Boost converter, perform small-signal linearization processing on the time-domain average model based on the steady-state operating point of the Boost converter, obtain the small-signal model of the Boost converter, and convert it into the frequency domain. Step S105: Establish the frequency domain equation of the mathematical model of the maximum power point tracking controller, and calculate the output impedance of the photovoltaic side by combining the small signal model of the photovoltaic cell.

[0010] As a preferred technical solution, the photovoltaic array is composed of photovoltaic cell modules connected in a series-parallel mode; The mathematical model of the external characteristics of the photovoltaic array is as follows: in N p and N s It refers to the number of photovoltaic cell modules connected in parallel and in series in a photovoltaic array; I scr It is the photocurrent generated by a photovoltaic cell under standard conditions; I on This is the saturation current of the diode under standard conditions; T This represents the actual value of the photovoltaic array's illumination temperature. The output voltage of the photovoltaic array is n; the quality factor of the diode is n. Linearizing the mathematical model of the external characteristics of the photovoltaic array, the small-signal model representation of the photovoltaic array is obtained as follows: in k p The dynamic admittance of the photovoltaic array; This refers to the small-signal component of the output current of the photovoltaic array. This refers to the small-signal component of the photovoltaic array output voltage. Will k p Rewritten as follows: in, This represents the steady-state value of the photovoltaic array output current. Based on the maximum power output characteristics of the photovoltaic array, the voltage-current relationship that satisfies the maximum power output is as follows: The small-signal model of the voltage and current at the maximum power point of the photovoltaic array is obtained: in k m The equivalent impedance corresponding to the maximum power point of the photovoltaic array is expressed as follows: in, The small-signal component of the maximum power point voltage; This is the steady-state value of the voltage at the maximum power point; Steady-state value of the maximum power point current.

[0011] As a preferred technical solution, the frequency domain representation of the small-signal model of the Boost converter is as follows: In the formula , These are the small-signal components of the photovoltaic array's output current and voltage, respectively. , These are the small-signal components of the inverter input DC bus voltage and current, respectively. This is the small-signal component of the inductor current; V dc0 , I L0 These are the steady-state components of the DC bus voltage and the inductor current, respectively. For the duty cycle of the Boost converter, the small-signal component is used. The MPPT controller uses the error signal to adjust the duty cycle of the Boost converter. Therefore, the frequency domain equation of the MPPT controller's mathematical model can be obtained as follows: Its frequency domain small-signal model can be represented as follows: In the formula H pv ( s )= k p + k i / s For the PI controller of the Boost converter; Combining the small-signal model of the photovoltaic cell above, the output impedance of the photovoltaic side is expressed as follows: = in For photovoltaic array voltage, and These are the input filter capacitor for the Boost converter and the DC bus filter capacitor, respectively. and These are the output currents on the photovoltaic side, Provides the DC bus voltage and current to the inverter.

[0012] As a preferred technical solution, step S2 specifically includes: adding a small signal disturbance of a harmonic frequency at the power frequency steady-state operating point, linearizing the small signal in the frequency domain through Fourier decomposition, and further combining it with the symmetric component method to obtain the sequence impedance model of the grid-type MMC photovoltaic system of the target system in the abc coordinate system.

[0013] As a preferred technical solution, the sequence impedance model of the grid-type MMC photovoltaic system in the abc coordinate system includes: the main circuit model, the small-signal model of the reference phase, the small-signal model of the control loop, and the frequency domain sequence impedance model. The main circuit model construction process includes: establishing a set of nonlinear differential equations describing its dynamic characteristics based on the MMC average value model; and superimposing at the steady-state operating point frequencies of... , The positive and negative sequence small-signal voltage disturbances are arranged into a small-signal column vector according to the steady-state frequency sequence. The process of constructing the small-signal model of the reference phase includes starting with VSG control, injecting voltage disturbances to cause power disturbances, causing disturbances in the MMC modulation phase, and deriving the reference angular frequency disturbance component and the small-signal component of the MMC modulation phase. The process of constructing the small-signal model of the control loop includes integrating AC current control and circulating current control to establish a small-signal model of the control signal; the small-signal model includes small-signal models of the differential-mode component and common-mode component of the modulation signal. The process of constructing the frequency domain sequence impedance model includes: establishing its frequency domain small-signal model based on the time domain steady-state model; establishing the relationship between DC side voltage and DC current according to Ohm's law; performing linearization processing to obtain the small-signal perturbation relationship; and obtaining the MMC AC port admittance matrix.

[0014] As a preferred technical solution, the MMC AC port admittance matrix is: in, , , These are the sum of the upper bridge arm current, the submodule capacitor voltage, and the modulation function, respectively; C eq Let C be the equivalent capacitance of the bridge arm, satisfying C eq =C sm / N, where N is the number of modules; A pd Y is the bridge arm current transformation matrix. Larm Z is the admittance matrix of the bridge arm inductor under small-signal frequency domain sequence; Ceq R is the equivalent capacitance-impedance matrix of the bridge arm under small-signal frequency domain sequence; mat =diag(0,0,0,1.5R,0,0,0), where the coefficient 1.5 depends on the weight of the three-phase current superimposed on the DC side.

[0015] As a preferred technical solution, the admittance impedance model of the grid-type MMC photovoltaic system is as follows: in, The element in the 4th row and 4th column of the system's total admittance matrix; The output impedance of the photovoltaic side; For MMC AC port admittance matrix; Finally, the sequence impedance is obtained. : Among them, (4,4) is the 4th row and 4th column of the MMC admittance matrix.

[0016] As a preferred technical solution, the correctness of the impedance model of the grid-connected MMC photovoltaic system is verified using a frequency sweep verification method; wherein the frequency sweep verification method specifically includes: Step S401: Establish a simulation model of the grid-connected MMC photovoltaic system based on Matlab; Step S402: Perform positive-sequence and negative-sequence disturbances sequentially at the common grid connection point; Step S403: Detect and process the current response at the frequency corresponding to the grid connection point to verify the AC port impedance model.

[0017] As a preferred technical solution, the positive-sequence perturbation includes: injecting a small positive-sequence voltage, corresponding to a positive-sequence impedance test; The negative sequence disturbance includes: injecting a small negative sequence voltage with a frequency of fn, corresponding to a negative sequence impedance test.

[0018] Compared with the prior art, the present invention has the following beneficial effects: 1. It fills the gap in the complete sequence impedance model of grid-connected MMC photovoltaic systems and solves the problem of insufficient coverage of existing technologies. Existing impedance modeling research largely focuses on wind power grid-connected systems via MMC-HVDC, with limited research on photovoltaic (PV) power plants connected via MMC-HVDC. Previously, a complete sequence impedance model encompassing the PV array, Boost converter, and overall characteristics of the grid-connected MMC was not established. This invention, for the first time, integrates the impedance characteristics of the PV side (including the PV array, Boost converter, and MPPT control) with those of the grid-connected MMC side, forming a full-link system sequence impedance model. This fills the modeling gap in this scenario and provides a complete model foundation for subsequent stability analysis.

[0019] 2. High modeling accuracy, effectively characterizing the nonlinear properties of the system. Traditional modeling methods struggle to handle the nonlinear characteristics of VSG control in grid-type MMCs and the strong nonlinear output characteristics of photovoltaic arrays. This invention employs harmonic linearization technology, superimposing positive and negative sequence small-signal disturbances at the steady-state operating point at power frequency, and deriving the sequence impedance using the symmetrical component method. Simultaneously, the external characteristics of the photovoltaic array are linearized, and small-signal modeling is performed based on the time-domain averaging model of the Boost converter. This fully considers photovoltaic output fluctuations, the inertia and damping characteristics of VSG control, the dynamic characteristics of the MMC bridge arms, and the influence of the third harmonic, avoiding the simplification errors of traditional methods. The final analytical results of the positive and negative sequence impedances of the model show a high degree of agreement with the amplitude and phase frequency characteristics of the frequency sweep simulation results, verifying the high-precision characteristics.

[0020] 3. Supports subsynchronous and supersynchronous oscillation mechanism analysis and accurate stability assessment The sequence impedance model established in this invention can clearly reflect the impedance characteristics of the system at different frequencies. Combined with impedance analysis, it can directly determine the risk of secondary and supersynchronous oscillations: when the grid impedance and the system output impedance intersect at amplitude points in the secondary and supersynchronous frequency bands and the phase margin is insufficient, the oscillation risk can be predicted. Compared with traditional methods that rely solely on time-domain simulation, this model can reveal the oscillation mechanism at the frequency domain level, significantly improving the efficiency and accuracy of stability analysis and providing clear guidance for the design of oscillation suppression strategies.

[0021] 4. It can provide quantitative basis for system parameter optimization and control strategy improvement. The model explicitly includes the influence of photovoltaic side parameters, MMC main circuit parameters, and VSG control parameters on impedance characteristics. Researchers can quickly optimize parameters by adjusting them and observing changes in impedance characteristics. They can also verify the effectiveness of improved control strategies based on the model, reducing on-site debugging costs and shortening the engineering development cycle.

[0022] 5. The model validation method is reliable and has strong engineering applicability. This invention constructs a full-system simulation model and verifies its correctness using a frequency sweep method that injects multi-frequency positive and negative sequence perturbation voltages at the PCC point. This method is consistent with the impedance testing approach in actual engineering, and the verification process is standardized and the results are reliable. The constructed model can be used for academic research and can also directly serve the stability verification of actual photovoltaic flexible DC grid-connected projects, possessing strong engineering application value. Attached Figure Description

[0023] Figure 1 The circuit topology and control block diagram of a grid-type MMC photovoltaic system; Figure 2 Here is the circuit topology diagram of the Boost converter; Figure 3 VSG control strategy diagram; Figure 4 The positive sequence impedance characteristic curve of a grid-type MMC photovoltaic system; Figure 5 The negative sequence impedance characteristic curve of a grid-type MMC photovoltaic system; Figure 6 This is the overall flowchart of the present invention. Detailed Implementation

[0024] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0025] Example 1: like Figure 1 The diagram shows the circuit topology and control block diagram of a grid-type MMC photovoltaic system: The grid-connected MMC photovoltaic system studied in this invention utilizes an equivalent voltage source formed on the DC side by boosting the photovoltaic array via a Boost converter. Power Supply. The photovoltaic array uses maximum power point tracking (MPPT) to adjust the duty cycle of the Boost converter, optimizing the extraction of photovoltaic power and maintaining a stable DC voltage on the DC bus. The MMC converter inverts the DC power into three-phase AC power. Each arm of the MMC consists of several half-bridge modules connected in series, and its modular design enables high-voltage, high-capacity, and low-harmonic output. The AC voltage output from the MMC is stepped up by the converter transformer before being connected to the AC grid. The converter transformer not only matches the voltage level but also provides necessary electrical isolation and impedance matching.

[0026] In the picture, , ( ) represent the upper and lower arm currents of the MMC three-phase bridge, respectively, and SM k ( ) represents the various sub-modules of the MMC bridge arm. For submodule capacitors, The inductance is for the bridge arm. The MMC inverter is connected to the AC grid via a converter transformer. For the converter transformer inductance, , These are the equivalent resistance and inductance of the AC power grid, respectively. For photovoltaic array voltage, and These are the input filter capacitor for the Boost converter and the DC bus filter capacitor, respectively. and These are the output currents on the photovoltaic side, Provide the DC bus voltage and current to the inverter. and For the boost converter's boost inductor and resistor.

[0027] The grid-connected MMC employs a VSG control strategy. At the grid connection point, active and reactive power are controlled via VSG to generate a reference phase. and reference voltage The modulation voltage reference signal is generated through dual closed-loop control of voltage and current and circulating current control. Finally, the turn-on and turn-off signals of the submodule IGBT are generated through a stepped wave modulation stage.

[0028] (2) Impedance modeling 1. Photovoltaic array impedance modeling A photovoltaic array consists of photovoltaic cell modules connected in a series-parallel configuration. It has a series connection... N s Modules and Parallel N p The external characteristics of the photovoltaic array of the module can be described by the following formula: In the formula N p and N s It refers to the number of photovoltaic cell modules connected in parallel and in series in a photovoltaic array. I scr It is the photocurrent generated by a photovoltaic cell under standard conditions. I on This is the saturation current of the diode under standard conditions. k The value is the Boltzmann constant (1.380625 × 10⁻²³ J / K). T This represents the actual value of the photovoltaic array's illumination temperature. q It is a unit charge (1.60217×10-23C).

[0029] Linearizing the above equation, we can obtain the small-signal model representation of the photovoltaic array as follows: In the formula k p To determine the dynamic admittance of the photovoltaic array, and to avoid complex exponential calculations, it can be... k p Rewritten as follows Based on the maximum power output characteristics of the photovoltaic array, the voltage-current relationship that satisfies the maximum power output can be obtained as follows: Then we can obtain the small-signal model of the maximum power point voltage and current of the photovoltaic array. In the formula k m The equivalent impedance corresponding to the maximum power point of the photovoltaic array is expressed as follows: Therefore, a small-signal model of the photovoltaic array near the maximum power point can be obtained.

[0030] To eliminate the nonlinear effects of switching action, this paper uses the average model of the Boost converter instead of the switching model, based on... Figure 2 The time-domain average model equation of the Boost converter can be expressed as: Based on the steady-state operating point of the Boost converter, the time-domain model of the converter is linearized using small-signal processing. Since the amplitude of higher-order small signals is much smaller than that of the first-order term, it can be ignored and does not significantly affect the modeling accuracy. This yields the time-domain small-signal model of the Boost converter, which can be represented in the frequency domain as follows: In the formula , These are the small-signal components of the photovoltaic array's output current and voltage, respectively. , These are the small-signal components of the inverter input DC bus voltage and current, respectively. This is the small-signal component of the inductor current; V dc0 , I L0 These are the steady-state components of the DC bus voltage and the inductor current, respectively. This refers to the duty cycle of the small-signal component of the Boost converter.

[0031] The MPPT controller uses the error signal to adjust the duty cycle of the Boost converter; therefore, the frequency domain equation of the MPPT controller's mathematical model can be obtained as follows: Its frequency domain small-signal model can be represented as follows: In the formula H pv ( s )= k p + k i / s This is the PI controller for the Boost converter.

[0032] Combining the small-signal model of the photovoltaic cell above, the output impedance of the photovoltaic side can be expressed as follows: 2. Network-based MMC sequence impedance model The VSG control block diagram is as follows: Figure 3 As shown, the active frequency simulates the rotor motion equation of the synchronous machine, giving it inertia and primary frequency regulation capability; the reactive voltage loop simulates the synchronous machine excitation, giving it voltage regulation capability.

[0033] Depend on Figure 3 It can be seen that the mathematical equations for the active power loop and the reactive power loop can be expressed as: In the formula P sref This is a reference value for active power at the point of common coupling; D This is the virtual damping coefficient; J This is the virtual inertia coefficient; ω ref Using the reference angular frequency as an integral, the reference phase θ is obtained. ω 0 represents the fundamental angular frequency; k Q This is the reactive power droop coefficient; V 0 represents the no-load voltage setting.

[0034] This section uses the harmonic linearization method to establish the sequence impedance model of the network-type MMC. This method adds a small signal disturbance of a harmonic frequency at the steady-state operating point of the power frequency, and linearizes it in the frequency domain through Fourier decomposition. By further combining it with the symmetric component method, the sequence impedance model of the target system in the abc coordinate system can be obtained.

[0035] Based on the principle of harmonic linearization, the sequence impedance modeling process is described in four parts: the main circuit model, the small-signal model of the reference phase, the small-signal model of the control loop, and the frequency domain sequence impedance model.

[0036] Based on the MMC average value model, its dynamic characteristics can be described by a set of nonlinear differential equations. Taking the upper arm of phase a as an example, that is... In the formula i au , v Cau , m au These are the sum of the upper bridge arm current, the submodule capacitor voltage, and the modulation function, respectively. C eq The equivalent capacitance of the bridge arm satisfies C eq = C sm / N ,in N This represents the number of modules.

[0037] Under normal operating conditions, the MMC operates at its steady-state operating point. The superposition frequencies at the steady-state operating point are as follows: f p , f n The positive-sequence and negative-sequence small-signal voltage disturbances can be expressed as the voltage at the grid connection point. In the formula V 1 represents the amplitude of the fundamental frequency phase voltage; ω 1 represents the fundamental angular frequency; v p , v n These represent the amplitudes of the positive-sequence and negative-sequence harmonic voltages, respectively. ω p , ω n These are the positive and negative sequence harmonic angular frequencies, respectively. ϕ p , ϕ n These are the initial phases of the positive and negative harmonics, respectively.

[0038] High accuracy can be achieved by considering the influence of the third harmonic in MMC impedance modeling. To describe the steady-state characteristics of the converter, the voltage components are arranged according to the steady-state frequency sequence {-3}. f 1,…,0,…,+3 f The numbers 1 and 2 are arranged in the order of 7 small signal column vectors, that is: To describe its small-signal frequency domain characteristics, this component is arranged according to the small-signal frequency sequence { f p -3 f 1,…,0,…, f p +3 f The numbers 1 and 2 are arranged in order to form a 7-row small signal column vector, i.e. In the formula For frequency f p -2 f The small-signal component of AC voltage 1, For frequency f p The small-signal component of AC voltage.

[0039] The small-signal model of the reference phase can be established by starting with VSG control. Injected voltage disturbances will cause power disturbances, thereby causing disturbances in the MMC modulation phase θ. Furthermore, compared to current disturbances, voltage disturbances have a smaller impact on output power; therefore, the power disturbance component caused by voltage disturbances is ignored here. In the formula , These are the active and reactive small signal components at the grid connection point, respectively. It is the conjugate of the fundamental frequency phase current; For frequency f p The small-signal component of alternating current.

[0040] Depend on Figure 3 As shown in the VSG control strategy diagram, the active power frequency control loop generates a disturbance component of the reference angular frequency based on power fluctuations, that is: In the formula The small signal component is the reference angular frequency.

[0041] The small-signal component of the MMC modulation phase is obtained from the above equation. That is, the reference phase for the subsequent Parker transformation. Depend on Figure 1 From the control links of the network-type MMC, we can see that: In the formula , These are the d-axis and q-axis small signal vectors of the common-mode component of the modulation signal, respectively. The decoupling coefficient for circulating control; , These are the d-axis and q-axis small-signal vectors of the bridge arm circulation, respectively. G cir For the circulating control matrix, G v , G i These are seventh-order control matrices for the outer voltage loop and the inner current loop, respectively, with the following specific expressions: Performing the inverse Parker transform on the above equation yields the small-signal model of the differential-mode component of the phase a modulation function, i.e. In the formula G 1. G 2 These are seventh-order control matrices, with the specific expressions as follows: Similarly, considering the influence of negative-sequence second harmonic circulating current control, a small-signal model for circulating current control is established. From... Figure 1 The control loop shown can be obtained as follows: In the formula , These are the common-mode components of the modulation signal. d , q Small-scale signal vector; K c The decoupling coefficient for circulating control; , These are the d-axis and q-axis small-signal vectors of the bridge arm circulation, respectively. right and By performing a negative-order second harmonic inverse Parker transform, the small-signal model of the common-mode component of the phase a modulation function can be obtained, i.e. In the formula, G3 is a seventh-order control matrix, with the following specific expression: The small-signal model of the control loop is derived from Figure 1 It can be seen that by combining AC current control and circulating current control, the small-signal model of the control signal for the upper arm of phase a can be obtained, i.e. Substituting the above equation, we get: in: In the formulaA pd The bridge arm current conversion matrix consists of half of the AC current, which is formed by the differential mode components of the upper and lower bridge arm currents. The frequency domain sequence impedance model can be based on the time-domain steady-state model, and its frequency domain small-signal model can be established accordingly. In the formula Y Larm The bridge arm inductance admittance matrix under small-signal frequency domain sequence; Z Ceq Given the equivalent capacitance and impedance matrix of the bridge arm in the small-signal frequency domain sequence, to simplify the convolution operation, the dot product is used instead of convolution, extending the steady-state component column vector into a Toplitz matrix form. The specific expression is as follows: According to Ohm's law, the relationship between DC-side voltage and DC current is as follows: Linearization is performed to obtain the small-signal perturbation relationship: In MMC, the relationship between DC current and the three-phase upper and lower arm currents can be expressed as: On the DC side of the MMC, the DC voltage With DC current and equivalent DC load resistance The relationship between them satisfies Ohm's law, that is To establish a frequency-domain small-signal impedance model, the DC voltage disturbance component in the above relationship needs to be expressed as a function of the DC current disturbance component. Therefore, the steady-state DC voltage... Replace with By applying a small-signal perturbation to both sides of the equation and ignoring higher-order nonlinear terms, we obtain the small-signal linearized expression in the frequency domain: In the frequency domain order impedance model This can be represented by introducing a DC load impedance matrix. Since R only acts on the DC component, in a 7x7 Toeplitz matrix, it mainly affects the center frequency, defined as follows: R mat =diag(0,0,0,1.5R,0,0,0), where the coefficient 1.5 depends on the weight of the three-phase current superimposed on the DC side.

[0042] After considering the load R, the MMC AC port admittance matrix is ​​corrected as follows: 3. Integration and Frequency Sweep Verification of Sequence Impedance Model for Grid-Based MMC Photovoltaic Systems Based on the topology of the grid-type MMC photovoltaic system, the output impedance of the PV side is added for analysis, and the admittance impedance model of the grid-type MMC photovoltaic system can be obtained. Finally, the sequence impedance is obtained. : To verify the correctness of the obtained impedance model of the grid-connected MMC photovoltaic system and to facilitate subsequent stability analysis, this paper establishes a model based on Matlab / Simlink. Figure 1 The simulation model of the grid-connected MMC photovoltaic system is shown. The AC port impedance model is verified by using a frequency sweep verification method, which involves sequentially injecting positive and negative sequence disturbance voltages at various frequencies at the PCC point, and then detecting and processing the current response at the corresponding frequency of the grid connection point. Figure 3 This paper compares the impedance analytical model and simulation results of a grid-connected MMC photovoltaic system. Tables 1 and 2 show the specific photovoltaic side parameters and grid-connected MMC parameters.

[0043] Table 1 PV-side parameter table Table 2. Parameters of Network-Type MMC Figure 4 and Figure 5 The figure shows a comparison between the analytical model of the positive-sequence impedance and the frequency sweep results of the grid-connected MMC photovoltaic system. The comparison results show that the theoretical curve and the simulated frequency sweep results agree well, verifying the correctness of the impedance model derived in this paper. It can be observed that the admittance matrix matches the amplitude-frequency and phase-frequency characteristics of the frequency sweep results, verifying the correctness of the analytical impedance model.

[0044] In summary, the impedance modeling method for grid-connected MMC photovoltaic systems based on harmonic linearization proposed in this invention can accurately establish a complete sequence impedance model for the entire grid-connected photovoltaic system, including the photovoltaic Boost converter and the VSG-controlled MMC converter. This method establishes small-signal models of the photovoltaic array near its maximum power point, frequency-domain small-signal models of the Boost converter, and output impedance models on the photovoltaic side. Using harmonic linearization, it establishes small-signal models of the main circuit, reference phase, control loop, and frequency-domain sequence impedance models of the grid-connected MMC. Finally, these are integrated to obtain a complete system sequence impedance model. Frequency sweep verification shows that the amplitude-frequency and phase-frequency characteristics of the analytical model and simulation results are highly consistent, proving the accuracy of the established model. This invention provides an accurate model foundation for the stability analysis and parameter optimization of grid-connected MMC photovoltaic systems.

[0045] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. An impedance modeling method for a grid-connected MMC photovoltaic system based on harmonic linearization, characterized in that, include: Step S1: Establish a small-signal model of the photovoltaic array and the Boost converter, and calculate the output impedance on the photovoltaic side; Step S2: Use the harmonic linearization method to establish the sequence impedance model of the grid-type MMC photovoltaic system; Step S3: Process the sequence impedance model of the grid-type MMC to obtain the admittance impedance model of the grid-type MMC photovoltaic system. Step S4: Integrate the output impedance of the photovoltaic side with the admittance impedance model of the grid-connected MMC photovoltaic system to obtain a complete impedance model of the grid-connected MMC photovoltaic system and verify the correctness of the impedance model.

2. The impedance modeling method for a grid-connected MMC photovoltaic grid-connected system based on harmonic linearization according to claim 1, characterized in that, Step S1 specifically includes: Step S101: Construct a photovoltaic array; Step S102: Construct the external characteristic mathematical model of the photovoltaic array, and linearize the external characteristic mathematical model to obtain the small signal model of the photovoltaic array; Step S103: Based on the maximum power output characteristics of the photovoltaic array, derive the small-signal model of the voltage and current at the maximum power point of the photovoltaic array; Step S104: Establish the time-domain average model of the Boost converter, perform small-signal linearization processing on the time-domain average model based on the steady-state operating point of the Boost converter, obtain the small-signal model of the Boost converter, and convert it into the frequency domain. Step S105: Establish the frequency domain equation of the mathematical model of the maximum power point tracking controller, and calculate the output impedance of the photovoltaic side by combining the small signal model of the photovoltaic cell.

3. The impedance modeling method for a grid-connected MMC photovoltaic grid-connected system based on harmonic linearization according to claim 2, characterized in that, The photovoltaic array consists of photovoltaic cell modules connected in a series-parallel configuration. The mathematical model of the external characteristics of the photovoltaic array is as follows: in N p and N s It refers to the number of photovoltaic cell modules connected in parallel and in series in a photovoltaic array; I scr It is the photocurrent generated by a photovoltaic cell under standard conditions; I on This is the saturation current of the diode under standard conditions; T This represents the actual value of the photovoltaic array's illumination temperature. The output voltage of the photovoltaic array is n; the quality factor of the diode is n. Linearizing the mathematical model of the external characteristics of the photovoltaic array, the small-signal model representation of the photovoltaic array is obtained as follows: in k p The dynamic admittance of the photovoltaic array; This refers to the small-signal component of the output current of the photovoltaic array. This refers to the small-signal component of the photovoltaic array output voltage. Will k p Rewritten as follows: in, This represents the steady-state value of the photovoltaic array output current. Based on the maximum power output characteristics of the photovoltaic array, the voltage-current relationship that satisfies the maximum power output is as follows: The small-signal model of the voltage and current at the maximum power point of the photovoltaic array is obtained: in k m The equivalent impedance corresponding to the maximum power point of the photovoltaic array is expressed as follows: in, The small-signal component of the maximum power point voltage; This is the steady-state value of the voltage at the maximum power point; Steady-state value of the maximum power point current.

4. The impedance modeling method for a grid-connected MMC photovoltaic grid-connected system based on harmonic linearization according to claim 2, characterized in that, The frequency domain representation of the small-signal model of the Boost converter is as follows: In the formula , These are the small-signal components of the photovoltaic array's output current and voltage, respectively. , These are the small-signal components of the inverter input DC bus voltage and current, respectively. This is the small-signal component of the inductor current; V dc0 , I L0 These are the steady-state components of the DC bus voltage and the inductor current, respectively. For the duty cycle of the Boost converter, the small-signal component is used. The MPPT controller uses the error signal to adjust the duty cycle of the Boost converter. Therefore, the frequency domain equation of the MPPT controller's mathematical model can be obtained as follows: Its frequency domain small-signal model can be represented as follows: In the formula H pv ( s )= k p + k i / s For the PI controller of the Boost converter; Combining the small-signal model of the photovoltaic cell above, the output impedance of the photovoltaic side is expressed as follows: = in For photovoltaic array voltage, and These are the input filter capacitor for the Boost converter and the DC bus filter capacitor, respectively. and These are the output currents on the photovoltaic side, Provides the DC bus voltage and current to the inverter.

5. The impedance modeling method for a grid-connected MMC photovoltaic grid-connected system based on harmonic linearization according to claim 1, characterized in that, Step S2 specifically includes: adding a small signal disturbance of a harmonic frequency at the steady-state operating point of the power frequency, linearizing the small signal in the frequency domain through Fourier decomposition, and further combining it with the symmetric component method to obtain the sequence impedance model of the grid-type MMC photovoltaic system of the target system in the abc coordinate system.

6. The impedance modeling method for a grid-connected MMC photovoltaic grid-connected system based on harmonic linearization according to claim 5, characterized in that, The sequence impedance model of the grid-type MMC photovoltaic system in the abc coordinate system includes: the main circuit model, the small-signal model of the reference phase, the small-signal model of the control loop, and the frequency domain sequence impedance model. The main circuit model construction process includes: establishing a set of nonlinear differential equations describing its dynamic characteristics based on the MMC average value model; and superimposing at the steady-state operating point frequencies of... , The positive and negative sequence small-signal voltage disturbances are arranged into a small-signal column vector according to the steady-state frequency sequence. The process of constructing the small-signal model of the reference phase includes starting with VSG control, injecting voltage disturbances to cause power disturbances, causing disturbances in the MMC modulation phase, and deriving the reference angular frequency disturbance component and the small-signal component of the MMC modulation phase. The process of constructing the small-signal model of the control loop includes integrating AC current control and circulating current control to establish a small-signal model of the control signal; the small-signal model includes small-signal models of the differential-mode component and common-mode component of the modulation signal. The process of constructing the frequency domain sequence impedance model includes: establishing its frequency domain small-signal model based on the time domain steady-state model; establishing the relationship between DC side voltage and DC current according to Ohm's law; performing linearization processing to obtain the small-signal perturbation relationship; and obtaining the MMC AC port admittance matrix.

7. The impedance modeling method for a grid-connected MMC photovoltaic system based on harmonic linearization according to claim 6, characterized in that, The MMC AC port admittance matrix is: in, , , These are the sum of the upper bridge arm current, the submodule capacitor voltage, and the modulation function, respectively; C eq Let C be the equivalent capacitance of the bridge arm, satisfying C eq =C sm / N, where N is the number of modules; A pd Y is the bridge arm current transformation matrix. Larm Z is the admittance matrix of the bridge arm inductor under small-signal frequency domain sequence; Ceq R is the equivalent capacitance-impedance matrix of the bridge arm under small-signal frequency domain sequence; mat =diag(0,0,0,1.5R,0,0,0), where the coefficient 1.5 depends on the weight of the three-phase current superimposed on the DC side.

8. The impedance modeling method for a grid-connected MMC photovoltaic grid-connected system based on harmonic linearization according to claim 1, characterized in that, The admittance impedance model of the grid-type MMC photovoltaic system: in, The element in the 4th row and 4th column of the system's total admittance matrix; The output impedance of the photovoltaic side; For MMC AC port admittance matrix; Finally, the sequence impedance is obtained. : Among them, (4,4) is the 4th row and 4th column of the MMC admittance matrix.

9. The impedance modeling method for a grid-connected MMC photovoltaic grid-connected system based on harmonic linearization according to claim 1, characterized in that, The correctness of the impedance model of the grid-connected MMC photovoltaic system is verified by frequency sweep verification method; The frequency sweep verification method specifically includes: Step S401: Establish a simulation model of the grid-connected MMC photovoltaic system based on Matlab; Step S402: Perform positive-sequence and negative-sequence disturbances sequentially at the common grid connection point; Step S403: Detect and process the current response at the frequency corresponding to the grid connection point to verify the AC port impedance model.

10. The impedance modeling method for a grid-connected MMC photovoltaic grid-connected system based on harmonic linearization according to claim 1, characterized in that... in, The positive-sequence perturbation includes: injecting a small positive-sequence voltage, corresponding to a positive-sequence impedance test; The negative sequence disturbance includes: injecting a small negative sequence voltage with a frequency of fn, corresponding to a negative sequence impedance test.

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