Photovoltaic MMC-APF fractional order sliding mode control method and medium

Abstract

The invention relates to a photovoltaic-containing MMC-APF fractional order sliding mode control method and a medium, and the method comprises the following steps: constructing a photovoltaic-containing MMC-APF equivalent mathematical model according to the topological structures of an MMC and an APF; carrying out dq coordinate system transformation based on the MMC-APF equivalent mathematical model containing photovoltaic power, and obtaining a voltage and current relation under a dq coordinate system; constructing an inner ring sliding mode current controller according to a sliding mode control principle and a fractional order theory based on the voltage and current relationship under the dq coordinate system; and generating a trigger pulse based on the inner ring sliding mode current controller so as to control the output of the MMC-APF containing photovoltaic power, and completing the control process. Compared with the prior art, the method has the advantages of high response speed, excellent control performance, remarkable power quality compensation effect and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of MMC-APF control, and in particular, to a fractional-order sliding mode control method and medium for MMC-APF with photovoltaic power generation. Background Art

[0002] With the increasing complexity of power systems and the widespread application of power electronic devices, harmonics in the power grid are intensifying, leading to a decline in current quality. An APF (Active Power Filter) can suppress harmonics and compensate for reactive power, thereby improving power quality and ensuring the stable operation of the power grid. However, in high-voltage power grids, the current recovery ability of three-level APFs is weak. Since the introduction of MMC (Modular Multilevel Converter) in 1980, its application in power electronic devices has significantly expanded the functional potential of APFs. With the increasing emphasis on energy efficiency and low-carbon emissions, renewable energy sources are increasingly integrated into the power grid. Among them, photovoltaic power generation stands out for its wide availability and cost-effectiveness. The combination of photovoltaic power generation and MMC-APF further promotes effective grid integration.

[0003] However, the volatility of photovoltaic power generation poses challenges to the control of MMCs. These challenges become more severe under unbalanced grid conditions, resulting in complex power quality problems and increased current fluctuations. Scholars have conducted research on the combination of photovoltaic power generation and MMCs to address these issues. For example, a photovoltaic grid-connected control method based on a modular multilevel converter proposed in Patent CN104092239B, and a control method based on unbalanced grid voltage for photovoltaic grid connection proposed in Patent Application CN118763694A. Existing literature has also proposed a minimum maximum power point tracking algorithm to maintain phase power balance under partial shading conditions of photovoltaic arrays. A new modular circuit configuration for connecting photovoltaic systems to the grid through MMCs has also been introduced. However, this structure connects the photovoltaic system through a DC-DC converter, resulting in higher costs. Currently, the control strategies for MMC-APF with photovoltaic power generation under unbalanced grid conditions face challenges such as slow response speed and limited robustness. In addition, the voltage control of PSM (Photovoltaic Sub-Module) under unbalanced grid conditions still requires further research. Summary of the Invention

[0004] The purpose of the present invention is to provide a fractional-order sliding mode control method and medium for MMC-APF with photovoltaic power generation to improve stability.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] A fractional - order sliding - mode control method for a photovoltaic - integrated MMC - APF, comprising the following steps:

[0007] Construct an equivalent mathematical model of the photovoltaic - integrated MMC - APF according to the topological structures of the MMC and the APF;

[0008] Based on the equivalent mathematical model of the photovoltaic - integrated MMC - APF, perform a dq - coordinate transformation to obtain the voltage - current relationship in the dq - coordinate system;

[0009] Based on the voltage - current relationship in the dq - coordinate system, construct an inner - loop sliding - mode current controller according to the sliding - mode control principle and the fractional - order theory;

[0010] Based on the inner - loop sliding - mode current controller, generate trigger pulses to control the output of the photovoltaic - integrated MMC - APF and complete the control process.

[0011] Furthermore, the expression of the equivalent mathematical model of the photovoltaic - integrated MMC - APF is:

[0012]

[0013] where \(u\) pk1 is the output voltage of the MMC, \(u\) pk is the differential - mode voltage between the upper and lower bridge arms, \(L\) peq is the equivalent inductance, \(i\) pk is the line current, and \(R1\) is the line resistance.

[0014] Furthermore, the voltage - current relationship in the dq - coordinate system is expressed as:

[0015]

[0016] where \(u\) pd1 , \(u\) pq1 are the output voltages of the MMC in the dq - coordinate system, \(u\) pd , \(u\) pq are the differential - mode voltages between the upper and lower bridge arms in the dq - coordinate system, \(L\) peq is the equivalent inductance, \(i\) pd , \(i\) pq are the line currents in the dq - coordinate system, \(R1\) is the line resistance, and \(\omega\) is the angular frequency.

[0017] Furthermore, the steps of constructing the inner - loop sliding - mode current controller include:

[0018] Based on the voltage - current relationship in the dq - coordinate system, according to the sliding - mode control principle, obtain the initial sliding - mode control law to form an initial inner - loop sliding - mode current controller;

[0019] Based on the initial inner - loop sliding - mode current controller, optimize the sliding - mode surface according to the fractional - order theory to obtain the final sliding - mode control law improved based on fractional - order integration, and form the final inner - loop sliding - mode current controller.

[0020] Furthermore, the steps of obtaining the initial sliding - mode control law include:

[0021] Set the expected value, expressed as:

[0022]

[0023] In the formula, is the expected value, are the dq reference values of the positive and negative sequence currents;

[0024] Based on the expected value, define the sliding - mode surface, expressed as:

[0025]

[0026] In the formula, s1 and s2 are the sliding - mode surfaces, E1 and E2 are the deviations between the expected value and the actual value, x + , x - are the positive and negative sequence inner - loop currents;

[0027] According to the sliding - mode surface and combined with the voltage - current relationship in the dq coordinate system, obtain the derivative of the current, expressed as:

[0028]

[0029] In the formula, is the derivative of the current, R1 is the line resistance, ω is the angular frequency, L peq is the equivalent inductance, are the dq - axis currents under the positive sequence, is the MMC output voltage under the positive sequence in the dq - axis, is the differential - mode voltage between the upper and lower bridge arms under the positive sequence in the dq - axis;

[0030] According to the derivative of the current, obtain the derivative of the sliding - mode surface, expressed as:

[0031]

[0032] Where:

[0033]

[0034] In the formula, is the derivative of the sliding - mode surface, ρ + , ρ - are the positive and negative sequence adjustment coefficients, and sgn is the sign function;

[0035] Replace the sign function with a saturation function, and the derivative expression of the sliding mode surface is transformed into:

[0036]

[0037] where ρ1, ρ2 are, and sat is the saturation function;

[0038] According to the derivative of the transformed sliding mode surface, the initial sliding mode control law is obtained, which is expressed as:

[0039]

[0040] where u + , u - is the initial sliding mode control law.

[0041] Furthermore, the steps for obtaining the sliding mode control law improved based on fractional integral include:

[0042] Define a fractional differential operator, and the expression is:

[0043]

[0044] where α and t represent the upper and lower limits of the operator respectively, represents the α - order derivative or integral of the function f(t);

[0045] Adopt the fractional derivative defined by Caputo, which is expressed as:

[0046]

[0047] where 1 < α < n, and Γ() is the gamma function;

[0048] According to the fractional derivative defined by Caputo, optimize the sliding mode surface, where the optimized sliding mode surface is expressed as:

[0049]

[0050] where s1, s2 are the optimized positive and negative sliding mode surfaces, and c2, c3 are the sliding mode gains;

[0051] According to the optimized sliding mode surface, obtain the positive and negative reaching rates, which are expressed as:

[0052]

[0053] where:

[0054]

[0055] where are the positive and negative arrival rates, k1 and k2 are the sliding mode surface coefficients, ε1 and ε2 are the reaching term coefficients, and k s is a positive number;

[0056] According to the positive and negative arrival rates and the initial sliding mode control rate, a sliding mode control rate improved based on fractional-order integration is obtained, which is expressed as:

[0057]

[0058] In the formula, u + and u - are the sliding mode control rates improved based on fractional-order integration.

[0059] Furthermore, it also includes using the maximum power point tracking algorithm to perform voltage stabilization control on the photovoltaic sub-module in the MMC-APF.

[0060] Furthermore, the steps of performing voltage stabilization control on the photovoltaic sub-module include:

[0061] The steps of constructing the capacitor voltage controller include:

[0062] Using the maximum power point tracking algorithm, calculate the conductance difference between two consecutive voltage points in the photovoltaic output characteristic curve to obtain the maximum power point, and based on the maximum power point, set the voltage of the photovoltaic sub-module when it outputs the maximum power;

[0063] Use the MMC modulation technology to determine the number of photovoltaic sub-modules that need to be activated on the upper and lower arms of each phase;

[0064] Obtain the capacitor voltage values of each photovoltaic sub-module and sort them;

[0065] According to the number of photovoltaic sub-modules that need to be activated on the upper and lower arms of each phase, the sorted capacitor voltage values, and the direction of the arm current, apply the following principles to ensure that the voltage on each photovoltaic sub-module capacitor is constant:

[0066] (1) If the arm current is charging the photovoltaic sub-module capacitor, then conduct the photovoltaic sub-modules in sequence, starting from the photovoltaic sub-module with the smallest capacitor voltage in the sorting, and disconnect the remaining photovoltaic sub-modules;

[0067] (2) If the arm current is discharging the photovoltaic sub-module capacitor, then conduct the photovoltaic sub-modules in sequence, starting from the photovoltaic sub-module with the largest capacitor voltage in the sorting, and disconnect the remaining photovoltaic sub-modules.

[0068] Furthermore, the maximum power point tracking algorithm is the conductance increment method, and the steps of obtaining the maximum power point include:

[0069] According to the rated power of the photovoltaic determined by P = UI, take the derivative of it to obtain:

[0070]

[0071] When dP / dU = 0, the output power of the photovoltaic sub-module reaches the maximum value, obtaining the maximum power point, and the expression is:

[0072]

[0073] In the formula, P is the rated power, U is the rated voltage, and I is the rated current.

[0074] The present invention also provides a computer-readable storage medium, including one or more programs executed by one or more processors of an electronic device, and the one or more programs include instructions for executing the photovoltaic-containing MMC-APF fractional-order sliding mode control method as described above.

[0075] Compared with the prior art, the present invention has the following beneficial effects:

[0076] (1) For the unbalanced power grid problem in medium and high voltage systems, the control method of the present invention introduces sliding mode control based on fractional-order theory. By introducing a fractional-order term into the sliding mode surface to optimize the sliding mode surface, the improved SMC can slow down the convergence rate of the system state near the sliding mode surface, thereby significantly enhancing the overall compensation effect on power quality, reducing the chattering amplitude, and having a shorter response time and better stability compared with the traditional SMC.

[0077] (2) The present invention also combines the maximum power point tracking algorithm into the voltage equalization control of the photovoltaic sub-module, effectively regulating the voltage of the photovoltaic sub-module, ensuring the stability of the voltage of the system photovoltaic sub-module, and providing voltage support for the operation of MMC-APF.

[0078] (3) The combined control method of photovoltaic and MMC-APF based on FOSMC proposed by the present invention can restore the current quality under conditions such as load change, voltage sag and swell, and harmonic injection. The simulation results verify the effectiveness of FOSMC in current quality restoration and PSM voltage control. Description of the Drawings

[0079] Figure 1 It is a schematic diagram of the method flow of the present invention;

[0080] Figure 2 It is the main circuit topology of the photovoltaic-containing MMC-APF of the present invention;

[0081] Figure 3 It is the voltage control strategy of the photovoltaic sub-module of the present invention;

[0082] Figure 4It is the FOSMC (Fractional-Order Sliding Mode Control) control block diagram of the MMC-APF with photovoltaic of the present invention;

[0083] Figure 5 It is the comparison of two control strategies under load switching in the embodiment of the present invention. Among them, (a) is the load current waveform, (b) is the grid current waveform under FOSMC control, (c) is the compensation current waveform under FOSMC control, (d) is the grid current waveform under conventional SMC control, and (e) is the compensation current waveform under conventional SMC control;

[0084] Figure 6 It is the comparison of two control strategies under voltage sag and swell in the embodiment of the present invention. Among them, (a) is the load current waveform, (b) is the grid current waveform under FOSMC control, (c) is the compensation current waveform under FOSMC control, (d) is the grid current waveform under conventional SMC control, and (e) is the compensation current waveform under conventional SMC control;

[0085] Figure 7 It is the comparison of two control strategies under harmonic injection in the embodiment of the present invention. Among them, (a) is the load current waveform, (b) is the grid current waveform under FOSMC control, (c) is the compensation current waveform under FOSMC control, (d) is the grid current waveform under conventional SMC control, and (e) is the compensation current waveform under conventional SMC control;

[0086] Figure 8 It is the voltage waveforms of PSM under the change of light intensity in the embodiment of the present invention. Among them, (a) is the voltage waveform of sub-module 1, (b) is the voltage waveform of sub-module 2, (c) is the voltage waveform of sub-module 3, and (d) is the voltage waveform of sub-module 4. Specific implementation mode

[0087] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and the detailed implementation manner and specific operation process are given, but the protection scope of the present invention is not limited to the following embodiments.

[0088] This embodiment provides a fractional-order sliding mode control method for MMC-APF with photovoltaic, as Figure 1 shown, and this method includes the following steps:

[0089] S1. According to the topological structures of MMC and APF, construct an equivalent mathematical model of MMC-APF with photovoltaic.

[0090] Figure 2Shows the MMC-APF topology with photovoltaic. The MMC is connected to the grid in parallel to provide current compensation. However, the presence of non-linear loads often introduces harmonic components into the grid-side current. The MMC actively generates compensation current to prevent harmonic current from entering the grid, effectively improving the power quality and reducing harmonic interference. The non-linear load in this paper uses a resistor R3 and an IGBT in series, and is connected in series with an RL buffer circuit and an inductive-resistive load, as shown in Figure 2 as shown. Figure 2 In, u a , u b and u c represent the grid voltage respectively, while u pk represents the output voltage. C1 is the DC-side capacitor. According to Kirchhoff's law and the equivalent circuit of MMC-APF, the mathematical model is obtained as follows:

[0091]

[0092] In the formula: u pk1 is the output voltage of MMC; u pk is the differential-mode voltage between the upper and lower bridge arms; L peq is the equivalent inductance; i pk1 is the line current; R1 is the line resistance.

[0093] S2. Based on the above mathematical model, the voltage-current relationship in the dq coordinate system is derived.

[0094] According to formula (1), the mathematical model of the photovoltaic MMC-APF in the dq coordinate system can be derived, which is specifically expressed as:

[0095]

[0096] In the formula: ω is the angular frequency.

[0097] S3. Based on the voltage-current relationship in the dq coordinate system, according to the principle of sliding mode control (SMC), an inner-loop sliding mode current controller is designed.

[0098] SMC (Sliding Mode Control) is a robust control method for complex non-linear systems and systems with uncertainties. Its core idea is to design a suitable sliding surface and force the system state to reach and stay on this sliding surface, so as to ensure the achievement of the desired control goal. SMC is known for its strong robustness, fast response and excellent interference suppression ability.

[0099] The expected value can be expressed as:

[0100]

[0101] In the formula: is the dq reference value of the positive and negative sequence of current.

[0102] The sliding mode surface is defined as:

[0103]

[0104] Then the derivative of the current can be derived as:

[0105]

[0106] The derivative of the sliding mode surface is:

[0107]

[0108] In the formula,

[0109] The saturation function is used to replace the sign function of the sliding mode surface to minimize the high-frequency jitter in SMC. Therefore, the following expression is obtained:

[0110]

[0111] The SMC control rate can be obtained as:

[0112]

[0113] S4. Based on the inner-loop sliding mode current controller, the sliding mode surface is further optimized using the fractional order theory (FO), enhancing the dynamic performance of the controller.

[0114] Specifically:

[0115] Traditional SMC often exhibits chattering phenomena on the sliding mode surface, which reduces its effectiveness in controlling complex systems. To address this issue, fractional calculus is introduced as an extension of integer calculus. Since in practical systems, some behaviors cannot be fully described by integer calculus, fractional calculus provides a more accurate representation. By introducing fractional terms into the original sliding mode surface, the improved SMC can slow down the convergence rate of the system state near the sliding mode surface, thereby reducing the chattering amplitude and effectively suppressing the oscillation of the system when moving along the sliding mode surface.

[0116] The fractional differential operator is defined as:

[0117]

[0118] In this expression, α and t represent the upper and lower limits of the operator respectively; represents the α-order derivative (or integral) of the function f(t). The Caputo-defined fractional derivative is adopted, and its definition is as follows:

[0119]

[0120] where: 1 < α < n and Γ() is the gamma function.

[0121] The positive and negative sliding mode surfaces are defined as:

[0122]

[0123] The positive and negative arrival rates are defined as:

[0124]

[0125] where:

[0126] Combining equations (8) and (12), the sliding mode control law improved based on fractional-order integration is:

[0127]

[0128] The sliding mode control law improved based on fractional-order integration can be used in the inner-loop current controller to generate trigger pulses to control the output of the PV MMC-APF and thus regulate the power quality.

[0129] S5. Combining the maximum power point tracking algorithm, a capacitor voltage controller for the PV MMC-APF is designed to ensure the stability of the voltage of the PV sub-module.

[0130] Since the PV output is volatile, to ensure the stable operation of the system, the voltage of the PV sub-module is controlled. The present invention combines the maximum power point tracking algorithm into the voltage balancing control of the PV sub-module, and designs a capacitor voltage controller to ensure the stability of the voltage of the system's PV sub-module (PSM).

[0131] Specifically:

[0132] The MMC-APF includes three phases, and each phase has upper and lower bridge arms. Each bridge arm is composed of multiple sub-modules (SMs) and can output a high-level voltage. Each SM is composed of two IGBTs, and its capacitor is connected to the PV. The PV can be distributed and better grid-connected through the sub-module. Since the SM system is equipped with the PV, it is necessary to combine the control of the PV system with the voltage balance of the PSM. The conductance increment method is a technique for determining the maximum power point tracking of the PSM. Through the maximum power point, the voltage at the maximum power can be obtained. Therefore, the output of the sub-module uses the voltage at the maximum power, which can ensure the power output of the SM. The basic principle of this maximum power point tracking technology is to calculate the conductance difference between two consecutive voltage points in the PV output characteristic curve to identify the maximum power point. The rated power of the PV is determined by P = UI. Taking the derivative of this formula, we get:

[0133]

[0134] When dP / dU = 0, the output power of the PSM reaches its maximum value, and the equation is:

[0135]

[0136] Due to the characteristics of the PSM, the photovoltaic is directly connected to the SM capacitor, resulting in continuous charging of the capacitor. The constant voltage on the PSM capacitor is maintained through the following three key processes: modulation, sorting, and selection. First, a modulation technique applicable to the MMC is used to determine the number of PSMs that need to be activated on the upper and lower arms of each phase. Then, the capacitance voltage values of each PSM are measured and sorted in ascending or descending order. Finally, according to the number of PSMs to be activated on the upper and lower arms, the sorted capacitance voltage, and the direction of the arm current, specific principles are applied to ensure a constant voltage on each PSM capacitor:

[0137] (1) If the arm current is charging the PSM capacitor, the PSMs are turned on in sequence, starting from the PSM with the smallest capacitance voltage in the sorting, and the remaining PSMs are turned off.

[0138] (2) If the arm current is discharging the PSM capacitor, the PSMs are turned on in sequence, starting from the PSM with the largest capacitance voltage in the sorting, and the remaining PSMs are turned off.

[0139] The designed PSM voltage control strategy is as Figure 3 shown. The reference voltage of the photovoltaic sub-module is obtained through the maximum power point tracking technology. After obtaining the reference voltage, it is compared with the sub-module capacitance voltage by taking the difference and enters the outer-loop PI control. Then, the current value obtained by the outer-loop PI is compared with the reference current, and the trigger pulse is obtained after entering the inner loop. Figure 4 shows the control flow chart of the photovoltaic MMC-APF based on FOSMC. The measured voltage and current values are decomposed into positive and negative sequences. After entering the FOSMC controller, the modulation waveform is obtained. At the same time, the maximum output power of the PSM is determined through the maximum power point tracking. Combining the voltage control strategy, the PSM can operate stably. Finally, the carrier phase-shift modulation strategy is used to generate the drive signal to drive the operation of the photovoltaic MMC-APF.

[0140] Table 1 System parameters for simulation and experiment

[0141]

[0142] This embodiment verifies and explains the technical effects adopted in this method. Different methods selected in this embodiment are compared and tested with this method, and the experimental results are compared by means of scientific demonstration. The simulation platform is used to verify the real effects of this method. In the environment of MATLAB / Simulink, the effectiveness of the proposed FOSMC with photovoltaic MMC-APF is verified. The main simulation parameters of the system are shown in Table 1. In order to verify the performance of the designed controller under unbalanced grid conditions, this invention compares the FOSMC method with the traditional SMC method. This invention focuses on studying the influence of nonlinear load switching, voltage sag and swell, and harmonic injection, and evaluates the superiority and feasibility of the proposed FOSMC strategy.

[0143] (1) Simulation results of load switching

[0144] At 0.3 s, the nonlinear load suddenly increases. Figure 5 Shows the simulation results of the two control methods during the load change process. When the nonlinear load is connected, the grid current is severely distorted, and the total harmonic distortion (THD) reaches 26%. Both control methods can compensate for the harmonic current, but when the load increases, the response speed of FOSMC is faster than that of the traditional SMC. After stabilizing at 0.3 s, the THD of the current under FOSMC is 1%, while the THD under SMC is 3%. This shows that FOSMC provides better control performance.

[0145] (2) Simulation results of voltage change

[0146] The grid voltage experiences a voltage sag between 0.1 s and 0.2 s and a voltage swell between 0.3 s and 0.4 s. Figure 6 Shows the results of the two control strategies under the condition of grid voltage change. As Figure 6 (d) shows, the traditional SMC can recover to a certain extent after the voltage fluctuation, but there is still an obvious overshoot. In contrast, under FOSMC, the voltage recovery is more stable and balanced, and the imbalance is smaller. This shows that FOSMC exhibits superior dynamic performance under the conditions of grid voltage sag and swell.

[0147] (3) Simulation results of harmonic injection

[0148] At 0.3 s, a 2500 V third harmonic is injected into phase a. Figure 7 Shows the simulation results of the two control strategies. After the harmonic injection, the total harmonic distortion of the grid current increases, making the recovery more difficult. Compared with the traditional SMC, the proposed FOSMC makes the grid current closer to a sine wave after recovery. From the perspective of compensation, the FOSMC strategy shows better stability.

[0149] (4) PSM Voltage Simulation Results

[0150] Figure 8 Shows the voltage changes of the PSM under different light intensities. Four PSMs operate under a solar radiation intensity of 1000 W / m 2 and a temperature of 25 °C. At 0.25 s, the solar radiation intensities of the four PSMs drop to 800 W / m 2 , 600 W / m 2 , 400 W / m 2 and 200 W / m 2 respectively. Due to the reduction in solar radiation intensity, each PSM needs to adjust to a new output power. Under the PSM voltage control strategy, after the solar radiation changes, all four PSMs remain stable and reach a new equilibrium, and the voltage does not deviate from the expected PSM voltage. Therefore, the proposed FOSMC strategy ensures the normal operation of the PSM.

[0151] In summary, the present invention has the advantages of fast response speed, excellent control performance, and significant power quality compensation effect.

[0152] If the above functions are implemented in the form of software function units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The foregoing storage medium includes: USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs, etc., which can store program codes.

[0153] Those skilled in the art should understand that the embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can be implemented in the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can be implemented in the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes. The solutions in the embodiments of the present invention can be implemented in various computer languages, for example, object-oriented programming languages such as Java and interpreted scripting languages such as JavaScript.

[0154] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, and the combinations of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processors of general-purpose computers, special-purpose computers, embedded processors, or other programmable data processing devices to generate a machine, such that the instructions executed by the processors of the computer or other programmable data processing devices generate means for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks.

[0155] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means that implement the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks.

[0156] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, so that the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks.

[0157] Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications once they learn the basic creative concepts. Therefore, the appended claims are intended to be construed to include the preferred embodiments as well as all changes and modifications falling within the scope of the present invention.

[0158] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these modifications and variations.

Claims

1. A fractional-order sliding mode control method for MMC-APF containing photovoltaics, characterized in that: The following steps are involved: According to the topological structure of MMC and APF, an equivalent mathematical model of MMC-APF with photovoltaic is constructed; Based on the photovoltaic-containing MMC-APF equivalent mathematical model, a dq coordinate system transformation is performed to obtain a voltage-current relationship in the dq coordinate system; Based on the voltage-current relationship in the dq coordinate system, an inner-loop sliding-mode current controller is constructed according to the sliding-mode control principle and fractional-order theory; Based on the inner loop sliding mode current controller, a trigger pulse is generated to control the output of the MMC-APF containing photovoltaics, thereby completing the control process.

2. A photovoltaic MMC-APF fractional-order sliding mode control method according to claim 1, characterized in that: The expression of the equivalent mathematical model of the photovoltaic MMC-APF is: In the formula, u pk1 is the MMC output voltage, u pk is the differential voltage of the upper and lower bridge arms, L peq is the equivalent inductance, i pk is the line current, and R1 is the line resistance.

3. A fractional-order sliding mode control method for MMC-APF containing photovoltaic according to claim 1, characterized in that: The voltage-current relationship in the dq coordinate system is expressed as: In the formula, u pd1 、u pq1 is the MMC output voltage in the dq coordinate system, u pd 、u pq is the differential voltage of the upper and lower bridge arms in the dq coordinate system, L peq is the equivalent inductance, i pd 、i pq is the line current in the dq coordinate system, R1 is the line resistance, and ω is the angular frequency.

4. A fractional-order sliding mode control method for MMC-APF containing photovoltaic according to claim 1, characterized in that: The steps of constructing the inner loop sliding mode current controller include: Based on the voltage-current relationship in the dq coordinate system and according to the sliding mode control principle, an initial sliding mode control rate is obtained to form an initial inner loop sliding mode current controller; Based on the initial inner-loop sliding-mode current controller, the sliding-mode surface is optimized according to the fractional-order theory to obtain the final sliding-mode control rate based on fractional-order integral improvement, thereby forming the final inner-loop sliding-mode current controller.

5. A fractional-order sliding mode control method for MMC-APF containing photovoltaic according to claim 4, characterized in that: The step of obtaining the initial sliding mode control rate comprises: Set the expected value, expressed as: In the formula, is the expected value, is the dq reference value of the positive and negative sequence of current; Based on the expected value, the sliding surface is defined as: Where s1 and s2 are sliding surfaces, E1 and E2 are the deviations between the expected value and the actual value, and x + 、x - is the positive and negative sequence inner loop current; According to the sliding surface and in combination with the voltage-current relationship in the dq coordinate system, the derivative of the current is obtained, which is expressed as: In the formula, is the derivative of the current, R1 is the line resistance, ω is the angular frequency, L peq is the equivalent inductance, is the dq axis current under positive sequence, is the dq axis MMC output voltage under positive sequence, is the differential mode voltage of the upper and lower bridge arms of the dq axis under positive sequence; According to the derivative of the current, the derivative of the sliding surface is obtained, which is expressed as: in: In the formula, is the derivative of the sliding surface, ρ + , - is the positive and negative sequence adjustment coefficient, sgn is the sign function; By using a saturation function instead of the sign function, the derivative expression of the sliding surface is transformed into: In the formula, ρ1 and ρ2 are adjustment coefficients, and sat is the saturation function; According to the derivative of the transformed sliding surface, the initial sliding mode control rate is obtained, which is expressed as: In the formula, u + 、u - is the initial sliding mode control rate.

6. A fractional-order sliding mode control method for MMC-APF containing photovoltaics according to claim 5, characterized in that: The step of obtaining the sliding mode control rate based on fractional order integral improvement includes: Define the fractional differential operator, the expression is: In the formula, α and t represent the upper and lower limits of the operator respectively. Represents the α-order derivative or integral of the function f(t); Using the fractional derivative defined by Caputo, it is expressed as: Where, 1<α<n, Γ() is the gamma function; According to the fractional derivative defined by Caputo, the sliding surface is optimized, where the optimized sliding surface is expressed as: Where s1 and s2 are the optimized positive and negative sliding surfaces, c2 and c3 are the sliding gains; According to the optimized sliding surface, the positive and negative arrival rates are obtained, which are expressed as: in: In the formula, are the positive and negative arrival rates, k1 and k2 are the sliding surface coefficients, ε1 and ε2 are the approach term coefficients, and k s is a positive number; According to the positive and negative arrival rates and the initial sliding mode control rate, the sliding mode control rate based on fractional order integration improvement is obtained, which is expressed as: In the formula, u + 、u - is the sliding mode control rate improved based on fractional order integration.

7. A photovoltaic MMC-APF fractional-order sliding mode control method according to claim 1, characterized in that: It also includes using the maximum power point tracking algorithm to stabilize the voltage of the photovoltaic sub-module in the MMC-APF.

8. A fractional-order sliding mode control method for MMC-APF containing photovoltaics according to claim 7, characterized in that: The steps of voltage stabilization control of the photovoltaic submodule include: The steps to build a capacitor voltage controller include: Using the maximum power point tracking algorithm, the conductance difference between two consecutive voltage points in the photovoltaic output characteristic curve is calculated to obtain the maximum power point, and based on the maximum power point, the output of the photovoltaic submodule adopts the voltage at the maximum power; The MMC modulation technology is used to determine the number of photovoltaic sub-modules that need to be activated in the upper and lower bridge arms of each phase; Obtain the capacitor voltage value of each photovoltaic sub-module and sort them; According to the number of PV sub-modules that need to be activated in the upper and lower bridge arms of each phase, the sorted capacitor voltage value, and the direction of the bridge arm current, the following principles are applied to ensure that the voltage on the capacitor of each PV sub-module is constant: (1) If the bridge arm current is charging the PV module capacitor, the PV modules are turned on in sequence, starting with the PV module with the smallest capacitor voltage in the sequence, and the remaining PV modules are disconnected; (2) If the bridge arm current is discharging the PV module capacitor, the PV modules are turned on in sequence, starting with the PV module with the largest capacitor voltage in the sequence, and the remaining PV modules are disconnected.

9. A fractional-order sliding mode control method for MMC-APF containing photovoltaics according to claim 8, characterized in that: The maximum power point tracking algorithm is a conductance increment method, and the step of obtaining the maximum power point includes: According to the rated power of photovoltaic power, P = UI, the following is derived: When dP / dU=0, the output power of the photovoltaic sub-module reaches the maximum value, and the maximum power point is obtained, which is expressed as: In the formula, P is the rated power, U is the rated voltage, and I is the rated current.

10. A computer-readable storage medium, characterized in that: It comprises one or more programs for execution by one or more processors of an electronic device, wherein the one or more programs comprise instructions for executing the photovoltaic-containing MMC-APF fractional-order sliding mode control method as claimed in any one of claims 1 to 9.

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