High-efficiency wide-gain combined grid-connected inverter for photovoltaic power generation grid-connected system

By adopting a combined structure of the main power circuit dual active bridge converter and a partial power circuit Boost converter in the photovoltaic power generation system, the existing grid-connected inverter has been solved, and an efficient and low-cost wide-gain grid-connected inverter design is achieved.

CN120237974APending Publication Date: 2025-07-01HUNAN UNIV OF TECH
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Patent Information

Application Number
CN202510405979.9
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-04-02
Publication Date
2025-07-01

AI Technical Summary

Technical Problem

Existing grid-connected inverters have problems such as high production cost, low energy conversion efficiency and narrow input voltage range, and it is difficult to take into account the advantages of single-stage and two-stage structures.

Method used

A high-efficiency wide-gain combined grid-connected inverter for photovoltaic power generation grid-connected systems is designed, and a combination structure of a dual active bridge converter for main power circuit and a Boost converter for partial power circuit is adopted. The soft switch and wide gain are realized using the LLC resonator cavity, which simplifies the connection of components and improves energy transmission efficiency.

Benefits of technology

The high frequency operation of the converter is realized, the device volume is reduced, the cost is reduced, the input voltage range is expanded, and the power density and energy transmission efficiency are improved.

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Abstract

The invention discloses a high-efficiency wide-gain combined grid-connected inverter for a photovoltaic power generation grid-connected system, and belongs to the technical field of grid-connected inverters. The inverter is formed by combining a main power circuit dual-active bridge converter and a partial power circuit Boost converter. The main power circuit is composed of a primary side H full bridge, an LLC resonant cavity, a secondary side bidirectional switch and a high-frequency transformer. The input of the partial power circuit and the input of the main power circuit share a direct current voltage source Vdc, and the output side of the Boost converter is connected with a first bridge arm of the H full bridge; a Boost converter of a part of power circuits works in a boost mode, zero-voltage switching-on of an alternating-current side switching tube and zero-current switching-off of a direct-current side switching tube are achieved while gain conditions are met by means of resonance characteristics of an LLC resonant cavity, and THD of output current is low; the grid-connected inverter topology provided by the invention is beneficial to high-frequency work of the converter and reduction of the size of the device, and has the advantages of wide gain range and high transmission efficiency.
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Description

Technical Field

[0001] The present invention belongs to the technical field of grid-connected inverters, and particularly relates to an efficient wide-gain combined grid-connected inverter for a photovoltaic power generation grid-connected system. Background Art

[0002] With the development of technology, the problems of depletion of fossil energy and environmental pollution are becoming increasingly serious. Using clean energy for power generation, such as photovoltaic power generation, to gradually replace fossil energy for power generation is one of the effective ways to solve this problem. As the core interface for new energy conversion, the DC-AC grid-connected inverter has been widely used in a new power system with new energy as the core. However, how to reduce the manufacturing cost, improve the energy conversion efficiency, and achieve a wide input voltage range are the main technical challenges faced by current grid-connected inverters. At present, various different types of single-phase photovoltaic grid-connected inverter topologies have been proposed. For example, topologies based on structures such as single-phase full-bridge, flyback, and neutral point clamped, and their derivative types. To simplify the design and control methods of grid-connected inverters, some inverters adopt a two-stage structure, but it has disadvantages such as low weighted efficiency, high cost, and large volume; while the single-stage structure can only achieve boost and inversion through one-stage conversion, and has problems such as a small input voltage range, difficult topology design, and complex control methods. Therefore, how to design a topology that takes into account the advantages of both single-stage and two-stage structure grid-connected inverters is becoming increasingly important. Summary of the Invention

[0003] The object of the present invention is to overcome the defects in the above background art, and propose an efficient wide-gain combined grid-connected inverter for a photovoltaic power generation grid-connected system. The topology of the present invention is a quasi-unipolar structure, which combines the advantages of single-stage and two-stage structure inverters, improves the power transmission efficiency of the converter, and has many advantages such as low cost, wide input voltage range, etc. while realizing soft switching of power tubes and improving power density.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] An efficient wide-gain combined grid-connected inverter for a photovoltaic power generation grid-connected system, characterized in that the inverter includes a DC voltage source U cd , a Boost output voltage stabilizing capacitor C in , a ninth power tube S9 of the Boost converter, a first diode D1, a storage inductor L, a first power tube S1, a second power tube S2, a third power tube S3, a fourth power tube S4, a fifth power tube S5, a sixth power tube S6, a seventh power tube S7, an eighth power tube S8, an exciting inductor L s , a series resonance capacitor C r , a series resonance inductor L r , a first capacitor C1, a second capacitor C2, an AC side filter inductor L ac, AC grid side voltage source V g ;

[0006] The inverter is composed of a main power circuit dual active bridge converter and a partial power circuit Boost converter. The dual active bridge converter consists of an H-bridge circuit, a resonant network, and a high-frequency transformer bidirectional switch. The Boost converter shares a DC voltage source U with the dual active bridge converter cd , and the output side of the Buck converter is connected to the first bridge arm of the H-bridge.

[0007] Furthermore, the primary circuit of the high-frequency transformer of the main power circuit dual active bridge converter includes the primary winding N of the transformer P , the H-bridge circuit, the DC voltage source U cd and the DC side capacitor C cd . The H-bridge circuit consists of the first power transistor S1, the second power transistor S2, the third power transistor S3, and the fourth power transistor S4 with junction capacitors and anti-parallel diodes. The drain of the first power transistor S1 is connected to the DC side capacitor C in , the drain of the second power transistor S2 is connected to the DC power supply U cd , and the sources of the third power transistor S3 and the fourth power transistor S4 are connected to the negative pole of the DC voltage source U cd .

[0008] Furthermore, the secondary circuit of the high-frequency transformer of the main power circuit dual active bridge converter includes the secondary winding N of the high-frequency transformer S , an LLC resonant cavity composed of an exciting inductor L s , a series resonant capacitor C r , and a series resonant inductor L r , and two groups of bidirectional switches composed of the fifth power transistor S5, the sixth power transistor S6, the seventh power transistor S7, and the eighth power transistor S8 with junction capacitors and anti-parallel diodes. The same-name terminal of the secondary winding N of the high-frequency transformer S is connected to the resonant inductor L r , and the different-name terminal of the secondary winding N S is connected to the series resonant capacitor C r . The resonant inductor L r and the resonant capacitor C r are respectively connected to the source of the sixth power transistor and the midpoint between the first capacitor C1 and the second capacitor C2. The drain of the fifth power transistor S5 and the upper end of the first capacitor C1 are connected to the filter inductor L ac , and the drain of the eighth power transistor S8 and the lower end of the second capacitor C2 are connected to the lower end of the AC side voltage source V g .

[0009] Furthermore, the partial power circuit Boost converter shares a DC voltage source U with the dual active bridge converter in, the output side of the Boost converter is connected to the first bridge arm composed of the first power transistor S1 and the second power transistor S2 in the H-bridge; the partial power circuit Boost converter includes a storage inductor L and a DC-side capacitor C in , the ninth power transistor S9 with an antiparallel diode, and the first diode D1; the left end of the storage inductor L is connected to the positive pole of the DC voltage source U cd and the drain of the third power transistor S3, and the right end of the storage inductor L is connected to the drain of the ninth power transistor and the anode of the first diode D1; the cathode of the first diode D1 is connected to the positive pole of the DC-side capacitor C in and the drain of the first power transistor S1, and the negative pole of the DC-side capacitor C in is connected to the negative pole of the DC voltage source U cd negative pole, the source of the second power transistor S2, the source of the fourth power transistor S4, and the source of the ninth power transistor S9.

[0010] Further, the switching frequency f of the main power circuit dual-active-bridge converter s operates at the resonant frequency with a fixed duty cycle; in the primary H-bridge circuit, the duty cycles of the first power transistor S1 and the fourth power transistor S4 are 0.5 and they are driven in the same way, the duty cycles of the second power transistor S2 and the third power transistor S3 are 0.5 and they are driven in the same way, the first power transistor S1 and the second power transistor S2 are complementary-conducted, the third power transistor S3 and the fourth power transistor S4 are complementary-conducted; the sixth power transistor S6 and the eighth power transistor S8 are always on during the positive half-cycle of the AC-side voltage source V g , and their duty cycles are both 0.5 and they are complementary-conducted during the negative half-cycle of the AC-side voltage source V g ; the fifth power transistor S5 and the seventh power transistor S7 are always on during the negative half-cycle of the AC-side voltage source V g , and their duty cycles are both 0.5 and they are complementary-conducted during the positive half-cycle of the AC-side voltage source V g ; there is an external phase-shift angle D1 between the first power transistor S1 and the fifth power transistor S5; the resonant frequency of the LLC resonant cavity is:

[0011]

[0012] where f r is the resonant frequency, C r is the series resonant capacitor, and L r is the series resonant inductor.

[0013] Further, the partial power circuit Boost converter adopts a modulation strategy with variable duty cycle, and the output voltage U of the partial power circuit Boost converter in is:

[0014]

[0015] Where D is the duty cycle of the Boost converter in the partial power circuit, and V dc is the voltage of the DC voltage source.

[0016] Furthermore, when driving the first power transistor S1 and the fourth power transistor S4 of the primary H-bridge circuit within half a switching cycle, the voltage U AB at the midpoint of the DC-side bridge arm of the transformer is the output voltage U in of the Boost converter in the partial power circuit. When driving the second power transistor S2 and the third power transistor S3 in the other half of the switching cycle, the voltage U AB at the midpoint of the DC-side bridge arm is the opposite of the DC voltage source U dc . It can be summarized as:

[0017]

[0018] Where V dc is the DC voltage source and D is the duty cycle of the Boost converter in the partial power circuit.

[0019] Furthermore, when driving the first power transistor S1 and the fourth power transistor S4 of the primary H-bridge circuit within a switching cycle, the magnitude of the voltage U CD at the midpoint of the AC-side bridge arm of the transformer is half of the instantaneous value of the AC voltage source on the AC side. To achieve energy transfer from the DC side to the AC side, the voltage U AB at the midpoint of the DC-side bridge arm needs to lead the voltage U CD at the midpoint of the AC-side bridge arm.

[0020] Furthermore, when driving the first power transistor S1 and the fourth power transistor S4 of the primary H-bridge circuit within a switching cycle, the value of the input current i g on the AC side of the transformer is related to the phase shift ratio D1. The control of the AC output current i g can be achieved by modulating the phase shift ratio D1. Among them, the input current i g is the integration of the power transistor current within this cycle, and the expression is:

[0021]

[0022] Where i g is the AC current output by the inverter, I ref is the output current reference value, and i lm is the current flowing through the excitation inductor L m .

[0023] Furthermore, according to the high-efficiency wide-gain combined grid-connected inverter for a photovoltaic power generation grid-connected system described in claim 1, it is characterized in that the expression of the voltage conversion ratio M n is:

[0024]

[0025] Among them, u g is the instantaneous value of the AC voltage source, and n is the turns ratio of the primary and secondary sides.

[0026] Compared with the prior art, the present invention adopts the above technical solutions and has the following beneficial effects:

[0027] (1) The structure of the high-efficiency wide-gain combined grid-connected inverter for the photovoltaic power generation grid-connected system of the present invention is relatively simple, realizing the soft-switching operation of the power transistors of the converter, reducing the switching loss of the converter, which is beneficial to the high-frequency operation of the converter and the reduction of the device volume.

[0028] (2) For the high-efficiency wide-gain combined grid-connected inverter for the photovoltaic power generation grid-connected system of the present invention, the main power circuit adopts a dual-active-bridge inverter, and part of the power circuit adopts a boost converter to increase the input voltage regulation range, enabling efficient energy flow and wide-range DC voltage input.

[0029] The high-efficiency wide-gain combined grid-connected inverter for the photovoltaic power generation grid-connected system of the present invention utilizes different input voltages of two bridge arms to achieve partial power processing, which is beneficial to reducing the total number of components and costs and realizing two connection architectures.

[0030] (4) The high-voltage AC side of the dual-active-bridge converter of the main power circuit of the high-efficiency wide-gain combined grid-connected inverter for the photovoltaic power generation grid-connected system of the present invention has an LLC resonant cavity, and the inverter operates at the resonant point, having high efficiency. Description of the Drawings

[0031] Attached Figure 1 is the circuit drawing of the present invention;

[0032] Attached Figure 2 is the schematic drawing of the main waveforms of the implementation circuit of the present invention;

[0033] Attached Figure 3 is the schematic drawing of the switching mode [t0~t1] of the embodiment of the present invention;

[0034] Attached Figure 4 is the schematic drawing of the switching mode [t1~t2] of the embodiment of the present invention;

[0035] Attached Figure 5 is the schematic drawing of the switching mode [t2~t3] of the embodiment of the present invention;

[0036] Attached Figure 6 is the schematic drawing of the switching mode [t3~t4] of the embodiment of the present invention;

[0037] Attached Figure 7It is the schematic drawing of the switching mode [t4 - t5] of the embodiment of the present invention;

[0038] Appendix Figure 8 It is the schematic drawing of the switching mode [t5 - t6] of the embodiment of the present invention;

[0039] Appendix Figure 9 It is the schematic drawing of the switching mode [t6 - ] of the embodiment of the present invention;

[0040] Appendix Figure 10 The input voltage V of the embodiment of the present invention dc is 25V, the duty cycle is 0.35, and the square - wave voltage U on the primary side of the provided transformer AB , the square - wave voltage U on the secondary side CD , and the resonant current I flowing through the resonant inductor L r . Lr .

[0041] Appendix Figure 11 It is the waveform diagram of the voltage V of the voltage source on the AC side and the output current I of the embodiment of the present invention g , g Waveform diagram. Specific embodiments

[0042] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without making creative efforts shall fall within the protection scope of the present invention.

[0043] The high - efficiency wide - gain combined grid - connected inverter for a photovoltaic power generation grid - connected system is characterized in that within one switching period, the positive - half - cycle working process of the invented converter can be divided into 7 modes, namely [t0 - t1], [t1 - t2], [t2 - t3], [t3 - t4], [t4 - t5], [t5 - t6], [t6 - ]. Among them, within the positive - half - cycle of the AC - side voltage source, the power tubes S6 and S8 are always on;

[0044] The specific simulation parameters are shown in Table 1:

[0045] Table 1 Simulation parameters under one working condition

[0046] <![CDATA[U in > D Turn ratio <![CDATA[f s > <![CDATA[f Boost > <![CDATA[C in > <![CDATA[L r > <![CDATA[C r > <![CDATA[L m > <![CDATA[I g Effective value]]> Operating condition 1 25V 0.35 4:21 150000 hz 100000 hz 500 uF 46.1 uH 55 nF 180 uH 1.62A

[0047] Among them, f s is the frequency of the dual - active - bridge converter of the main - power circuit, and f boost is the frequency of the Boost converter of the partial - power circuit.

[0048] The circuit topology in Mode 1 [t0 - t1] is as follows Figure 3 shown:

[0049] At time t0, the AC - side power transistor S5 is turned on, and the DC - side power transistors S1 and S4 are turned on. Energy is transferred from the DC - side to the AC - side;

[0050] The circuit topology in Mode 2 [t1 - t2] is as follows Figure 4 shown:

[0051] At time t1, the DC - side power transistors S1 and S4 are turned off, entering the dead - time. At this time, if the inductor current direction is as shown in the figure, the inductor current charges the junction capacitors of S1 and S4 to voltage V dc , and discharges the junction capacitors of S2 and S3 to 0. If the inductor current is in the reverse direction or 0, the soft - switching condition will be lost;

[0052] The circuit topology in Mode 3 [t2 - t3] is as follows Figure 5 shown:

[0053] During the dead - time, the body diodes of S2 and S3 conduct naturally. The inductor current loop passes through the body diodes of S2 and S3, creating conditions for zero - voltage turn - on;

[0054] The circuit topology in Mode 4 [t3 - t4] is as follows Figure 6 shown:

[0055] At this time, the AC - side power transistor S5 is still on, and the DC - side power transistors S2 and S3 are turned on with zero voltage. Energy is transferred from the DC - side to the AC - side;

[0056] The circuit topology in Mode 5 [t4 - t5] is as follows Figure 7 shown:

[0057] At this time, the AC - side power transistor S5 is turned off, entering the AC - side dead - time. At this time, if the inductor current direction is as shown in the figure, the inductor current charges the junction capacitor of S5 to voltage u g , and discharges the junction capacitor of S7 to 0. If the inductor current is in the reverse direction or 0, the soft - switching condition will be lost;

[0058] The circuit topology in Mode 6 [t5 - t6] is as follows Figure 8 shown:

[0059] During the dead - time, the body diode of S7 conducts naturally. The inductor current loop passes through the body diode of S7, creating conditions for zero - voltage turn - on;

[0060] The circuit topology in Mode 7 [t5 - t6] is as follows Figure 9 shown:

[0061] The power transistor S7 turns on with zero voltage and enters the symmetric second half cycle. The principle of the second half cycle mode is similar to that of the first half cycle and will not be elaborated here.

[0062] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A high-efficiency wide-gain combined grid-connected inverter for a photovoltaic power generation grid-connected system, characterized in that: The inverter comprises a DC voltage source U cd , Boost output voltage stabilizing capacitor C in , Boost converter ninth power tube S9, first diode D1, energy storage inductor L, first power tube S1, second power tube S2, third power tube S3, fourth power tube S4, fifth power tube S5, sixth power tube S6, seventh power tube S7, eighth power tube S8, excitation inductor L s , series resonant capacitor C r , series resonant inductor L r , first capacitor C1, second capacitor C2, AC filter inductor L ac , AC grid side voltage source V g ; The inverter is composed of a main power circuit dual active bridge converter and a partial power circuit Boost converter. The dual active bridge converter is composed of an H-bridge circuit, a resonant network, and a high-frequency transformer bidirectional switch. The Boost converter and the dual active bridge converter share a DC voltage source U cd , the output side of the Buck converter is connected to the first arm of the H bridge.

2. The high-efficiency wide-gain combined grid-connected inverter for the photovoltaic power generation grid-connected system according to claim 1, characterized in that: The high-frequency transformer primary circuit of the main power circuit dual active bridge converter includes a transformer primary winding N P , H-bridge circuit, DC voltage source U cd and DC link capacitor C cd , where the H-bridge circuit consists of a first power tube S1 with a junction capacitor and an anti-parallel diode, a second power tube S2, a third power tube S3, and a fourth power tube S4; the drain of the first power tube S1 is connected to the DC side capacitor C in , the drain of the second power tube S2 is connected to the DC side power supply U cd The sources of the third power tube S3 and the fourth power tube S4 are connected to the DC voltage source U cd of the negative electrode.

3. The high-efficiency wide-gain combined grid-connected inverter for the photovoltaic power generation grid-connected system according to claim 1, characterized in that: The secondary circuit of the main power circuit dual active bridge converter includes a secondary winding N of a high frequency transformer S , by the excitation inductance L s , series resonant capacitor C r , series resonant inductor L r The LLC resonant cavity is composed of two sets of bidirectional switches composed of a fifth power tube S5, a sixth power tube S6, a seventh power tube S7, and an eighth power tube S8 with a junction capacitor and an anti-parallel diode; the secondary winding N of the high-frequency transformer S The same name terminated resonant inductor L r , secondary winding N S Differential termination series resonant capacitor C r , resonant inductor L r and resonant capacitor C r The source of the sixth power tube and the midpoint between the first capacitor C1 and the second capacitor C2 are connected respectively, and the drain of the fifth power tube S5 and the upper end of the first capacitor C1 are connected to the filter inductor L ac The drain of the eighth power tube S8 and the lower end of the second capacitor C2 are connected to the AC voltage source V g Lower end.

4. The high-efficiency wide-gain combined grid-connected inverter for the photovoltaic power generation grid-connected system according to claim 1, characterized in that: The boost converter of the partial power circuit and the dual active bridge converter share a DC voltage source U in The output side of the Boost converter is connected to the first bridge arm composed of the first power tube S1 and the second power tube S2 in the H bridge; the partial power circuit Boost converter includes an energy storage inductor L, a DC side capacitor C in , the ninth power tube S9 of the anti-parallel diode, the first diode D1; the left end of the energy storage inductor L is connected to the DC voltage source U cd The positive electrode and the drain of the third power tube S3, the right end of the energy storage inductor L is connected to the drain of the ninth power tube and the anode of the first diode D1; the cathode of the first diode D1 is connected to the DC side capacitor C in The positive electrode and the drain of the first power tube S1, the DC side capacitor C in The negative pole is connected to the DC voltage source U cd The cathode, the source of the second power tube S2, the source of the fourth power tube S4, and the source of the ninth power tube S9.

5. The high-efficiency wide-gain combined grid-connected inverter for the photovoltaic power generation grid-connected system according to claim 1, characterized in that: The switching frequency f of the main power circuit dual active bridge converter s Work at the resonant frequency, the duty cycle is fixed; the duty cycle of the first power tube S1 and the fourth power tube S4 of the primary side H-bridge circuit is 0.5 and the same drive is adopted, the duty cycle of the second power tube S2 and the third power tube S3 is 0.5 and the same drive is adopted, the first power tube S1 and the second power tube S2 are complementary conduction, the third power tube S3 and the fourth power tube S4 are complementary conduction; the sixth power tube S6 and the eighth power tube S8 are connected to the AC voltage source V g The positive half cycle is always on, and the AC voltage source V g The duty cycle of the negative half cycle is 0.5 and they are complementary. The fifth power tube S5 and the seventh power tube S7 are connected to the AC voltage source V g The negative half cycle is always on, and the AC voltage source V g The duty cycle of the positive half cycle is 0.5 and they are complementary to each other. There is an external phase shift angle D1 between the first power tube S1 and the fifth power tube S5. The resonant frequency of the LLC resonant cavity is: where f r is the resonant frequency, C r is the series resonant capacitor, L r is the series resonant inductor.

6. The high-efficiency wide-gain combined grid-connected inverter for the photovoltaic power generation grid-connected system according to claim 1, characterized in that: The partial power circuit Boost converter adopts a variable duty cycle modulation strategy, and the output voltage U in for: Where D is the duty cycle of the boost converter in the power circuit, V dc is a DC voltage source.

7. The high-efficiency wide-gain combined grid-connected inverter for the photovoltaic power generation grid-connected system according to claim 1, characterized in that: When the first power tube S1 and the fourth power tube S4 of the primary H-bridge circuit are driven in half a switching cycle, the midpoint voltage U AB is the output voltage U of the boost converter of the partial power circuit in When the second power tube S2 and the third power tube S3 are driven in the other half of the switching cycle, the DC side bridge arm midpoint voltage U AB is the DC voltage source U dc The opposite number of can be summarized as: Where V dc is a DC voltage source, and D is the duty cycle of the boost converter of the partial power circuit.

8. The high-efficiency wide-gain combined grid-connected inverter for the photovoltaic power generation grid-connected system according to claim 7, characterized in that: When the first power tube S1 and the fourth power tube S4 of the primary H-bridge circuit are driven during the switching cycle, the midpoint voltage U CD The magnitude is half of the instantaneous value of the AC voltage source on the AC side. In order to realize the energy transmission from the DC side to the AC side, the DC side bridge arm midpoint voltage U AB The AC side bridge arm midpoint voltage U must be ahead CD .

9. The high-efficiency wide-gain combined grid-connected inverter for the photovoltaic power generation grid-connected system according to claim 8, characterized in that: When the first power tube S1 and the fourth power tube S4 of the primary H-bridge circuit are driven during the switching cycle, the input current i g The value of the shift phase D1 is related to the AC output current i g The control of the input current i g is the integral of the power tube current in this cycle, and the expression is: where i g is the AC current output by the inverter, I ref is the output current reference value, i lm is the current flowing through the magnetizing inductance L m of current.

10. The high-efficiency wide-gain combined grid-connected inverter for the photovoltaic power generation grid-connected system according to claim 1, characterized in that: The voltage conversion ratio M n The expression is: Among them, u g is the instantaneous value of the AC voltage source, and n is the primary to secondary turns ratio.