A single-phase three-level heterogeneous hybrid bridge arm type energy storage inverter
By using the heterogeneous hybrid bridge arm structure and independent diode design of the single-phase three-level heterogeneous hybrid bridge arm type energy storage inverter, the problem of unstable output of new energy power generation is solved, the three-level function is realized, the voltage and current stress of the switching tube is reduced, the life is extended, and the power conversion efficiency and system reliability are improved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHINA THREE GORGES UNIV
- Filing Date
- 2022-11-09
- Publication Date
- 2026-05-08
AI Technical Summary
The randomness and volatility of the output power of existing new energy power generation lead to low efficiency of energy storage inverters, high voltage stress on switching transistors, short lifespan, high losses, and the risk of shoot-through of bridge arm power switching transistors.
A single-phase three-level heterogeneous hybrid bridge arm type energy storage inverter is adopted. The heterogeneous hybrid bridge arm structure increases the power flow path, uses electrolytic capacitors with equal capacitance values and independent diodes, reduces the voltage and current stress of the switching transistors, avoids the risk of bridge arm shoot-through, and improves the power conversion efficiency.
It achieves three-level functionality, reduces voltage and current stress on the switching transistor, extends the lifespan of the switching transistor, reduces losses, improves power conversion efficiency, and enhances system reliability.
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Figure CN115912960B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power electronic energy conversion, specifically a single-phase three-level heterogeneous hybrid bridge arm type energy storage inverter. Background Technology
[0002] With the increasing severity of the traditional fossil fuel crisis and environmental problems, the government is continuously increasing its investment and support for the new energy industry, and new energy power generation technology is developing rapidly. However, due to the influence of natural conditions, the output power of new energy power generation has considerable randomness and fluctuation. Energy storage inverter technology can effectively solve the problem of unstable power output of new energy power generation, playing an important role in the effective utilization of new energy.
[0003] Compared to traditional two-level inverters, three-level inverters have many advantages, such as lower voltage stress on the switching transistors, which facilitates transistor selection and extends transistor lifespan; lower output harmonic content, allowing the use of filter inductors with smaller inductance, thereby reducing overall cost and losses; and lower switching losses and higher power conversion efficiency. Summary of the Invention
[0004] This invention provides a single-phase three-level heterogeneous hybrid bridge-arm type energy storage inverter. This inverter employs a heterogeneous hybrid bridge-arm structure, increasing the power flow path and improving the stability of the topology circuit. Compared to a two-level inverter, this invention increases the number of output levels, reduces the voltage and current stress on the switching transistors, decreases switching losses, and improves energy conversion efficiency.
[0005] The technical solution adopted in this invention is as follows:
[0006] A single-phase three-level heterogeneous hybrid bridge arm type energy storage inverter includes switching transistors S1, S2, S3, S4, S5, S6, and S7, diodes D1, D2, and D3, inductors L1 and L2, and capacitors C1 and C2.
[0007] The positive terminal of capacitor C1 is connected to the drain of switching transistor S1, and the connection node forms the terminal p.
[0008] The negative terminal of capacitor C2 is connected to the source of switch S7, and the connection node forms the terminal m.
[0009] The negative terminal of capacitor C1 is connected to the positive terminal of capacitor C2 and the drain of switching transistor S4, and the connection node forms the terminal n.
[0010] The source of the switching transistor S4 is connected to the anode of diode D1 and the cathode of diode D2, and the connection node forms the terminal e.
[0011] The drain of switch S7 is connected to the source of switch S5, the source of switch S6, the anode of diode D2, and the anode of diode D3, and the connection node forms the endpoint d.
[0012] The source of switch S1 is connected to the drain of switch S2 and the drain of switch S3 respectively, and their connection nodes form the endpoint c.
[0013] The source of the switching transistor S2 is connected to one end of the inductor L1 and the cathode of the diode D1, and the connection node forms the endpoint a.
[0014] The source of the switching transistor S3 is connected to the other end of the inductor L2 and the cathode of the diode D3, and the connection node forms the endpoint b.
[0015] The drain of the switching transistor S5 is connected to the load R respectively. L One end, the other end of inductor L1;
[0016] The drain of the switching transistor S6 is connected to the load R respectively. L The other end is one end of inductor L2.
[0017] In this energy storage inverter, the switching transistor S2, diode D1, and diode D2 are connected to form a heterogeneous hybrid bridge arm. In this heterogeneous hybrid bridge arm, diodes D1 and D2 are connected to the switching transistor S4, providing an additional power flow path.
[0018] In this energy storage inverter, endpoints p and m are connected to the output side of the bidirectional DC-DC converter, and the input side of the bidirectional DC-DC converter is connected to the energy storage battery.
[0019] In this energy storage inverter, capacitors C1 and C2 are two electrolytic capacitors with equal capacitance values, each bearing the DC voltage U on the output side of the bidirectional DC-DC converter. s Half of that, which is the level ±1 / 2U s This provides the conditions for its implementation.
[0020] When the energy storage inverter is working normally, it includes the following six operating modes:
[0021] Operating mode 1: The circuit operates at output voltage u o During the positive half-cycle, switches S1, S2, S6, and S7 are turned on, while the remaining switches are turned off. The energy storage battery supplies power to inductor L1 and load R. L Power supply, inductor L1 current i L1 Linear increase, output current i o =i L1 In this mode, the voltage u between endpoints a and b is... ab =+U s .
[0022] Operating mode 2: The circuit operates at output voltage u oDuring the positive half-cycle, switches S4, S6, and S7 are turned on, while the remaining switches are turned off. The energy storage battery charges capacitor C1, causing the voltage across capacitor C1 to rise. Capacitor C2 then charges inductor L1 and load R. L With power supply, the voltage across capacitor C2 drops, and the current i in inductor L1 increases. L1 Linear increase, output current i o =i L1 In this mode, the voltage u between endpoints a and b is... ab =+1 / 2U s .
[0023] Operating mode 3: The circuit operates at output voltage u o During the positive half-cycle, switch S6 is turned on, and the other switches are turned off. The energy storage battery charges capacitors C1 and C2, causing the voltages of capacitors C1 and C2 to rise, and the current i in inductor L1 to increase. L1 The current flows through diodes D2 and D1 and is distributed to the load R. L Power supply, inductor L1 current i L1 Linear decrease, output current i o =i L1 In this mode, the voltage u between endpoints a and b is... ab =0.
[0024] Operating mode four: The circuit operates at output voltage u o During the negative half-cycle, switch S5 is turned on, and the other switches are turned off. The energy storage battery charges capacitors C1 and C2, causing the voltages of capacitors C1 and C2 to rise, and the current i in inductor L2 increases. L2 Freewheeling current through diode D3 and flowing to load R L Power supply, inductor L2 current i L2 Linear decrease, output current i o =-i L2 In this mode, the voltage u between endpoints a and b is... ab =0.
[0025] Operating mode 5: The circuit operates at output voltage u o During the negative half-cycle, switches S1, S3, and S5 are turned on, while the remaining switches are turned off. The energy storage battery charges capacitor C2, causing the voltage across capacitor C2 to rise. Capacitor C1 then charges inductor L2 and load R. L With power supply, the voltage across capacitor C1 drops, and the current i in inductor L2 increases. L2 Linear increase, output current i o =-i L2 In this mode, the voltage u between endpoints a and b is... ab =-1 / 2U s .
[0026] Operating mode six: The circuit operates at output voltage uo During the negative half-cycle, switches S1, S3, S5, and S7 are turned on, while the remaining switches are turned off. The energy storage battery supplies power to inductor L2 and load R. L Power supply, inductor L2 current i L2 Linear increase, output current i o =-i L2 In this mode, the voltage u between endpoints a and b is... ab =-U s .
[0027] This invention discloses a single-phase three-level heterogeneous hybrid bridge-arm type energy storage inverter, with the following technical advantages:
[0028] 1) The circuit of the energy storage inverter of the present invention adopts a heterogeneous hybrid bridge arm structure. In this heterogeneous hybrid bridge arm structure, diodes D1 and D2 are connected to the switching transistor S4, which increases the power flow path and improves the utilization rate of components.
[0029] 2) The circuit of the energy storage inverter of the present invention has a three-level function. Compared with the traditional two-level inverter, it reduces the voltage and current stress of the switching transistor, extends the service life of the switching transistor, reduces switching losses, and improves the power conversion efficiency.
[0030] 3) Compared with the traditional bridge inverter circuit, the circuit of the energy storage inverter of this invention does not have the risk of shoot-through of the bridge arm power switch, which improves reliability. At the same time, the freewheeling current does not pass through the body diode of the switch, but through an independent diode, eliminating the reverse recovery problem of the body diode of the switch and reducing losses.
[0031] 4) The circuit of the energy storage inverter of the present invention uses switching transistors S1 and S7 to clamp the input DC side voltage, thereby improving the working reliability of the inverter. Attached Figure Description
[0032] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0033] Figure 1 This is a diagram of the main topology of a single-phase three-level heterogeneous hybrid bridge arm type energy storage inverter according to the present invention.
[0034] Figure 2 This is a schematic diagram of the working mode of a single-phase three-level heterogeneous hybrid bridge arm type energy storage inverter according to the present invention;
[0035] Figure 3 This is a schematic diagram of the second working mode of a single-phase three-level heterogeneous hybrid bridge arm type energy storage inverter according to the present invention;
[0036] Figure 4 This is a schematic diagram of the three working modes of a single-phase three-level heterogeneous hybrid bridge arm type energy storage inverter according to the present invention;
[0037] Figure 5 This is a schematic diagram of the fourth working mode of a single-phase three-level heterogeneous hybrid bridge arm type energy storage inverter according to the present invention;
[0038] Figure 6 This is a schematic diagram of the fifth working mode of a single-phase three-level heterogeneous hybrid bridge arm type energy storage inverter of the present invention;
[0039] Figure 7 This is a schematic diagram of the sixth working mode of a single-phase three-level heterogeneous hybrid bridge arm type energy storage inverter according to the present invention.
[0040] Figure 8 This diagram shows the six operating modes of the switching transistors S1 to S7 in the circuit of this invention.
[0041] Figure 9 This is a diagram showing the pulse signal distribution for the switching transistors S1 to S7 in the circuit of this invention.
[0042] Figure 10 The output voltage u of the circuit of this invention in steady state o and output current i o Waveform diagram.
[0043] Figure 11 The circuit of this invention provides the current i flowing through inductor L1 in steady state. L1 Waveform diagram.
[0044] Figure 12 The circuit of this invention provides the current i flowing through inductor L2 in steady state. L2 Waveform diagram.
[0045] Figure 13 The voltage u between terminals a and b in the circuit of this invention under steady state. ab Waveform diagram.
[0046] Figure 14 The voltage u across capacitors C1 and C2 in the circuit of this invention under steady state. c1 u c2 Waveform diagram. Detailed Implementation
[0047] like Figure 1 As shown, a single-phase three-level heterogeneous hybrid bridge-arm type energy storage inverter includes an energy storage battery, a bidirectional DC-DC converter, switching transistors S1 to S7, diodes D1 and D2, inductors L1 and L2, and capacitors C1 and C2; the connection relationships between the components are as follows:
[0048] The positive terminal of capacitor C1 is connected to the drain of switching transistor S1, and the connection node forms the terminal p.
[0049] The negative terminal of capacitor C2 is connected to the source of switch S7, and the connection node forms the terminal m.
[0050] The negative terminal of capacitor C1 is connected to the positive terminal of capacitor C2 and the drain of switching transistor S4, and the connection node forms the terminal n.
[0051] The source of the switching transistor S4 is connected to the anode of diode D1 and the cathode of diode D2, and the connection node forms the terminal e.
[0052] The drain of switch S7 is connected to the source of switch S5, the source of switch S6, the anode of diode D2, and the anode of diode D3, and the connection node forms the endpoint d.
[0053] The source of switch S1 is connected to the drain of switch S2 and the drain of switch S3 respectively, and their connection nodes form the endpoint c.
[0054] The source of the switching transistor S2 is connected to one end of the inductor L1 and the cathode of the diode D1, and the connection node forms the endpoint a.
[0055] The source of the switching transistor S3 is connected to the other end of the inductor L2 and the cathode of the diode D3, and the connection node forms the endpoint b.
[0056] The drain of the switching transistor S5 is connected to the load R respectively. L One end, the other end of inductor L1;
[0057] The drain of the switching transistor S6 is connected to the load R respectively. L The other end is one end of inductor L2.
[0058] In the inverter topology circuit of this invention, the switch S2, diode D1, and diode D2 are connected to form a heterogeneous hybrid bridge arm. Diodes D1 and D2 in this bridge arm are connected to the switch S4, and the voltage is ±1 / 2U. s The implementation of the voltage levels provides a power flow path, ensuring the realization of the three-level function of the invented inverter.
[0059] In the inverter topology circuit of this invention, capacitors C1 and C2 are two electrolytic capacitors with equal capacitance values, each capacitor bearing 1 / 2U. s The voltage is ±1 / 2U. s The implementation of voltage levels provides the necessary conditions.
[0060] The specific experimental parameters of the circuit of this invention are as follows:
[0061] Output AC voltage u o The effective value is 220V, the frequency is 50Hz, and the DC voltage U on the output side of the bidirectional DC-DC converter is... s The voltage is 400V, the capacitors C1 and C2 are 4700μF, the inductors L1 and L2 are 3mH, the switching frequency is 20kHz, and the load R is...L The resistance is 80Ω.
[0062] A single-phase three-level heterogeneous hybrid bridge-arm type energy storage inverter has the following six operating modes during normal operation:
[0063] like Figure 2 As shown, operating mode one: the circuit operates at output voltage u o During the positive half-cycle, switches S1, S2, S6, and S7 are turned on, while the remaining switches are turned off. The energy storage battery supplies power to inductor L1 and load R. L Power supply, inductor L1 current i L1 Linear increase, output current i o =i L1 In this mode, the voltage u between endpoints a and b is... ab =+U s .
[0064] like Figure 3 As shown, operating mode two: the circuit operates at output voltage u o During the positive half-cycle, switches S4, S6, and S7 are turned on, while the remaining switches are turned off. The energy storage battery charges capacitor C1, causing the voltage across capacitor C1 to rise. Capacitor C2 then charges inductor L1 and load R. L With power supply, the voltage across capacitor C2 drops, and the current i in inductor L1 increases. L1 Linear increase, output current i o =i L1 In this mode, the voltage u between endpoints a and b is... ab =+1 / 2U s .
[0065] like Figure 4 As shown, operating mode three: the circuit operates at output voltage u o During the positive half-cycle, switch S6 is turned on, and the other switches are turned off. The energy storage battery charges capacitors C1 and C2, causing the voltages of capacitors C1 and C2 to rise, and the current i in inductor L1 to increase. L1 The current flows through diodes D2 and D1 and is distributed to the load R. L Power supply, inductor L1 current i L1 Linear decrease, output current i o =i L1 In this mode, the voltage u between endpoints a and b is... ab =0.
[0066] like Figure 5 As shown, operating mode four: the circuit operates at output voltage u o During the negative half-cycle, switch S5 is turned on, and the other switches are turned off. The energy storage battery charges capacitors C1 and C2, causing the voltages of capacitors C1 and C2 to rise, and the current i in inductor L2 increases.L2 Freewheeling current through diode D3 and flowing to load R L Power supply, inductor L2 current i L2 Linear decrease, output current i o =-i L2 In this mode, the voltage u between endpoints a and b is... ab =0.
[0067] like Figure 6 As shown, operating mode five: the circuit operates at output voltage u o During the negative half-cycle, switches S1, S3, and S5 are turned on, while the remaining switches are turned off. The energy storage battery charges capacitor C2, causing the voltage across capacitor C2 to rise. Capacitor C1 then charges inductor L2 and load R. L With power supply, the voltage across capacitor C1 drops, and the current i in inductor L2 increases. L2 Linear increase, output current i o =-i L2 In this mode, the voltage u between endpoints a and b is... ab =-1 / 2U s .
[0068] like Figure 7 As shown, operating mode six: the circuit operates at output voltage u o During the negative half-cycle, switches S1, S3, S5, and S7 are turned on, while the remaining switches are turned off. The energy storage battery supplies power to inductor L2 and load R. L Power supply, inductor L2 current i L2 Linear increase, output current i o =-i L2 In this mode, the voltage u between endpoints a and b is... ab =-U s .
[0069] Figure 8 This diagram illustrates the six operating modes of the switching transistors S1 to S7 in the circuit of this invention. The on / off states of the switching transistors are represented by "1" and "0", where "1" indicates conduction and "0" indicates off. Figure 8 It can be seen that the circuit has three operating modes in both the positive and negative half-cycles. Among them, in the positive half-cycle, the output voltage u o >0, voltage u ab There are 0 and +U s / 2、+U s Three states; during the negative half-cycle, the output voltage u o <0, voltage u ab There are 0 and -U s / 2、-U s Three states.
[0070] Figure 9This is a pulse signal distribution diagram corresponding to the switching transistors S1 to S7 in the circuit of this invention, where the voltage u ab The range of change is divided into four sub-intervals, where interval 1 represents 0. ab ≤1 / 2U s Interval 2 represents 1 / 2U s ab ≤U s Interval 3 represents -1 / 2U s ab ≤0, the interval 4 represents -U s ab ≤-1 / 2U s Within one operating cycle, by continuously switching the switching states of each switching transistor, the voltage u is adjusted. ab The sequence of the changing intervals is: [interval 1] → [interval 2] → [interval 1] → [interval 3] → [interval 4] → [interval 3], thus achieving three levels.
[0071] Figure 10 The output voltage u of the circuit of this invention in steady state o and output current i o Waveform diagram, for easy observation of current i o With voltage u o The relationship between current i o After multiplying the original value by a gain of 10, and then comparing it with the voltage u... o Comparing within the same oscilloscope window, from Figure 10 It can be seen that the voltage u o With current i o The waveforms all maintain good sinusoidal characteristics.
[0072] Figure 11 The circuit of this invention provides the current i flowing through inductor L1 in steady state. L1 Waveform diagram, from Figure 11 It can be seen that inductor L1 only has current flowing through it during the positive half of the operating cycle, which is consistent with the theoretical analysis.
[0073] Figure 12 The circuit of this invention provides the current i flowing through inductor L2 in steady state. L2 Waveform diagram, from Figure 12 It can be seen that inductor L2 only has current flowing through it during the negative half-cycle, which is consistent with the theoretical analysis.
[0074] Figure 13 The voltage u between terminals a and b in the circuit of this invention under steady state. ab Waveform diagram, from Figure 13 It can be seen that during the positive half-cycle, the voltage u ab There are three states: 0V, 200V, and 400V. During the negative half-cycle, the voltage u...ab It has three states: 0, -200V, and -400V, which conforms to the working characteristics of a three-level circuit, proving that the invented inverter has a three-level function.
[0075] Figure 14 The voltage u across capacitors C1 and C2 in the circuit of this invention under steady state. c1 u c2 Waveform diagram, from Figure 14 It can be seen that the voltage u c1 and u c2 Maintaining dynamic balance at around 200V proves that the invented inverter has the characteristic of capacitor voltage self-balancing.
[0076] Compared to traditional bridge inverters, the single-phase three-level heterogeneous hybrid bridge arm energy storage inverter of this invention does not have the risk of shoot-through of bridge arm power switches or the reverse recovery problem of power switch body diodes, thus improving operational reliability. At the same time, compared to traditional two-level inverters, this inverter increases the number of output levels, reduces voltage and current stress on the switching transistors, reduces switching losses, and improves power conversion efficiency.
Claims
1. A single-phase three-level heterogeneous hybrid bridge-arm type energy storage inverter, comprising switching transistors S1, S2, S3, S4, S5, S6, and S7, diodes D1, D2, and D3, inductors L1 and L2, and capacitors C1 and C2; characterized in that: The positive terminal of capacitor C1 is connected to the drain of switching transistor S1, and the connection node forms the terminal p. The negative terminal of capacitor C2 is connected to the source of switch S7, and the connection node forms the terminal m. The negative terminal of capacitor C1 is connected to the positive terminal of capacitor C2 and the drain of switching transistor S4, and the connection node forms the terminal n. The source of the switching transistor S4 is connected to the anode of diode D1 and the cathode of diode D2, and the connection node forms the terminal e. The drain of switch S7 is connected to the source of switch S5, the source of switch S6, the anode of diode D2, and the anode of diode D3, and the connection node forms the endpoint d. The source of switch S1 is connected to the drain of switch S2 and the drain of switch S3 respectively, and their connection nodes form the endpoint c. The source of the switching transistor S2 is connected to one end of the inductor L1 and the cathode of the diode D1, and the connection node forms the endpoint a. The source of the switching transistor S3 is connected to the other end of the inductor L2 and the cathode of the diode D3, and the connection node forms the endpoint b. The drain of the switching transistor S5 is connected to the load R respectively. L One end, the other end of inductor L1; The drain of the switching transistor S6 is connected to the load R respectively. L The other end is one end of inductor L2.
2. The single-phase three-level heterogeneous hybrid bridge arm type energy storage inverter according to claim 1, characterized in that: In this energy storage inverter, the switching transistor S2, diode D1, and diode D2 are connected to form a heterogeneous hybrid bridge arm. In this heterogeneous hybrid bridge arm, diodes D1 and D2 are connected to the switching transistor S4, providing an additional power flow path.
3. The single-phase three-level heterogeneous hybrid bridge arm type energy storage inverter according to claim 1, characterized in that: In this energy storage inverter, endpoints p and m are connected to the output side of the bidirectional DC-DC converter, and the input side of the bidirectional DC-DC converter is connected to the energy storage battery.
4. The single-phase three-level heterogeneous hybrid bridge arm type energy storage inverter according to claim 1, characterized in that: In this energy storage inverter, capacitors C1 and C2 are two electrolytic capacitors with equal capacitance values, each bearing the DC voltage U on the output side of the bidirectional DC-DC converter. s Half of it.
5. The single-phase three-level heterogeneous hybrid bridge arm type energy storage inverter according to any one of claims 1 to 4, characterized in that: When the energy storage inverter is working normally, it includes the following six operating modes: Operating mode 1: The circuit operates at the output voltage. u o During the positive half-cycle, switching transistors S1, S2, S6, and S7 are turned on, while the remaining switching transistors are turned off. The energy storage battery affects the inductor L1 and the load R. L Power supply, current in inductor L1 i L1 Linear increase, output current i o = i L1 In this mode, the voltage between endpoints a and b u ab =+U s ; Operating mode two: The circuit operates at the output voltage. u o During the positive half-cycle, switches S4, S6, and S7 are turned on, while the remaining switches are turned off; the energy storage battery charges capacitor C1, causing the voltage across capacitor C1 to rise, and capacitor C2 charges inductor L1 and load R. L With power supply, the voltage across capacitor C2 drops, and the current through inductor L1 increases. i L1 Linear increase, output current i o = i L1 In this mode, the voltage between endpoints a and b u ab =+1 / 2U s ; Operating mode 3: The circuit operates at the output voltage. u o During the positive half-cycle, switch S6 is turned on, and the other switches are turned off; the energy storage battery charges capacitors C1 and C2, causing the voltages of capacitors C1 and C2 to rise, and the current in inductor L1 to increase. i L1 The current flows through diodes D2 and D1 and is distributed to the load R. L Power supply, current in inductor L1 i L1 Linear decrease, output current i o = i L1 In this mode, the voltage between endpoints a and b u ab =0; Operating mode four: The circuit operates at the output voltage. u o During the negative half-cycle, switch S5 is turned on, and the other switches are turned off; the energy storage battery charges capacitors C1 and C2, causing the voltages of capacitors C1 and C2 to rise, and the current in inductor L2 to increase. i L2 Freewheeling current through diode D3 and flowing to load R L Power supply, inductor L2 current i L2 Linear decrease, output current i o =- i L2 In this mode, the voltage between endpoints a and b u ab =0; Operating mode 5: The circuit operates at the output voltage. u o During the negative half-cycle, switches S1, S3, and S5 are turned on, while the remaining switches are turned off; the energy storage battery charges capacitor C2, causing the voltage across capacitor C2 to rise, and capacitor C1 charges inductor L2 and load R. L With power supply, the voltage across capacitor C1 drops, and the current in inductor L2 increases. i L2 Linear increase, output current i o =- i L2 In this mode, the voltage between endpoints a and b u ab =-1 / 2U s ; Operating mode six: The circuit operates at the output voltage. u o During the negative half-cycle, switching transistors S1, S3, S5, and S7 are turned on, while the remaining switching transistors are turned off. Energy storage battery to inductor L2 and load R L Power supply, inductor L2 current i L2 Linear increase, output current i o =- i L2 In this mode, the voltage between endpoints a and b u ab =-U s .
Citation Information
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