CN115328263B - MPPT method of fuel cell based on double-sliding-mode-surface self-adaptive equivalent sliding mode control - Google Patents

MPPT method of fuel cell based on double-sliding-mode-surface self-adaptive equivalent sliding mode control Download PDF

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CN115328263B
CN115328263B CN202210960176.6A CN202210960176A CN115328263B CN 115328263 B CN115328263 B CN 115328263B CN 202210960176 A CN202210960176 A CN 202210960176A CN 115328263 B CN115328263 B CN 115328263B
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sliding mode
slip
control
fuel cell
sliding
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CN115328263A (en
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汪昊桢
秦灏
戚志东
陈豹
曹义航
袁文舒
姚楚豪
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Nanjing University of Science and Technology
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    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05FSYSTEMS FOR REGULATING ELECTRIC OR MAGNETIC VARIABLES
    • G05F1/00Automatic systems in which deviations of an electric quantity from one or more predetermined values are detected at the output of the system and fed back to a device within the system to restore the detected quantity to its predetermined value or values, i.e. retroactive systems
    • G05F1/66Regulating electric power
    • G05F1/67Regulating electric power to the maximum power available from a generator, e.g. from solar cell
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02MAPPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M3/00Conversion of dc power input into dc power output
    • H02M3/02Conversion of dc power input into dc power output without intermediate conversion into ac
    • H02M3/04Conversion of dc power input into dc power output without intermediate conversion into ac by static converters
    • H02M3/10Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M3/145Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M3/155Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
    • H02M3/156Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/30Hydrogen technology
    • Y02E60/50Fuel cells

Abstract

The invention discloses a maximum power point tracking method of a fuel cell based on double-sliding-mode-surface self-adaptive equivalent sliding mode control. First, a sliding mode surface of sliding mode control is designed according to the output characteristics of the proton exchange membrane fuel cell, wherein the sliding mode surface comprises a sliding mode surface for searching a maximum power point and a sliding mode surface for tracking and stabilizing in a maximum power output state. By using a dual slip-form surface, the complex optimization problem is converted into a traditional tracking problem, so that more flexibility is provided in the design of the slip-form surface. Secondly, a generalized supercoiled algorithm is selected as a control law, and an equivalent sliding mode control method is applied. And designing a sliding mode surface switching strategy, and judging whether the current working point is MPP by monitoring whether the operation condition is changed or is in the change process, and setting a state flag to switch the current sliding mode surface to cope with environmental change. The invention can greatly weaken buffeting and improve the tracking capability of MPP.

Description

MPPT method of fuel cell based on double-sliding-mode-surface self-adaptive equivalent sliding mode control
Technical Field
The invention belongs to the field of new energy, and particularly relates to a maximum power point tracking (Maximum Power Point Tracking, MPPT) method of a fuel cell based on double-sliding-mode-surface self-adaptive equivalent sliding mode control.
Background
Hydrogen is an emerging energy source, and Proton Exchange Membrane Fuel Cells (PEMFCs) are devices that utilize hydrogen to generate electricity. In order to improve the instability of the electric energy output, the reactant fuel hydrogen can be fully utilized, and the service life of the PEMFC is prolonged. MPPT technology is indispensable. At present, the MPPT technology is studied very much, but the situation discussion under the continuous change of the environment is less, and the MPPT technology is difficult to apply to practical situations.
Disclosure of Invention
The invention aims to provide an MPPT method of a proton exchange membrane fuel cell.
The technical scheme for realizing the purpose of the invention is as follows: an MPPT method of a fuel cell based on double-sliding-mode-surface self-adaptive equivalent sliding mode control comprises the following steps:
Step 1, establishing a PEMFC mechanism model according to the working characteristics and the working principle of the PEMFC;
step 2, acquiring output voltage, output current and load end voltage of the PEMFC by using a Boost converter, and establishing equivalent sliding mode control by using the acquired voltage and current;
step 3, designing an optimal sliding mode surface for tracking a maximum power point;
step4, designing a steady-state tracking sliding die surface;
step 5, designing a switching strategy of a sliding mode surface, and ensuring correct tracking of an algorithm under any condition;
and 6, designing self-adaptive equivalent sliding mode control by using a GSTA method.
Compared with the prior art, the invention has the remarkable advantages that:
1. The invention discovers and solves the oscillation problem of the sliding mode surface which is frequently used in the maximum power point tracking and takes the internal resistance of the fuel cell as an influence factor, and through the design of the double sliding mode surfaces and the application of a perfect switching strategy, one sliding mode surface is used for optimizing, and the other sliding mode surface is used for steady state tracking, so that buffeting is greatly weakened and stability is improved;
2. The invention provides a method suitable for tracking the self-adaptive gain of the maximum power point of the fuel cell, which partially weakens buffeting, improves tracking speed, reduces the gain of a controller and improves system stability and robustness.
3. The invention is not only suitable for the condition of stable external environment, but also can well cope with the continuously-changing working condition, tracks the maximum power point of the fuel cell in real time, and has strong applicability.
Drawings
Fig. 1 is a Boost converter topology and waveforms.
Fig. 2 is a flow chart of a sliding mode face switching strategy.
Fig. 3 is a block diagram of the MPPT system of the present invention.
Fig. 4 is a graph of fuel cell output power versus algorithm.
Fig. 5 is a graph of fuel cell load power versus algorithm to algorithm.
Fig. 6 is a graph of power change at the time of temperature change.
Fig. 7 is a fuel cell output power tracking path diagram.
Detailed Description
The invention will be further described with reference to the drawings and the specific embodiments.
The MPPT method of the fuel cell based on the double-sliding-mode-surface self-adaptive equivalent sliding mode control comprises the following steps:
step 1, a PEMFC mechanism model is established according to the working characteristics and the working principle of the PEMFC. The PEMFC has only one maximum power point.
Further, in the step 1, temperature and water content in the membrane are selected as input variables of a PEMFC mechanism model, and output voltage, current and power are selected as output variables. According to the output characteristic of the PEMFC, the output power characteristic curve is determined to be a convex curve, and the unique maximum point exists.
Step 2, collecting output voltage V in, output current I in(iL) and load terminal voltage V 0 of the PEMFC by using a Boost converter, wherein the output voltage V in, the output current I in(iL) and the load terminal voltage V 0 are used for designing equivalent sliding mode control, and the specific process is as follows:
step 2.1, the Boost converter is as shown in fig. 1, and a state space model of the Boost converter is built:
Wherein D is the duty cycle, X 1 is the state when the switching tube is on, and X 2 is the state when the switching tube is off.
Wherein i L is an inductor current, that is, an output current of the fuel cell, V 0 is a load voltage, i L_on、V0_on is an inductor current and a load voltage when the switching tube is turned on, and i L_off、V0_off is an inductor current and a load voltage when the switching tube is turned off, respectively.
The dynamic differential equation for the converter system is:
Wherein L, C, R is the inductance value, capacitance value and load size in the converter, respectively, and V in is the output voltage of the fuel cell.
Converting a state space model of a Boost converter into a general form of a nonlinear time-invariant system:
Step 2.2, equivalent sliding mode control:
a general nonlinear time-invariant system is described as follows:
when the desired sliding mode control is achieved:
The equivalent sliding mode control is as follows:
For a system with uncertainty and interference, the adopted control law is a combination of equivalent control and switching control, and the switching control is used for realizing robust control on the uncertainty and the external interference, and the control law is as follows:
u=ueq-v (11)
wherein v is the offset switching control.
Step 3, designing an optimal sliding mode surface s 1 for tracking a maximum power point, wherein the specific process is as follows:
Wherein P st、Ist、Vst is the stack power, the stack current, and the stack voltage, respectively.
Namely the slip form surface s 1 is:
And 4, designing a steady tracking sliding die surface s 2 according to the optimizing sliding die surface s 1, and reducing sliding die buffeting.
When the system is stable, s 1 = 0, obtainable according to equation (14):
r=-dr (17)
Where r is the instantaneous impedance of the fuel cell and dr is the impedance variation. The impedance change dr=0 when the system is stable in an ideal case, however, the internal resistance r must exist in any case in the fuel cell, and r+.0. The condition s=0 cannot be satisfied, and the system inevitably oscillates with the impedance r as an influence factor. Therefore, the slip mold surface s 2 needs to be designed to avoid the influence of the slip mold surface s 1 on the steady state, so that buffeting can be greatly weakened, and the tracking capability is improved. Meanwhile, the design of the double sliding mode surfaces also provides enough flexibility for the algorithm, the design of the sliding mode surface s 2 is very flexible, the simplest error sliding mode surface can be used, and the sliding mode surface can also be designed into a quasi-sliding mode or a terminal sliding mode and the like. Since the slip form surface s 1 is used for optimizing, the slip form surface s 2 releases the design constraint of the slip form surface s 1 to meet the optimizing function, and only the steady state needs to be tracked, the slip form surface s 2 can be described as:
s2=Iref-Ist (18)
When the sliding mode surface s 1 is used for tracking the maximum power point, the inductance current value at the moment is used as a reference current value I ref corresponding to the maximum power point to construct the sliding mode surface s 2.
And (3) combining the step (3) and the step (4) to obtain a double sliding mode surface as follows:
Step 5, designing a sliding mode surface switching strategy to ensure the correct tracking of the algorithm under any condition, wherein the specific process is shown in fig. 2:
The state flag is switched to the slip form surface s 1 when the state flag=0, and is switched to the slip form surface s 2 when the state flag=1. When the system does not track the MPP, the flag=0 is in an optimizing mode; when the system tracks the MPP, flag=1 is the steady state tracking mode. The operation condition of the PEMFC is changed or is in the process of change (namely, the environment is changed, the membrane water content is changed and the like), and the flag=0 is switched into an optimizing mode; when the operating conditions are stable and the MPP has been tracked, flag=1 switches to steady state tracking mode. According to the switching strategy, the effectiveness of the algorithm under any condition is ensured.
Wherein, whether the operating point reaches the MPP can be judged by whether s 1_old·s1_current is less than or equal to 0 (i.e. detecting s 1 =0). The inductance current value corresponding to the MPP can be obtained at the moment of detecting s 1 =0, and is used as the reference current I ref to construct a sliding mode surface s 2.
Step 6, designing an adaptive GSTA. GSTA is a second order sliding mode algorithm, is an expansion of Super-spiral algorithm (STA-Twisting Algorithm), has the main advantages of direct applicability to a relative 1-order system, does not need information of sliding variable time derivative, maintains the characteristics of a first order sliding mode, and is not interfered by output measurement noise and estimation error. The expression of GSTA is as follows:
Wherein the method comprises the steps of
S is a sliding mode variable, and t is time.
Then GSTA expansion is as
Where k 3 is the coefficient of the exponential approach and k 1(t)、k2 (t) is the variable gain.
An adaptive variable gain k 1(t)、k2 (t) according to the following relation:
where α 12, β, δ, ε >0 are gain parameters and δ is the desired convergence accuracy, which can be understood as the boundary layer thickness.
According to the formula (11), the global control law is the combined action of the equivalent control item and the switching control item, and is used for stabilizing the system, avoiding buffeting and enabling the system to converge to a specified target in a limited time. The global control law expression is as follows:
Wherein u n = -v, u e 0, 1.
The stability of the designed sliding mode MPPT method is proved, and the method is specifically described as follows:
System stability was verified using Lyapunov (Lyapunov) function:
The Lyapunov function V is constant for 0, v=0 if and only if s=0.
To ensure that V converges to zero in a finite time, its time derivativeMust be semi-negative. For the slip plane s 1、s2, the Lyapunov function stability proved as follows:
the PEMFC power-current characteristic curve is a convex curve, and the properties of the concave-convex curve are as follows: if the convex curve f (x) is second-order, the second-order derivative f "(x) is less than or equal to 0 and is constant. From this, it can be seen that the following relationship exists for the slip plane s 1
The following relationship exists for the slip plane s 2
From the equations (27) and (28), equation (29) is always true for the slide surface s 1、s2.
Considering three cases of s > 0, s=0 and s < 0 respectively, the slip form surface s 1、s2 is the same, and the relation between u n and s is as follows:
(a) When 0 < u < 1, there are
According to the formulas (30) and (31),This is true.
(B) When u=0, the number of the cells,
Wherein the method comprises the steps ofThe constant holds.
U=0 there are two cases:
according to the formulas (32) and (33), This is true.
(C) When u=1, the number of the cells,
U=1 there are two cases:
According to the formulas (34) and (35), This is true.
To sum up three conditions (a), (b) and (c)The constant holds. And because of the formula (33)Constant is established, so that
In summary, according to the Lyapunov theory, the stability of the slip plane s 1、s2 and the control law are both demonstrated.
Examples
The MPPT method of the fuel cell based on the double-sliding-mode surface self-adaptive equivalent sliding-mode control mainly comprises an MPPT system structure, double-sliding-mode surface selection, control law design, a self-adaptive gain method, sliding-mode surface switching strategy design and the like, and the specific process is as follows:
1) And analyzing the power generation characteristics of the PEMFC, and establishing a mechanism model. The PEMFC power-current characteristic has and only has one maximum value as a maximum value, i.e., a maximum power point.
2) Using a Boost converter, a state space model of the Boost converter is built. The output voltage V in, the output current i L and the load terminal voltage V 0 of the PEMFC are collected and used for the equivalent sliding mode control design.
3) Slip form surface for designing optimizing modeAnd the method is used for searching the maximum power point, and detecting whether the MPP is reached or not through s 1_old·s1_current is less than or equal to 0, so as to obtain a corresponding current value I ref.
4) The sliding mode surface s 2=Iref-Ist of the tracking mode is designed to attenuate steady-state sliding mode buffeting.
5) And a switching strategy of the sliding mode surface is designed to ensure the correct tracking of the algorithm under any condition. When the state flag is=0, the mode is switched to the optimizing mode, the current sliding mode surface is s 1, and when the state flag is=1, the mode is switched to the steady tracking mode, and the current sliding mode surface is s 2. When the system does not track the MPP, the flag=0 is in an optimizing mode; when the system tracks the MPP, flag=1 is the steady state tracking mode. The operation condition of the PEMFC is changed or is in the process of change (namely, the environment is changed, the membrane water content is changed and the like), and the flag=0 is switched into an optimizing mode; when the operation condition is stable, flag=1 is switched to the steady-state tracking mode. According to the switching strategy, the effectiveness of the algorithm under any condition is ensured.
6) And the GSTA control law is used for designing self-adaptive equivalent sliding mode control, so that the response speed is improved, the gain of the controller is reduced, and the robustness is improved.
7) The stability of the sliding mode MPPT method is proved through Lyapunov functions.
8) Simulation results
The MPPT system structure of the fuel cell is shown in fig. 3. By carrying out simulation analysis and verification on the MPPT method provided by the patent, and comparing the MPPT algorithm under the condition of load disturbance, fig. 4 and 5 show that the method has obvious advantages in the aspects of tracking speed and steady-state performance.
When the temperature change is slowly rising or falling as shown in fig. 6, the algorithm can still accurately track the maximum power point and stably work at the maximum power point. The curve of the output power tracking path of the fuel cell along with the temperature is shown in fig. 7, wherein the red curve is the tracking condition of the MPPT algorithm, and the other two curves are the power characteristic curves of the fuel cell at different temperatures. The temperature starts to linearly rise from 0.01s to 0.02s, the working point moves from A to B, the temperature linearly drops from 0.03s to 0.04s, and the working point moves from B to A, so that the change of the external environment and the operation condition can be responded in real time.
As can be seen from fig. 6 and 7, under the condition that the temperature is continuously changed, the improved sliding mode algorithm can well cope with the temperature change, can adjust and track the MPP in real time, and verifies the dynamic performance of the improved sliding mode algorithm. And (3) switching the sliding mode surface s 2 to the sliding mode surface s 1 at 0.01s to search MPP, and switching the sliding mode surface s 1 to the sliding mode surface s 2 to perform steady tracking when the system is stable after 0.02 s. And then, when the working environment of the system changes, switching to the sliding mode surface s 1 to search the MPP, and when the working environment is stable and unchanged and the system reaches the MPP in the current state, switching to the sliding mode surface s 2 to keep the maximum power output.

Claims (7)

1. The MPPT method of the fuel cell based on the double-sliding-mode-surface self-adaptive equivalent sliding mode control is characterized by comprising the following steps of:
Step 1, establishing a PEMFC mechanism model according to the working characteristics and the working principle of the PEMFC;
Step 2, acquiring output voltage, output current and load end voltage of the PEMFC by using a Boost converter, and establishing equivalent sliding mode control by using the acquired voltage and current, wherein the equivalent sliding mode control comprises the following specific steps of:
step 2.1, establishing a state space model of the Boost converter:
wherein D is the duty ratio, X 1 is the state when the switching tube is on, and X 2 is the state when the switching tube is off;
Wherein i L is an inductor current, V 0 is a load voltage, i L_on、V0_on is an inductor current and a load voltage when the switching tube is turned on, and i L_off、V0_off is an inductor current and a load voltage when the switching tube is turned off;
the dynamic differential equation for the converter system is:
wherein L, C, R is the inductance value, capacitance value and load size in the converter, and V in is the output voltage of the fuel cell;
converting a state space model of a Boost converter into a general form of a nonlinear time-invariant system:
Step 2.2, equivalent sliding mode control:
a general nonlinear time-invariant system is described as follows:
when the desired sliding mode control is achieved:
The equivalent sliding mode control is as follows:
For a system with uncertainty and interference, the adopted control law is a combination of equivalent control and switching control, and the switching control is used for realizing robust control on the uncertainty and the external interference, and the control law is as follows:
u=u eq -v (11), where v is the offset handover control;
step 3, designing an optimal sliding mode surface for tracking a maximum power point;
step4, designing a steady-state tracking sliding die surface;
step 5, designing a switching strategy of a sliding mode surface, and ensuring correct tracking of an algorithm under any condition;
and 6, designing self-adaptive equivalent sliding mode control by using a GSTA method.
2. The MPPT method of a fuel cell based on dual-slip-mode face adaptive equivalent slip-mode control of claim 1, wherein in step 1, temperature and water content in a membrane are selected as input variables of a PEMFC model, output voltage, current and power are selected as output variables, and according to the output characteristics of the PEMFC, an output power characteristic curve is a convex curve, and only one maximum power point exists.
3. The MPPT method of the fuel cell based on the dual-slip-plane adaptive equivalent slip-mode control as claimed in claim 1, wherein the optimizing slip-plane s 1 is designed in the step 3, specifically described as:
Wherein P st、Ist、Vst is pile power, pile current and pile voltage respectively;
Namely the slip form surface s 1 is:
4. the MPPT method of a fuel cell based on dual-slip-plane adaptive equivalent slip-mode control of claim 1, wherein the steady-state tracking slip-plane s 2 designed in step 4 is described as:
s2=Iref-Ist (15)
When the sliding mode surface s 1 is used for tracking the maximum power point, the inductance current value at the moment is used as a reference current value I ref corresponding to the maximum power point to construct the sliding mode surface s 2.
5. The MPPT method of the fuel cell based on the dual-slip-plane adaptive equivalent slip-mode control of claim 1, wherein the slip-plane switching strategy formulated in step 5 is specifically:
The state flag bit is switched to the sliding mode surface s 1 when the state flag bit is=0, the state flag bit is switched to the sliding mode surface s 2 when the state flag bit is=1, and the specific determination mode of flag bit=0 or flag bit=1 is as follows:
when the system does not track the MPP, the flag=0 is in an optimizing mode;
When the system tracks MPP, flag=1 is a steady state tracking mode;
the operation condition of the PEMFC is changed or is in a changing process, and the flag=0 is switched into an optimizing mode;
When the operating conditions are stable and the MPP has been tracked, flag=1 switches to steady state tracking mode.
6. The MPPT method of claim 5, wherein determining whether the operating point reaches the MPP is performed by determining whether s 1_old·s1_current is less than or equal to 0.
7. The MPPT method of a fuel cell based on dual-slip-plane adaptive equivalent slip-mode control of claim 1, wherein the specific method for designing the adaptive equivalent slip-mode control using GSTA method is:
the expression of GSTA is as follows:
Wherein the method comprises the steps of
S is a sliding mode variable, and t is time;
Then GSTA expansion is as
Where k 3 is the coefficient of the exponential approach, and k 1(t)、k2 (t) is the variable gain;
An adaptive variable gain k 1(t)、k2 (t) according to the following relation:
k2(t)=2εk1(t)
Wherein alpha 12, beta, delta, epsilon > 0 are gain parameters, delta is the expected convergence accuracy;
the global control law expression is as follows:
u=ueq+un
Wherein u n = -v, u e 0, 1.
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CN104298296A (en) * 2014-09-24 2015-01-21 上海电力学院 Fuel cell maximum power tracking control method
CN112421080A (en) * 2020-11-18 2021-02-26 上海恒劲动力科技有限公司 Power control system of proton exchange membrane fuel cell
CN113054842A (en) * 2021-03-22 2021-06-29 武汉博日电气自动化有限公司 Control method and system for DC/DC boost converter of fuel cell
CN114448238A (en) * 2022-01-14 2022-05-06 江苏大学 Boost converter control method based on adaptive second-order sliding mode

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Publication number Priority date Publication date Assignee Title
IT1393858B1 (en) * 2009-04-24 2012-05-11 Univ Degli Studi Salerno CONTROLLER EQUIPMENT FOLLOWING THE MAXIMUM POWER POINT OF AN ELECTRIC POWER GENERATION SYSTEM BASED ON PHOTOVOLTAIC SOURCES, CONTROL METHOD AND RELATIVE ELECTRIC POWER GENERATION SYSTEM.

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Publication number Priority date Publication date Assignee Title
CN104298296A (en) * 2014-09-24 2015-01-21 上海电力学院 Fuel cell maximum power tracking control method
CN112421080A (en) * 2020-11-18 2021-02-26 上海恒劲动力科技有限公司 Power control system of proton exchange membrane fuel cell
CN113054842A (en) * 2021-03-22 2021-06-29 武汉博日电气自动化有限公司 Control method and system for DC/DC boost converter of fuel cell
CN114448238A (en) * 2022-01-14 2022-05-06 江苏大学 Boost converter control method based on adaptive second-order sliding mode

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