Sliding-mode control-based current stress optimization method for dual-active bridge converter

Abstract

The invention belongs to the technical field of direct-current converters, and particularly relates to a sliding mode control-based dual-active bridge converter current stress optimization method, which is suitable for a direct-current micro-grid cluster interconnection converter which is a dual-active bridge converter. The method comprises the following specific steps: constructing mathematical models of transmission power and current stress of the dual active bridge converter in two signal modulation modes of single phase shift modulation and expanded phase shift modulation and soft switching characteristics under mode correspondence; constructing an order reduction model of the dual-active bridge converter; constructing an expression which takes the current stress as an optimization target and then adopts a Karush-Kuhn-Tucker (KKT) algorithm to solve an optimal phase shift ratio; and constructing a single-integral sliding mode controller and a double-integral sliding mode controller based on the double-active-bridge reduced-order model and carrying out equivalence. According to the method, single-integral and double-integral sliding mode control and single phase shift and expanded phase shift modulation are compared, and current stress optimization is adopted under integral sliding mode control, so that the converter has relatively good dynamic performance under integral sliding mode control, and meanwhile, current stress is relatively well reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of DC converters, and particularly relates to a method for optimizing the current stress of a dual-active-bridge converter based on sliding mode control, where the interconnection converter of a DC microgrid cluster is a dual-active-bridge converter. Background Art

[0002] With the penetration of distributed renewable energy sources (such as photovoltaic and wind power) and the development of DC power conversion technology, DC microgrids (DCMGs) have received increasing attention due to their advantages such as high efficiency, low cost, and flexible and convenient construction, and have gradually been regarded as an effective way to efficiently integrate distributed renewable energy sources. Compared with AC microgrids (ACMGs), DC microgrids do not need to consider factors such as system frequency, phase, and reactive power, so the control design is relatively simple, and grid connection and island (off-grid) operation can be flexibly achieved. In a DC microgrid cluster, using an interconnection converter to flexibly connect different power grids to form a DC microgrid system for power transmission is an important method to improve system efficiency and reliability.

[0003] There are mainly three interconnection forms of DC microgrids, namely: multi-bus interconnection, parallel connection to the bus, and direct interconnection. When the bus voltage levels are the same, the direct interconnection of buses has a simpler and more applicable structure; when the bus voltage levels are different, converters can be connected in parallel to the bus, and the failure of a single DC microgrid may cause the instability of the entire system; the multi-bus interconnection method can connect DC microgrids with the same or different voltage levels together through a bidirectional interconnection converter, and achieve power transmission between DC microgrids through different coordinated control strategies.

[0004] In the selection of interconnection converters, dual-active-bridge converters (DABs) are more widely used in DC microgrids, electric vehicles, and energy storage systems due to their high power density, electrical isolation ability, easy implementation of soft switching, and bi-directional energy transmission ability.

[0005] In a DAB converter, to improve the converter efficiency, it can be mainly carried out from three aspects, namely: reducing the converter current stress, decreasing the converter reverse power, and achieving soft-switching conduction of the switching tubes. Among the above three optimization methods, the duty cycle when the switching tubes of the DAB converter are conducting needs to be utilized. There are four commonly used modulation methods for DAB converters, single-phase-shift (SPS), double-phase-shift (DPS), extended-phase-shift (EPS), and triple-phase-shift (TPS).

[0006] Single-phase-shift modulation only has a phase-shift angle between the primary full-bridge and the secondary full-bridge, so the control is relatively simple, but there are certain limitations in optimizing the current stress and the circulating power. Extended-phase-shift modulation has a phase-shift angle within the primary full-bridge and another phase-shift angle between the primary full-bridge and the secondary full-bridge. Dual-phase-shift modulation has a phase-shift angle in each of the primary full-bridge and the secondary full-bridge. Extended-phase-shift and dual-phase-shift modulation have better control freedom, so the control can be designed according to the transmitted power to improve the efficiency of the converter. Triple-phase-shift modulation has three phase-shift angles, with higher control freedom but more complex control due to more degrees of freedom. The literature "Optimal Control Strategy of Dual Active Bridge DC-DC Converter with Extended Phase-Shift Modulation" combines the optimization of the steady-state and dynamic performance of the dual active bridge DC-DC converter and proposes in-loop direct power control to better optimize the current stress. The literature "Transmission Power Characteristics of Dual Active Bridge DC-DC Converter Based on Switching Combination Rules" divides the working states of the DAB into 12 modes by arbitrarily combining the three degrees of freedom of triple-phase-shift modulation, and compares with other three modulation methods by special assignment of the three degrees of freedom. The literature "Dynamic Modeling and Minimum Circulating Power Control of Bidirectional Full-Bridge DC-DC Converter Based on Dual Phase-Shift Modulation" analyzes the soft-switching constraint conditions and transmission power characteristics under dual-phase-shift modulation and proposes a minimum circulating power control strategy that meets the soft-switching constraint conditions. The literature "Multi-objective Optimal Control Method of Dual Active Full-Bridge DC-DC Converter Based on Extended Phase-Shift" proposes an optimized power control method while improving the efficiency and dynamic performance of the converter. By comprehensively analyzing the phase-shift amount relationship of the converter under extended phase-shift, the global optimal solution of the current stress is obtained to further improve the efficiency of the converter. The literature "Nonlinear Integral Sliding Mode Control Strategy for Voltage and Current of Dual Active Bridge DC-DC Converter" proposes a nonlinear integral sliding mode control strategy for DC voltage and charging current control. The state-space model of the converter is established under single-phase-shift modulation, and the smooth nonlinear saturation function is combined with the sliding mode control. The literature "Super-Twisting Sliding Mode Control of DC Microgrid DC-DC Converter Based on Circulating Power Optimization" proposes a super-twisting sliding mode control strategy combined with circulating power optimization under extended phase-shift modulation. The literature "Sliding Mode Control of Bi-directional Dual Active Bridge DC / DC Converters for Battery Energy Storage Systems" proposes a double-integral sliding mode control. Based on the harmonic model of the single-phase-shift modulation DAB converter, the mathematical model of nonlinear control design is derived, effectively reducing the error.The literature "Voltage and Current Regulations of Bidirectional Isolated Dual-Active-Bridge DC-DC Converters Based on a Double-Integral Sliding Mode Control" designs a new controller for the output voltage and current of the DAB converter using the double-integral sliding mode control theory to reduce the dynamic error and improve the dynamic response.

[0007] In summary, in order to improve the dynamic performance of the DAB converter and reduce losses, for the dual-active-bridge converter used as a bidirectional interconnection converter in the DC microgrid system, the inventors expect to design a method for optimizing the current stress of the dual-active-bridge converter based on sliding mode control. Summary of the Invention

[0008] The purpose of the present invention is to overcome the above problems existing in the traditional technology and provide a method for optimizing the current stress of a dual-active-bridge converter based on sliding mode control, where the DC microgrid cluster interconnection converter is a dual-active-bridge converter.

[0009] To achieve the above technical objectives and reach the above technical effects, the present invention is realized through the following technical solutions:

[0010] The present invention provides a method for optimizing the current stress of a dual-active-bridge converter based on sliding mode control, including the following steps:

[0011] S1. Construct a mathematical model of the basic transmission power and current stress of the dual-active-bridge converter under two signal modulation methods of single-phase-shift modulation and extended-phase-shift modulation, and the soft-switching characteristics corresponding to the modes.

[0012] S2. Construct a reduced-order model of the dual-active-bridge converter according to the mathematical model constructed in step S1.

[0013] S3. Construct a function equation with the current stress as the optimization objective and the transmission power and soft-switching characteristics as the constraint conditions, and use the Karush-Kuhn-Tucker (KKT) algorithm to solve the expression of the optimal phase-shift ratio.

[0014] S4. Construct a single-integral and double-integral sliding mode controller based on the reduced-order model of the dual-active-bridge and make them equivalent.

[0015] S5. Conduct a simulation experiment to verify the current stress optimization effect and the response speed optimization effect through simulation.

[0016] Furthermore, in step S1, under single-phase-shift modulation, the basic transmission power and current stress models and soft-switching characteristics of the dual-active-bridge converter are as follows:

[0017] In this mode, the inductor current i L is symmetric during the half cycle of the switch. The inductor current values at each moment within this half cycle are as follows:

[0018]

[0019] where: K = U1 / nU2;

[0020] The transmission power P sps and the maximum current stress i Lmax under the single-phase shift modulation mode are obtained from the average power algorithm and the symmetry within the half cycle, respectively, as follows:

[0021]

[0022] The duty cycle D and P sps are found to have the following relationship:

[0023]

[0024] Select a reference transmission power P N :

[0025]

[0026] Based on the current reference value i N and the normalized maximum current stress expression i Lmax ' after per-unit unification is as follows:

[0027]

[0028] i Lmax ' = 2(1 - K - 2D) (7)

[0029] Enabling all switching devices to achieve soft switching is an important method to reduce the switching losses of the converter and improve the transmission efficiency of the system. Under the single-phase shift modulation mode, from the analysis of the switching states of the dual-active-bridge converter, the requirements for achieving ZVS are:

[0030]

[0031] In summary, the conditions for achieving ZVS are:

[0032]

[0033] Furthermore, in step S1, under the extended phase shift modulation, the basic transmission power, current stress model, and soft switching characteristics of the dual-active-bridge converter are:

[0034] Mode 1: 0 ≤ D1 ≤ D2 ≤ 1;

[0035]

[0036] Where: K = U1 / nU2;

[0037] The transmission power P under the single-phase shift modulation mode is obtained from the average power algorithm and the symmetry within a half cycle eps1 and the maximum current stress i Lmax1 are respectively:

[0038]

[0039] Select the reference transmission power P N and the current reference value i N to perform the normalization and unification of the transmission power and the current stress, and obtain P' and i Lmax ' as follows:

[0040]

[0041] The condition for achieving ZVS in this mode is:

[0042]

[0043] Mode 2: 0 ≤ D2 ≤ D1 ≤ 1;

[0044]

[0045] Where: K = U1 / nU2;

[0046] The transmission power P under the single-phase shift modulation mode is obtained from the average power algorithm and the symmetry within a half cycle eps2 and the maximum current stress i Lmax2 are respectively:

[0047]

[0048] Select the reference transmission power P N and the current reference value i N to perform the normalization and unification of the transmission power and the current stress, and obtain P' and i Lmax ' as follows:

[0049]

[0050]

[0051] The condition for achieving ZVS in this mode is:

[0052]

[0053] Furthermore, in step S4, the dynamic equation of the output side of the dual-active-bridge converter is:

[0054] P C = P - P out = i out * u out (29)

[0055] Where P C represents the power on the output capacitor side, P is the transmission power after the converter passes through the secondary full-bridge, and P out is the output power, i out is the output current, and u out is the output voltage;

[0056] Combined with the dynamic equation of the output capacitor C, we get:

[0057]

[0058] For single-phase shift modulation, the following dynamic equation on the output side is obtained:

[0059]

[0060] For extended phase shift modulation, the following dynamic equation on the output side is obtained:

[0061]

[0062] Furthermore, in step S3, aiming at optimizing the current stress, the Karush-Kuhn-Tucker (KKT) algorithm is used to solve the expression of the optimal phase shift ratio:

[0063] The Lagrange function polynomial in Mode 1:

[0064]

[0065] The solved expression of the optimal phase shift duty cycle is:

[0066]

[0067] The corresponding transmission power P' is:

[0068]

[0069] The Lagrange function polynomial in Mode 2:

[0070]

[0071] The solved expression of the optimal phase shift duty cycle is:

[0072]

[0073] The corresponding transmission power P' is:

[0074]

[0075] Furthermore, in step S4, the sliding mode controller based on the reduced-order model of the dual active bridge is constructed as a single integral sliding mode controller;

[0076] Define the output voltage error where is the standard value of the output voltage, and u out is the output voltage; The sliding surface of Sliding-Mode-Control (SMC) is selected as follows:

[0077] S = k1e + k2∫edt (39)

[0078] where k1 and k2 are sliding mode gains that determine the dynamic convergence speed of the error; When moving on the sliding surface of S = 0:

[0079] k1e + k2∫edt = 0 (40)

[0080] The expression of the dynamic error is solved as:

[0081]

[0082] where K0 is the initial error of the output voltage at steady state. When k1 and k2 are greater than 0, the dynamic error will converge to zero as t approaches ∞;

[0083] The expression obtained by differentiating the sliding surface S is as follows:

[0084]

[0085] The equivalent sliding mode control law u eq is:

[0086]

[0087] where S represents the sliding surface, k3 is the sliding mode gain, and sgn(S) is the sign function expressed as:

[0088]

[0089] To reduce chattering, the sign function is replaced by the hyperbolic tangent function tanh, and the replaced equivalent control law is:

[0090]

[0091] where μ is a positive real number, is the boundary of the tanh function, E is the disturbance quantity, and f(x) and g(x) are time-varying nonlinear functions;

[0092] Obtained from the harmonic model of DAB

[0093]

[0094] Obtained:

[0095]

[0096] For single-phase shift modulation, substituting Equation (31) gives:

[0097]

[0098] Let Obtained:

[0099]

[0100] Let u eq = D(1 - D), and the equivalent duty cycle D of single-phase shift based on single-integral sliding mode control is obtained:

[0101]

[0102] For extended phase shift modulation, substituting Equation (32) gives:

[0103]

[0104] Let Then use u eq to replace M, where M is:

[0105]

[0106] The expression D2 related to u eq and the phase shift angle D1 under single-integral sliding mode control is obtained:

[0107]

[0108] Use the current stress optimization algorithm to first find the internal phase shift ratio D1 and then substitute it into the above formula to find D2;

[0109] Stability analysis:

[0110]

[0111] When g(x) and k2 are positive, the sliding mode controller is asymptotically stable.

[0112] Furthermore, in step S4, the sliding mode controller based on the reduced-order model of the dual active bridge is constructed as a double-integral sliding mode controller;

[0113] For single-phase shift modulation:

[0114] The dynamic error e is expressed as The double integral sliding mode surface is expressed as:

[0115] S = k1e + k2∫edt + k3∫∫edtdt (55)

[0116] After taking the derivative of S, we get:

[0117]

[0118] Let We obtain:

[0119]

[0120] The equivalent sliding mode control rate u eq is:

[0121]

[0122] Let u eq = D(1 - D) to obtain the equivalent duty cycle D of single-phase phase-shift modulation based on double integral sliding mode control:

[0123]

[0124] For extended phase-shift modulation, substituting Equation (32) gives:

[0125]

[0126] Let Then use u eq to replace M, where M is:

[0127]

[0128] We obtain the expression D2 related to u eq and the phase-shift angle D1 under single integral sliding mode control:

[0129]

[0130] Furthermore, in step S5, comparative simulation experiments are respectively carried out for only using PI control, single-phase phase-shift modulation based on single integral sliding mode control, single-phase phase-shift modulation based on double integral sliding mode control, extended phase-shift current stress optimization modulation based on single integral sliding mode control, and extended phase-shift current stress optimization modulation based on double integral sliding mode control.

[0131] The beneficial effects of the present invention are:

[0132] 1. The scheme for optimizing current stress based on sliding mode control designed by the present invention does not require complex modeling of the converter and is applicable to most traditional dual-active-bridge DC converter topologies, having universality.

[0133] 2. The single-integral sliding mode control has better dynamic performance than the DAB converter that only uses PI control. The double-integral sliding mode control has better dynamic response than the single-integral sliding mode control without a significant increase in control complexity.

[0134] 3. The extended phase-shift modulation current stress optimization strategy based on single-integral sliding mode control and the extended phase-shift modulation strategy based on double-integral sliding mode control significantly reduce the current stress while maintaining the better dynamic response of the integral sliding mode control compared to the ordinary PI control.

[0135] 4. Through the load jump simulation, it can be seen that as the load changes, the converter using integral sliding mode control has better dynamic performance than the ordinary PI control, and the extended phase-shift modulation current stress optimization strategy using integral sliding mode control inherits the excellent dynamic response ability.

[0136] Of course, it is not necessary for any product implementing the present invention to achieve all of the above advantages simultaneously. BRIEF DESCRIPTION OF THE DRAWINGS

[0137] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0138] Figure 1 It is a schematic diagram of the DC microgrid system structure containing an interconnected converter of the present invention;

[0139] Figure 2 It is the basic topology structure of the interconnected converter used in the present invention;

[0140] Figure 3 It is the waveform of the DAB converter under single-phase shift modulation (SPS);

[0141] Figure 4 It is the waveform of the DAB converter under extended phase-shift modulation (EPS);

[0142] Figure 5 It is the optimized control block diagram of the DAB converter;

[0143] Figure 6(a) is the output voltage waveform under PI control;

[0144] Figure 6(b) is the output voltage waveform of single-phase shift modulation based on single-integral sliding mode control;

[0145] Figure 6(c) is the output voltage waveform of single-phase shift modulation based on double-integral sliding mode control;

[0146] Figure 6(d) shows the optimized output voltage waveform of the extended phase-shifted current stress based on single-integral sliding mode control;

[0147] Figure 6(e) shows the optimized output voltage waveform of the extended phase-shifted current stress based on double-integral sliding mode control;

[0148] Figure 7(a) shows the transient output voltage waveform under PI control during load jump;

[0149] Figure 7(b) shows the transient output voltage waveform of single-phase-shift modulation during load jump based on single-integral sliding mode control;

[0150] Figure 7(c) shows the transient output voltage waveform of single-phase-shift modulation during load jump based on double-integral sliding mode control;

[0151] Figure 7(d) shows the optimized output voltage waveform of the extended phase-shifted current stress during load jump based on single-integral sliding mode control;

[0152] Figure 7(e) shows the optimized output voltage waveform of the extended phase-shifted current stress during load jump based on double-integral sliding mode control;

[0153] Figure 8(a) shows the steady-state waveform of inductor current under PI control;

[0154] Figure 8(b) shows the steady-state waveform of inductor current of single-phase-shift modulation based on single-integral sliding mode control;

[0155] Figure 8(c) shows the steady-state waveform of inductor current of single-phase-shift modulation based on double-integral sliding mode control;

[0156] Figure 8(d) shows the optimized steady-state waveform of inductor current of the extended phase-shifted current stress based on single-integral sliding mode control;

[0157] Figure 8(e) shows the optimized steady-state waveform of inductor current of the extended phase-shifted current stress based on double-integral sliding mode control;

[0158] Figure 9(a) shows the transient waveform of inductor current under PI control;

[0159] Figure 9(b) shows the transient waveform of inductor current of single-phase-shift modulation based on single-integral sliding mode control;

[0160] Figure 9(c) shows the transient waveform of inductor current of single-phase-shift modulation based on double-integral sliding mode control;

[0161] Figure 9(d) shows the optimized transient waveform of inductor current of the extended phase-shifted current stress based on single-integral sliding mode control;

[0162] Figure 9(e) shows the optimized transient waveform of inductor current of the extended phase-shifted current stress based on double-integral sliding mode control;

[0163] Figure 10(a) shows the transient waveform of the inductor current load after a jump under PI control;

[0164] Figure 10(b) shows the transient waveform of the inductor current load after a jump under single-phase-shift modulation based on single-integral sliding-mode control;

[0165] Figure 10(c) shows the transient waveform of the inductor current load after a jump under single-phase-shift modulation based on double-integral sliding-mode control;

[0166] Figure 10(d) shows the transient waveform of the inductor current load after a jump under extended-phase-shift current stress optimization based on single-integral sliding-mode control;

[0167] Figure 10(e) shows the transient waveform of the inductor current load after a jump under extended-phase-shift current stress optimization based on double-integral sliding-mode control. Detailed implementation manners

[0168] 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 the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0169] Embodiment

[0170] This embodiment provides a method for optimizing the current stress of a dual-active-bridge converter based on sliding-mode control, where the DC microgrid cluster interconnection converter is a dual-active-bridge converter, including the following steps:

[0171] S1. Construct a mathematical model of the dual-active-bridge converter regarding the basic transmission power and current stress under two signal modulation methods of single-phase-shift modulation and extended-phase-shift modulation, and the soft-switching characteristics corresponding to the modes:

[0172] S2. Construct a reduced-order model of the dual-active-bridge converter according to the mathematical model constructed in step S1;

[0173] S3. Construct a functional equation with the current stress as the optimization target and the transmission power and soft-switching characteristics as the constraint conditions, and use the Karush-Kuhn-Tucker (KKT) algorithm to solve the expression of the optimal phase-shift ratio;

[0174] S4. Construct single-integral and double-integral sliding-mode controllers based on the reduced-order model of the dual-active-bridge and make them equivalent;

[0175] S5. Conduct a simulation experiment to verify the current stress optimization effect and the response speed optimization effect through simulation.

[0176] The circuit topology of the dual-active-bridge converter is as shown in Figure 2 , where S1 to S4 are the primary-side switching transistors, S5 to S8 are the secondary-side switching transistors, C1 and C2 are the input and output capacitors respectively, T is a high-frequency transformer with a turns ratio of n:1, and an external series auxiliary inductor L is connected. U AB is the midpoint voltage of the full bridge on the primary side, and U CD is the midpoint voltage of the full bridge on the secondary side; K = U AB / nU CD , the input voltage is V in , the output voltage is u out , and i C is the current flowing through the output capacitor.

[0177] In the embodiment, the input voltage V in = 100V, the output voltage u out = 48V, and the transformer turns ratio n = 1.

[0178] In step S1, according to the quantity and magnitude relationship of the duty cycle, the power transfer model of the DAB converter can be divided into single-phase-shift modulation and extended phase-shift modulation, and the extended phase-shift modulation is divided into two types:

[0179] Mode 1: 0 ≤ D1 ≤ D2 ≤ 1;

[0180] Mode 2: 0 ≤ D2 ≤ D1 ≤ 1;

[0181] Figure 3 And Figure 4 are the working principle diagrams of the single-phase-shift modulation and extended phase-shift modulation respectively. In this embodiment, the working principle analysis and comparison are carried out taking the single-phase-shift and the second mode of the extended phase-shift as examples.

[0182] Since the inductor current i L is symmetric in the switching period, the inductor current values at each moment in half of the switching period are:

[0183] During single-phase-shift modulation:

[0184]

[0185] During the second mode of extended phase-shift modulation:

[0186]

[0187] where K = U1 / nU2, U1 = U AB , U2 = U CD .

[0188] The average transfer power P sps , P eps2The sum current stress expression is as follows:

[0189] During single-phase-shift modulation:

[0190]

[0191] The maximum transmission power under single-phase-shift modulation is P N :

[0192]

[0193] Based on the current reference value i N The maximum current stress expression i Lmax ' after normalization is as follows:

[0194]

[0195] i Lmax ' = 2(1 - K - 2D) (7)

[0196] Enabling all switching devices to achieve soft switching is an important method to reduce the switching losses of the converter and improve the transmission efficiency of the system. Under the single-phase-shift modulation mode, from the analysis of the switching states of the dual-active-bridge converter, the requirements for achieving ZVS are:

[0197]

[0198] In summary, the conditions for achieving ZVS are:

[0199]

[0200] During the second mode of extended phase-shift modulation:

[0201] From the average power algorithm and the symmetry within a half cycle, the transmission power P eps2 and the maximum current stress i Lmax2 under the single-phase-shift modulation mode are respectively:

[0202]

[0203] Selecting the reference transmission power P N and the current reference value i N to normalize and unify the transmission power and current stress, we obtain P' and i Lmax ' as follows:

[0204]

[0205] The conditions for achieving ZVS in this mode are:

[0206]

[0207] S2: Dynamic equation on the output side of the dual-active-bridge converter:

[0208] P C = P - P out = i out * u out (29)

[0209] where P C represents the power on the output capacitor side, P is the transmission power after the converter passes through the secondary full-bridge, P out is the output power, i out is the output current, and u out is the output voltage.

[0210] Combined with the dynamic equation of the output capacitor C, we can obtain:

[0211]

[0212] For single-phase-shift modulation, the following dynamic equation on the output side is obtained:

[0213]

[0214] For extended phase-shift mode 2, the following dynamic equation on the output side is obtained:

[0215]

[0216] S3: Aiming at optimizing the current stress, the Karush-Kuhn-Tucker (KKT) algorithm is used to solve the expression of the optimal phase-shift ratio:

[0217] Lagrange function polynomial in mode 2:

[0218]

[0219] The obtained expression of the optimal phase-shift duty cycle is:

[0220]

[0221] The corresponding transmission power P' is:

[0222]

[0223] In step S4, a sliding-mode controller based on the reduced-order model of the dual-active bridge is constructed

[0224] I. Single-integral sliding-mode controller

[0225] Define the output voltage error where is the standard value of the output voltage, u outis the output voltage. The sliding surface of Sliding-Mode-Control (SMC) is selected as follows:

[0226] S = k1e + k2∫edt (36)

[0227] where k1 and k2 are sliding mode gains that determine the dynamic convergence speed of the error. When moving on the sliding surface of S = 0

[0228] k1e + k2∫edt = 0 (37)

[0229] The expression for the dynamic error is solved as:

[0230]

[0231] where K0 is the initial error of the output voltage at steady state. When k1 and k2 are greater than 0, the dynamic error will converge to zero as t approaches ∞.

[0232] The expression obtained by differentiating the sliding surface S is as follows:

[0233]

[0234] The equivalent sliding mode control law u eq is:

[0235]

[0236] where S represents the sliding surface, k3 is the sliding mode gain, and sgn(S) is the sign function, which can be expressed as:

[0237]

[0238] To reduce chattering, the sign function can be replaced by the hyperbolic tangent function tanh. The equivalent control law after replacement is:

[0239]

[0240] where μ is the boundary layer thickness, a positive real number, E is the disturbance amount, and f(x) and g(x) are time-varying nonlinear functions.

[0241] Obtained from the harmonic model of DAB

[0242]

[0243] It can be obtained that:

[0244]

[0245] For single-phase shift modulation, substituting Equation (31) gives:

[0246]

[0247] Let obtain:

[0248]

[0249] Let u eq = D(1 - D) to obtain the single-phase shift equivalent duty cycle D based on single integral sliding mode control:

[0250]

[0251] For extended phase shift modulation, substituting Equation (32) gives:

[0252]

[0253] Let Then use u eq to replace M, where M is:

[0254]

[0255] The expression D2 related to u eq and the phase shift angle D1 under single integral sliding mode control can be obtained:

[0256]

[0257] Use the current stress optimization algorithm to first find the internal phase shift ratio D1 and then substitute it into the above formula to find D2. Stability analysis:

[0258]

[0259] When g(x) and k2 are positive, the sliding mode controller is asymptotically stable.

[0260] II. Double integral sliding mode controller

[0261] For single-phase shift modulation:

[0262] The dynamic error e is expressed as The double integral sliding mode surface can be expressed as:

[0263] S = k1e + k2∫∫edt + k3∫∫edtdt (52)

[0264] After differentiating S, we get

[0265]

[0266] Let obtain:

[0267]

[0268] The equivalent sliding mode control rate u eq is as follows:

[0269]

[0270] Let u eq = D(1 - D) to obtain the equivalent duty cycle D of single-phase phase-shift modulation based on double-integral sliding mode control:

[0271]

[0272] For extended phase-shift modulation, substituting Equation (32) gives:

[0273]

[0274] Let Then use u eq to replace M, where M is:

[0275]

[0276] The expression D2 related to u eq and the phase-shift angle D1 under single-integral sliding mode control can be obtained:

[0277]

[0278] First, use the current stress optimization algorithm to find the inner phase-shift ratio D1, and then substitute it into the above formula to find D2.

[0279] The main parameters of the simulation circuit are shown in Table 1 below:

[0280] Table 1

[0281] Main parameters of the simulation circuit Value <![CDATA[Input voltage V in / V]]> 100 <![CDATA[Output voltage u out / V]]> 48 Transformer turns ratio n 1 Inductance L / mH 30 Switching frequency fs / Hz 20000 <![CDATA[Input capacitance C1 / uF]]> 110 <![CDATA[Output capacitance C2 / uF]]> 110

[0282] According to the simulation and the attached drawings in step S5, the result analysis of this embodiment is carried out:

[0283] As can be seen from Fig. 6(a), the response time for the output voltage to reach 48V when only PI control is adopted is 0.025s; as can be seen from Fig. 6(b), when single-phase phase-shift modulation based on single-integral sliding-mode control is adopted, the response time for the output voltage to reach 48V is 0.018s; as can be seen from Fig. 6(c), when single-phase phase-shift modulation based on double-integral sliding-mode control is adopted, the response time for the output voltage to reach 48V is 0.0076s. By comparing the three figures of Fig. 6(a), (b) and (c), it can be obtained that the single-phase phase-shift modulation based on single-integral sliding-mode control has a faster response than the single-phase phase-shift modulation with only PI control, and at the same time, the response time of the single-phase phase-shift modulation based on double-integral sliding-mode control is faster than that of the single-phase phase-shift modulation under single-integral sliding-mode control. As can be seen from Fig. 6(d), when extended phase-shift current stress optimization control based on single-integral sliding-mode control is adopted, the response time for the output voltage to reach 48V is 0.017s; as can be seen from Fig. 6(e), when extended phase-shift current stress optimization control based on double-integral sliding-mode control is adopted, the response time for the output voltage to reach 48V is 0.0062s. By comparing Fig. 6(d) with Fig. 6(b), and Fig. 6(e) with Fig. 6(c), it can be obtained that while the current stress is optimized, the response time of the converter is faster than that with only integral sliding-mode control. Therefore, it can be concluded that the current stress optimization scheme adopted in this case has a fast response time.

[0284] Figure 7(a) - Figure 7(e)It is the waveform diagram of the output voltage variation when the converter undergoes load changes under different control modes. Figure 7(a) shows that when only PI control is adopted and the converter undergoes a load change at 0.1 s, the output voltage changes by 7.57 V and recovers to 48 V after a response time of 0.013 s; Figure 7(b) shows that when single-phase phase-shift modulation based on single-integral sliding-mode control is adopted and the converter undergoes a load change at 0.1 s, the output voltage changes by 4.16 V and recovers to 48 V after a response time of 0.0038 s; Figure 7(c) shows that when single-phase phase-shift modulation based on double-integral sliding-mode control is adopted and the converter undergoes a load change at 0.1 s, the output voltage changes by 1.21 V and recovers to 48 V after a response time of 0.00017 s. It can be seen from Figure 7(a), (b), and (c) that the single-phase phase-shift modulation with single-integral sliding-mode control has a faster response recovery time and smaller voltage change than the single-phase phase-shift modulation with only PI control. At the same time, the single-phase phase-shift modulation with double-integral sliding-mode control has a faster response recovery time and smaller voltage change than the single-phase phase-shift modulation with single-integral sliding-mode control. Therefore, the converter with integral sliding-mode control has better dynamic response. Figure 7(d) shows the extended phase-shift current stress optimization control based on double-integral sliding-mode control. It can be seen that when the converter undergoes a load change at 0.1 s, the output voltage changes by 3.11 V and recovers to 48 V after a response time of 0.004 s; Figure 7(e) shows the extended phase-shift current stress optimization control based on double-integral sliding-mode control. It can be seen that when the converter undergoes a load change at 0.1 s, the output voltage changes by 1.97 V and recovers to 48 V after a response time of 0.00015 s. By comparing Figure 7(d), (e) with Figure 7(b), (c), it can be concluded that while adopting current stress optimization, the converter still has better dynamic response ability compared to the case without current stress optimization.

[0285] Figure 9(a) - Figure 9(e)It is the transient waveform diagram of the inductor current variation of the converter under different controls. Figure 9(a) is the transient waveform diagram of the inductor current when only PI control is adopted. It can be seen from the figure that the maximum value of the inductor current is ±22.02 A; Figure 9(b) is the transient waveform diagram of the inductor current when single-phase phase-shift modulation based on single-integral sliding-mode control is adopted. It can be seen from the figure that the maximum value of the inductor current is ±21.89 A; Figure 9(c) is the transient waveform diagram of the inductor current when single-phase phase-shift modulation based on double-integral sliding-mode control is adopted. It can be seen from the figure that the maximum value of the inductor current is ±22.29 A; Figure 9(d) is the transient waveform diagram of the inductor current under the extended phase-shift optimization current stress based on single-integral sliding-mode control. It can be seen from the figure that the maximum value of the inductor current is ±17.21 A; Figure 9(e) is the transient waveform diagram of the inductor current under the extended phase-shift optimization current stress based on double-integral sliding-mode control. It can be seen from the figure that the maximum value of the inductor current is ±17.19 A. Through the comparison of the five figures, it can be seen that when the extended phase-shift optimization current stress is adopted, both the single-integral and double-integral sliding-mode controls have significantly reduced current stress compared with only adopting PI control and only adopting single-integral or double-integral control.

[0286] Figure 10(a) - Figure 10(e) It is the transient waveform diagram of the inductor current variation of the converter after load jump under different controls. Figure 10(a) is the transient waveform diagram of the inductor current after load jump when only PI control is adopted. It can be seen from the figure that the maximum value of the inductor current is ±23.89 A; Figure 10(b) is the transient waveform diagram of the inductor current after load jump when single-phase phase-shift modulation based on single-integral sliding-mode control is adopted. It can be seen from the figure that the maximum value of the inductor current is ±23.78 A; Figure 10(c) is the transient waveform diagram of the inductor current after load jump when single-phase phase-shift modulation based on double-integral sliding-mode control is adopted. It can be seen from the figure that the maximum value of the inductor current is ±23.88 A; Figure 10(d) is the transient waveform diagram of the inductor current after load jump under the extended phase-shift optimization current stress based on single-integral sliding-mode control. It can be seen from the figure that the maximum value of the inductor current is ±18.48 A; Figure 10(e) is the transient waveform diagram of the inductor current after load jump under the extended phase-shift optimization current stress based on double-integral sliding-mode control. It can be seen from the figure that the maximum value of the inductor current is ±17.91 A. Through the comparison of the five figures, it can be seen that after load jump, both the single-integral and double-integral sliding-mode controls with extended phase-shift optimization current stress have significantly reduced current stress compared with only adopting PI control and only adopting single-integral or double-integral control. Therefore, the current stress optimization using the two integral sliding-mode controls has good optimization effects and good dynamic response capabilities.

[0287] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to only the specific embodiments. Obviously, many modifications and variations can be made according to the content of this specification. These embodiments are selected and specifically described in this specification in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can well understand and utilize the present invention. The present invention is only limited by the claims and their full scope and equivalents.

Claims

1. A method for optimizing the current stress of a dual-active-bridge converter based on sliding-mode control, which is applicable to the dual-active-bridge converter as the interconnection converter of a DC microgrid cluster, and is characterized in that, Specifically, it includes the following steps: S1. Construct the mathematical models of the basic transmission power and current stress of the dual-active-bridge converter under two signal modulation methods, namely single-phase-shift modulation and extended-phase-shift modulation, and the soft-switching characteristics corresponding to different modes; S2. Construct a reduced-order model of the dual-active-bridge converter according to the mathematical model constructed in step S1; S3. Construct a functional equation with the current stress as the optimization objective and the transmission power and soft-switching characteristics as the constraint conditions, and use the Karush-Kuhn-Tucker algorithm to solve the expression of the optimal phase-shift ratio; S4. Construct single-integral and double-integral sliding-mode controllers based on the reduced-order model of the dual-active bridge and perform equivalence; S5. Conduct simulation experiments to verify the optimization effect of the current stress and the optimization effect of the response speed through simulation.

2. The method according to claim 1, wherein In step S1, under single-phase-shift modulation, the basic transmission power and current stress models and soft-switching characteristics of the dual-active-bridge converter are as follows: In this mode, the inductor current i L is symmetric during the half cycle of the switch. The inductor current values at each moment within this half cycle are as follows: Where: K = U1 / nU2; The transmission power P under the single-phase phase-shift modulation mode is obtained from the average power algorithm and the symmetry within half a period sps and the maximum current stress i Lmax respectively as follows: Find the relationship between the duty cycle D and P sps as follows: Select the reference transmission power P N : Based on the current reference value i N The maximum current stress expression i Lmax ' after per-unit normalization is as follows: i Lmax ' = 2(1 - K - 2D)(7) Enabling all switching devices to achieve soft switching is an important method to reduce the switching losses of the converter and improve the transmission efficiency of the system; under the single-phase-shift modulation method, from the analysis of the switching states of the dual-active-bridge converter, the requirements for achieving ZVS are: In summary, the conditions for achieving ZVS are:

3. The method according to claim 1, wherein In step S1, under extended-phase-shift modulation, the basic transmission power and current stress models and soft-switching characteristics of the dual-active-bridge converter are as follows: Mode 1: 0 ≤ D1 ≤ D2 ≤ 1; Where: K = U1 / nU2; The transmission power P under the single-phase phase-shift modulation mode is obtained from the average power algorithm and the symmetry within a half cycle eps1 and the maximum current stress i Lmax1 respectively as follows: Select the reference transmission power P N and the current reference value i N Perform normalization and unification of the transmission power and current stress to obtain P' and i Lmax ' as follows: The conditions for achieving ZVS in this mode are: Mode 2: 0 ≤ D2 ≤ D1 ≤ 1; Where: K = U1 / nU2; The transmission power P under the single-phase phase-shift modulation method is obtained from the average power algorithm and the symmetry within a half cycle eps2 and the maximum current stress i Lmax2 which are respectively as follows: Select the reference transmission power P N and the current reference value i N Perform the per-unit unification of the transmission power and current stress to obtain P' and i Lmax ' as follows: The conditions for achieving ZVS in this mode are:

4. The method according to claim 1, wherein In step S4, the dynamic equation of the output side of the dual-active-bridge converter is: P C = P - P out = i out * u out (29) Among which P C represents the power on the output capacitor side. P is the transmission power of the converter after the secondary full-bridge, and P out is the output power, i out is the output current, and u out is the output voltage; Combined with the dynamic equation of the output capacitor C, we get: For single-phase-shift modulation, the following dynamic equation of the output side is obtained: For extended-phase-shift modulation, the following dynamic equation of the output side is obtained:

5. The method according to claim 1, characterized in that, In step S3, with the goal of optimizing the current stress, the Karush-Kuhn-Tucker algorithm is used to solve the expression of the optimal phase-shift ratio: The Lagrange function polynomial in Mode 1: The solved expression of the optimal phase-shift duty cycle is: The corresponding transmission power P' is: The Lagrange function polynomial in Mode 2: The solved expression of the optimal phase-shift duty cycle is: The corresponding transmission power P' is:

6. The method according to claim 1, wherein In step S4, the sliding-mode controller constructed based on the reduced-order model of the dual-active bridge is a single-integral sliding-mode controller; Define the output voltage error where is the standard value of the output voltage, and u out is the output voltage; The sliding surface of Sliding-Mode-Control (SMC) is selected as follows: S = k1e + k2∫edt (39) Where k1 and k2 are the sliding-mode gains that determine the dynamic convergence speed of the error; when moving on the sliding surface of S = 0: k1e + k2∫edt = 0 (40) The solved expression of the dynamic error is: Where K0 is the initial error of the output voltage at steady state. When k1 and k2 are greater than 0, the dynamic error will converge to zero when t approaches ∞; The expression obtained by differentiating the sliding surface S is as follows: Equivalent sliding mode control law u eq is as follows: Where S represents the sliding surface, k3 is the sliding-mode gain, and sgn(S) is the sign function expressed as: To reduce chattering, the sign function is replaced by the hyperbolic tangent function tanh, and the replaced equivalent control law is: where μ is a positive real number, is the boundary of the tanh function, E is the perturbation amount, and f(x) and g(x) are time-varying nonlinear functions; obtained from the harmonic model of DAB obtained: For single-phase shift modulation, substituting Equation (31) gives: Let Obtain: Let u eq = D(1 - D), and the single-phase shift equivalent duty cycle D based on single-integral sliding mode control is obtained: For extended phase shift modulation, substituting Equation (32) gives: Let Then use u eq to replace M, where M is: Obtain the expression D2 related to u eq and the phase shift angle D1 under single integral sliding mode control: Use the current stress optimization algorithm to first find the internal phase shift ratio D1 and then substitute it into the above formula to find D2; Stability analysis: When g(x) and k2 are positive, the sliding mode controller is asymptotically stable.

7. The method according to claim 1, characterized in that, In step S4, the sliding mode controller based on the reduced-order model of the dual active bridge is constructed as a double-integral sliding mode controller; For single-phase shift modulation: The dynamic error e is expressed as The double-integral sliding surface is expressed as: S = k1e + k2∫∫edt + k3∫∫edtdt (55) After taking the derivative of S, we get: Let Obtain: Equivalent sliding-mode control law \(u\) eq is as follows: Let u eq = D(1 - D) to obtain the equivalent duty cycle D of the single-phase phase-shift modulation based on the double-integral sliding-mode control: For extended phase shift modulation, substituting Equation (32) gives: Let Then use u eq to replace M, where M is: Obtain the expression D2 related to u eq and the phase-shift angle D1 under single-integral sliding mode control:

8. The method according to claim 1, wherein In step S5, comparative simulation experiments are carried out respectively for only using PI control, single-phase shift modulation based on single-integral sliding mode control, single-phase shift modulation based on double-integral sliding mode control, extended phase shift current stress optimization modulation based on single-integral sliding mode control, and extended phase shift current stress optimization modulation based on double-integral sliding mode control.

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