Sliding mode active disturbance rejection control method for bidirectional DC-DC converter based on flat theory

Abstract

The present invention discloses a sliding mode anti-disturbance control method for a bidirectional DC-DC converter based on flat theory. Based on the system state equation, an inner loop control model that satisfies the flat system is derived. Differential flat control is used for the current inner loop, and control parameters are obtained according to the equivalent second-order system. Then, the power changes and internal losses of the photovoltaic unit and the load in the voltage loop energy function are regarded as total disturbances, and an increased-order filter extended state observer is designed to estimate them. A sliding mode anti-disturbance control controller is constructed for the voltage outer loop based on the disturbance estimation information and the sliding mode control algorithm. The present invention effectively improves the dynamic response speed of the bus voltage under power disturbances and the robustness of the system under uncertain disturbances.

Description

Technical Field

[0001] The invention belongs to the technical field of converters, and in particular relates to a sliding mode anti-disturbance control method of a bidirectional DC-DC converter based on flat theory. Background Art

[0002] In recent years, microgrid systems with new energy as the main component have developed rapidly. Among them, DC microgrids have attracted widespread attention because their distributed power sources only need single-stage conversion when connected to the bus, reducing construction costs and process losses. DC microgrids contain energy storage units, distributed power sources, and different types of loads connected to the bus. The state of the bus voltage reflects the operating stability of the entire system. The energy storage unit transfers energy to the bus through a bidirectional DC-DC converter to balance the power demand caused by changes in distributed power sources and loads. Therefore, how to optimize the control of the bidirectional DC-DC converter, improve the dynamic performance of the system, and reduce the impact of power fluctuations of distributed power sources and loads on the stability of the bus voltage has become a hot topic for researchers.

[0003] The bidirectional DC-DC converter in the DC microgrid makes the system nonlinear. The traditional PI controller can no longer meet the bus voltage stability requirements when there are large disturbances in the new energy and load. At the same time, the uncertainty disturbances caused by temperature changes, noise, and device parameter perturbations also limit the performance of the PI controller. Therefore, many scholars use nonlinear control methods in the DC microgrid bus voltage control, such as adaptive control, state feedback linearization control, differential flatness control, and self-disturbance rejection control. Among them, differential flatness based control (DFBC) has gradually been widely used due to its advantages such as fast flat output and accurate following of reference trajectory. However, differential flatness control is used as the energy balance of the voltage outer loop management system, and the influence of uncertain disturbances is not considered. At the same time, differential flatness control relies on the accuracy of the model, which also increases the difficulty of control and the number of sensors.

[0004] Active Disturbance Rejection Control (ADRC) is a nonlinear robust control method with Extended State Observer (ESO) as its core. It does not require an accurate model of the controlled object. At the same time, ESO is used to observe the state variables and disturbances of the system, and uses the observed values ​​to compensate in the feedforward channel, which can greatly improve the rapidity and control accuracy of the system. Reference Huangfu Y, Zhuo S, Chen F, et al. Robust voltage control of floating interleaved boost converter for fuel cell systems [J]. IEEE Transactions on Industry Applications, 2018, 54(1): 665-674. It is proposed to form a dual closed-loop structure of ADRC and second-order sliding mode control to control the output series boost converter in the fuel cell power supply system. The total disturbance of the system is estimated by ESO, and the PD controller is used to compensate, so as to achieve the overall reduction of the total disturbance; Reference Research on the self-disturbance rejection control method of photovoltaic energy storage bidirectional DC-DC converter [J]. Acta Energiae Solaris Sinica, 2018, 39(05): 1342-1350. Yang Hui, Luo Shan, Sun Xiangdong, et al. proposed a dual closed-loop control structure of nonlinear ADRC and PI for photovoltaic energy storage system, which improved the anti-disturbance performance and rapidity of the system. However, due to the use of independent PWM control method and the complex problem of nonlinear ADRC control parameter setting, the control difficulty is increased. Literature PMLSM current deviation decoupling control based on sliding mode anti-disturbance control[J]. Optics and Precision Engineering, 2022, 30(04): 431-441. Zhao Ximei, Wu Cen. The permanent magnet linear synchronous motor is completely decoupled by using sliding mode control combined with ADRC, which simplifies the control structure and further improves the system robustness. Summary of the invention

[0005] The purpose of the present invention is to provide a bidirectional DC-DC converter sliding mode anti-disturbance control method based on flat theory, which effectively improves the dynamic response speed of bus voltage under power disturbance and the robustness of the system under uncertain disturbance.

[0006] The technical solution adopted by the present invention is a sliding mode anti-disturbance control method for a bidirectional DC-DC converter based on flat theory, an inner loop control model satisfying a flat system is derived based on a system state equation, differential flat control is adopted for the current inner loop, and control parameters are obtained according to an equivalent second-order system; then, the power changes and internal losses of the photovoltaic unit and the load in the voltage loop energy function are regarded as total disturbances, an increased-order filter extended state observer is designed to estimate them, and a sliding mode anti-disturbance control controller is constructed for the voltage outer loop based on disturbance estimation information and a sliding mode control algorithm, which specifically includes the following steps:

[0007] Step 1: Build a simplified model of the DC microgrid and obtain the state equation of the energy storage unit;

[0008] Step 2: Model the bidirectional DC-DC converter control system for the DC microgrid

[0009] Step 2.1: Modeling the flat inner loop of the current;

[0010] Step 2.2: Modeling of flat voltage outer loop;

[0011] Step 3: Design of controller for bidirectional DC-DC converter of energy storage unit

[0012] Step 3.1: Design of current inner loop differential flat control;

[0013] Step 3.2: Design of voltage outer loop sliding mode anti-disturbance control

[0014] Step 3.2.1: Establish the voltage outer loop model;

[0015] Step 3.2.2: Design of enhanced-order filter extended state observer;

[0016] Step 3.2.3: Sliding mode ADRC design.

[0017] The present invention is also characterized in that:

[0018] In step 1, the DC microgrid structure is that the distributed power source is controlled by the maximum power point tracking MPPT and connected to the DC bus through a single-stage conversion. The energy storage unit is connected to the DC bus through a bidirectional DC-DC converter to balance the system power. The load types include resistive loads and constant power loads, among which the constant power loads include DC loads connected to the bus through a DC-DC converter and AC loads connected to the bus through a DC-AC inverter.

[0019] The distributed power source selects photovoltaic units, and the energy storage unit selects batteries. In the energy storage unit, v bat and v bus are the energy storage battery output voltage and DC bus voltage respectively; i L is the current flowing through the energy storage inductor L; C 1is the battery filter capacitor; C bus is the DC bus capacitance; VT 1 VT 2 is the power switch tube of the energy storage unit, d and d′ are VT 1 VT 2 The duty cycle of the two switch tubes is d+d′=1, and the control signals of the two switch tubes are complementary, that is, d+d′=1. Only one of the switch tubes needs to be controlled, and the other switch tube can be operated at the same time.

[0020] The state equation of the energy storage unit is:

[0021]

[0022] In formula (1), P L is an equivalent constant power load, which is the sum of the photovoltaic unit output power and the AC load power.

[0023] Step 2.1 is as follows:

[0024] Select the bidirectional DC-DC converter inductor current as the flat output variable y c and the state variable x c , that is:

[0025] y c =x c =i L =ψ x (y c ) (4)

[0026] In formula (4), ψ(y c ) is the flat output variable y c The mapping function of

[0027] Switching tube VT 1 The duty cycle is used as the control variable u c , after transforming formula (1), we get:

[0028]

[0029] Equations (4) and (5) meet the flatness requirements of the system.

[0030] Step 2.2 is as follows:

[0031] System DC bus capacitor C bus The stored energy E bus It is expressed as:

[0032]

[0033] When the internal loss of the system is ignored, the derivative of the DC bus capacitor energy is expressed as:

[0034]

[0035] In formula (7), P bat is the power output from the energy storage battery to the DC bus, P pv is the power output from the photovoltaic unit to the DC bus, P load is the load power, where P bat It is expressed as:

[0036] P bat =i L v Bat (8)

[0037] The energy stored in the capacitor and the voltage across the capacitor are taken as flat output variables y v and the state variable x v ,Right now:

[0038]

[0039]

[0040] The control variable u v Defined as i Lref According to formula (7), we can get:

[0041]

[0042] Equations (9)-(11) meet the flatness requirements of the system.

[0043] Step 3.1 is as follows:

[0044] Define the expected value of the current loop as i Lref =y cref , from equations (3)-(5), when the current inner loop controlled system is in steady state and the flat output variable strictly follows its reference trajectory, we have:

[0045]

[0046] When the current inner loop controlled system is in the dynamic adjustment process, the deviation of the flat output variable from its reference trajectory and the derivative and integral terms of the deviation have the following relationship:

[0047]

[0048] In formula (13), k 1 , k 2 is the feedback gain of the inner loop controller.

[0049] The control object is equivalent to a second-order system to eliminate the steady-state error. The closed-loop transfer function of the system is:

[0050]

[0051] The current loop error is defined as According to formula (13) and (14), we can get:

[0052]

[0053] Combining equation (14) and equation (15), we can get:

[0054]

[0055] In formula (16), ξ c is the damping ratio of the inner loop system, ω nc is the inner ring oscillation frequency.

[0056] Combining equations (13) and (16), we can obtain the differential term of the flat output variable:

[0057]

[0058] According to formula (17), k 1 , k 2 When it is positive, the inner loop system is stable and the controller parameter ξ c and ω nc The selection of determines the transient characteristics of the inner loop system. c When fixed, ω nc The larger the value, the faster the response of the inner loop system. nc It cannot be increased infinitely. The stability of the inner loop system requires that the inner loop bandwidth is much smaller than the system switching frequency, that is, the following relationship is satisfied:

[0059] ω nc <<ω s =2πf s (18).

[0060] Step 3.2.1 is as follows:

[0061] According to formula (11), the energy function of the DC bus capacitor is:

[0062]

[0063] In formula (19), f is the total static loss of the photovoltaic unit and the energy storage unit;

[0064] The first-order system that defines the energy function according to the ADRC paradigm is:

[0065]

[0066] In formula (20), ω = f(y v ,d,t)+(bb0 )u is the total disturbance required; y v is the DC bus capacitor energy E bus ,u v is the expected current signal output by the outer loop control to the inner loop, b is the precise value of the control gain, f(y v ,d,t) is the comprehensive characteristics of the time-varying dynamics and external disturbances generated in the system, and the easily available estimated value b 0 As the control quantity gain b.

[0067] From the combined equations (19) and (20), we can know that:

[0068]

[0069] Step 3.2.2 is as follows:

[0070] According to formula (20), the state variables of the outer loop model are defined as:

[0071]

[0072] The outer loop system model can be written as:

[0073]

[0074] In formula (23),

[0075] C=[1 0 0].

[0076] According to formula (23), the designed ESO is:

[0077]

[0078] In formula (24), θ = [θ 1 ,θ 2 ,θ 3 ] T θ 1 ,θ 2 ,θ 3 are η 1 , η 2 , η 3 The observed value of a =η 1 -θ 1 =y v -θ 1 is the observation error of ESO; L = [l 1 ,l 2 ,l 3 ] T is the gain of the observer;

[0079] The characteristic polynomial of ESO can be obtained by Laplace transforming equation (24), and then configured with the observer bandwidth:

[0080] s 3 +l 1 s 2 +l 2 s+l 3 =(s+ω 1 ) 3 (25)

[0081] In formula (25), ω 1 is the bandwidth of ESO, the observer gain can be configured as l 1 =3ω 1 , l 2 =3ω 1 2 , l 3 =ω 1 3 If the observer gain is adjusted based on the system bandwidth, the observed value can maintain a good tracking effect on the output and the total disturbance, that is, θ 1 →η 1 ,θ 2 →η 2 ,θ 3 →η 3 .

[0082] Step 3.2.3 is as follows:

[0083] Define the expected value of the voltage outer loop as E ref , the capacitance energy error is:

[0084] e v =θ 4 -E ref (27)

[0085] Derivative of formula (27) yields:

[0086]

[0087] Select the sliding surface S as:

[0088] S=e v +c∫e v (29)

[0089] The sliding mode reaching law is chosen as:

[0090]

[0091] In formula (30), w 1 >0,w 2 >0.

[0092] According to equations (27)-(30), the voltage outer loop control law is:

[0093]

[0094] According to formula (24), the state variable η representing the disturbance is expanded in the voltage outer loop model 2 That is, ω is replaced by the state variable θ of ESO 2 Tracking, after the low-pass filter link θ of formula (26) 2 becomes θ 5 , Substituting equation (31) into equation (23) reduces the total disturbance η 2 That is, θ 5 , the original object is simplified to a single integral system, namely:

[0095]

[0096] In formula (32), u 0 =-w 1 Sw 2 sign(S)-c(θ 4 -E ref ).

[0097] The beneficial effects of the present invention are:

[0098] 1) The bidirectional DC-DC converter sliding mode anti-disturbance control method of the present invention based on the flat theory solves the problems of poor stability and slow dynamic response of the photovoltaic storage DC microgrid system caused by the output power fluctuation of the distributed power supply, the sudden change of load power and the uncertain disturbance;

[0099] 2) For the control of the bidirectional DC-DC converter of the energy storage unit, based on the system model, the inner and outer loop models that meet the flatness requirements are obtained, and a dual closed-loop control structure of inner loop DFBC and outer loop ISM-ADRC is constructed. By treating power changes and uncertain disturbances as total disturbances for estimation and compensation, the control is less dependent on the model and the control difficulty is reduced.

[0100] 3) Compared with the traditional dual-loop PI control and dual-loop DFBC, the control strategy in this paper can effectively suppress the transient shock caused by load mutation and photovoltaic power fluctuation, alleviate the fluctuation of the DC bus, and significantly improve the response speed and anti-interference ability of the DC bus voltage.

[0101] 4) When the system circuit parameters are perturbed and high-frequency noise exists, the bus voltage does not oscillate significantly or become unstable, which improves the robustness of the system. The control strategy in this paper is conducive to application in actual working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0102] Figure 1It is a DC microgrid structure diagram in the bidirectional DC-DC converter sliding mode anti-disturbance control method based on the flat theory of the present invention;

[0103] Figure 2 It is a simplified model diagram of a DC microgrid in a bidirectional DC-DC converter sliding mode anti-disturbance control method based on flat theory of the present invention;

[0104] Figure 3 It is a control block diagram of a bidirectional DC-DC converter of an energy storage unit in a bidirectional DC-DC converter sliding mode self-disturbance rejection control method based on flat theory of the present invention;

[0105] Figure 4 It is a current inner loop DFBC control block diagram of the bidirectional DC-DC converter sliding mode anti-disturbance control method based on the flat theory of the present invention;

[0106] Figure 5 It is a voltage outer loop ISM-ADRC control block diagram of the bidirectional DC-DC converter sliding mode anti-disturbance control method based on the flat theory of the present invention;

[0107] FIG6 is a simulation comparison diagram of different control strategies when the constant power load fluctuates, wherein FIG6(a) is a curve diagram of the active power output of the inverter when the constant power load fluctuates, FIG6(b) is a diagram of the remaining capacity of the battery when the constant power load fluctuates, FIG6(c) is a waveform diagram of the bus voltage under the dual-loop PI control when the constant power load fluctuates, FIG6(d) is a waveform diagram of the bus voltage under the dual-loop DFBC control when the constant power load fluctuates, and FIG6(e) is a waveform diagram of the bus voltage under the control of the present invention when the constant power load fluctuates;

[0108] FIG7 is a simulation comparison diagram of different control strategies when the output of the photovoltaic unit fluctuates, wherein FIG7(a) is a photovoltaic output power curve diagram under different light intensities when the output of the photovoltaic unit fluctuates, FIG7(b) is a diagram of the remaining capacity of the battery when the output of the photovoltaic unit fluctuates, FIG7(c) is a bus voltage waveform diagram under dual-loop PI control when the output of the photovoltaic unit fluctuates, FIG7(d) is a bus voltage waveform diagram under dual-loop DFBC control when the output of the photovoltaic unit fluctuates, and FIG7(e) is a bus voltage waveform diagram under the control of the present invention when the output of the photovoltaic unit fluctuates;

[0109] FIG8 is a bus voltage simulation waveform diagram when the inductance parameter is perturbed, wherein FIG8(a) is a bus voltage simulation waveform diagram when the inductance parameter is perturbed, FIG8(b) is an enlarged view of range A in FIG8(a), and FIG8(c) is an enlarged view of range B in FIG8(a);

[0110] FIG9 is a bus voltage simulation waveform diagram when the capacitor parameters are perturbed, wherein FIG9(a) is a bus voltage simulation waveform diagram when the capacitor parameters are perturbed, FIG9(b) is an enlarged view of range C in FIG9(a), and FIG9(c) is an enlarged view of range D in FIG9(a);

[0111] FIG10 is a waveform diagram of the system simulation after adding measurement noise, wherein FIG10(a) is a waveform diagram of the capacitor energy observation value under the influence of noise, and FIG10(b) is a waveform diagram of the bus voltage simulation under the influence of noise. DETAILED DESCRIPTION

[0112] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0113] The present invention is based on the flat theory of the bidirectional DC-DC converter sliding mode anti-disturbance control method, based on the system state equation to derive the inner loop control model that satisfies the flat system, the current inner loop adopts differential flat control and obtains the control parameters according to the equivalent second-order system; then, the power change of the photovoltaic unit and the load in the voltage loop energy function and its internal loss are regarded as the total disturbance, the increased order filter extended state observer is designed to estimate it, and the sliding mode anti-disturbance controller is constructed for the voltage outer loop based on the disturbance estimation information and the sliding mode control algorithm, which specifically includes the following steps:

[0114] Step 1: Build a simplified model of the DC microgrid and obtain the state equation of the energy storage unit;

[0115] like Figure 1 As shown, the DC microgrid structure is that the distributed power source is controlled by Maximum Power Point Tracking (MPPT) and connected to the DC bus through a single-stage conversion. The energy storage unit is connected to the DC bus through a bidirectional DC-DC converter to balance the system power. The load types include resistive loads and constant power loads, wherein the constant power loads include DC loads connected to the bus through a DC-DC converter and AC loads connected to the bus through a DC-AC inverter. For the DC microgrid in the off-grid mode, the present invention selects to control the battery bidirectional DC-DC converter to maintain the system power balance and the stability of the bus voltage.

[0116] The simplified model of DC microgrid is as follows: Figure 2 As shown, the distributed power source selects photovoltaic units, and the energy storage unit selects batteries. In the energy storage unit, v bat and v bus are the energy storage battery output voltage and DC bus voltage respectively; i L is the current flowing through the energy storage inductor L; C 1 is the battery filter capacitor; C bus is the DC bus capacitance; VT 1 VT 2 is the power switch tube of the energy storage unit, d and d′ are VT 1 VT 2The duty cycle of the two switches is d+d′=1, and the control signals of the two switches are complementary, that is, d+d′=1. Only one of the switches needs to be controlled, and the other switch can be operated at the same time, which improves the response speed of the system.

[0117] The state equation of the energy storage unit is:

[0118]

[0119] In formula (1), P L is an equivalent constant power load, which is the sum of the photovoltaic unit output power and the AC load power.

[0120] Step 2: Model the bidirectional DC-DC converter control system for the DC microgrid

[0121] Differential flat control is to linearly represent the nonlinear system with state variables x and input variables u by selecting flat output and its derivatives of various orders. Assuming there is a nonlinear system, its mathematical model can be expressed as:

[0122]

[0123] If there is an output y and its finite differential, it can be expressed as:

[0124]

[0125] Then the system is called a differentially flat system. In formula (3), u∈R n , x∈R m , y∈R n , m, n are positive integers, and m≥n. ψ x (·),ψ u (·) is the mapping function.

[0126] Step 2.1: Modeling the flat inner loop of the current;

[0127] Select the bidirectional DC-DC converter inductor current as the flat output variable y c and the state variable x c , that is:

[0128] y c =x c =i L =ψ x (y c ) (4)

[0129] In formula (4), ψ ( yc ) is the flat output variable y c The mapping function of

[0130] Switching tube VT 1The duty cycle is used as the control variable u c , after transforming formula (1), we can get:

[0131]

[0132] Equations (4) and (5) meet the flatness requirements of the system.

[0133] Step 2.2: Modeling of flat voltage outer loop;

[0134] In the design process of the voltage outer loop, different from the traditional direct voltage control, by adjusting the DC bus capacitor C bus The energy on the bus is used to maintain the system power balance and indirectly stabilize the bus voltage;

[0135] System DC bus capacitor C bus The stored energy E bus It is expressed as:

[0136]

[0137] When the internal loss of the system is ignored, the derivative of the DC bus capacitor energy is expressed as:

[0138]

[0139] In formula (7), P bat is the power output from the energy storage battery to the DC bus, P pv is the power output from the photovoltaic unit to the DC bus, P load is the load power,

[0140] P bat =i L v bat (8)

[0141] The energy stored in the capacitor and the voltage across the capacitor are taken as flat output variables y v and the state variable x v ,Right now:

[0142]

[0143]

[0144] The control variable u v Defined as i Lref According to formula (7), we can get:

[0145]

[0146] Equations (9)-(11) meet the flatness requirements of the system.

[0147] Step 3: Design of controller for bidirectional DC-DC converter of energy storage unit

[0148] The block diagram of the sliding mode anti-disturbance control of the bidirectional DC-DC converter of the energy storage unit based on the flat theory is shown in Figure 3. This paper adopts a dual-loop control structure and designs the controllers for the current inner loop and the voltage outer loop in turn.

[0149] Step 3.1: Design of current inner loop differential flat control;

[0150] First, the current inner loop with differential flat control is designed to quickly track the dynamic changes of the system and improve the dynamic response capability of the system. The expected value of the current loop is defined as i Lref =y cref , from equations (3)-(5), when the current inner loop controlled system is in steady state and the flat output variable strictly follows its reference trajectory, we have:

[0151]

[0152] When the current inner loop controlled system is in the dynamic adjustment process, the deviation of the flat output variable from its reference trajectory and the derivative and integral terms of the deviation have the following relationship:

[0153]

[0154] In formula (13), k 1 , k 2 is the feedback gain of the inner loop controller.

[0155] The control object is equivalent to a second-order system to eliminate the steady-state error. The closed-loop transfer function of the system is:

[0156]

[0157] The current loop error is defined as According to formula (13) and (14), we can get:

[0158]

[0159] Combining equation (14) and equation (15), we can get:

[0160]

[0161] In formula (16), ξ c is the damping ratio of the inner loop system, ω nc is the inner ring oscillation frequency.

[0162] Combining equations (13) and (16), we can obtain the differential term of the flat output variable:

[0163]

[0164] According to formula (17), k 1 , k 2 When it is positive, the inner loop system is stable and the controller parameter ξ c and ω nc The selection of determines the transient characteristics of the inner loop system. c When fixed, ω nc The larger the value, the faster the response of the inner loop system. nc It cannot be increased infinitely. The stability of the inner loop system requires that the inner loop bandwidth is much smaller than the system switching frequency, that is, the following relationship is satisfied:

[0165] ω nc <<ω s =2πf s (18)

[0166] In summary, the current inner loop control block diagram is as follows: Figure 4 shown.

[0167] Step 3.2: Design of voltage outer loop sliding mode anti-disturbance control

[0168] On the basis of the stability of the inner loop, a first-order flat system with single input and single output of the outer loop is constructed and the outer loop controller is designed to ensure the stability of the bus voltage and provide a reference value for the current inner loop. Since DFBC as an outer loop control depends on the accuracy of the model, it will also increase the use of sensors. In order to reduce the control difficulty and improve the robustness of the system, according to the characteristics of ADRC that it does not depend on the object model, the outer loop auto-disturbance rejection model is first derived from the relationship between the energy and power of the DC microgrid capacitor, and then an increased-order filter ESO is established based on the auto-disturbance rejection model. Finally, a sliding mode auto-disturbance rejection controller is designed based on the increased-order filter ESO as the framework.

[0169] Step 3.2.1: Establish the voltage outer loop model;

[0170] According to formula (11), the energy function of the DC bus capacitor is:

[0171]

[0172] In formula (19), f is the total static loss of the photovoltaic unit and the energy storage unit;

[0173] The first-order system that defines the energy function according to the ADRC paradigm is:

[0174]

[0175] In formula (20), ω = f(y v ,d,t)+(bb 0 )u is the total disturbance required; y v is the DC bus capacitor energy Ebus ,u v is the expected current signal output by the outer loop control to the inner loop, b is the precise value of the control gain, f(y v ,d,t) is the comprehensive characteristics of the time-varying dynamics and external disturbances generated in the system, and the easily available estimated value b 0 As the control quantity gain b.

[0176] From the combined equations (19) and (20), we can know that:

[0177]

[0178] Note 1: b 0 As the disturbance compensation factor of the observer, a value that is too large or too small will affect the compensation effect and dynamic performance. Therefore, after the circuit parameters are initially determined according to formula (21), they are gradually adjusted based on this value according to the response speed of the system.

[0179] Step 3.2.2: Design of enhanced-order filter extended state observer;

[0180] In order to ensure the stable operation of the system under relatively harsh conditions, it is necessary to improve the observation ability of ESO for state quantities and disturbance quantities, thereby improving the bus voltage quality. Therefore, combined with the literature

[17] , the ESO is subjected to an order-enhancing treatment;

[0181] According to formula (20), the state variables of the outer loop model are defined as:

[0182]

[0183] The outer ring system model is written as:

[0184]

[0185] In formula (23),

[0186] C=[1 0 0].

[0187] According to formula (23), the designed ESO is:

[0188]

[0189] In formula (24), θ = [θ 1 ,θ 2 ,θ 3 ] T θ 1 ,θ 2 ,θ 3 are η 1 , η 2 , η 3 The observed value of a =η1 -θ 1 =y v -θ 1 is the observation error of ESO; L = [l 1 ,l 2 ,l 3 ] T is the gain of the observer;

[0190] The characteristic polynomial of ESO can be obtained by Laplace transforming equation (24), and then configured with the observer bandwidth:

[0191] s 3 +l 1 s 2 +l 2 s+l 3 =(s+ω 1 ) 3 (25)

[0192] In formula (25), ω 1 is the bandwidth of ESO, the observer gain can be configured as l 1 =3ω 1 , l 2 =3ω 1 2 , l 3 =ω 1 3 If the observer gain is adjusted based on the system bandwidth, the observed value can maintain a good tracking effect on the output and the total disturbance, that is, θ 1 →η 1 ,θ 2 →η 2 ,θ 3 →η 3 .

[0193] Note 2: ESO uses 3 to 5 times the voltage loop bandwidth of the equivalent second-order system to configure the observer bandwidth, so that the observation rate of ESO is much higher than the system operation rate. Then, feedforward compensation can be performed by estimating the disturbance and state quantity, which plays a role in eliminating steady-state errors and reducing the influence of disturbances in control.

[18] .

[0194] Considering that the energy density of the battery is large and the power density is small, it is difficult to respond quickly to compensate for the bus energy loss when dealing with high-frequency power fluctuations, and it will affect the service life of the energy storage unit. Therefore, a low-pass filter is used to suppress the high-frequency power noise caused by the sensor measurement link, that is:

[0195]

[0196] Where σ = 1 / ω 1 .

[0197] Step 3.2.3: Sliding Mode Active Disturbance Rejection Controller Design

[0198] Define the expected value of the voltage outer loop as E ref , the capacitance energy error is:

[0199] e v =θ 4 -E ref (27)

[0200] Derivative of formula (27) yields:

[0201]

[0202] Select the sliding surface S as:

[0203] S=e v +c∫e v (29)

[0204] The sliding mode reaching law is chosen as:

[0205]

[0206] In formula (30), w 1 >0,w 2 >0.

[0207] According to equations (27)-(30), the voltage outer loop control law is:

[0208]

[0209] According to formula (24), the state variable η representing the disturbance is expanded in the voltage outer loop model 2 That is, ω is replaced by the state variable θ of ESO 2 Tracking, after the low-pass filter link θ of formula (26) 2 becomes θ 5 , Substituting equation (31) into equation (23) reduces the total disturbance η 2 That is, θ 5 , the original object is simplified to a single integral system, namely:

[0210]

[0211] In formula (32), u 0 =-w 1 Sw 2 sign(S)-c(θ 4 -E ref )

[0212] In summary, the voltage outer loop control block diagram is as follows: Figure 5 shown.

[0213] The stability analysis of ESO and outer loop control system is as follows:

[0214] The ESO tracking error is defined as:

[0215]

[0216] In the formula, e a 、e b is the error between the observed value and the actual value.

[0217] By Laplace transforming equation (33), the characteristic equation of the ESO error system can be obtained as follows:

[0218]

[0219] Analyzing equation (34), we can see that the characteristic roots of the characteristic equation are all located in the left half plane of the s plane, so the ESO error system is stable. According to the terminal value theorem of Laplace transform, when t→∞, the observation error in equation (33) tends to 0.

[0220] Define the Lyapunov function V as:

[0221]

[0222] Ignoring the observation error, taking the derivative of equation (35) yields:

[0223]

[0224] From formula (36), we can see that That is, the designed voltage outer loop control system is asymptotically stable.

[0225] Simulation Analysis

[0226] In order to verify the effectiveness of the control algorithm, the simulation models of dual-loop PI control, dual-loop DFBC and the control strategy of this paper were built for the bidirectional converter in the photovoltaic storage DC microgrid system in MATLAB / Simulink simulation software. The initial conditions of the system are set as follows: ambient temperature 25℃, light intensity 1000W / m 2 , the initial SOC of the battery is 50%, and the rated bus voltage is 650V. The photovoltaic unit adopts the particle swarm algorithm for MPPT control, and the inverter DC / AC unit adopts instantaneous voltage and current double closed-loop control. The simulation circuit parameters are shown in Table 1, and the controller parameters are shown in Table 2.

[0227] Table 1 Simulation circuit parameters of photovoltaic storage DC microgrid system

[0228]

[0229] Table 2 Controller parameters

[0230]

[0231] (I) Simulation comparison of different control strategies

[0232] Power load fluctuation

[0233] The AC load is connected to the DC bus through a DC / AC inverter. There may be a sudden increase or decrease in active power due to changes in user demand, which causes bus voltage fluctuations. Therefore, this section simulates and compares different control methods to control the energy storage unit bidirectional converter to suppress load power mutations, as shown in Figure 6.

[0234] Figure 6 shows the light intensity maintained at 1000W / m 2 The inverter power suddenly increases from 5.5kW to 10.5kW at 0.7s. The load power demand is greater than the output power of the photovoltaic unit. The battery discharges to compensate the DC bus. The inverter power suddenly increases from 10.5kW to 18kW at 1s. The battery discharge rate accelerates. It suddenly decreases from 18kW to 5.5kW at 1.3s. The output power of the photovoltaic unit is greater than the power required by the load. The battery starts to charge slowly again.

[0235] From the analysis of Figure 6(a) and Figure 6(b), we can see that, taking the conversion of the battery from discharge to charge at 1.3s as an example, the battery state conversion response rate under the control strategy of this paper is better than that of the dual-loop PI control and the dual-loop DFBC. From the analysis of Figure 6(c), (d), (e) and Table 3, we can see that the battery energy storage unit under the control strategy of this paper can coordinate well with the photovoltaic unit to maintain the stable operation of the bus voltage. The bus voltage overshoot under the control strategy of this paper is similar to that of the dual-loop DFBC. When the load increases or decreases, the adjustment time is fast and the change range is not large, which reflects the ability of the ESO in the control strategy of this paper to quickly estimate and compensate when facing load fluctuations.

[0236] Table 3 Output performance when constant power load fluctuates

[0237]

[0238] PV cell output fluctuations

[0239] Under actual working conditions, the output power of the photovoltaic unit will change with the change of light intensity, thus affecting the bus voltage. Therefore, this section simulates and compares different control methods to control the energy storage unit bidirectional converter to suppress the sudden change of photovoltaic unit power, as shown in Figure 7.

[0240] Figure 7 shows that the output power of the inverter remains unchanged at 5.5kW, and the light intensity of the photovoltaic unit suddenly drops to 500W / m at 0.7s.2 , the output power of the photovoltaic unit is less than the power required by the load, and the battery discharges to compensate the DC bus for energy. The light intensity of the photovoltaic unit suddenly increases to 1200W / m at 1s. 2 The output power of the photovoltaic unit is greater than the power required by the load. The DC bus uses the excess energy to charge the battery. The light intensity of the photovoltaic unit returns to 1000W / m at 1.4s. 2 , the battery charging rate slows down.

[0241] From the analysis of Figure 7(a) and Figure 7(b), we can see that, taking the conversion of the battery from charging to discharging state at 0.7s as an example, the battery state conversion response rate under the control strategy of this paper is better than that of the dual-loop PI control and the dual-loop DFBC. From the analysis of Figure 7(c), (d), (e) and Table 4, we can see that when the output of the photovoltaic unit fluctuates, the bus voltage fluctuation overshoot under the control strategy of this paper is the smallest and the adjustment time is the shortest. This shows the superiority of the control strategy of this paper in suppressing the fluctuation of photovoltaic output.

[0242] Table 4 Output performance when photovoltaic output fluctuates

[0243]

[0244] (II) Impact of converter circuit parameter perturbations

[0245] Due to differences in manufacturing processes of electronic components and the impact of environmental factors such as temperature changes, the actual values ​​of inductance and capacitance will not match the nominal values. Under high-power operation, the deviations caused by process and aging of components will be greater. Therefore, in this section, the parameter perturbation is set to +25% and -25% to simulate the worst working conditions. The robustness of the proposed control strategy to circuit parameter uncertainty is verified by simulation. As shown in Figures 8 and 9.

[0246] From the analysis of Figure 8, we can see that the inductance parameter perturbation of ±25% of the energy storage bidirectional converter is simulated using 3mH and 5mH inductors respectively. The expected value of the bus voltage drops to 620V at 1s, and the expected value of the bus voltage rises to 680V at 1.5s. It can be seen from Figure 8(b) and Figure 8(c) that the dynamic performance of the bus voltage under different inductance parameters is basically the same, and both can stably follow the expected voltage, reflecting the strong robustness of ISM-ADRC.

[0247] From the analysis of Figure 9, we can see that the bus capacitance ±25% parameter perturbation is simulated using capacitors of 15000μH and 25000μH, respectively. It can be seen from Figure 9(b) and Figure 9(c) that the expected value of the bus voltage drops to 620V at 1s, and the dynamic performance of the bus voltage under different capacitance values ​​is basically the same. The expected value of the bus voltage rises to 680V at 1.5s. The bus voltage under different capacitance values ​​only changes in voltage ripple, with similar fall times and a difference of about 0.7% in overshoot. Therefore, the ISM-ADRC used in this paper can effectively suppress the component parameter perturbation problem in actual working conditions.

[0248] (III) Impact of system high-frequency noise

[0249] Considering the actual working conditions, the DC microgrid system is not an idealized model. Due to the influence of the high-frequency component of the load power and the external environment, the sensor measurement signal of the bus voltage is usually contaminated with high-frequency noise. Therefore, this section verifies the effectiveness of the proposed control strategy for noise suppression through simulation. As shown in Figure 10, the control structure of the traditional SM-ADRC in the figure is consistent with the literature Zhao Ximei, Wu Cen. PMLSM current deviation decoupling control based on sliding mode self-disturbance rejection [J]. Optics and Precision Engineering, 2022, 30(04): 431-441.

[0250] From the analysis of Figure 10(a), it can be seen that after adding noise to the bus voltage signal, the observation value of the bus capacitor energy by the traditional SM-ADRC is affected by high-frequency noise, while the observation value of the bus capacitor energy by the ISM-ADRC is significantly smoother, effectively suppressing the high-frequency component. From the analysis of Figure 10(b), it can be seen that under the influence of noise, the control of the bus voltage by the traditional SM-ADRC diverges, causing system instability, while the bus voltage of the ISM-ADRC only fluctuates slightly under the same noise influence, and the noise amplitude is about 0.6% of the rated value. The bus voltage can be stabilized near the expected value to ensure the normal operation of the system.

[0251] From the above content, we can know that, firstly, DFBC control is used for the inner current loop to improve the rapidity and load capacity of the system. Secondly, ISM-ADRC is designed for the energy function of the voltage loop to maintain the power balance of the system, and the ESO in ADRC is processed by increasing the order to improve the observation ability of the disturbance term, thereby improving the anti-disturbance performance of the bus voltage; the high-frequency noise generated by the measurement link is suppressed by a low-pass filter to protect the life of the battery energy storage system and improve the charging and discharging response speed. In view of the influence of circuit parameter perturbations and other uncertain disturbances, ADRC is combined with sliding mode control to improve the overall robustness of the system. Finally, simulation verifies the effectiveness of the control strategy in this paper.

Claims

1. A sliding mode anti-disturbance control method for a bidirectional DC-DC converter based on flat theory, characterized in that: Based on the system state equation, the inner loop control model that satisfies the flat system is derived. Differential flat control is adopted for the current inner loop and the control parameters are obtained according to the equivalent second-order system. Then, the power changes of the photovoltaic unit and the load in the voltage loop energy function and their internal losses are regarded as total disturbances, and an increased-order filter extended state observer is designed to estimate them. Based on the disturbance estimation information and the sliding mode control algorithm, a sliding mode anti-disturbance control is constructed for the voltage outer loop. The specific steps include: Step 1: Build a simplified model of the DC microgrid and obtain the state equation of the energy storage unit; In step 1, the DC microgrid structure is that the distributed power source is controlled by the maximum power point tracking MPPT and connected to the DC bus through a single-stage conversion. The energy storage unit is connected to the DC bus through a bidirectional DC-DC converter to balance the system power. The load types include resistive loads and constant power loads, among which the constant power loads include DC loads connected to the bus through a DC-DC converter and AC loads connected to the bus through a DC-AC inverter. The distributed power source selects photovoltaic units, and the energy storage unit selects batteries. In the energy storage unit, v bat and v bus are the energy storage battery output voltage and DC bus voltage respectively; i L is the current flowing through the energy storage inductor L; C1 is the battery filter capacitor; C bus is the DC bus capacitor; VT1 and VT2 are the power switch tubes of the energy storage unit, d and d′ are the duty ratios of VT1 and VT2 respectively, and the control signals of the two switch tubes are complementary, that is, d+d′=1. Only one of the switch tubes needs to be controlled, and the other switch tube can be operated at the same time; The state equation of the energy storage unit is: In formula (1), P L is the equivalent constant power load, which is the sum of the PV unit output power and the AC load power; Step 2: Model the bidirectional DC-DC converter control system for the DC microgrid Step 2.1: Modeling the flat inner loop of the current; Step 2.1 is as follows: Select the bidirectional DC-DC converter inductor current as the flat output variable y c and the state variable x c , that is: and c =x c =i L =ψ x (and c ) (4) In formula (4), ψ ( yc ) is the flat output variable y c The mapping function of The duty cycle of the switch tube VT1 is used as the control variable u c , after transforming formula (1), we get: Equations (4) and (5) meet the flatness requirements of the system; Step 2.2: Modeling of flat voltage outer loop; Step 2.2 is as follows: System DC bus capacitor C bus The stored energy E bus It is expressed as: When the internal loss of the system is ignored, the derivative of the DC bus capacitor energy is expressed as: In formula (7), P bat is the power output from the energy storage battery to the DC bus, P pv is the power output from the photovoltaic unit to the DC bus, P load is the load power, where P bat It is expressed as: P bat =i L v Bat (8) The energy stored in the capacitor and the voltage across the capacitor are taken as flat output variables y v and the state variable x v ,Right now: The control variable u v Defined as i Lref According to formula (7), we can get: Equations (9)-(11) meet the flatness requirements of the system; Step 3: Design of controller for bidirectional DC-DC converter of energy storage unit Step 3.1: Design of current inner loop differential flat control; Step 3.2: Design of voltage outer loop sliding mode anti-disturbance control Step 3.2.1: Establish the voltage outer loop model; Step 3.2.2: Design of enhanced-order filter extended state observer; Step 3.2.3: Sliding mode ADRC design.

2. The bidirectional DC-DC converter sliding mode auto-disturbance rejection control method based on flat theory according to claim 1 is characterized in that: Step 3.1 is as follows: Define the expected value of the current loop as i Lref =y cref , from equations (3)-(5), when the current inner loop controlled system is in steady state and the flat output variable strictly follows its reference trajectory, we have: When the current inner loop controlled system is in the dynamic adjustment process, the deviation of the flat output variable from its reference trajectory and the derivative and integral terms of the deviation have the following relationship: In formula (13), k1 and k2 are the feedback gains of the inner loop controller; The control object is equivalent to a second-order system to eliminate the steady-state error. The closed-loop transfer function of the system is: The current loop error is defined as According to formula (13) and (14), we can get: Combining equation (14) and equation (15), we get: In formula (16), ξ c is the damping ratio of the inner loop system, ω nc is the inner ring oscillation frequency; Combining equations (13) and (16), the differential term of the flat output variable is: According to formula (17), when k1 and k2 are positive, the inner loop system is stable and the controller parameter ξ c and ω nc The selection of determines the transient characteristics of the inner loop system. c When fixed, ω nc The larger the value, the faster the response of the inner loop system. nc It cannot be increased infinitely. The stability of the inner loop system requires that the inner loop bandwidth is much smaller than the system switching frequency, that is, the following relationship is satisfied: oh nc <<ω s =2πf s (18)。 3. The bidirectional DC-DC converter sliding mode auto-disturbance rejection control method based on flat theory according to claim 2 is characterized in that: Step 3.2.1 is as follows: According to formula (11), the energy function of the DC bus capacitor is: In formula (19), f is the total static loss of the photovoltaic unit and the energy storage unit; The first-order system that defines the energy function according to the ADRC paradigm is: In formula (20), ω = f(y v ,d,t)+(b-b0)u is the total disturbance required; y v is the DC bus capacitor energy E bus ,u v is the expected current signal output by the outer loop control to the inner loop, b is the precise value of the control gain, f(y v ,d,t) is the comprehensive characteristic of the time-varying dynamics and external disturbances generated in the system, and the easily available estimated value b0 is used as the control quantity gain b; From the combined equations (19) and (20), we can know that:

4. The sliding mode anti-disturbance control method of a bidirectional DC-DC converter based on flat theory according to claim 3 is characterized in that: Step 3.2.2 is as follows: According to formula (20), the state variables of the outer loop model are defined as: The outer loop system model is written as: In formula (23), According to formula (23), the designed ESO is: In formula (24), θ = [θ1, θ2, θ3] T ; θ1, θ2, θ3 are the observed values ​​of η1, η2, η3 respectively; e a =η1-θ1=y v -θ1 is the observation error of ESO; L = [l1, l2, l3] T is the gain of the observer; The characteristic polynomial of ESO is obtained by Laplace transforming equation (24) and then configured with the observer bandwidth: s 3 +l1s 2 +l2s+l3=(s+ω1) 3 (25) In formula (25), ω1 is the bandwidth of ESO, and the observer gain can be configured as l1 = 3ω1, l2 = 3ω1 2 , l3=ω1 3 , if the observer gain is adjusted based on the system bandwidth, the observation value can maintain a good tracking effect on the output and the total disturbance, that is, θ1→η1, θ2→η2, θ3→η3.

5. The sliding mode anti-disturbance control method of a bidirectional DC-DC converter based on flat theory according to claim 4 is characterized in that: Step 3.2.3 is as follows: Define the expected value of the voltage outer loop as E ref , the capacitance energy error is: And v =θ4-E ref (27) Derivative of formula (27) yields: Select the sliding surface S as: S=e v +c∫e v (29) The sliding mode reaching law is chosen as: In formula (30), w1>0, w2>0; According to equations (27)-(30), the voltage outer loop control law is: According to formula (24), the state variable η2, i.e., ω, representing the disturbance is expanded in the voltage outer loop model and tracked by the state variable θ2 of the ESO. After the low-pass filtering link of formula (26), θ2 becomes θ5. Substituting formula (31) into formula (23) eliminates the total disturbance η2, i.e., θ5. The original object is simplified to a single integral system, i.e.: In formula (32), u0 = -w1S - w2sign(S) - c(θ4 - E ref ).

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