Non-singular fast terminal sliding mode control method for bipolar DC micro-grid

Abstract

The invention relates to the technical field of bipolar direct-current micro-grid control, in particular to a nonsingular fast terminal sliding mode control method for a bipolar direct-current micro-grid. The method comprises the following steps: firstly, fitting a control system into a first-order system model according to an active-disturbance-rejection theory, and converting the first-order system model into an active-disturbance-rejection control system normal form; secondly, designing an extended state observer according to the first-order system model, improving the state observer into a finite time extended state observer, and defining an error function; then, according to the error function, defining a non-singular fast terminal sliding mode surface; then, designing a non-singular fast terminal sliding mode control law according to the singular fast terminal sliding mode surface; and finally, according to the finite time expansion state observer, obtaining a final nonsingular fast terminal sliding mode active-disturbance-rejection control law based on the finite time expansion state observer.

Description

Technical Field

[0001] The present invention relates to the technical field of bipolar direct current microgrid control, and in particular to a non-singular fast terminal sliding mode control method for a bipolar direct current microgrid. Background Art

[0002] With the rapid development of new energy industries and power electronics technology, DC microgrid systems are gaining widespread adoption due to their advantages, such as their lack of consideration for reactive power, harmonics, and synchronization issues. By simplifying the energy conversion process, DC microgrids reduce energy losses, improve system controllability, and effectively integrate and optimize distributed resources, adapting to the integration of new energy sources and new loads, while also promoting the modernization of the power market system. Bipolar DC microgrids effectively increase the utilization rate of DC bus power supply compared to unipolar structures. However, traditional control methods cannot meet the high speed and interference immunity requirements of bidirectional DC-DC converters.

[0003] In DC microgrids, traditional PI control can lead to large output voltage fluctuations and slow dynamic response when faced with sudden load changes or photovoltaic output variations due to its inherent characteristics and difficulty in parameter adjustment. Furthermore, the PI control strategy can also face DC bus voltage fluctuations and shocks due to difficulty in parameter adjustment and insufficient anti-interference capability, which can lead to reduced system stability. The integral control inherent in PI control can also lead to longer bus voltage regulation times and larger fluctuations.

[0004] To this end, a non-singular fast terminal sliding mode control method for bipolar DC microgrid is proposed. Summary of the Invention

[0005] The present invention provides a non-singular fast terminal sliding mode control method for a bipolar DC microgrid, which is used to solve the above-mentioned technical problems. First, based on the active disturbance rejection theory, the control system is fitted into a first-order system model and converted into an active disturbance rejection control system paradigm. Second, based on the first-order system model, an extended state observer is designed, which is improved into a finite-time extended state observer, and an error function is defined. Next, based on the error function, a non-singular fast terminal sliding mode surface is defined. Then, based on the non-singular fast terminal sliding mode surface, a non-singular fast terminal sliding mode control law is designed. Finally, based on the finite-time extended state observer, a final non-singular fast terminal sliding mode active disturbance rejection control law based on the finite-time extended state observer is obtained.

[0006] A non-singular fast terminal sliding mode control method for a bipolar DC microgrid comprises the following steps:

[0007] S1. According to the active disturbance rejection theory, the control system is fitted into a first-order system model and transformed into an active disturbance rejection control system paradigm;

[0008] S2. Designing an extended state observer based on the first-order system model, improving the extended state observer into a finite-time extended state observer and defining an error function;

[0009] S3. defining a sliding mode surface of a non-singular fast terminal sliding mode according to the error function;

[0010] S4. Designing a non-singular fast terminal sliding mode control law based on the non-singular fast terminal sliding mode surface;

[0011] S5. According to the finite-time extended state observer, a final non-singular fast terminal sliding mode active disturbance rejection control law based on the finite-time extended state observer is obtained.

[0012] Furthermore, according to the active disturbance rejection theory, the control system is fitted into a first-order system model and converted into an active disturbance rejection control system paradigm. The first-order system model is:

[0013]

[0014] Among them, a is the system parameter, y is the system output, is the first-order derivative of y, u is the input of the system, γ is the external disturbance of the system, and b is the input gain of the system;

[0015] The first-order system model is rewritten as:

[0016]

[0017] Where b0 is the estimated value of b and f(y,γ,t) is the total disturbance of the system.

[0018] Furthermore, based on the first-order system model, an extended state observer is designed, and the extended state observer is:

[0019]

[0020] Among them, x1 and x2 are state variables, expressed as:

[0021]

[0022] Where y is the system output, u is the system input, b0 is the estimated value of b, and f is the total disturbance of the system. is the first-order derivative of x1, is the first derivative of x2, is the first-order derivative of f.

[0023] Furthermore, according to the first-order system model, the extended state observer is improved into a finite-time extended state observer, which is:

[0024]

[0025] where sign(e1) is the sign function, expressed as:

[0026]

[0027] where e1 is the estimation error of the state variable x1, expressed as:

[0028]

[0029] where x1 and x2 are state variables, is the state estimate of x1, is the state estimate of x2, is the first derivative of, is the first derivative of, b0 is the estimate of b, e1 is the estimation error of the state variable x1, and λ1, λ2, and δ are parameters to be designed, with λ1 > 0, λ2 > 0, and δ ∈ (0, 1).

[0030] Furthermore, based on the first-order system model, an error function is defined, and the error function is:

[0031] e = y d - y;

[0032] where e is the error function, y is the output of the system, and y d is the expected output of the system.

[0033] Furthermore, based on the first-order system model, the sliding surface of the nonsingular fast terminal sliding mode is defined, and the sliding surface is:

[0034]

[0035] where the sign function sgn(e) and are used to ensure the rapid approach of the error and avoid steady-state oscillation; and achieve finite-time convergence by adjusting the power to improve the dynamic response speed;

[0036] where s is the sliding surface, e is the estimation error of the state variable x1, and a1, a2, b1, and b2 are parameters to be designed. a1 and a2 are sliding surface gains used to balance the weights of the error and its derivative, and need to satisfy being positive constants. b1 and b2 are power parameters and need to satisfy b1 > b2 and 1 < b2 < 2 to ensure the singularity and rapid convergence of the sliding surface, is the first derivative of e.

[0037] Furthermore, according to the sliding mode surface, a nonsingular fast terminal sliding mode control law is designed, and the nonsingular fast terminal sliding mode control law is as follows:

[0038]

[0039] where b0 is the estimated value of b, a1, a2, b1, b2, and α are parameters to be designed, a1 and a2 are positive constants, b1 > b2 and 1 < b2 < 2, e is the error function, is the second derivative of e, is the first derivative of e, k is the reaching law coefficient, is the first derivative of y d f is the total disturbance of the system, sgn(e) and sgn(s) are sign functions.

[0040] Furthermore, according to the finite-time extended state observer, the final nonsingular fast terminal sliding mode active disturbance rejection control law based on finite-time extended state observation is obtained, and the nonsingular fast terminal sliding mode active disturbance rejection control law based on finite-time extended state observation is as follows:

[0041]

[0042] where b0 is the estimated value of b, a1, a2, b1, b2, and α are parameters to be designed, a1 and a2 are positive constants, b1 > b2 and 1 < b2 < 2, e is the error function, is the second derivative of e, is the first derivative of e, k is the reaching law coefficient, is the first derivative of y d sgn(e) and sgn(se) are sign functions, is the estimated value of the disturbance.

[0043] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0044] 1. By adopting active disturbance rejection control, it does not depend on an accurate mathematical model, can effectively cope with external disturbances existing in the system, can thus achieve fast output and high tracking accuracy, can further improve the stability of the DC bus voltage under dynamic power disturbances, and进而提高直流微电网的稳定性。

[0045] ​2. Combined with the finite-time expanded state observer, it can ensure that the observation error is bounded within a finite time and can converge to a given range at a speed no less than exponential convergence, thereby improving the system's response speed and control accuracy, and effectively improving the stability of the system output; it can also quickly and accurately observe unknown disturbances in the system, avoid DC bus voltage overshoot, improve the reliability of the converter, and effectively suppress current fluctuations.

[0046] 3. The use of a non-singular fast terminal sliding mode controller can enable the system state to converge quickly to zero within a finite time, which is beneficial to improving the dynamic response speed of the bipolar DC microgrid; when a disturbance is applied, the non-singular fast terminal sliding mode controller can avoid using a large switching gain through feedforward compensation, reducing the system's jitter; in the face of parameter changes and external interference, the non-singular fast terminal sliding mode controller can improve the robustness of the system, so that the bipolar DC microgrid can maintain stability even when various load and power supply conditions change, thereby effectively improving the DC bus power supply utilization. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a flow chart of a non-singular fast terminal sliding mode control method for a bipolar DC microgrid provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0048] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0049] Compared with the unipolar structure, the bipolar DC microgrid contains two voltage levels and can be connected to loads, distributed power supplies and energy storage systems of different voltage levels. It can effectively improve the utilization rate of DC bus power supply and has been widely used. However, when the positive and negative power deviations of the bipolar DC microgrid are large, it is difficult to balance the neutral voltage; and multiple voltage balancers are also difficult to coordinate and control. However, the traditional PI control parameters are difficult to adjust, so the anti-interference ability is not strong, and the control speed and accuracy are low. To this end, the present invention provides a non-singular fast terminal sliding mode self-disturbance rejection control method for a bipolar DC microgrid. By designing a finite time extended state observer and a non-singular fast terminal sliding mode control, the method can accurately and quickly observe interference, so that the system parameters can be quickly adjusted according to the interference, and can improve the response speed and control accuracy of the system, effectively improving the stability of the system output. In order to illustrate the feasibility of the present invention, two specific embodiments will be described below.

[0050] Example 1

[0051] In the embodiment of the present application, a non-singular fast terminal sliding mode control method for a bipolar DC microgrid is adopted; the specific implementation process is as follows Figure 1 As shown in the figure, first, according to the active disturbance rejection theory, the control system is defined as a first-order system model and converted into an active disturbance rejection control system paradigm; then, according to the first-order system model, an extended state observer is designed, and the state observer is improved into a finite-time extended state observer and an error function is defined; then, according to the error function, the sliding surface of the non-singular fast terminal sliding mode is defined; then, according to the non-singular fast terminal sliding mode surface, a non-singular fast terminal sliding mode control law is designed; finally, according to the finite-time extended state observer, the final non-singular fast terminal sliding mode active disturbance rejection control law based on the finite-time extended state observer is obtained.

[0052] Furthermore, the specific implementation process of the embodiment of the present application is as follows: In the embodiment of the present application, based on the simulation system of wind-solar complementary, the initial conditions of the system are set as follows: the light intensity is 1000W / m 2 ; The ambient temperature is 25℃; the wind speed is 5m / s; the switching frequency is 20kHz; the parameter values ​​of the non-singular fast terminal sliding mode active disturbance rejection control system are: a1=250, a2=35, b1=1.05, b2=1.02, b0=200; the DC bus voltage is 700V, and the two-stage voltage is 350V; the system load jumps from 23A to 46A at 0.5s, and from 46A to 23A at 1s.

[0053] According to the active disturbance rejection theory, the control system is fitted into a first-order system model and transformed into an active disturbance rejection control system paradigm. The first-order system model is:

[0054]

[0055] Among them, a is the system parameter, y is the system output, is the first-order derivative of y, u is the input of the system, γ is the external disturbance of the system, and b is the input gain of the system;

[0056] The first-order system model is rewritten as:

[0057]

[0058] Where f(y,γ,t) is the total disturbance of the system.

[0059] In an embodiment of the present application, the system is simplified into a first-order system model based on the self-disturbance rejection theory, so that the system does not rely on the accurate model of the system and simplifies the complexity of the design. The strong robustness of the self-disturbance rejection control to model uncertainty and external interference enables the system to maintain system stability when facing uncertain disturbances and parameter mutations, thereby improving the stability of the bus voltage.

[0060] Furthermore, based on the first-order system model, an extended state observer is designed, and the extended state observer is:

[0061]

[0062] Among them, x1 and x2 are state variables, expressed as:

[0063]

[0064] Where y is the system output, u is the system input, b0 is the estimated value of b, and f is the total disturbance of the system. is the first-order derivative of x1, is the first derivative of x2, is the first-order derivative of f.

[0065] In an embodiment of the present application, an extended state observer is designed to observe the total disturbance of the system. The system can accurately estimate the unknown dynamics and external disturbances within the system in real time, so that the system can respond quickly and accurately, and adjust parameters to compensate for disturbances, thereby improving the system's anti-interference ability, enhancing the system's robustness and improving control accuracy.

[0066] Furthermore, according to the first-order system model, the extended state observer is improved into a finite-time extended state observer, which is:

[0067]

[0068] Among them, sgn(e1) is the sign function, which is expressed as:

[0069]

[0070] Among them, e1 is the estimated error of the state variable x1, expressed as:

[0071]

[0072] Among them, x1 and x2 are state variables, is the state estimate of x1, is the state estimate of x2, for The first derivative of for The first derivative, where a1 is the estimation error of the state variable x1, λ1, λ2, and δ are parameters to be designed, λ1 > 0, λ2 > 0, and δ ∈ (0, 1).

[0073] In the embodiment of the present application, the extended state observer is improved to a finite-time extended state observer. By introducing a non-linear term, the finite-time estimation of the extended state is guaranteed, enhancing the robustness of the control system; moreover, it can make the observation error of the extended state converge to zero within a finite time, thereby improving the response speed of the microgrid system and the stability of the output voltage.

[0074] Furthermore, according to the first-order system model, an error function is defined, and the error function is as follows:

[0075] e = y d - y;

[0076] where e is the error function, y is the output of the system, and y d is the desired output of the system.

[0077] In the embodiment of the present application, the output error function of the system is defined. By clarifying the output error, the control system can be adjusted to reduce the error. This method can effectively reflect the problems existing in the system through the error function, enabling the system to be corrected in real time to ensure the stability of the output voltage of the microgrid and is conducive to improving the control accuracy of the system.

[0078] Furthermore, according to the first-order system model, the sliding surface of the non-singular fast terminal sliding mode is defined, and the sliding surface is:

[0079]

[0080] where the sign function sgn(e) and are used to ensure the rapid approach of the error and avoid steady-state oscillation; |e| 1.05 [[ID=三十二]]and achieve finite-time convergence by adjusting the power to improve the dynamic response speed;

[0081] where s is the sliding surface, e is the estimation error of the state variable x1, a1, a2, b1, and b2 are parameters to be designed, a1 and a2 are sliding surface gains used to balance the weights of the error and its derivative, and need to satisfy being positive constants, b1 and b2 are power parameters, and need to satisfy b1 > b2 and 1 < b2 < 2 to ensure the singularity and fast convergence of the sliding surface, is the first derivative of e.

[0082] In an embodiment of the present application, a sliding surface of a non-singular fast terminal sliding mode is defined so that the system trajectory can reach the sliding surface within a finite time. When reaching the sliding surface, the system slides along the sliding surface, thereby enabling the system to converge quickly, thereby improving the response speed and control accuracy of the system, and enabling the microgrid system to maintain the stability of the output voltage even when subjected to external interference or parameter mutations.

[0083] Furthermore, according to the sliding surface, a non-singular fast terminal sliding mode control law is designed. The non-singular fast terminal sliding mode control law is:

[0084]

[0085] Wherein, e is the error function, is the second-order derivative of e, is the first-order derivative of e, α is the parameter to be designed, k is the reaching law coefficient, y d The first-order derivative of , f is the total disturbance of the system.

[0086] In an embodiment of the present application, a non-singular fast terminal sliding mode controller is designed, which can enable the system to quickly approach the equilibrium state and converge within a finite time, thereby improving the response speed of the system; moreover, the non-singular fast terminal sliding mode control can effectively suppress chattering, so that the output voltage can remain stable; in the presence of external disturbances or parameter mutations, the non-singular fast terminal sliding mode control can enable the system to maintain stability and good performance, thereby improving the stability and control accuracy of the system.

[0087] Furthermore, according to the finite-time extended state observer, the final non-singular fast terminal sliding mode active disturbance rejection control law based on the finite-time extended state observation is obtained. The non-singular fast terminal sliding mode active disturbance rejection control law based on the finite-time extended state observation is:

[0088]

[0089] Wherein, e is the error function, is the second-order derivative of e, is the first-order derivative of e, k is the reaching law coefficient, α is the parameter to be designed, y d The first derivative of The perturbation estimate of

[0090] In the embodiments of the present application, active disturbance rejection control and a finite-time extended state observer are introduced into a non-singular fast terminal sliding mode controller. The active disturbance rejection control technology can directly handle unknown disturbances in the system by estimating and compensating for the internal and external disturbances of the system, thereby improving the performance of the system in the face of complex environments and uncertainties, enabling the system to more accurately estimate and compensate for disturbances, thereby improving the control accuracy of the system; the finite-time extended state observer can more accurately estimate and compensate for disturbances;

[0091] When the disturbance to the system changes, the system can respond quickly and accurately, thereby improving the system's anti-interference ability and control accuracy; non-singular fast terminal sliding mode control can enable the system to quickly converge to an equilibrium state within a certain period of time. The combination of the three improves the anti-interference ability and response speed of the microgrid system and ensures the stability of the output voltage.

[0092] Example 2

[0093] The following table is a comparison table of the effects of dual closed-loop PI control and non-singular fast terminal sliding mode control in the above embodiment;

[0094] Table 10. Comparison of bus voltage transient performance between dual closed-loop PI and non-singular fast terminal sliding mode active disturbance rejection control at 5s

[0095] Control strategy Voltage overshoot / V Overshoot adjustment time / s Double closed-loop PI 30 0.22 Non-singular fast terminal sliding mode active disturbance rejection control 18 0.07

[0096] Table 2 Comparison of bus voltage transient performance of dual closed-loop PI and non-singular fast terminal sliding mode active disturbance rejection control at 1s

[0097] Control strategy Voltage overshoot / V Overshoot adjustment time / s Double closed-loop PI 31 0.21 Non-singular fast terminal sliding mode active disturbance rejection control 15 0.09

[0098] These two tables show the impact of dual closed-loop PI control and non-singular fast terminal sliding mode active disturbance rejection control on bus voltage transient performance under two different time conditions: 0.5 seconds and 1 second. Specifically, the tables compare the performance of these two control strategies on bus voltage overshoot and overshoot adjustment time at different time points.

[0099] At 0.5 seconds, the voltage overshoot for dual closed-loop PI control was 30 volts, with an overshoot adjustment time of 0.22 seconds, while the voltage overshoot for non-singular fast-terminal sliding-mode active disturbance rejection control was 18 volts, with an overshoot adjustment time of 0.07 seconds. At 1 second, the voltage overshoot for dual closed-loop PI control increased slightly to 31 volts, with an overshoot adjustment time of 0.21 seconds, while the voltage overshoot for non-singular fast-terminal sliding-mode active disturbance rejection control decreased to 15 volts, with an overshoot adjustment time of 0.09 seconds.

[0100] Comparing the data in the two tables, we can see that non-singular fast terminal sliding mode ADRC outperforms dual closed-loop PI control in both voltage overshoot and regulation time. Non-singular fast terminal sliding mode ADRC not only more effectively suppresses voltage overshoot but also more quickly adjusts the voltage back to normal. Furthermore, over time, the voltage overshoot of dual closed-loop PI control increases, while that of non-singular fast terminal sliding mode ADRC decreases. This may indicate that non-singular fast terminal sliding mode ADRC is more stable over longer timescales. Overall, non-singular fast terminal sliding mode ADRC demonstrates superior control effectiveness.

[0101] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A non-singular fast terminal sliding mode control method for a bipolar DC microgrid, characterized in that: The following steps are involved: S1. According to the active disturbance rejection theory, the control system is fitted into a first-order system model and transformed into an active disturbance rejection control system paradigm; S2. Designing an extended state observer based on the first-order system model, improving the extended state observer into a finite-time extended state observer and defining an error function; S3. defining a sliding mode surface of a non-singular fast terminal sliding mode according to the error function; S4. Designing a non-singular fast terminal sliding mode control law based on the sliding surface; S5. According to the finite-time extended state observer, a final non-singular fast terminal sliding mode control law based on the finite-time extended state observer is obtained.

2. The non-singular fast terminal sliding mode control method for a bipolar DC microgrid according to claim 1, characterized in that: According to the active disturbance rejection theory, the control system is fitted into a first-order system model and transformed into an active disturbance rejection control system paradigm. The first-order system model is: Among them, a is the system parameter, y is the system output, is the first-order derivative of y, u is the input of the system, γ is the external disturbance of the system, and b is the input gain of the system; The first-order system model is rewritten as: Where b0 is the estimated value of b and f(y,γ,t) is the total disturbance of the system.

3. The non-singular fast terminal sliding mode control method for a bipolar DC microgrid according to claim 1, characterized in that: According to the first-order system model, an extended state observer is designed, which is: Among them, x1 and x2 are state variables, expressed as: Where y is the system output, u is the system input, b0 is the estimated value of b, and f is the total disturbance of the system. is the first-order derivative of x1, is the first derivative of x2, is the first-order derivative of f.

4. The non-singular fast terminal sliding mode control method for a bipolar DC microgrid according to claim 1, characterized in that: According to the first-order system model, the extended state observer is improved into a finite-time extended state observer, which is: Among them, sgn(e1) is the sign function, which is expressed as: Among them, e1 is the estimated error of the state variable x1, expressed as: Among them, x1 and x2 are state variables, is the state estimate of x1, is the state estimate of x2, for The first derivative of for The first-order derivative of , b0 is the estimated value of b, e1 is the estimated error of the state variable x1, λ1, λ2 and δ are the parameters to be designed, λ1>0, λ2>0, δ∈(0,1).

5. The non-singular fast terminal sliding mode control method for a bipolar DC microgrid according to claim 1, characterized in that: According to the first-order system model, an error function is defined, which is: e=y d -and; Wherein, e is the error function, y is the output of the system, and y d is the expected output of the system.

6. The non-singular fast terminal sliding mode control method for a bipolar DC microgrid according to claim 4, characterized in that: According to the first-order system model, the sliding surface of the non-singular fast terminal sliding mode is defined, and the sliding surface is: Where s is the sliding surface, e is the error function, a1, a2, b1 and b2 are the parameters to be designed, a1 and a2 are positive constants, b1>b2 and 1 <b2<2, is the first-order derivative of e, and sgn(e) is the sign function.

7. The non-singular fast terminal sliding mode control method for a bipolar DC microgrid according to claim 1, characterized in that: According to the sliding surface, a non-singular fast terminal sliding mode control law is designed. The non-singular fast terminal sliding mode control law is: where, b0 is the estimated value of b, a1, a2, b1, b2 and α are parameters to be designed, a1 and a2 are positive constants, b1 > b2 and 1 < b2 < 2, e is the error function, is the second derivative of e, is the first derivative of e, k is the reaching law coefficient, is the first derivative of y d , f is the total disturbance of the system, sgn(e) and sgn(s) are sign functions.

8. The non-singular fast terminal sliding mode control method for a bipolar DC microgrid according to claim 1, characterized in that: According to the finite-time extended state observer, the final non-singular fast terminal sliding mode active disturbance rejection control law based on the finite-time extended state observation is obtained. The non-singular fast terminal sliding mode active disturbance rejection control law based on the finite-time extended state observation is: where, b0 is the estimated value of b, a1, a2, b1, b2 and α are parameters to be designed, a1 and a2 are positive constants, b1 > b2 and 1 < b2 < 2, e is the error function, is the second derivative of e, is the first derivative of e, k is the reaching law coefficient, is the first derivative of y d , sgn(e) and sgn(s) are sign functions, is the estimated value of the disturbance.

Images