Non-singular terminal sliding mode active disturbance rejection control method for two-stage energy storage converter

Abstract

The present invention discloses a non-singular terminal sliding mode auto-disturbance rejection control method for a two-stage energy storage converter. Based on the auto-disturbance rejection theory, the state equation of the energy storage converter in the dq coordinate system is converted into an auto-disturbance rejection paradigm, the system coupling term and the part unrelated to the control quantity are equivalent to a lumped disturbance, observation compensation is performed through a fixed-time observer, and then a non-singular terminal sliding mode control law is designed as a feedback control law to replace the linear feedback in the auto-disturbance rejection, thereby improving the speed of error convergence; the transient time of the short state can be effectively shortened, the overshoot is reduced, and the grid-connected power quality is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of power electronic converters, and in particular relates to a non-singular terminal sliding mode auto-disturbance rejection control method for a two-stage energy storage converter. Background Art

[0002] With the rapid development of renewable energy generation technologies, the scale of renewable energy power station construction is increasing. However, renewable energy generation is subject to climate change, resulting in a certain degree of randomness and volatility. Therefore, the construction of renewable energy power stations is often accompanied by energy storage devices to improve energy utilization. In energy storage systems, the power conversion system (PCS), as the hub connecting the energy storage battery and the main power grid, is crucial for the reliable operation of the entire energy storage system. Existing PCS control strategies mostly use linear proportional-integral (PI) control, but PI control has certain shortcomings, such as large overshoot, long transition times, and poor disturbance rejection during transient conditions. Existing nonlinear control methods include model predictive control, fuzzy control, active disturbance rejection control (ADRC), and sliding mode control. While model predictive control and fuzzy control can effectively handle nonlinear systems and exhibit good robustness, they are computationally intensive or require extensive data training, are highly dependent on the model, and also rely on the designer's subjective experience. Summary of the Invention

[0003] The purpose of the present invention is to provide a non-singular terminal sliding mode auto-disturbance rejection control method for a two-stage energy storage converter, which solves the problems of large overshoot and long transition time when the energy storage converter experiences power fluctuations and DC bus voltage fluctuations under the existing PI control strategy.

[0004] The technical solution adopted by the present invention is a non-singular terminal sliding mode active disturbance rejection control method for a two-stage energy storage converter, which is specifically implemented according to the following steps:

[0005] Step 1: Establish a mathematical model of the energy storage converter in the abc coordinate system, and convert the mathematical model in the abc coordinate system into the state equation of the dq rotating coordinate system through Park transformation;

[0006] Step 2: Based on the dq coordinate system state equation, the coupling terms of the converter system and other parts unrelated to the controlled variables are equivalent to the total disturbance to design a fixed-time convergence observer;

[0007] Step 3: Design a non-singular terminal sliding mode combined with a fast power reaching law as the feedback control law to replace the PD feedback in the linear active disturbance rejection control.

[0008] The present invention is also characterized in that:

[0009] Step 1 is specifically as follows:

[0010] The two-stage energy storage converter structure includes a battery energy storage system, a bidirectional DC / DC converter, a DC / AC converter, and a filter. The mathematical model of the energy storage converter in the abc stationary coordinate system is:

[0011]

[0012] In formula (1), u a 、u b 、u c is the three-phase voltage on the grid side, i a 、i b 、i c is the three-phase current on the grid side, u ga 、u gb 、u gc is the AC grid voltage, L and C are filter parameters, R is the line equivalent resistance parameter, C dc is the voltage stabilizing capacitor, i dc is the DC bus current, u dc is the DC bus voltage, i r is the battery current, s j is the switching function representing the on-off state of each bridge arm switch in the converter, j = a, b, c,

[0013]

[0014] The equation (1) in the stationary coordinate system is transformed into the AC side differential equation in the dq rotating coordinate system:

[0015]

[0016] In formula (3), ω is the grid voltage angular frequency, u dr =s d u dc ,u qr =s q u dc , s d 、s q are the d and q axis switching functions, u d 、u q are the components of the converter output voltage on the d and q axes, i d 、i q are the components of the grid-side current on the d-axis and q-axis respectively.

[0017] Step 2 is specifically as follows:

[0018] Converting Equation (3) into the ADRC paradigm is:

[0019]

[0020] In formula (6), b1 and b2 are the gains of the d-axis and q-axis control variables, respectively. f1 and f2 are the equivalent lumped disturbances of the d-axis and q-axis, respectively. The lumped disturbance includes the unmodeled part of the system, the coupled part, and the internal and external disturbances of the system. The lumped disturbance expression is:

[0021]

[0022] Let the state variable x d1 =i d , x d2 =f1,x q1 =i q , x q2 =f2, then formula (6) can be written as follows:

[0023]

[0024] According to formula (8), the form of the fixed time convergence observer is designed as follows:

[0025]

[0026] In formula (9), z1, z3, are the system state variables i d 、i q The observed values of z2 and z4, the observed values of the total disturbance f1 and f2, α i =iα-(i-1),β i =iβ-(i-1), i=1,2, l1, l2 are both greater than 0, h1, h2 are both greater than 0, l1, l2, h1, h2 are observer gains, α=(1-ε,1), β=(1,1+γ), 0<ε<1, 0<γ<1;

[0027] Operator sig in the observer α The specific form of (e) is:

[0028] sig α (e)=|e| α sign(e) (10)

[0029] sign(e) is the sign function, and its specific content is:

[0030]

[0031] Step 3 is as follows:

[0032] Let i after coordinate transformation d 、i q The deviations e1 and e2 from their corresponding reference values are:

[0033]

[0034] In formula (12), i dref for i d Reference value, i qref for i q Reference value of

[0035] Based on formula (12), the non-singular terminal sliding mode functions s1 and s2 of the d and q axes are constructed as follows:

[0036]

[0037] In formula (13), c1, c2>0, 1 <p / q<2;

[0038] The fast power reaching law is selected as the sliding mode switching control law:

[0039]

[0040] In formula (14), k1, k2>0, 0 <a<1;

[0041] The inner loop current control law is calculated by combining equations (8) to (14):

[0042]

[0043] i dref and i qref The specific form is as follows:

[0044] On the basis of the three-phase balance of the grid voltage, the d-axis direction of the grid voltage is taken as the direction of the voltage vector, that is, u d =u g ,u q =0, according to the instantaneous power theory, the instantaneous power on the AC side of the converter is:

[0045]

[0046] In formula (4), P is the active power output of the converter on the AC side, and Q is the reactive power output of the converter on the AC side;

[0047] The dq axis current reference value i is calculated by formula (4): dref 、i qref The relationship with power is:

[0048]

[0049] The beneficial effects of the present invention are:

[0050] The present invention discloses a non-singular terminal sliding mode auto-disturbance rejection control method for a two-stage energy storage converter. Based on the auto-disturbance rejection theory, the state equation of the energy storage converter in the dq coordinate system is converted into an auto-disturbance rejection paradigm. The system coupling terms and the parts unrelated to the control quantity are equivalent to lumped disturbances. Observation compensation is performed through a fixed-time observer. Then, a non-singular terminal sliding mode control law is designed as a feedback control law to replace the linear feedback in the auto-disturbance rejection method, thereby improving the error convergence speed. The method can effectively shorten the transition time of the short state, reduce the overshoot, and improve the grid-connected power quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a structural diagram of a two-stage energy storage converter;

[0052] Figure 2 This is the circuit topology diagram of the subsequent DC / AC converter;

[0053] Figure 3 is the block diagram of the fixed-time convergence observer;

[0054] Figure 4 This is a block diagram of non-singular terminal sliding mode feedback control;

[0055] Figure 5 It is the overall control diagram of the two-stage energy storage converter;

[0056] Figure 6 shows the power response diagrams under different control strategies, where Figure 6(a) is the PCS output active power response diagram, and Figure 6(b) is the active power transient magnification diagram;

[0057] Figure 7 is the DC bus voltage response diagram;

[0058] FIG8 is a harmonic analysis diagram under different control strategies, wherein FIG8(a) is a harmonic analysis diagram of PI control, FIG8(b) is a harmonic analysis diagram of ADRC, and FIG8(c) is a harmonic analysis diagram of the control method of the present invention. DETAILED DESCRIPTION

[0059] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0060] Example 1

[0061] This embodiment provides a non-singular terminal sliding mode active disturbance rejection control method for a two-stage energy storage converter, which is specifically implemented according to the following steps:

[0062] Step 1: Establish a mathematical model of the energy storage converter in the abc coordinate system, and convert the mathematical model in the abc coordinate system into the state equation of the dq rotating coordinate system through Park transformation;

[0063] like Figure 1As shown in Figure 2, the two-stage energy storage converter structure includes a battery energy storage system (BESS), a bidirectional DC / DC converter, a DC / AC converter and a filter. Figure 2 It can be seen that according to Kirchhoff's law, the mathematical model of the energy storage converter in the abc stationary coordinate system is:

[0064]

[0065] In formula (1), u a 、u b 、u c is the three-phase voltage on the grid side, i a 、i b 、i c is the three-phase current on the grid side, u ga 、u gb 、u gc is the AC grid voltage, L and C are filter parameters, R is the line equivalent resistance parameter, C dc is the voltage stabilizing capacitor, i dc is the DC bus current, u dc is the DC bus voltage, i r is the battery current, s j is the switching function representing the on-off state of each bridge arm switch in the converter, j = a, b, c,

[0066]

[0067] The equation (1) in the stationary coordinate system is transformed into the AC side differential equation in the dq rotating coordinate system:

[0068]

[0069] In formula (3), ω is the grid voltage angular frequency, u dr =s d u dc ,u qr =s q u dc , s d 、s q are the d and q axis switching functions, u d 、u q are the components of the converter output voltage on the d and q axes, i d 、i q are the components of the grid-side current on the d-axis and q-axis respectively;

[0070] Step 2: Based on the dq coordinate system state equation, the coupling terms of the converter system and other parts unrelated to the controlled variables are equivalent to the total disturbance to design a fixed-time convergence observer;

[0071] Step 3: Design a non-singular terminal sliding mode combined with a fast power reaching law as the feedback control law to replace the PD feedback in the linear active disturbance rejection control.

[0072] Example 2

[0073] This embodiment provides a non-singular terminal sliding mode active disturbance rejection control method for a two-stage energy storage converter. Based on embodiment 1, step 2 is specifically as follows:

[0074] Converting Equation (3) into the ADRC paradigm is:

[0075]

[0076] In formula (6), b1 and b2 are the gains of the d-axis and q-axis control variables, respectively. f1 and f2 are the equivalent lumped disturbances of the d-axis and q-axis, respectively. The lumped disturbance includes the unmodeled part of the system, the coupled part, and the internal and external disturbances of the system. The lumped disturbance expression is:

[0077]

[0078] Let the state variable x d1 =i d , x d2 =f1,x q1 =i q , x q2 =f2, then formula (6) can be written as follows:

[0079]

[0080] like Figure 3 As shown, the form of designing a fixed-time convergence observer according to formula (8) is:

[0081]

[0082] In formula (9), z1, z3, are the system state variables i d 、i q The observed values of z2 and z4, the observed values of the total disturbance f1 and f2, α i =iα-(i-1),β i =iβ-(i-1), i=1,2, l1, l2 are both greater than 0, h1, h2 are both greater than 0, l1, l2, h1, h2 are observer gains, α=(1-ε,1), β=(1,1+γ), 0<ε<1, 0<γ<1;

[0083] Operator sig in the observer α The specific form of (e) is:

[0084] sigα (e)=|e| α sign(e) (10)

[0085] sign(e) is the sign function, and its specific content is:

[0086]

[0087] Example 3

[0088] This embodiment provides a non-singular terminal sliding mode auto-disturbance rejection control method for a two-stage energy storage converter. Based on the embodiment 1-2, as shown in FIG. Figure 4 As shown in Figure 3, step 3 designs a non-singular terminal sliding mode control law as the feedback control law in the active disturbance rejection control. Compared with the ordinary sliding mode control, the non-singular terminal sliding mode can converge to the equilibrium point in a finite time and solve the singular point problem of the terminal sliding mode surface. Step 3 is specifically as follows:

[0089] Let i after coordinate transformation d 、i q The deviations e1 and e2 from their corresponding reference values are:

[0090]

[0091] In formula (12), i dref for i d Reference value, i qref for i q Reference value; On the basis of the three-phase balance of the grid voltage, the d-axis direction of the grid voltage is taken as the direction of the voltage vector, that is, u d =u g ,u q =0, according to the instantaneous power theory, the instantaneous power on the AC side of the converter is:

[0092]

[0093] In formula (4), P is the active power output of the converter on the AC side, and Q is the reactive power output of the converter on the AC side;

[0094] The dq axis current reference value i is calculated by formula (4): dref 、i qref The relationship with power is:

[0095]

[0096] Based on formula (12), the non-singular terminal sliding mode functions s1 and s2 of the d and q axes are constructed as follows:

[0097]

[0098] In Equation (13), \(c_1, c_2 \gt 0\), and \(1 \lt \frac{p}{q} \lt 2\);

[0099] Select the fast power approaching law as the sliding mode switching control law:

[0100]

[0101] In Equation (14), \(k_1, k_2 \gt 0\), and \(0 \lt a \lt 1\); when the initial state of the system is far from the sliding mode surface, the exponential term can ensure a relatively fast approaching speed, and when the system state is close to the sliding mode surface, the power term plays a major role. The power term can change the approaching speed according to the magnitude of the system state and effectively reduce the chattering phenomenon in the approaching motion;

[0102] By combining Equations (8) to (14) and calculating, the inner-loop current control law is obtained as:

[0103]

[0104] The non-singular terminal sliding mode active disturbance rejection control method of the two-stage energy storage converter in the present invention realizes a non-singular terminal sliding mode active disturbance rejection control strategy for the stable output power and DC bus voltage in the transient state of the two-stage energy storage converter. In the energy storage system, the DC / DC converter is used to control and manage the voltage of the energy storage battery to supply power to the subsequent DC / AC converter, and then the electric energy output by the energy storage converter is connected to the grid for use. The energy storage system can achieve bidirectional flow, so the grid electric energy can also charge the energy storage battery through the energy storage converter. The control block diagram of the present invention is as Figure 5 shown. The active disturbance rejection control (ADRC) and sliding mode control are used in combination. The active disturbance rejection control takes the extended state observer as the core, does not rely on the accurate modeling of the system, and has good application prospects in nonlinear systems. The sliding mode control is insensitive to parameters and has the characteristics of fast convergence speed and strong anti-disturbance performance. The present invention obtains the current loop reference value from the power reference value and designs according to the current state equation to improve the transient performance of the system.

[0105] Simulation analysis

[0106] To verify the feasibility of the non-singular terminal sliding mode active disturbance rejection control method of the two-stage energy storage converter in the present invention, a two-stage energy storage converter circuit is built in the Simulink software, and the control proposed in the present invention is compared and analyzed with the traditional PI control and active disturbance rejection control. The simulation circuit parameters are: battery voltage \(V\) bat \( = 500V\), voltage stabilizing capacitor \(C\) dc \( = 1mF\), DC bus voltage \(V\) dc \( = 800V\), filter inductor \(L = 2mH\), filter capacitor \(C = 50\mu F\), equivalent resistance \(R = 0.01\Omega\), grid voltage \(u\) g=220V, switching frequency f=20kHz; controller parameters are: k1=4000, k2=700, p=7, q=5, α=0.75, β=1.5, a=0.8, l1=6×10 3 , l2=9×10 6 , h1=4×10 3 , h2=4×10 6 , c 1,2 =40.

[0107] Figure 6 shows the output power waveform of the energy storage converter under different control strategies. As shown in Figure 6(a), three power jumps were set in the simulation: the output power jumped from 20kW to 60kW at 0.25s, the power jumped from 60kW to 30kW at 0.3s, and the power jumped from 30kW to -20kW at 0.35s ("-" indicates that the energy storage system switches from emitting power to absorbing power). Figure 6(b) is an enlarged view of the transient moment. It can be seen from the enlarged view that the control proposed by the present invention has a faster convergence speed than PI control and anti-disturbance control, and the transient transition is smoother with basically no overshoot. Figure 7 Table 1 shows the transient fluctuations of the DC bus voltage under different control strategies. The transient moments correspond to three power fluctuations. Table 1 shows the transient transition time and overshoot of the DC bus voltage. As can be seen from the table, the transition time from transient to steady state under the proposed control strategy is significantly shorter than that under PI control and active disturbance rejection control, and the overshoot generated during this transition is also significantly smaller than that under PI control and active disturbance rejection control. Figure 8 shows the harmonic analysis of the grid-connected current under different control strategies. The figure shows that the THD under PI control is 3.24%, the THD under active disturbance rejection control is 1.97%, and the THD under the proposed control is 0.92%. The proposed control strategy has lower harmonic content and provides higher power quality.

[0108] Table 1 DC bus voltage transient transition time and overshoot

[0109]

[0110]

Claims

1. A non-singular terminal sliding mode active disturbance rejection control method for a two-stage energy storage converter, characterized in that: Please follow the steps below to implement it: Step 1: Establish a mathematical model of the energy storage converter in the abc coordinate system, and convert the mathematical model in the abc coordinate system into the state equation of the dq rotating coordinate system through Park transformation; The step 1 is specifically as follows: The two-stage energy storage converter structure includes a battery energy storage system, a bidirectional DC / DC converter, a DC / AC converter, and a filter. The mathematical model of the energy storage converter in the abc stationary coordinate system is: (1) In formula (1), u a 、 u b 、 u c is the three-phase voltage on the grid side, i a 、 i b 、 i c is the three-phase current on the grid side, u ga 、 u gb 、 u gc is the AC grid voltage, L, C is the filtering parameter, R is the line equivalent resistance parameter, C dc is the voltage stabilizing capacitor, i dc is the DC bus current, u dc is the DC bus voltage, i r is the battery current, s j is the switching function that represents the on-off state of each bridge arm switch in the converter, j = a,b,c , (2)； The equation (1) in the stationary coordinate system is transformed into the AC side differential equation in the dq rotating coordinate system: (3) In formula (3), ω is the grid voltage angular frequency, u dr = s d u dc , u qr = s q u dc , s d 、 s q are the d-axis and q-axis switching functions, u d 、 u q are the components of the converter output voltage on the d and q axes, i d 、 i q are the components of the grid-side current on the d-axis and q-axis respectively; Step 2: Based on the dq coordinate system state equation, the coupling terms of the converter system and other parts unrelated to the controlled variables are equivalent to the total disturbance to design a fixed-time convergence observer; The step 2 is specifically as follows: Converting Equation (3) into the ADRC paradigm is: (4) In formula (4), b 1. b 2 are the control gain of d-axis and q-axis respectively, f 1. f 2 are the equivalent lumped disturbances of the d-axis and q-axis respectively. The lumped disturbances include the unmodeled part of the system, the coupled part, and the internal and external disturbances of the system. The lumped disturbance expression is: (5) Let the state variable x d1 = i d , x d2 = f 1, x q1 =i q , x q2 = f 2, then formula (4) can be written as follows: (6) According to formula (6), the form of the fixed time convergence observer is designed as follows: (7) In formula (7), z 1. z 3. System state quantity i d 、 i q The observed value of z 2. z 4 Total disturbance f 1. f 2 observations, α i = iα -( i -1), β i = iβ -( i -1), i =1,2, l 1. l 2 are both greater than 0, h 1. h 2 are both greater than 0, l 1. l 2. h 1. h 2 is the observer gain, α =(1- ε ,1), β =(1,1+ γ ), 0< ε< 1,0< γ< 1; Operators in the Observer sig α ( e ) is in the form of: (8) sign( e ) is a symbolic function, and its specific content is: (9)； Step 3: Design a non-singular terminal sliding mode combined with a fast power reaching law as the feedback control law to replace the PD feedback in the linear active disturbance rejection control; The step 3 is specifically as follows: After coordinate transformation i d 、 i q The deviations from their corresponding reference values e 1. e 2 is: (10) In formula (10), i dref for i d The reference value, i qref for i q Reference value of described i dref and i qref The specific form is as follows: On the basis of the three-phase balance of the grid voltage, the d-axis direction of the grid voltage is taken as the direction of the voltage vector, that is, u d = u g , u q =0, according to the instantaneous power theory, the instantaneous power on the AC side of the converter is: (11) In formula (11), P is the active power output on the AC side of the converter, Q Measure the output reactive power of the converter AC; The dq axis current reference value is calculated by formula (11): i dref 、 i qref The relationship with power is: (12)； Based on formula (10), the d and q axis non-singular terminal sliding mode functions are constructed. s 1. s 2 is: (13) In formula (13), c 1. c 2>0,1< p / q <2; The fast power reaching law is selected as the sliding mode switching control law: (14) In formula (14), k 1, k 2>0,0< a <1; The inner loop current control law is calculated by combining equations (8) to (14): (15)。

Images