An Adaptive Passive Control Method for DC Microgrid Buck Converter Based on Large-Signal Stability

Abstract

The present invention proposes an adaptive passive control method for a DC microgrid Buck converter based on large-signal stability. This control method is based on the passive control theory, and the system impedance is re-optimized and adjusted through virtual impedance technology to make the entire system in a passive stable state. Aiming at the steady-state error caused by the deviation from the rated operating state due to system uncertainties, the present invention designs and applies a high-order disturbance observer technology to perform feed-forward compensation on the steady-state error caused by uncertainties, thereby ensuring the stable and error-free operation of the system in the presence of disturbances and uncertainties. In addition, in order to ensure the large-signal stability of the proposed algorithm, the hybrid potential energy function theory is used for stability analysis and the parameter selection criteria are given. Finally, the effectiveness and superiority of the proposed algorithm are verified through a simulation platform.

Description

Technical Field

[0001] The present invention relates to the technical field of DC microgrids, and particularly to an adaptive passive control method for a Buck converter in a DC microgrid based on large-signal stability. Background Art

[0002] In recent years, microgrids, as small-scale distribution systems that effectively integrate renewable energy sources, energy storage devices, and different types of loads, have received extensive attention. Since there is no reactive power, phase, and frequency in a DC microgrid, the DC microgrid also has the advantages of low system cost, low loss, and easy control. It is precisely because of these advantages that the DC microgrid can absorb the output of distributed energy more efficiently and reliably. Different from the traditional AC grid architecture system, due to the DC power supply mode, the only index for measuring the stable operation of the grid in the DC microgrid is the amplitude of the DC bus voltage. In addition, as one of the most common interfaces in the DC microgrid, the Buck converter can reduce the redundant energy conversion stage between the DC power supply and the load. However, the negative incremental impedance characteristic exhibited by constant power loads seriously threatens the stable operation of the system. Therefore, it is very necessary to explore a controller that can achieve fast bus voltage regulation and maintain the stable operation of the DC microgrid.

[0003] To eliminate the instability problems caused by constant power loads, the initially proposed solutions can be classified into passive damping methods and active damping methods based on linear control techniques. Passive damping methods mainly optimize the impedance distribution of the system by adding components such as inductors, capacitors, or LC filters, improve the damping characteristics of the system, and thus suppress the occurrence of limit cycle oscillations. Although the stability of the system is ensured, this method will lead to an increase in system weight and energy loss. Active damping methods rely on virtual impedance technology to suppress system oscillations by changing the system control loop to ensure system stability. However, since a small-signal model is used to analyze the system near the steady-state operating point and a linear control algorithm is used to suppress the system oscillations, the above active damping method can only ensure the normal and stable operation of the system in the neighborhood of the steady-state operating point. To overcome the above defects, a series of non-linear control strategies based on large-signal stability have been proposed and applied to solve the instability problems caused by constant power loads, such as: robust control, backstepping control, sliding mode control, model predictive control, deep reinforcement learning control, etc. However, the above non-linear controllers cannot avoid problems such as difficult design and complex parameter tuning. Due to its advantages of simplicity, high efficiency, and easy application, passive control has achieved great development in the industrial field including the power electronics field. When this method is used to solve the instability problem caused by constant power loads, passive control ensures the passivity of the controlled system through damping injection to eliminate the limit cycle oscillation phenomenon, and makes the energy absorbed, stored, and dissipated in the system maintain a dynamic balance through energy reshaping, thus finally ensuring the stable operation of the system under its rated operating state. In addition, to eliminate the static error caused by system uncertainty, a control strategy combining an integral link with passive control is proposed. However, it has defects such as a relatively high overshoot and a slow dynamic response due to the influence of the feedback link. Summary of the Invention

[0004] The object of the present invention is to solve the problems in the prior art to meet the actual situation needs, and a self-adaptive passive control method for a DC microgrid Buck converter based on large-signal stability is proposed.

[0005] The present invention is realized through the following technical solutions. The present invention proposes a self-adaptive passive control method for a DC microgrid Buck converter based on large-signal stability. The control method is based on the passive control theory, and re-optimizes and adjusts the impedance of the DC microgrid system through virtual impedance technology to make the entire DC microgrid system in a passively stable state. The specific method is as follows:

[0006] A high-order disturbance observer based on circuit topology is used to online estimate and feedforward compensate the steady-state error caused by lumped disturbances; an improved passivity-based control algorithm is used to ensure the large-signal stability of the DC microgrid system and compensate for lumped disturbances; the large-signal stability of the improved passivity-based control algorithm is analyzed through the hybrid potential function theory, and the stability boundary conditions and parameter selection criteria are given.

[0007] Furthermore, assuming that the Buck converter and its connected CPL operate in continuous current mode, the average state model of the DC microgrid system is expressed as:

[0008]

[0009] In the above formula, P CPL is the power of the constant power load, and μ is the duty cycle; it can be seen from Equation (1) that the changes in the inductance and its equivalent series resistance value, the capacitance and its equivalent series resistance value, the input voltage, the resistance, and the constant power load power can all affect the output voltage; and the disturbances involved in the control method are mainly the changes in the input voltage, the constant power load, and the constant impedance load. When the above factors are taken into account, Equation (1) is rewritten as:

[0010]

[0011] In Equation (2), d1 and d2 respectively represent the disturbances caused by the input voltage and the load fluctuation, expressed as

[0012]

[0013] In Equation (3), E0, R0, P CPL0 are respectively the rated values of the input voltage, the constant impedance load, and the constant power load power;

[0014] Define the following vector group:

[0015]

[0016] Then Equations (1) and (2) can be rewritten in the following matrix forms respectively:

[0017]

[0018]

[0019] The goal of the control method is to achieve global asymptotic stability in the presence of disturbances, that is, to achieve

[0020]

[0021] In the above formula, for the initial value z of the elements in matrix Z10 , z 20 , there exists z 10 ≥0, z 20 > ε; Z d is the reference trajectory matrix of the vector group Z, and ε is an arbitrarily small positive real number.

[0022] Furthermore, the design of the passive controller in the improved passive control algorithm is specifically as follows: According to the passive control theory, when the energy provided by the power source in the DC microgrid system is equal to the sum of the energy dissipated by the DC microgrid system and the energy stored in the DC microgrid system, the entire DC microgrid system is passive; based on the passive control theory, by means of a virtual resistor, that is, by adjusting the inductance in the DC microgrid system in series with the virtual resistor R 1d and the capacitance in parallel with the virtual resistor R 2d , while not generating additional energy loss in the DC microgrid system, optimize the impedance distribution of the DC microgrid system to ensure the passivity of the DC microgrid system, and balance the energy of each part through energy reshaping to achieve stable control of the Buck circuit with constant power load and constant impedance load.

[0023] Furthermore, the energy reshaping of the DC microgrid system is specifically as follows: Considering the change trend of the energy to be reshaped, the energy in the inductor and capacitor both reaches the minimum value at the new balance. Therefore, the following transformation is performed on Equation (6) to achieve the reshaping of the energy;

[0024]

[0025] where represents the amplitude of the deviation of Z from the reference value vector group Z d of the trajectory.

[0026] Furthermore, damping injection is performed on the DC microgrid system. The damping injection changes the system impedance distribution to a passive state by introducing a virtual impedance into the DC microgrid system, so as to ultimately achieve the purpose of eliminating the energy oscillation in the system. Among them, the introduction process of the virtual impedance is realized by modifying Equation (8).

[0027] Furthermore, construct a virtual impedance matrix as shown in Equation (9)

[0028]

[0029] Let R i = R(z r ) + R d , and add to both sides of Equation (8) respectively,

[0030]

[0031] When a virtual resistor with appropriate value is introduced into the system, it can ensure that the redundant transient energy in the system is fully dissipated and the global asymptotic stability of the system is ensured, so that Therefore, it can be known that the left side of Equation (10) will approach zero, that is

[0032]

[0033] The above can be proved by implementing the Lyapunov stability criterion; let be the equilibrium point of Equation (11), and at the same time be the domain containing ; let S: D → R be a continuous integral function, S(0) = 0 and in D - {0}, in D, then the equilibrium point is stable, and if in D - {0}, then the equilibrium point is asymptotically stable; let the total energy stored in the system be

[0034]

[0035] Since the matrix H is a positive definite matrix, the energy storage function of the system Taking the derivative of Equation (12) gives

[0036]

[0037] Transform Equation (11) and substitute Equation (13) into Equation (11) to get

[0038]

[0039] In Equation (14), since G is an anti-symmetric matrix, so And R(z) is a symmetric matrix. Only by ensuring that the diagonal elements are all positive can it be guaranteed that the value of Equation (14) is a negative value less than zero. According to the definition of the Lyapunov direct method, the entire system will finally approach the globally stable asymptotic equilibrium point, regardless of the action of the converter switch; therefore, the left side of the equal sign in Equation (10) is equal to zero, and rewriting it gives

[0040]

[0041] Rewriting the above into the form of a system of equations, the dynamic characteristic equation of the passive control as shown below can be obtained

[0042]

[0043] Since the Buck converter is a non-minimum phase system, so use i Lref and v Cref to replace iLd With v Cd , and let i Ld With v Cd The derivative value is zero, and the tracking of the reference voltage can be achieved

[0044]

[0045] After arranging Equation (17), the voltage loop control equation and the current loop control equation for the Buck converter PBC control algorithm are shown in Equations (18) and (19) respectively

[0046] μ=(v Cref +R 1d (i Lref -i L )) / E (18)

[0047]

[0048] Under the rated condition, a passive control algorithm is constructed according to Equations (18) and (19). The passive control algorithm is based on a double-loop control architecture. The voltage outer loop calculates the difference between the output voltage and the voltage reference value through Equation (19) to generate the reference value of the inductor current while achieving the tracking of the reference voltage. The current inner loop then compares the inductor current with the reference current and calculates through Equation (18) to generate the corresponding PWM signal to achieve current tracking

[0049] Furthermore, the design of the high-order disturbance observer is specifically as follows: transform the dynamic characteristic equation into a general nonlinear equation mode:

[0050]

[0051] where x∈R n , u∈R m , d∈R r are the state variable matrix, the controlled input matrix, and the disturbance matrix of the system respectively. f(x,μ;t) is the system equation, and both it and the matrix F with rank r are known; assuming that the disturbance changes slowly, that is the disturbance can be regarded as a constant disturbance, and since the state variable x is measurable and its initial value is known, the system shown in Equation (20) can be reduced order to

[0052]

[0053] In the above formula, F+ is the pseudo-inverse matrix of matrix F. The general form of the constant disturbance observer of the system shown in Equation (20) is shown as follows

[0054]

[0055] In the above formula, is a disturbance estimation vector group, and Γ0 = diag{γ 01 , γ 02 ..., γ 0i}, where γ 0i > 0 (i = 1, 2..., r) is the observer gain coefficient matrix to be debugged; let the observer error be

[0056]

[0057] By combining equations (21) to (23), the following observer error derivative equation can be obtained

[0058]

[0059] As can be seen from the above equation, when the observer gain coefficient matrix -Γ0 is a Hurwitz matrix, the disturbance estimation value will approach the disturbance value d at infinity; thus, the high-order disturbance observer for observing the input voltage disturbance is as follows

[0060]

[0061] The high-order disturbance observer for constant impedance load and constant power load disturbances is as follows

[0062]

[0063] By substituting equations (18), (19), (25), and (26) into equation (2), the control equation of the adaptive passive control algorithm considering the disturbance can be obtained

[0064]

[0065]

[0066] Furthermore, the large-signal stability is judged by the following large-signal stability criterion;

[0067]

[0068] The present invention also proposes an electronic device, including a memory and a processor, where the memory stores a computer program, and when the processor executes the computer program, the steps of the adaptive passive control method for a DC microgrid Buck converter based on large-signal stability are implemented.

[0069] The present invention also proposes a computer-readable storage medium for storing computer instructions, and when the computer instructions are executed by a processor, the steps of the adaptive passive control method for a DC microgrid Buck converter based on large-signal stability are implemented.

[0070] Advantages of the present invention:

[0071] The present invention proposes an adaptive passive control method for a Buck converter in a DC microgrid based on large-signal stability, which eliminates the influence of the negative impedance characteristic of a constant power load on the stable operation of the Buck converter in the DC microgrid and improves the transient performance of the system during load disturbances in the DC microgrid. This control method is based on the passive control theory, and the system impedance is re-optimized and adjusted through virtual impedance technology to make the entire system in a passively stable state. Aiming at the steady-state error caused by the deviation from the rated operating state due to system uncertainties, the present invention designs and applies a high-order disturbance observer technology to perform feedforward compensation on the steady-state error caused by uncertainties, thereby ensuring the stable and error-free operation of the system in the presence of disturbances and uncertainties. In addition, in order to ensure the large-signal stability of the proposed algorithm, the hybrid potential energy function theory is used for stability analysis and the parameter selection criteria are given. Finally, the effectiveness and superiority of the proposed algorithm are verified through a simulation platform. Brief Description of the Drawings

[0072] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts.

[0073] Figure 1 is a schematic diagram of the topology structure of a Buck converter with a constant impedance load and a constant power load;

[0074] Figure 2 is a schematic diagram of the passive control principle of a Buck converter with a constant impedance load and a constant power load;

[0075] Figure 3 is a schematic diagram of the large-signal equivalent model of a Buck converter with a constant impedance load and a constant power load;

[0076] Figure 4 is a large-signal stability boundary diagram of the system of the proposed algorithm; where (a) is the large-signal boundary diagram of the system when the constant impedance load changes, and (b) is the large-signal boundary diagram of the system when the constant power load changes;

[0077] Figure 5 is a comparison waveform diagram of the outputs of the adaptive PBC and the traditional PBC when the input voltage changes;

[0078] Figure 6 is a comparison waveform diagram of the outputs of the adaptive PBC and the traditional PBC when the constant power load changes;

[0079] Figure 7 It is the comparison waveform diagram of the output of the adaptive PBC and the traditional PBC when the constant impedance load changes;

[0080] Figure 8 It is the comparison waveform diagram of the output of the adaptive PBC, IPBC, and PBC+NDO when the input voltage changes;

[0081] Figure 9 It is the comparison waveform diagram of the output of the adaptive PBC, IPBC, and PBC+NDO when the constant power load changes;

[0082] Figure 10 It is the comparison waveform diagram of the output of the adaptive PBC, IPBC, and PBC+NDO when the constant impedance load changes;

[0083] Figure 11 It is the schematic diagram of the overall system structure of the DC microgrid. Specific implementation manners

[0084] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0085] To ensure the stable and error-free operation of the DC microgrid Buck converter with a constant power load under system uncertainties including resistance, constant power load power, input voltage disturbance, etc., the present invention proposes an adaptive passive control method. In this method, a high-order disturbance observer based on the circuit topology is used for online estimation and feedforward compensation of the lumped disturbance, and an improved passive control algorithm is used to ensure the large-signal stability of the studied circuit system (DC microgrid system) and the compensation of the lumped disturbance. In addition, the large-signal stability analysis of the proposed algorithm is carried out through the hybrid potential function theory, and the stability boundary conditions and parameter selection criteria are given. Finally, the effectiveness and superiority of the proposed algorithm are verified through MATLAB / Simulink simulation.

[0086] Specifically, in combination with Figures 1 - 11 , the present invention proposes an adaptive passive control method for the DC microgrid Buck converter based on large-signal stability. The control method is based on the passive control theory, and the impedance of the DC microgrid system is re-optimized and adjusted through virtual impedance technology to make the entire DC microgrid system in a passively stable state; the method is specifically as follows:

[0087] A high-order disturbance observer based on circuit topology is used for online estimation and feed-forward compensation of the steady-state error caused by concentrated disturbances; an improved passive control algorithm is used to ensure the large-signal stability of the DC microgrid system and compensation for concentrated disturbances; the large-signal stability of the improved passive control algorithm is analyzed through the hybrid potential function theory, and the stability boundary conditions and parameter selection criteria are given.

[0088] The method of the present invention is designed based on a buck converter with a parallel constant impedance load and a constant power load as shown in Figure 1 , where E, L, C, and R are the input voltage, inductance, capacitance, and resistance value of the constant impedance load of the system, respectively, and i L , v C , i C , i R , i CPL represent the inductor current, capacitor voltage, capacitor current, resistor current, and current of the constant power load, respectively. The power bus is powered by a power generation unit, and the DC / DC buck converter is used to reduce the voltage and supply energy to the load bus. The resistive load and the constant power load absorb electrical energy from the load bus, and the negative impedance characteristic of the constant power load is not conducive to system stability. Therefore, it is necessary to design a suitable controller for the interface converter to achieve the stable operation of the DC microgrid.

[0089] Assume that Figure 2 the Buck converter in and the CPL it drives operate in continuous current mode, then the average state model of the DC microgrid system is expressed as:

[0090]

[0091] In the above formula, P CPL is the power of the constant power load, μ is the duty cycle; it can be seen from Equation (1) that the changes in the inductor and its equivalent series resistance value, capacitor and its equivalent series resistance value, input voltage, resistor, and constant power load power can all affect the output voltage; however, when a virtual resistor is introduced in the passive control, the equivalent series resistance of the inductor and capacitor can be ignored, and under normal operating conditions, the inductor value and capacitor value are not likely to change significantly, and the change in the input voltage will directly cause the change in the output voltage, and the changes in the constant power load and the constant impedance load will change the passive state of the system and cause output errors, and in severe cases, even the appearance of limit cycle oscillations. The disturbances involved in the control method are mainly the changes in the input voltage, constant power load, and constant impedance load. When the above factors are taken into account, Equation (1) is rewritten as:

[0092]

[0093] In Equation (2), d1 and d2 respectively represent the perturbations caused by the input voltage and the load fluctuation, expressed as

[0094]

[0095] In Equation (3), E0, R0, P CPL0 are respectively the rated values of the input voltage, the constant impedance load, and the constant power load power;

[0096] Define the following vector group:

[0097]

[0098] Then, Equation (1) and Equation (2) can be respectively rewritten into the following matrix forms:

[0099]

[0100] The goal of the described control method is to achieve global asymptotic stability in the presence of perturbations, that is, to achieve

[0101]

[0102] In the above formula, for the initial value z of the elements in matrix Z 10 , z 20 , there exists z 10 ≥0, z 20 > ε; Z d is the reference trajectory matrix of the vector group Z, and ε is an arbitrarily small positive real number.

[0103] In the described improved passive control algorithm, the design of the passive controller is specifically as follows: According to the passive control theory, when the energy provided by the power source in the DC microgrid system is equal to the sum of the dissipated energy and the stored energy in the DC microgrid system, the entire DC microgrid system is passive; however, due to the negative incremental impedance introduced by the constant power load, the transient energy stored in the capacitors and inductors in the circuit system cannot be dissipated. Therefore, the system is in a limit oscillation state, causing energy oscillation between the energy storage elements and resulting in unstable system output. Therefore, based on the passive control theory, the present invention uses the means of a virtual resistor, that is, by adjusting Figure 2 as shown in the DC microgrid system, a virtual resistor R 1d is connected in series with the inductor and a virtual resistor R 2d is connected in parallel with the capacitor. While not generating additional energy loss in the DC microgrid system, the impedance distribution of the DC microgrid system is optimized to ensure the passivity of the DC microgrid system, and the energy of each part is balanced through energy reshaping, thereby achieving stable control of the Buck circuit with constant power load and constant impedance load.

[0104] The energy reshaping of the DC microgrid system is specifically as follows: Considering the changing trend of the energy to be reshaped, the energies in the inductor and capacitor both reach the minimum value at the new equilibrium. Therefore, the following transformation is performed on Equation (6) to achieve energy reshaping;

[0105]

[0106] where represents the vector group Z of the deviation of Z from the trajectory reference value d amplitude.

[0107] Damping injection is performed on the DC microgrid system. Damping injection changes the system impedance distribution to a passive state by introducing virtual impedance into the DC microgrid system, so as to ultimately eliminate the energy oscillation in the system. Among them, the process of introducing virtual impedance is achieved by modifying Equation (8).

[0108] Construct a virtual impedance matrix as shown in Equation (9)

[0109]

[0110] Let R i =R(z r )+R d , and add to both sides of Equation (8), respectively, to obtain

[0111]

[0112] When an appropriately valued virtual resistor is introduced into the system, it can ensure that the excess transient energy in the system is fully dissipated and ensure the global asymptotic stability of the system, so that Therefore, it can be known that the left side of Equation (10) will approach zero, that is

[0113]

[0114] The above proof can be implemented through Lyapunov's stability criterion; let be the equilibrium point of Equation (11), and at the same time be the domain containing ; let S:D→R be a continuous integral function, S(0)=0 and in D-{0}, in D, then the equilibrium point is stable, and if in D-{0}, then the equilibrium point is asymptotically stable; let the total energy stored in the system be

[0115]

[0116] Since the matrix H is a positive definite matrix, the system energy storage function Taking the derivative of Equation (12) gives

[0117]

[0118] Performing a transformation on Equation (11) and substituting Equation (13) into Equation (11) gives

[0119]

[0120] In Equation (14), since G is an anti-symmetric matrix, therefore And R(z) is a symmetric matrix. Only by ensuring that all diagonal elements are positive can the value of Equation (14) be guaranteed to be a negative value less than zero. According to the definition of Lyapunov's direct method, the entire system will ultimately approach the globally stable asymptotic equilibrium point, regardless of the actions of the converter switches; therefore, the left side of the equal sign in Equation (10) is equal to zero, and rewriting it gives

[0121]

[0122] Rewriting the above equation in the form of a system of equations, the dynamic characteristic equation of the passive control as shown below can be obtained

[0123]

[0124] Since the Buck converter is a non-minimum phase system, therefore using i Lref and v Cref to replace i Ld and v Cd respectively, and setting the derivative values of i Ld and v Cd to zero can achieve tracking of the reference voltage

[0125]

[0126] Rearranging Equation (17), the voltage loop control equation and current loop control equation for the Buck converter PBC control algorithm are shown in Equations (18) and (19) respectively

[0127] μ=(v Cref +R 1d (i Lref -i L )) / E (18)

[0128]

[0129] Under the rated condition, a passive control algorithm is constructed according to Equations (18) and (19). The passive control algorithm is based on a double-loop control architecture. The voltage outer loop calculates the difference between the output voltage and the voltage reference value through Equation (19), and while achieving the tracking of the reference voltage, it generates the reference value of the inductor current. The current inner loop then compares the inductor current with the reference current and calculates through Equation (18) to generate the corresponding PWM signal to achieve current tracking.

[0130] The design of the high-order disturbance observer is specifically as follows: The PBC control algorithm proposed by the present invention can ensure Figure 2 the stable and error-free operation of the circuit system shown under the rated operating condition. However, considering the randomness and uncertainty of the source-load end, Figure 2 the power of the constant power load, the constant impedance load, and the input voltage in the circuit shown usually change with time. In order to enable the system to still achieve stable and error-free tracking of the reference value when the above variables change, a control algorithm architecture based on the disturbance observer technology will be adopted. The control algorithm designed based on this architecture can realize the real-time observation of the concentrated disturbance in the system through the disturbance observer, and compensate it through the modified control algorithm, thereby ensuring the stable and error-free operation of the system. Therefore, the present invention realizes the online estimation of the concentrated disturbance information based on the high-order disturbance observer technology, and compensates the influence of the disturbance by making corresponding adaptive modifications to the PBC, thereby improving its robustness so that it can still operate normally in the presence of disturbances. First, the dynamic characteristic equation is transformed into the general nonlinear equation mode:

[0131]

[0132] where \(x\in R\) n , \(u\in R\) m , \(d\in R\) r are the state variable matrix, the controlled input matrix, and the disturbance matrix of the system respectively, \(f(x,\mu;t)\) is the system equation, and both it and the matrix \(F\) with rank \(r\) are known; assuming that the disturbance changes slowly, that is the disturbance can be regarded as a constant disturbance, and since the state variable \(x\) is measurable and its initial value is known, the system shown in Equation (20) can be reduced to

[0133]

[0134] In the above formula, \(F^+\) is the pseudo-inverse matrix of the matrix \(F\). Since \(F\) is the identity matrix in this article, \(F^+\) can also take the value of the identity matrix. The general form of the constant disturbance observer of the system shown in Equation (20) is as follows

[0135]

[0136] In the above formula, is a disturbance estimation vector group, and Γ0 = diag{γ 01 , γ 02 ..., γ 0i}, where γ 0i > 0 (i = 1, 2..., r) is the observer gain coefficient matrix to be debugged; let the observer error be

[0137]

[0138] By combining equations (21) to (23), the following observer error derivative equation can be obtained

[0139]

[0140] It can be seen from the above equation that when the observer gain coefficient matrix -Γ0 is a Hurwitz matrix, the disturbance estimation value will approach the disturbance value d at infinity; thus, the high-order disturbance observer for observing the input voltage disturbance is as follows

[0141]

[0142] The high-order disturbance observer for constant impedance load and constant power load disturbances is as follows

[0143]

[0144] By substituting equations (18), (19), (25), and (26) into equation (2), the control equation of the adaptive passive control algorithm considering the disturbance can be obtained

[0145]

[0146] Large-signal stability analysis based on the hybrid potential function: The large-signal stability analysis method based on the hybrid potential function theory was first proposed in 1960. Before being applied to the field of power electronics, it was mainly used for the stability analysis of nonlinear circuits. The general form of the hybrid potential function is as follows

[0147] P(i, v) = -A(i) + B(v) + (i, γv - a) (29)

[0148] In the above equation, A(i) is the current potential energy equation, B(v) is the voltage potential energy equation, γ is a constant equation related to the circuit structure, and α is a constant vector. There are three theorems in the hybrid potential energy theory. However, since the current potential energy function in the first theorem and the voltage potential energy function in the second theorem are both linear, the third theorem is used for the large-signal stability analysis of the system proposed in the present invention. Let μ1 and μ2 be L -1 / 2 Aii (i)L -1 / 2 and C -1 / 2 B vv (v)C -1 / 2 The minimum eigenvalue of. If the condition is satisfied

[0149] μ1 + μ2 ≥ δ(δ > 0) (30)

[0150] And when |i| + |v| → ∞, there exists

[0151]

[0152] In the above formula, P i is the partial derivative of P(i, v) with respect to current. When time approaches infinity, all solutions corresponding to the system tend to the stable operating point. For the circuit system in the present invention, the output current of the power supply is proportional to the output terminal voltage, and the current absorbed by the constant power load from the bus is also proportional to the bus voltage. Therefore, the power supply and the constant power load in the circuit system can be equivalently regarded as a controlled current source. The equivalent circuit of the system described in the present invention is as Figure 3 shown.

[0153] Based on Figure 3 the equivalent model shown, the hybrid potential energy function of the DC microgrid system described in the present invention can be written as

[0154]

[0155] For the convenience of large-signal stability analysis of the system, equation (32) is rewritten into the general form of the hybrid potential energy function as shown below

[0156]

[0157] After the damping injection by the PBC algorithm, the power supply can achieve fast tracking of the reference current, that is, i L = i Lref . Therefore, the following expressions of μ1 and μ2 can be obtained as

[0158]

[0159] Therefore, the large-signal stability is judged by the following large-signal stability criterion;

[0160]

[0161] It can be seen from equation (35) that for the system under different working conditions, only the virtual parallel resistance R of the capacitor needs to be adjusted 2dThe large-signal stability of the system can be achieved. Although for a buck circuit system with a constant-impedance load as the single load, the change of the constant-impedance load within the power supply capacity range of the power supply does not affect the large-signal stability of the system. However, in the present invention, the considered load is a hybrid load. When the value of the constant-impedance load changes to the point where it loses its dominant position, the large-signal stability of the system will be damaged. Therefore, it is necessary to analyze the large-signal stability when the constant-power load and the constant-impedance load fluctuate. When the constant-power load and the constant-impedance load change separately, the large-signal stability boundary diagram of the system is as shown in Figure 4 . In the large-signal stability boundary diagram, the blue area is the large-signal stable area. When the point formed with the power of the constant-power load or the constant-impedance load as the abscissa and the virtual parallel resistance R of the capacitor as the ordinate is located within the blue area, the system is in a large-signal stable state. In the simulation and experiment corresponding to the present invention, the value of R 2d is not only related to the large-signal stability of the system. An excessively high value of R 2d will reduce the system response characteristics and cause output errors, while a lower value of R 2d can ensure that the system obtains fast dynamic response characteristics, but at the same time will also cause severe ripples in the output waveform. Therefore, after weighing the above factors, the virtual capacitor parallel resistance R in the present invention 2d 2d is finally selected as 0.16. Combining the two large-signal stability boundary diagrams in Figure 4 shows that this value can ensure the large-signal stability of the system when the constant-impedance load and the constant-power load fluctuate.

[0162] Next, the method proposed in the present invention is verified through MATLAB / Simulink simulation. In addition, the values of the virtual resistors R 1d , R 2d in the method described in the present invention are 10 6 and 0.16 respectively, and the disturbance observer coefficients are Γ1 = 1000 and Γ2 = 4000 respectively. On this basis, two types of case studies are carried out: a) Steady-state performance comparison test under various source-load side disturbances; b) Transient performance comparison test under various source-load side disturbances. The detailed parameters of the system are shown in Table 1.

[0163] Table 1 System parameter configuration

[0164]

[0165] Case a): This case study examines the steady-state performance of the proposed controller in the face of step disturbances on the source-load side to verify the effectiveness of the method proposed in the present invention. Figure 5 ​The figure shows the simulation results of the output comparison between the proposed adaptive passive control method (in red in the figure) and the traditional passive control algorithm (in blue in the figure) when the input and voltage change. At 0.04 s, the input voltage of the system increases from the rated value of 1500 V to 2000 V and returns to the rated value after 0.02 s. As Figure 5 can be seen, the change in the input voltage has no obvious effect on the output voltage of the proposed algorithm, while there is a steady-state error in the output voltage of the traditional passive control.

[0166] Figure 6 The figure shows the simulation results of the output comparison between the proposed adaptive passive control algorithm (in red in the figure) and the traditional passive control algorithm (in blue in the figure) when the constant power load undergoes a step change. At 0.04 s, the power of the constant power load steps from 14.4 kW to 21.7 kW and returns to 14.4 kW after 0.06 s. From Figure 6 the figure, it can be seen that the traditional passive control does not take into account the change of the constant power load. Therefore, although the system is in a stable state, there is a steady-state error in its output voltage compared with the rated value. The proposed adaptive passive control algorithm produces a certain overshoot when the constant power load changes and its output returns to the rated value of 750 V after about 2 ms.

[0167] Figure 7 The figure shows the simulation results of the output comparison between the adaptive passive control method (in red in the figure) and the traditional passive control method (in blue in the figure) when the constant impedance load undergoes a step change. The constant impedance load of the system changes from 50 Ω to 33.33 Ω at 0.04 s and returns to 50 Ω at 0.06 s. From Figure 7 the figure, it can be seen that there is a steady-state error in the output voltage of the traditional passive control. When the load resistance decreases, the proposed adaptive passive control algorithm produces an overshoot of 0.4 V and returns to the rated value after 2 ms.

[0168] Case b): This case studies the transient performance of the proposed controller in the face of step disturbances on the source and load sides to verify the superiority of the method proposed in the present invention. To further verify the transient performance of the adaptive passive control algorithm, the present invention conducts a comparative simulation with the passivity-based control with integrator (IPBC) and the passivity-based control with a nonlinear disturbance observer (PBC+NDO). In the construction of the passive control with an integral link, the virtual resistances R 1d , R 2d take the same values as those of the proposed algorithm, and the integral coefficient is selected as 300. Figures 8 to 10Comparison simulation diagrams of the outputs of the proposed algorithm (red in the figure), IPBC (green in the figure), and PBC+NDO (blue in the figure) when the input voltage, constant-power load, and constant-impedance load are disturbed respectively.

[0169] Figure 8 The input voltage change in Figure 5 is consistent with the Figure 8 operating conditions. As can be seen from Figure 9 the constant-power load change in Figure 6 is consistent with the Figure 9 operating conditions. As can be seen from Figure 10 the constant-impedance load change in Figure 7 is consistent with the Figure 10 operating conditions. As can be seen from

[0170] The schematic diagram of the DC microgrid structure is as Figure 11 shown, which consists of a DC / DC buck converter topology and the corresponding controller. Among them, the present invention proposes an adaptive passive control algorithm based on high-order disturbance observer technology, which can solve the instability problem caused by the constant-power load in the buck circuit. In the proposed algorithm, the high-order disturbance observer is used to realize the real-time observation of the disturbance quantity, while the passive control balances the impedance distribution in the system through virtual impedance technology to ensure the large-signal stability of the system, and realizes the stable tracking of the reference voltage through the reshaping of the system energy. In addition, the improved passive control algorithm also realizes the compensation of the concentrated disturbance to improve the robustness of the algorithm. In order to verify the large-signal stability of the proposed algorithm, the present invention analyzes the large-signal stability of the system based on the hybrid potential energy theory, and proves the large-signal stability of the system of the present invention. Through MATLAB simulation, the proposed control algorithm can successfully suppress the influence of disturbances such as input voltage and load fluctuations on the output, and has good dynamic response performance.

[0171] The present invention also proposes an electronic device, including a memory and a processor, where the memory stores a computer program, and when the processor executes the computer program, it realizes the steps of the adaptive passive control method for the DC microgrid buck converter based on large-signal stability.

[0172] The present invention also provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the above-described adaptive passive control method for a DC microgrid Buck converter based on large-signal stability.

[0173] The memory in the embodiments of the present application may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read-only memory (ROM), a programmable ROM (PROM), an erasable programmable ROM (EPROM), an electrically erasable programmable ROM (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example but not limitation, many forms of RAM are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchlink DRAM (SLDRAM), and direct rambus RAM (DRRAM). It should be noted that the memory for the methods described in the present invention is intended to include but not be limited to these and any other suitable types of memory.

[0174] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, the processes or functions described in the embodiments of the present application are generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center by wire (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wirelessly (such as infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium accessible by a computer or a data storage device such as a server, data center, etc. that contains one or more integrated available media. The available media can be magnetic media (such as floppy disks, hard disks, magnetic tapes), optical media (such as high-density digital video discs (DVDs)), or semiconductor media (such as solid state discs (SSDs)), etc.

[0175] In the implementation process, each step of the above method can be completed by the integrated logic circuit of the hardware in the processor or the instructions in the form of software. The steps of the method disclosed in combination with the embodiments of the present application can be directly embodied as being executed by the hardware processor or executed by the combination of the hardware and software modules in the processor. The software module can be located in a mature storage medium in the art such as random access memory, flash memory, read-only memory, programmable read-only memory, or electrically erasable programmable memory, registers, etc. This storage medium is located in the memory, and the processor reads the information in the memory and combines its hardware to complete the steps of the above method. To avoid repetition, it will not be described in detail here.

[0176] It should be noted that the processor in the embodiments of the present application can be an integrated circuit chip with signal processing capabilities. In the implementation process, the steps of the above method embodiments can be completed by the integrated logic circuit in the hardware of the processor or instructions in software form. The above-mentioned processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. It can implement or execute the various methods, steps and logic block diagrams disclosed in the embodiments of the present application. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc. The steps of the method disclosed in combination with the embodiments of the present application can be directly embodied as being executed and completed by the hardware decoding processor, or executed and completed by the combination of the hardware and software modules in the decoding processor. The software module can be located in a mature storage medium in the art such as random access memory, flash memory, read-only memory, programmable read-only memory or electrically erasable programmable memory, register, etc. This storage medium is located in the memory, and the processor reads the information in the memory and combines its hardware to complete the steps of the above method.

[0177] The above has introduced in detail a self-adaptive passive control method for a DC microgrid Buck converter based on large-signal stability. Specific examples are used in this article to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. An adaptive passive control method for a DC microgrid Buck converter based on large-signal stability, characterized in that, The control method is based on the passive control theory. Through the virtual impedance technology, the impedance of the DC microgrid system is re-optimized and adjusted to make the entire DC microgrid system in a passive stable state. Specifically, the method is as follows: A high-order disturbance observer based on the circuit topology is used to online estimate and feedforward compensate the steady-state error caused by the concentrated disturbance. An improved passive control algorithm is used to ensure the large-signal stability of the DC microgrid system and the compensation for the concentrated disturbance. The large-signal stability of the improved passive control algorithm is analyzed through the hybrid potential function theory, and the stability boundary conditions and parameter selection criteria are given. Assume that the Buck converter and the CPL it drives operate in the continuous current mode. Then the average state model of the DC microgrid system is expressed as: (1) In the above formula, P CPL is the power of the constant-power load, μ is the duty cycle; it can be seen from Equation (1) that the changes in the inductor and its equivalent series resistance value, the capacitor and its equivalent series resistance value, the input voltage, the resistor, and the constant-power load power can all affect the output voltage; and the disturbances involved in the control method are mainly the changes in the input voltage, the constant-power load, and the constant-impedance load. When the above factors are taken into account, Equation (1) is rewritten as: (2) In formula (2), d 1 and d 2 respectively represent the disturbances caused by the input voltage and the load fluctuation, expressed as (3) In formula (3), E 0, R 0, P CPL0 are respectively the rated values of the input voltage, the constant impedance load, and the constant power load power; Define the following vector group: (4) Then formula (1) and formula (2) can be rewritten as the following matrix forms respectively: (5) (6) The objective of the control method is to achieve global asymptotic stability in the presence of disturbances, that is, to achieve D in the case of a non-empty matrix (7) In the above formula, for the matrix Z the initial value of the elements in z 10 , z 20 there exists z 10 ≥ 0, z 20 > ε; Z d is the reference trajectory matrix of the vector group Z , ε is an arbitrarily small positive real number; The design of the passive controller in the improved passive control algorithm is specifically as follows: According to the passive control theory, when the energy provided by the power source in the DC microgrid system is equal to the sum of the energy dissipated by the DC microgrid system and the energy stored in the DC microgrid system, the entire DC microgrid system is passive; based on the passive control theory, by means of a virtual resistor, that is, by adjusting the inductance in the DC microgrid system in series with a virtual resistor R 1d and a capacitor in parallel with a virtual resistor R 2d , while not generating additional energy losses in the DC microgrid system, optimize the impedance distribution of the DC microgrid system to ensure the passivity of the DC microgrid system, and balance the energy of each part through energy reshaping to achieve stable control of the Buck circuit with constant power load and constant impedance load; The energy reshaping of the DC microgrid system is specifically as follows: Considering the change trend of the energy to be reshaped, the energy in the inductor and capacitor both reaches the minimum value at the new balance. Therefore, the following transformation is performed on formula (6) to achieve the energy reshaping. (8) Among them represents Z off-track reference value vector group Z d amplitude; Damping injection is carried out on the DC microgrid system. Damping injection is achieved by introducing virtual impedance into the DC microgrid system, thereby changing the system impedance distribution to make it in a passive state to ultimately achieve the purpose of eliminating the energy oscillation in the system. Among them, the introduction process of the virtual impedance is realized by modifying equation (8). Construct the virtual impedance matrix as shown in formula (9) (9) Let R i = R ( z r )+ R d , and adding to both sides of Equation (8), we can obtain (10) When a virtual resistor with an appropriate value is introduced into the system, it can ensure that the redundant transient energy in the system is fully dissipated and the global asymptotic stability of the system is ensured, so that , so it can be seen that the left side of equation (10) will approach zero, that is (11) The above proof can be implemented by Lyapunov stability criterion; let be the equilibrium point of Equation (11), and at the same time be the domain containing ; assume is a continuous integral function, and within , within D , then the equilibrium point is stable, and if within , then the equilibrium point is asymptotically stable; assume the total energy stored in the system is (12) Since the matrix H is a positive definite matrix, the system energy storage function , taking the derivative of Equation (12) gives (13) Perform transformation on formula (11), and substitute formula (13) into formula (11) to obtain (14) In Equation (14), since G is an anti-symmetric matrix, so ; and R ( z ) is a symmetric matrix. Only by ensuring that all diagonal elements are positive can it guarantee that the value of Equation (14) is a negative value less than zero. According to the definition of Lyapunov's direct method, the entire system will eventually approach the globally stable asymptotic equilibrium point, regardless of the actions of the converter switches; therefore, the left side of the equal sign in Equation (10) is equal to zero, and by rewriting it, we can get (15) Rewrite the above formula into the form of a system of equations, and the dynamic characteristic equation of the passive control can be obtained as follows (16) Since the Buck converter is a non-minimum phase system, i Lref and v Cref are respectively replaced with i Ld and v Cd , and by setting i Ld and v Cd to have zero derivative values, the tracking of the reference voltage can be achieved (17) Arrange formula (17). The voltage loop control equation and current loop control equation for the Buck converter PBC control algorithm are shown in formula (18) and formula (19) respectively (18) (19) Under the rated state, according to formula (18) and (19), construct a passive control algorithm. The passive control algorithm is based on a double-loop control architecture. The voltage outer loop calculates the difference between the output voltage and the voltage reference value through formula (19) to generate the reference value of the inductor current while achieving the tracking of the reference voltage. The current inner loop then generates the corresponding PWN signal through comparing the inductor current with the reference current and calculating through formula (18) to achieve the current tracking. The design of the high-order disturbance observer is specifically as follows: Transform the dynamic characteristic equation into the general nonlinear equation mode: (20) Among them , , are the state variable matrix, the controlled input matrix, and the disturbance matrix of the system respectively, is the system equation, which is related to the matrix of rank r and F are all known; assuming that the disturbance changes slowly, that is , the disturbance can be regarded as a constant disturbance, and since the state variable x is measurable and its initial value is known, the system shown in Equation (20) can be reduced to (21) In the above formula, F + is the pseudo-inverse matrix of the matrix F As shown in Equation (20), the general form of the constant disturbance observer of the system is as follows (22) In the above formula, is a disturbance estimation vector group, and , is an observer gain coefficient matrix to be debugged; Let the observer error be (23) Combine formula (21) to formula (23) to obtain the following observer error derivative equation (24) As can be seen from the above formula, when the observer gain coefficient matrix is a Hurwitz matrix, the disturbance estimation value will approach the disturbance value d at infinity; thus, the high-order disturbance observer for observing the input voltage disturbance is as follows (25) The high-order disturbance observer for constant impedance load and constant power load disturbance is as follows (26) By substituting formula (18), (19), (25), (26) into formula (2), the control equation of the adaptive passive control algorithm considering the disturbance can be obtained (27) (28)。 2. The method according to claim 1, wherein The large-signal stability is judged by the following large-signal stability criterion; (35)。 3. An electronic device, comprising a memory and a processor, the memory storing a computer program, characterized in that, When the processor executes the computer program, it realizes the steps of the method described in any one of claims 1-2.

4. A computer-readable storage medium for storing computer instructions, characterized in that, When the computer instruction is executed by the processor, it realizes the steps of the method described in any one of claims 1-2.

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