An Adaptive Composite Model Predictive Control Method for a DC Microgrid with Constant Power Loads and a Large-Signal Stability Analysis Method

Abstract

An adaptive composite model predictive control method and a large-signal stability analysis method for a DC microgrid with constant power loads, belonging to the technical field of DC microgrid control. To achieve the stable operation and good transient performance of a boost converter with constant power loads, the present invention includes an adaptive proportional-integral control voltage loop model, a model predictive control current loop model, and a nonlinear disturbance observer model. The present invention consists of a feedback loop composed of adaptive proportional-integral control and model predictive control for tracking the voltage reference value, and a feedforward loop composed of a nonlinear disturbance observer for online estimating and feedforward compensating the load disturbance current, thereby significantly improving the robustness of the system on the basis of the stable control of the boost converter. The large-signal stability analysis based on the hybrid potential function theory shows that the large-signal stability of the controlled object is ensured when the controlled object deviates from the rated operating state due to uncertainties and has high-penetration constant power loads.

Description

Technical Field

[0001] The present invention belongs to the technical field of DC microgrid control, and particularly relates to an adaptive composite model predictive control method and a large-signal stability analysis method for a DC microgrid with constant power loads. Background Art

[0002] In recent years, microgrids, as simple, compact, and reliable power distribution systems, have attracted wide attention by integrating renewable energy sources, energy storage systems, distributed generation units, and modern power electronic loads. Compared with AC microgrids, the control structure of DC microgrids is relatively simple, which can avoid problems such as reactive power, phase synchronization, and frequency regulation. In addition, most power sources and electronic loads are inherently DC characteristics. Therefore, the most common DC / DC boost converter interface in DC microgrids reduces redundant energy conversion stages and improves transmission efficiency. Therefore, it is very important to explore a controller that can quickly regulate the bus voltage and stabilize the DC microgrid interface converter.

[0003] DC microgrids usually contain traditional resistive loads and constant power loads. The normal operation of the former resistive load usually requires a constant voltage, while the latter constant power load usually manifests itself as a strictly regulated power electronic converter load, that is, the input voltage (current) decreases as the input current (voltage) increases, thereby ensuring constant power operation. Therefore, its unique negative incremental impedance characteristics will interact with the source converter, reduce the system damping, and thus threaten the stable operation of the system. In order to eliminate the stability problems caused by constant power loads, many control methods have been proposed, which are mainly divided into passive damping methods and active damping methods. Among them, the passive damping method improves the system damping by adding passive components such as resistors, inductors, capacitors, and LC filters to the system, but increases the volume and cost of the system and reduces efficiency; the active damping method reshapes the damping stability system by modifying the control loop. Although the design method is relatively simple, the small signal stability analysis corresponding to the linearized model can only guarantee the stability of the system near the steady-state operating point. When there are large signal interferences such as step changes on the source and load side and plug-and-play, the system may become unstable. Therefore, many nonlinear controllers have been proposed to ensure the large signal stability of the system, including backstepping control, model predictive control, passive control, robust control, control based on deep reinforcement learning, and sliding mode control. It is worth noting that the design of the above nonlinear controllers depends on an accurate system model, so steady-state errors will occur when facing uncertain parameters and source-load disturbances. Therefore, in order to improve the robustness of nonlinear control, most of the above nonlinear controls use nonlinear control feedback links to ensure the stability of the system's large signals, and use nonlinear disturbance observers as feedforward auxiliary links for online estimation and feedforward compensation of uncertain disturbances. However, it cannot avoid the problems of complex nonlinear controller design, difficult parameter setting, and heavy computational burden. In addition, the current large signal stability analysis method for nonlinear controllers usually uses the Lyapunov analysis method. However, the construction of the Lyapunov function can only be determined by empirical methods and cannot give large signal stability. Summary of the invention

[0004] The problem to be solved by the present invention is to achieve stable operation and good transient performance of a boost converter with a constant power load in a DC microgrid, and propose an adaptive composite model predictive control method and a large signal stability analysis method for a DC microgrid with a constant power load.

[0005] To achieve the above object, the present invention is implemented through the following technical solutions:

[0006] An adaptive composite model predictive control method for a DC microgrid with a constant power load, wherein the control method is designed in three parts, including an adaptive proportional integral control voltage loop model, a model predictive control current loop model, and a nonlinear disturbance observer model;

[0007] The feedback loop is composed of an adaptive proportional-integral control voltage loop model and a model predictive control current loop model, and the non-linear disturbance observer is the feed-forward compensation loop;

[0008] The adaptive proportional-integral control voltage loop model outputs the current reference value result to the model predictive control current loop model by inputting the reference voltage value collected by the input acquisition and the output voltage data of the boost converter collected by the voltage signal sensor;

[0009] The model predictive control current loop model outputs the duty cycle signal of the boost converter to the non-linear disturbance observer model by inputting the current reference value result obtained from the adaptive proportional-integral control voltage loop model and the inductor current data of the boost converter collected by the current signal sensor;

[0010] The non-linear disturbance observer model outputs the concentrated disturbance estimation value by inputting the output voltage data of the boost converter collected by the voltage signal sensor, the inductor current data of the boost converter collected by the current signal sensor, and the duty cycle signal of the boost converter obtained from the model predictive control current loop model. Then, the non-linear disturbance observer model feeds forward and compensates the concentrated disturbance estimation value to the adaptive proportional-integral control voltage loop model.

[0011] Furthermore, the control method is based on the boost converter with a parallel resistive load and a constant power load operating in continuous conduction mode;

[0012] First, construct the average dynamic model of the boost converter, and the expression is:

[0013]

[0014] where L, C, v s , v o , i L , μ, R and P CPL are the inductance value, capacitance value, input voltage, output voltage, inductor current, switching duty cycle, resistive load and constant power load power of the DC / DC boost converter respectively;

[0015] According to Equation (1), construct the open-loop transfer function G(s) with a resistive load and a constant power load, and the expression is:

[0016]

[0017] where, represents the small-signal disturbance of the output voltage steady-state operating point, represents the small-signal disturbance of the duty cycle steady-state operating point.

[0018] Furthermore, design the adaptive proportional-integral control voltage loop model, and the expression is:

[0019]

[0020] Among them, I d is the current reference value result, k p is the proportionality coefficient, k i is the integral coefficient, k p ′, k p ″ are respectively the first adaptive correction coefficient and the second adaptive correction coefficient of the proportionality coefficient, k i ′, k i ″ are respectively the first adaptive correction coefficient and the second adaptive correction coefficient of the integral coefficient, β is the adaptive correction coefficient of the integral link, v ref is the output voltage reference value.

[0021] Furthermore, the designed model predictive control current loop model is a model predictive control based on an offline single-step period, which adopts tracking triangular wave PWM modulation, the carrier is an isosceles triangular wave, and set i L (k) and i L (k + 1) are respectively the predicted values of the inductor current at the current moment and the inductor current at the next moment;

[0022] According to Equation (1), combined with the duty cycle μ = 1 or 0 of the isosceles triangular wave, calculate the current slope h as follows:

[0023]

[0024] Among them, E(k) is the input voltage of the boost converter at the current moment, v o (k) is the output voltage of the boost converter at the current moment;

[0025] According to the inductor current i L (k) at the current moment and the turn-on time t1 = t3, obtain the predicted value i L (k + 1) of the inductor current at the next moment, which is expressed as:

[0026]

[0027] Among them, i S1 is the first inductor current extreme point, i S2 is the second inductor current extreme point, i S3 is the third inductor current extreme point;

[0028] Set to adopt the average tracking mode to track the reference value of the inductor current, and its cost function J(k) is as follows:

[0029] J(k) = (I d - i S1 ) 2 + (I d - iS2 ) 2 +(I d -i S3 ) 2 (7)

[0030] By substituting the equation (6) for solving the extreme point of the inductor current into equation (7), the expression is obtained as follows:

[0031] J(k) = (I d -i S0 -h1t1) 2 +(I d -i S0 -h1t1 - h2t2) 2 +(I d -i S0 -2h1t1 - h2t2) 2 (8)

[0032] Considering that in equation (8), one switching period T s = t1 + t2 + t3 = 2t1 + t2, so equation (8) is regarded as a quadratic equation with one variable with t1 as the independent variable and J(k) as the dependent variable; by taking the derivative and finding the value of t1 corresponding to when its derivative is zero, the corresponding times of different actions of the switch within one period are obtained as follows for the case of optimal tracking of the reference current:

[0033]

[0034] According to equation (9), the duty cycle in the boost converter operating mode is expressed as:

[0035] μ = 2t1 / T s (10).

[0036] Furthermore, design a non - linear disturbance observer model, introduce a feed - forward loop based on the non - linear disturbance observer, and transform equation (1) into a non - linear system form, with the expression as follows:

[0037]

[0038] where d is the lumped disturbance in the system;

[0039] In order to improve the response speed of the controlled system, a disturbance observer is adopted. The constructed disturbance observer is only used to estimate the load disturbance current value and perform feed - forward compensation through the feed - forward channel, and its specific form is as follows:

[0040]

[0041] where R0 and P CPL0 are the rated resistance load value and the rated power of the constant - power load respectively;

[0042] According to the form of the nonlinear system in Equation (11), the basic nonlinear disturbance observer model is expressed as follows:

[0043]

[0044] where λ represents the nonlinear disturbance observer gain coefficient, and p(Z) represents the nonlinear function to be designed;

[0045] Define the estimation error e of the nonlinear disturbance observer d as follows:

[0046]

[0047] Derive Equation (14), and substitute the general equation of the nonlinear system and the basic nonlinear disturbance observer model represented by Equation (13) into the derivative equation of the estimated error after derivation, we can get:

[0048]

[0049] where is the derivative of the estimation error of the nonlinear disturbance observer;

[0050] By selecting the disturbance observer gain λ, the estimation error of the disturbance observer will finally converge to zero;

[0051] Based on the above construction process, the expression of the nonlinear disturbance observer model for observing the load uncertainty of the boost converter is:

[0052]

[0053] A large-signal stability analysis method for a DC microgrid with a constant power load is realized based on the adaptive composite model predictive control method for a DC microgrid with a constant power load described above. Based on the mixed potential function theorem and the Lyapunov theorem, combined with the large-signal equivalent circuit structure of the boost converter, a mixed potential function is constructed, and a large-signal stability criterion is derived to judge the stability of the system;

[0054] The tracking of the converter output voltage of the large-signal equivalent circuit structure of the boost converter under the proposed control strategy is indirectly realized through current tracking, and the current absorbed by the constant power load from the bus is also proportional to the bus voltage. The power supply and the constant power load in the circuit system are equivalent to a controlled current source, and at the same time, the constant impedance load is modeled separately and equivalent to a power-consuming element with a constant resistance value.

[0055] Furthermore, it includes the following steps:

[0056] S1. Construct the general form of the hybrid potential function \(P(i, v)\) used in the non - linear circuit as follows:

[0057] \(P(i, v)=-A(i)+B(v)+(i, \gamma v-\alpha)\quad(17)\)

[0058] Where \(A(i)\) is the current potential energy equation, \(B(v)\) is the voltage potential energy equation, \(\gamma\) is a constant equation related to the circuit structure, and \(\alpha\) is a constant vector;

[0059] S2. Analyze the large - signal stability of the object under study using the third theorem;

[0060] Let \(\mu_1\) and \(\mu_2\) be the minimum eigenvalues of \(L\) -1 / 2 \(A\) ii (i) \(L\) -1 / 2 and \(C\) -1 / 2 \(B\) vv (v) \(C\) -1 / 2 respectively;

[0061] If the condition

[0062] \(\mu_1+\mu_2\geq\delta\quad\delta > 0\quad(18)\)

[0063] is satisfied and when \(i + v\rightarrow\infty\), there exists

[0064]

[0065] Then as time approaches infinity, all solutions corresponding to the system tend to the stable operating point, that is, the verified system is a large - signal stable system;

[0066] According to the large - signal equivalent circuit of the boost converter, the expression of the hybrid potential function used in the non - linear circuit is obtained as:

[0067]

[0068] For the convenience of large - signal stability analysis, equation (20) is rewritten as the unified expression of the hybrid potential function as follows:

[0069]

[0070] S3. Based on the fast tracking of the reference current by the model - predictive control current - loop model, let \(i\) in (21) L \(=I\) d ;

[0071] Combined with the adaptive proportional - integral control voltage - loop model in formula (4), the expressions of \(\mu_1\) and \(\mu_2\) are obtained as:

[0072]

[0073] According to the third theorem of the hybrid potential function, the large-signal stability criterion is derived as follows:

[0074]

[0075] Advantages of the present invention:

[0076] For the adaptive composite model predictive control method of a DC microgrid with a constant power load of the present invention, the proposed controller includes a parameter adaptive proportional-integral control based on the error signal, a model predictive control feedback loop with a single-step prediction period, and a feedforward loop of a nonlinear disturbance observer, significantly improving the robustness of the system on the basis of the stability control of the boost converter. In addition, the large-signal stability analysis based on the hybrid potential function shows that when the controlled object deviates from the rated operating state due to uncertainties and there are constant power loads with high permeability, the proposed control algorithm can still ensure the stability of the controlled object when meeting the obtained large-signal stability criterion. The hardware-in-the-loop comparison experiment shows that the proposed controller has excellent robustness.

[0077] For the adaptive composite model predictive control method of a DC microgrid with a constant power load of the present invention, an adaptive composite model predictive control strategy is proposed to alleviate the instability problem caused by the negative impedance characteristic of the constant power load and improve the transient performance of the system during disturbances on the source-load side in the DC microgrid. The controller of the proposed invention method consists of a feedback loop composed of an adaptive proportional-integral control and a model predictive control for tracking the voltage reference value, and a feedforward loop composed of a nonlinear disturbance observer for online estimating and feedforward compensating the load disturbance current, thus significantly improving the robustness of the system on the basis of the stable control of the boost converter. In addition, the large-signal stability analysis based on the hybrid potential function theory shows that when the controlled object deviates from the rated operating state due to uncertainties and there are constant power loads with high permeability, the proposed invention method can ensure the large-signal stability of the controlled object. Finally, the effectiveness and superiority of the proposed control method are verified through hardware-in-the-loop experiments in multiple scenarios. Brief Description of the Drawings

[0078] Figure 1 is the typical DC microgrid structure and its equivalent circuit of the present invention;

[0079] Figure 2 is the waveform diagram of the inductor current and the duty cycle within a switching period;

[0080] Figure 3 is the adaptive composite model predictive control block diagram of a DC microgrid with a constant power load of the present invention;

[0081] Figure 4It is the equivalent model for the large-signal stability analysis of the present invention;

[0082] Figure 5 It is the large-signal stability boundary diagram of the present invention;

[0083] Figure 6 It is the waveform diagram of the hardware-in-the-loop comparison experiment of the control method proposed by the present invention under the change of resistive load;

[0084] Figure 7 It is the waveform diagram of the hardware-in-the-loop comparison experiment of the control method proposed by the present invention under the change of constant-power load;

[0085] Figure 8 It is the waveform diagram of the hardware-in-the-loop comparison experiment of the control method proposed by the present invention under the change of input voltage;

[0086] Figure 9 It is the structural schematic diagram of the present invention. Specific Embodiments

[0087] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in combination with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the specific embodiments described are only a part of the embodiments of the present invention, rather than all of the specific embodiments. The components of the specific embodiments of the present invention usually described and shown in the accompanying drawings here can be arranged and designed in various different configurations, and the present invention can also have other embodiments.

[0088] Therefore, the detailed description of the specific embodiments of the present invention provided in the accompanying drawings below is not intended to limit the scope of the claimed invention, but merely represents the selected specific embodiments of the present invention. All other specific embodiments obtained by those skilled in the art based on the specific embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0089] To further understand the content, features and effects of the present invention, the following specific embodiments are cited and are accompanied by Figure 1 -Accompanying Figure 9 The details are as follows:

[0090] Example 1:

[0091] A DC microgrid adaptive composite model predictive control method with a constant-power load, and the control method is designed in three parts, including an adaptive proportional-integral control voltage loop model, a model predictive control current loop model and a non-linear disturbance observer model;

[0092] The feedback loop is composed of an adaptive proportional-integral control voltage loop model and a model predictive control current loop model, and the nonlinear disturbance observer is the feedforward compensation loop;

[0093] The adaptive proportional-integral control voltage loop model outputs the current reference value result to the model predictive control current loop model by inputting the reference voltage value collected by the input and the output voltage data of the boost converter collected by the voltage signal sensor;

[0094] The model predictive control current loop model outputs the duty cycle signal of the boost converter to the nonlinear disturbance observer model by inputting the current reference value result obtained from the adaptive proportional-integral control voltage loop model and the inductor current data of the boost converter collected by the current signal sensor;

[0095] The nonlinear disturbance observer model outputs the concentrated disturbance estimation value by inputting the output voltage data of the boost converter collected by the voltage signal sensor, the inductor current data of the boost converter collected by the current signal sensor, and the duty cycle signal of the boost converter obtained from the model predictive control current loop model. Then, the nonlinear disturbance observer model feeds forward and compensates the concentrated disturbance estimation value to the adaptive proportional-integral control voltage loop model.

[0096] Furthermore, the control method is based on the boost converter with a parallel resistive load and a constant power load operating in continuous conduction mode;

[0097] Based on the Figure 1 general DC microgrid structure shown and the equivalent circuit of the boost converter with a parallel resistive load and a constant power load. The source bus is powered by multiple power generation units, and the DC / DC boost converter is used to increase the voltage and provide energy for 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.

[0098] First, construct the average dynamic model of the boost converter, and the expression is:

[0099]

[0100] where L, C, v s , v o , i L , μ, R, and P CPL are the inductor value, capacitor value, input voltage, output voltage, inductor current, switch duty cycle, resistive load, and constant power load power of the DC / DC boost converter, respectively;

[0101] According to Equation (1), construct the open-loop transfer function G(s) with a resistive load and a constant power load, and the expression is:

[0102]

[0103] Among them, represents the small-signal perturbation of the steady-state operating point of the output voltage, represents the small-signal perturbation of the steady-state operating point of the duty cycle.

[0104] According to the small-signal model of Equation (2), when , that is, the resistive load dominates, the pole is located on the left half-axis of the plane, and the system remains stable; while when , that is, the equivalent resistance of the constant-power load dominates, the pole is located on the right half-axis of the plane, and the system remains unstable.

[0105] The expected goal for the design of the voltage controller is to propose an adaptive proportional-integral control loop to achieve fast voltage regulation (v ref -v o = 0) under system perturbations and without rated parameters. Traditional proportional-integral control tracks the reference value of the state variable by adjusting the proportional coefficient k p and the integral coefficient k i ; its formula is as follows:

[0106] I d = k p (v ref -v o ) + k i ∫(v ref -v o )dt (3)

[0107] However, traditional proportional-integral control usually relies on manual trial and error or empirical methods to select fixed coefficient gains, so its dynamic performance shows differences under different operating conditions. For example, if the control gain is selected conservatively, the system shows poor transient performance when subjected to large-signal interference; if the control gain is selected aggressively, the system shows redundant robustness when subjected to small-signal interference.

[0108] Considering that when the voltage signal deviates greatly from the reference value, the larger the proportional gain coefficient, the faster the voltage error converges. However, when the system voltage signal deviates slightly from the reference value, the larger the proportional gain coefficient may cause the voltage to directly cross its reference value and produce voltage overshoot. For the integral link, a larger integral gain coefficient can shorten the recovery time of the system, but it also makes the system stability worse. Therefore, when the voltage error is large, the control coefficient value should be made larger to improve the transient performance of the system and avoid static error; while when the error is small, the control coefficient value should be reduced to improve the stability of the system.

[0109] Furthermore, an adaptive proportional-integral control voltage loop model is designed, and its expression is:

[0110]

[0111] where I d is the result of the current reference value, k p is the proportional coefficient, k i is the integral coefficient, k p ′ and k p ″ are the first and second adaptive correction coefficients of the proportional coefficient respectively, k i ′ and k i ″ are the first and second adaptive correction coefficients of the integral coefficient respectively, β is the adaptive correction coefficient of the integral link, and v ref is the output voltage reference value.

[0112] Furthermore, the model predictive control current loop model is designed as a model predictive control based on an offline single-step cycle, which adopts tracking triangular wave PWM modulation, and the carrier is an isosceles triangular wave. Let i L (k) and i L (k + 1) be the predicted values of the inductor current at the current moment and the predicted value of the inductor current at the next moment respectively, as Figure 2 shown;

[0113] According to Equation (1), combined with the duty cycle μ = 1 or 0 of the isosceles triangular wave, the current slope h is calculated as follows:

[0114]

[0115] where E(k) is the input voltage of the boost converter at the current moment, and v o (k) is the output voltage of the boost converter at the current moment;

[0116] According to the inductor current i L (k) at the current moment and the turn-on time t1 = t3, the predicted value i L (k + 1) of the inductor current at the next moment is expressed as:

[0117]

[0118] where i S1 is the first inductor current extreme point, i S2 is the second inductor current extreme point, and i S3 is the third inductor current extreme point;

[0119] When using the predictive current control algorithm to track the reference current, there are usually three modes of tracking the current reference value, namely, the peak tracking of the current waveform, the valley tracking of the current waveform, and the average tracking of the current waveform. However, there are certain errors between the peak and valley tracking modes and the current reference value. The current predictive control adopting the average tracking mode is not affected by the duty cycle and can achieve error-free tracking of the reference current.

[0120] Set the reference value of the inductor current to be tracked in the average tracking mode, and its cost function J(k) is as follows:

[0121] J(k) = (I d - i S1 ) 2 + (I d - i S2 ) 2 + (I d - i S3 ) 2 (7)

[0122] By substituting the inductor current extreme point solving equation (6) into equation (7), the expression is obtained:

[0123] J(k) = (I d - i S0 - h1t1) 2 + (I d - i S0 - h1t1 - h2t2) 2 + (I d - i S0 - 2h1t1 - h2t2) 2 (8)

[0124] Considering that in equation (8), a switching period T s = t1 + t2 + t3 = 2t1 + t2, so equation (8) is regarded as a quadratic equation with one variable with t1 as the independent variable and J(k) as the dependent variable; by taking the derivative and finding the value of t1 corresponding to when the derivative is zero, the corresponding times of different actions of the switch within one period are obtained as follows when the effect of tracking the reference current is optimal:

[0125]

[0126] According to equation (9), the duty cycle in the boost converter working mode is expressed as:

[0127] μ = 2t1 / T s (10).

[0128] Furthermore, a non - linear disturbance observer model is designed, and a feed - forward loop based on the non - linear disturbance observer is introduced to convert Equation (1) into a non - linear system form, and the expression is as follows:

[0129]

[0130] where d is the lumped disturbance in the system;

[0131] In order to improve the response speed of the controlled system, a disturbance observer is adopted. The constructed disturbance observer is only used to estimate the load disturbance current value and perform feed - forward compensation through the feed - forward channel. Its specific form is as follows:

[0132]

[0133] where R0 and P CPL0 are the rated resistance load value and the rated power of the constant - power load respectively;

[0134] According to the non - linear system form of Equation (11), the basic non - linear disturbance observer model is expressed as follows:

[0135]

[0136] where λ represents the non - linear disturbance observer gain coefficient, and p(Z) represents the non - linear function to be designed;

[0137] Define the estimation error e of the non - linear disturbance observer d as follows:

[0138]

[0139] Taking the derivative of Equation (14) and substituting the general equation of the non - linear system and the basic non - linear disturbance observer model represented by Equation (13) into the derivative equation of the error estimation, we can get:

[0140]

[0141] where is the derivative of the estimation error of the non - linear disturbance observer;

[0142] By selecting the disturbance observer gain λ, the estimation error of the disturbance observer will finally converge to zero;

[0143] Based on the above construction process, the expression of the non - linear disturbance observer model for observing the load uncertainty of the boost converter is:

[0144]

[0145] Combining the adaptive proportional-integral voltage controller in Equation (4), the model predictive controls in Equations (5), (9), and (10), and the nonlinear disturbance observer (16), the proposed adaptive composite model predictive control for the boost converter can be obtained. Its detailed control block diagram is as shown in Figure 3 Figure 1. When selecting the parameters of the disturbance observer, a trade-off needs to be made between the convergence speed and the overshoot ripple. After multiple simulations, λ = 1000 is finally selected as the parameter of the nonlinear disturbance observer.

[0146] Embodiment 2:

[0147] A large-signal stability analysis method for a DC microgrid with a constant power load is realized based on the adaptive composite model predictive control method for a DC microgrid with a constant power load described in Embodiment 1. Based on the mixed potential function theorem and the Lyapunov theorem, combined with the large-signal equivalent circuit structure of the boost converter, a mixed potential function is constructed, and the large-signal stability criterion is derived to judge the stability of the system.

[0148] The tracking of the converter output voltage in the large-signal equivalent circuit structure of the boost converter under the proposed control strategy is indirectly realized through current tracking, and the current absorbed by the constant power load from the bus is also proportional to the bus voltage. The power supply and the constant power load in the circuit system are equivalent to controlled current sources, and at the same time, the constant impedance load is modeled separately and equivalent to an energy-consuming element with a constant resistance value.

[0149] Considering that the small-signal stability analysis is only applicable to the system parameter analysis and stability estimation under small disturbances, and is not applicable to the DC microgrid under large disturbances such as step changes on the source and load sides and plug-and-play, and high-penetration constant power loads, it is necessary to conduct a large-signal stability analysis on the proposed controller. Compared with other large-signal stability analysis methods, the mixed potential function theorem is based on the Lyapunov theorem, combined with the characteristics of the circuit structure, constructs a mixed potential function, and derives a large-signal stability criterion to judge the stability of the system. Its advantages are simple construction, clear physical meaning, and no need for complex frequency-domain analysis, which is a powerful tool for large-signal analysis of power electronic systems. There are three theorems in the mixed potential function 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, and the research objects in this paper are all DC / DC boost converters with nonlinear characteristics, the third theorem is used to analyze the large-signal stability of the research objects.

[0150] Further, it specifically includes the following steps:

[0151] S1. Construct the general form of the mixed potential function P(i, v) used in the nonlinear circuit as follows:

[0152] P(i, v) = -A(i) + B(v) + (i, γv - α) (17)

[0153] Wherein, 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;

[0154] S2. Analyze the large-signal stability of the object under study using the third theorem;

[0155] Let μ1 and μ2 be the minimum eigenvalues of L -1 / 2 A ii (i)L -1 / 2 and C -1 / 2 B vv (v)C -1 / 2 respectively;

[0156] If the condition

[0157] μ1 + μ2 ≥ δ, δ > 0 (18)

[0158] is satisfied and when i + v → ∞, there exists

[0159]

[0160] then as time approaches infinity, all solutions corresponding to the system tend to the stable operating point, that is, the verified system is a large-signal stable system;

[0161] Considering the existence of the current inner-loop controller in the DC / DC boost converter, it has the characteristics of a controlled current source. In addition, the current absorbed by the constant power load from the bus is also proportional to the bus voltage, so the constant power load can also be equivalent to a controlled current source. As Figure 4 shown:

[0162] According to the large-signal equivalent circuit of the boost converter, the expression of the hybrid potential function used in the nonlinear circuit is obtained as:

[0163]

[0164] For the convenience of large-signal stability analysis, Equation (20) is rewritten as the unified expression of the hybrid potential function as follows:

[0165]

[0166] S3. Based on the rapid tracking of the reference current by the model predictive control current loop model, let i in (21) L = I d ; Combining with the adaptive proportional-integral control voltage loop model in Equation (4), the expressions of μ1 and μ2 are obtained as:

[0167]

[0168] According to the third theorem of the hybrid potential function, the large-signal stability criterion is derived as follows:

[0169]

[0170] When the constant-power load and resistive load in the system change, the large-signal stability boundary of the system is as Figure 5 shown. It can be seen from Figure 5 that the upper part of the three-dimensional surface is the large-signal stable region. When the value range of the proportional parameter is located in the upper part of the three-dimensional surface, the system is in a large-signal stable state. After simulation comparison and analysis of the converter performance under different parameter values, the adaptive correction coefficients k p = 0.5, k i = 35, k p ' = 1.5, k p '' = 0.5, k i ' = 1, k i '' = 0.5 and β = 10 of the proportional and integral links are finally selected. Combining the large-signal stability criterion of formula (23) and the Figure 5 large-signal stability boundary diagram shown, the adaptive composite model predictive control proposed by the method of the present invention ensures the large-signal stability of the system.

[0171] The present invention proposes an adaptive composite model predictive control and large-signal stability analysis method for a DC microgrid with a constant-power load to alleviate the instability problem caused by the negative impedance characteristic of the constant-power load and improve the transient performance of the system during source-load side disturbances in the DC microgrid. This control method combines adaptive proportional-integral control, model predictive control, and observer technology. First, a parameter adaptive proportional-integral feedback link and a feedforward link based on nonlinear disturbance observation technology are introduced to enhance the robustness of the system on the basis of the stable control of the boost converter. Then, a model predictive control with a single-step prediction period is designed to reduce the computational burden and improve the dynamic performance. In addition, the large-signal stability analysis based on the hybrid potential theory shows that when the controlled object deviates from the rated operating state due to uncertainty and there is a constant-power load with high permeability, the proposed control algorithm can still ensure the stability of the controlled object when meeting the obtained large-signal stability criterion.

[0172] To verify the effectiveness of the method of the present invention, it is constructed on the hardware-in-the-loop experimental platform as Figure 1The boost converter model with resistive load and constant power load shown is used to further verify the effectiveness and superiority of the proposed adaptive composite model predictive control. The platform includes a MATLAB / Simulink model, an OPAL-RT OP5600 digital real-time simulator, and a digital signal processor. On this basis, two case studies are carried out: a) multiple load step change tests; b) input voltage step change tests. The detailed parameters of the system are shown in Table 1.

[0173] Table 1 System parameter configuration

[0174]

[0175] Case 1: This case study examines the robustness of the proposed controller in the face of step disturbances of resistive and constant power loads to verify the superiority of the proposed method. Figure 6 It shows the comparison of experimental waveforms between adaptive composite model predictive control (API-MPC) and traditional proportional-integral predictive control (PI-MPC) when the resistive load has a step change. The resistive load changes from 50 Ω to 25 Ω and then returns to 50 Ω after a period of time. From Figure 6 it can be seen that when the resistive load changes, the maximum overshoot and recovery time of the output voltage of the proposed method are 3.5 V and 25 ms respectively, while those of the traditional proportional-integral predictive control are 5.5 V and 75 ms respectively. Figure 7 It shows the experimental waveforms of adaptive composite model predictive control and traditional proportional-integral predictive control under the step disturbance of constant power load. The power of the constant power load changes from 250 W to 500 W and then returns to 250 W after a period of time. From Figure 7 it can be seen that when the power of the constant power load changes, the maximum overshoot and recovery time of the output voltage of the proposed method are 4.5 V and 20 ms respectively, while those of the traditional proportional-integral predictive control are 8 V and 60 ms respectively.

[0176] This case examines the robustness of the proposed method in the face of step disturbance of input voltage to verify the superiority of the proposed controller. Figure 8 It shows the comparison of experimental waveforms between adaptive composite model predictive control and traditional proportional-integral predictive control under the step disturbance of input voltage. The input voltage changes from 50 V to 80 V and then returns to 50 V after a period of time. From Figure 8 it can be seen that when the input voltage changes, the maximum overshoot and recovery time of the output voltage of the proposed method are 3.5 V and 25 ms respectively, while those of the traditional proportional-integral predictive control are 6.5 V and 60 ms respectively.

[0177] It should be noted that relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprising", "including" or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising an..." does not exclude the presence of additional identical elements in the process, method, article or device comprising said element.

[0178] Although the present application has been described above with reference to specific embodiments, various improvements can be made thereto and components thereof can be replaced with equivalents without departing from the scope of the present application. In particular, as long as there is no structural conflict, the features in the specific embodiments disclosed in the present application can be combined with each other in any way, and the exhaustive description of these combinations is not given in this specification only for the sake of saving space and resources. Therefore, the present application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. An adaptive composite model predictive control method for a DC microgrid with a constant power load, characterized in that, The control method is designed in three parts, including an adaptive proportional-integral control voltage loop model, a model predictive control current loop model, and a nonlinear disturbance observer model; The adaptive proportional-integral control voltage loop model and the model predictive control current loop model form a feedback loop, and the nonlinear disturbance observer is a feedforward compensation loop; The adaptive proportional-integral control voltage loop model inputs the reference voltage value collected by the input, and the output voltage data of the boost converter collected by the voltage signal sensor, and outputs the current reference value result to the model predictive control current loop model; The model predictive control current loop model inputs the current reference value result obtained from the adaptive proportional-integral control voltage loop model and the inductor current data of the boost converter collected by the current signal sensor, and outputs the duty cycle signal of the boost converter to the nonlinear disturbance observer model; The nonlinear disturbance observer model inputs the output voltage data of the boost converter collected by the voltage signal sensor, the inductor current data of the boost converter collected by the current signal sensor, and the duty cycle signal of the boost converter obtained from the model predictive control current loop model, and outputs the lumped disturbance estimate value. Then, the nonlinear disturbance observer model feeds forward the lumped disturbance estimate value to the adaptive proportional-integral control voltage loop model.

2. The adaptive composite model predictive control method for a DC microgrid with a constant power load according to claim 1, characterized in that The control method is based on a boost converter with a parallel resistive load and a constant power load operating in continuous conduction mode; First, construct the average dynamic model of the boost converter, and the expression is: where L, C, v s , v o , i L , μ, R, and P CPL are the inductance value, capacitance value, input voltage, output voltage, inductor current, switch duty cycle, resistive load, and constant power load power of the DC / DC boost converter, respectively; According to Equation (1), construct the open-loop transfer function G(s) with a resistive load and a constant power load, and the expression is: Among them, represents the small-signal perturbation of the steady-state operating point of the output voltage, represents the small-signal perturbation of the steady-state operating point of the duty cycle.

3. An adaptive composite model predictive control method for a DC microgrid with a constant power load according to claim 2, characterized in that, Design the adaptive proportional-integral control voltage loop model, and the expression is: Among them, I d is the current reference value result, k p is the proportionality coefficient, k i is the integral coefficient, k p ′, k p ″ are the first and second adaptive correction coefficients of the proportionality coefficient respectively, k i ′, k i ″ are the first and second adaptive correction coefficients of the integral coefficient respectively, β is the adaptive correction coefficient of the integral link, v ref is the output voltage reference value.

4. An adaptive composite model predictive control method for a DC microgrid with a constant power load according to claim 3, characterized in that The design model predictive control current loop model is based on the off-line single-step cycle model predictive control, which adopts the tracking triangular wave PWM modulation. The carrier wave is an isosceles triangular wave. Set i L (k) and i L (k + 1) are the predicted values of the inductor current at the current moment and the predicted value of the inductor current at the next moment respectively; According to Equation (1), combined with the duty cycle μ = 1 or 0 of the isosceles triangular wave, calculate the current slope h as follows: Among them, E(k) is the input voltage of the boost converter at the current moment, and v o (k) is the output voltage of the boost converter at the current moment; According to the inductor current i at the current moment L (k) and the turn-on time t1 = t3, the predicted value of the inductor current at the next moment i L (k + 1) is expressed as: wherein, i S1 is the first inductor current extreme point, i S2 is the second inductor current extreme point, i S3 is the third inductor current extreme point; Set the average tracking mode to track the reference value of the inductor current, and its cost function J(k) is as follows: J(k) = (I d - i S1 ) 2 + (I d - i S2 ) 2 + (I d - i S3 ) 2 (7) By substituting the inductor current extreme point solution equation (6) into Equation (7), the expression is obtained: J(k) = (I d -i S0 -h1t1) 2 +(I d -i S0 -h1t1 - h2t2) 2 +(I d -i S0 -2h1t1 - h2t2) 2 (8) Considering a switching period T in Equation (8) s = t1 + t2 + t3 = 2t1 + t2, so Equation (8) is regarded as a quadratic equation with one variable, where t1 is the independent variable and J(k) is the dependent variable; by taking the derivative and finding the value of t1 corresponding to the zero derivative, the corresponding times of different actions of the switch within one period are obtained as follows when the effect of tracking the reference current is optimal: According to Equation (9), the duty cycle in the operating mode of the boost converter is expressed as: μ = 2t1 / T s (10).

5. A self - adaptive composite model predictive control method for a DC micro - grid with a constant - power load according to claim 4, characterized in that Design the nonlinear disturbance observer model, introduce a feedforward loop based on the nonlinear disturbance observer, and convert Equation (1) into a nonlinear system form, and the expression is: where d is the lumped disturbance in the system; In order to improve the response speed of the controlled system, a disturbance observer is used. The constructed disturbance observer is only used to estimate the load disturbance current value and perform feedforward compensation through the feedforward channel. Its specific form is as follows: wherein, R0 and P CPL0 are the rated resistance load value and the rated power of the constant power load respectively; According to the nonlinear system form of Equation (11), the basic nonlinear disturbance observer model is expressed as follows: where λ represents the nonlinear disturbance observer gain coefficient, and p(Z) represents the nonlinear function to be designed; Define the estimation error \(e\) of the nonlinear disturbance observer d as follows: Derive Equation (14), and substitute the general equation of the nonlinear system and the basic nonlinear disturbance observer model represented by Equation (13) into the derivative equation of the error estimate after derivation to obtain: Among them, is the derivative of the estimation error of the non-linear disturbance observer; By selecting the disturbance observer gain λ, the estimation error of the disturbance observer will finally converge to zero; Based on the above construction process, the expression of the nonlinear disturbance observer model for observing the load uncertainty of the boost converter is:

6. A large-signal stability analysis method for a DC microgrid with constant-power loads, which is implemented based on an adaptive composite model predictive control method for a DC microgrid with constant-power loads according to any one of claims 1-5, characterized in that Based on the hybrid potential function theorem and Lyapunov's theorem, combined with the large signal equivalent circuit structure of the boost converter, the hybrid potential function is constructed and the large signal stability criterion is derived to judge the stability of the system; The large signal equivalent circuit structure of the boost converter tracks the converter output voltage indirectly under the proposed control strategy through current tracking, and the current absorbed by the constant power load from the bus is also proportional to the bus voltage. The power supply and constant power load in the circuit system are equivalent to controlled current sources. At the same time, the constant impedance load is modeled separately and is equivalent to an energy-consuming element with a constant resistance.

7. A large-signal stability analysis method for a DC microgrid with a constant-power load according to claim 6, characterized in that The steps include: S1. The general form of the mixed potential function P(i,v) used in constructing nonlinear circuits is as follows: P(i,v)=-A(i)+B(v)+(i,γv-α) (17) Among them, 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; S2. Use the third theorem to analyze the large signal stability of the object under study; Let μ1 and μ2 be the minimum eigenvalues of L -1 / 2 A ii (i)L -1 / 2 and C -1 / 2 B vv (v)C -1 / 2 respectively; If the conditions are met μ1+μ2≥δδ>0 (18) And when |i|+|v|→∞, there exists Then when time approaches infinity, all solutions corresponding to the system tend to the stable working point, that is, the verified system is a large signal stable system; According to the large signal equivalent circuit of the boost converter, the expression of the mixed potential function used in the nonlinear circuit is obtained as follows: To facilitate large signal stability analysis, equation (20) is rewritten as a unified expression of the mixed potential function as follows: S3. Based on the model predictive control current loop model to rapidly track the reference current, let \(i\) in (21) L \(= I\) d ; Combining with the adaptive proportional-integral control voltage loop model in formula (4), the expressions of \(\mu_1\) and \(\mu_2\) are obtained as follows: According to the third theorem of mixed potential function, the large signal stability criterion is derived as:

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