Adaptive composite model predictive control method and large signal stability analysis method for DC micro-grid with constant power load

Abstract

The invention discloses an adaptive composite model prediction control method and a large signal stability analysis method for a direct current micro-grid with a constant power load, and belongs to the technical field of direct current micro-grid control. In order to realize stable operation and good transient performance of the boost converter with the constant power load, the method comprises an adaptive proportional-integral control voltage loop model, a model prediction control current loop model and a nonlinear disturbance observer model. According to the invention, a feedback loop composed of adaptive proportional integral control and model prediction control is used for tracking a voltage reference value, and a feed-forward loop composed of a nonlinear disturbance observer is used for online estimation and feed-forward compensation of load disturbance current. Therefore, the robustness of the system is obviously improved on the basis of stable control of the boost converter. Large signal stability analysis based on a mixed potential function theory shows that when a controlled object deviates from a rated operation state due to uncertainty and has a high-permeability constant-power load, the large signal stability of the controlled object is ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of direct current microgrid control, and in particular relates to an adaptive composite model predictive control method and a large signal stability analysis method for a direct current microgrid with a constant power load. Background Art

[0002] In recent years, microgrids have attracted extensive attention as simple, compact, and reliable power distribution systems that bring together renewable energy, energy storage systems, distributed generation units, and modern power electronic loads. Compared with AC microgrids, DC microgrids have a relatively simple control structure that avoids problems such as reactive power, phase synchronization, and frequency regulation. In addition, most power supplies and electronic loads are inherently DC. Therefore, the most common DC / DC boost converter interface for DC microgrids reduces redundant energy conversion stages and improves transmission efficiency. Therefore, it is very important to explore controllers that can quickly adjust 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 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;

[0008] The adaptive proportional integral control voltage loop model inputs the collected reference voltage value and the boost converter output voltage data collected by the voltage signal sensor, and outputs the current reference value result to the model prediction control current loop model;

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

[0010] The nonlinear disturbance observer model outputs a concentrated disturbance estimate through the boost converter output voltage data collected by the input voltage signal sensor, the boost converter inductor current data collected by the current signal sensor, and the boost converter duty cycle signal obtained by the model predictive control current loop model. The nonlinear disturbance observer model then feed-forwards the concentrated disturbance estimate to the adaptive proportional-integral control voltage loop model.

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

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

[0013]

[0014] Among them, L, C, v s , v o ,i L , μ, R and P CPL They 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;

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

[0016]

[0017] in, Represents the small signal disturbance of the output voltage steady-state operating point, Represents a small signal perturbation at the steady-state operating point of the duty cycle.

[0018] Furthermore, an adaptive proportional-integral control voltage loop model is designed, 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 integration coefficient, k p ′, k p ″ are the first adaptive correction coefficient and the second adaptive correction coefficient of the proportional coefficient, respectively, i ′, k i ″ are 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 model predictive control current loop model is designed to be based on the offline single-step cycle model predictive control using tracking triangle wave PWM modulation, the carrier is an isosceles triangle wave, and i is set L (k) and i L (k+1) is the inductor current at the current moment and the predicted value of the inductor current at the next moment;

[0022] According to formula (1), combined with the duty cycle μ of the isosceles triangle wave = 1 or 0, the current slope h is calculated as follows:

[0023]

[0024] Where 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 at the current moment L (k) and opening time t 1 =t 3 , get the predicted value of the inductor current at the next moment i L (k+1) 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 It is the third inductor current extreme point;

[0028] The reference value of the inductor current is set to track using the average tracking mode. The cost function J(k) is as follows:

[0029] J(k)=(I d -i S1 ) 2+(I d -i S2 ) 2 +(I d -i S3 ) 2 (7)

[0030] By substituting equation (6) for the inductor current extreme point into equation (7), we get the expression:

[0031] J(k)=(I d -i S0 -h 1 t 1 ) 2 +(I d -i S0 -h 1 t 1 -h 2 t 2 ) 2 +(I d -i S0 -2h 1 t 1 -h 2 t 2 ) 2 (8)

[0032] Considering a switching cycle T in equation (8) s =t 1 +t 2 +t 3 =2t 1 +t 2 , so we regard formula (8) as 1 A quadratic equation with J(k) as the independent variable and J(k) as the dependent variable; by taking the derivative and finding the corresponding t when the derivative is zero 1 The corresponding time of different actions of the switch in one cycle is as follows when the tracking reference current is optimal:

[0033]

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

[0035] μ=2t 1 / T s (10).

[0036] Furthermore, a nonlinear disturbance observer model is designed, and a feedforward loop based on the nonlinear disturbance observer is introduced to transform equation (1) into a nonlinear system form, which is expressed as follows:

[0037]

[0038] Where d is the total disturbance in the system;

[0039] 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:

[0040]

[0041] Among them, R 0 and P CPL0 They are the rated resistance load value and the constant power load rated power respectively;

[0042] According to the nonlinear system form of 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 shown below:

[0046]

[0047] By taking the derivative of equation (14) and bringing the general equation of the nonlinear system and the basic nonlinear disturbance observer model represented by equation (13) into the derivative error estimation derivative equation, we can obtain:

[0048]

[0049] in, 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 eventually 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 implemented based on the adaptive composite model predictive control method for a DC microgrid with a constant power load. Based on the hybrid potential function theorem and Lyapunov's theorem, combined with the large signal equivalent circuit structure of the boost converter, a hybrid potential function is constructed, and a large signal stability criterion is derived, thereby judging the stability of the system.

[0054] 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.

[0055] Further, the following steps are included:

[0056] S1. The general form of the mixed potential function P(i,v) used in constructing nonlinear circuits is as follows:

[0057] P(i,v)=-A(i)+B(v)+(i,γv-α) (17)

[0058] 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;

[0059] S2. Use the third theorem to analyze the large signal stability of the object under study;

[0060] set up μ 1 With μ 2 L -1 / 2 A ii (i)L -1 / 2 and C -1 / 2 B vv (v)C -1 / 2 The minimum eigenvalue of ;

[0061] If the conditions are met

[0062] μ 1 +μ 2 ≥δδ>0 (18)

[0063] And when i+v→∞, there exists

[0064]

[0065] 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;

[0066] 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:

[0067]

[0068] To facilitate large signal stability analysis, equation (20) is rewritten as a unified expression of the mixed potential function as follows:

[0069]

[0070] S3. Based on the model predictive control current loop model, the reference current is quickly tracked. Let i in (21) L =I d ;

[0071] Combining the adaptive proportional-integral control voltage loop model in formula (4), we get μ 1 , μ 2 The expression is:

[0072]

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

[0074]

[0075] Beneficial effects of the present invention:

[0076] The present invention discloses an adaptive composite model predictive control method for a DC microgrid with a constant power load. The proposed controller includes a parameter adaptive proportional integral control based on an error signal and a model predictive control feedback loop of a single-step prediction cycle, as well as a feedforward loop of a nonlinear disturbance observer, which significantly improves 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 uncertainty and has a constant power load with high penetration, the proposed control algorithm can still ensure the stability of the controlled object when the obtained large signal stability criterion is met. The hardware-in-the-loop comparison experiment shows that the proposed controller has excellent robustness.

[0077] The invention discloses an adaptive composite model predictive control method for a DC microgrid with a constant power load, and proposes an adaptive composite model predictive control strategy to alleviate the instability problem caused by the negative impedance characteristics of the constant power load, and improve the transient performance of the system when the source load side of the DC microgrid is disturbed. The controller of the proposed invention method is composed of a feedback loop consisting of an adaptive proportional integral control and a model predictive control, which is used to track the voltage reference value, and a feedforward loop consisting of a nonlinear disturbance observer, which is used to online estimate and feedforward compensate the load disturbance current, thereby 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 mixed potential function theory shows that when the controlled object deviates from the rated operating state due to uncertainty and has a high penetration constant power load, the proposed Fang Ming method can ensure the large signal stability of the controlled object. Finally, the effectiveness and superiority of the proposed control method are verified by hardware-in-the-loop experiments in various scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0079] Figure 2 It is the waveform diagram of inductor current and duty cycle in one switching cycle;

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

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

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

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

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

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

[0086] Fig. 9 It is a schematic diagram of the structure of the present invention. DETAILED DESCRIPTION

[0087] In order to make the purpose, technical solution and advantages of the present invention more clear, the present invention is further described in detail below in conjunction 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 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 described and shown in the drawings herein can be arranged and designed in various different configurations, and the present invention can also have other embodiments.

[0088] Therefore, the following detailed description of the specific embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents the selected specific embodiments of the present invention. Based on the specific embodiments of the present invention, all other specific embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present invention.

[0089] In order to further understand the content, features and effects of the present invention, the following specific implementation methods are given as examples, and the attached Figure 1 -Attached Fig. 9 The detailed instructions are as follows:

[0090] Embodiment 1:

[0091] 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;

[0092] 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;

[0093] The adaptive proportional integral control voltage loop model inputs the collected reference voltage value and the boost converter output voltage data collected by the voltage signal sensor, and outputs the current reference value result to the model prediction control current loop model;

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

[0095] The nonlinear disturbance observer model outputs a concentrated disturbance estimate through the boost converter output voltage data collected by the input voltage signal sensor, the boost converter inductor current data collected by the current signal sensor, and the boost converter duty cycle signal obtained by the model predictive control current loop model. The nonlinear disturbance observer model then feed-forwards the concentrated disturbance estimate to the adaptive proportional-integral control voltage loop model.

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

[0097] Based on Figure 1 The general DC microgrid structure and its equivalent circuit design of boost converter with parallel resistive load and constant power load are shown. The source bus is powered by a variety of power generation units, and the DC / DC boost converter is used to increase the voltage and provide energy to the load bus. Resistive load and constant power load as loads absorb electrical energy from the load bus, and the negative impedance characteristics of the constant power load are not conducive to system stability. Therefore, it is necessary to design a suitable controller for the interface converter to achieve stable operation of the DC microgrid.

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

[0099]

[0100] Among them, L, C, v s , v o ,i L , μ, R and P CPL They 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;

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

[0102]

[0103] in, Represents the small signal disturbance of the output voltage steady-state operating point, Represents a small signal perturbation at the steady-state operating point of the duty cycle.

[0104] According to the small signal model of formula (2), when When , the resistance load is dominant, the pole is located on the left half axis of the plane, and the system remains stable; when 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 intended goal for the voltage controller design is to propose an adaptive proportional-integral control loop that achieves fast voltage regulation (v) in the presence of system disturbances and without rated parameters. ref -v o =0). Traditional proportional-integral control adjusts the proportional coefficient k p and the integration coefficient k i to track the reference value of the state variable; 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 conservatively selected, the system will show poor transient performance when subjected to large signal interference; if the control gain is aggressively selected, the system will show redundant robustness when subjected to small signal interference.

[0108] Considering that when the voltage signal deviates from the reference value by a large margin, the larger the proportional gain coefficient, the faster the voltage error convergence speed will be. However, when the system voltage signal deviates from the reference value by a small margin, the larger the proportional gain coefficient, the more likely it is that the voltage will directly exceed its reference value and cause voltage overshoot. For the integral link, a larger integral gain coefficient can shorten the system recovery time, but it will also make the system stability worse. Therefore, when the voltage error is large, the control coefficient value should be larger to improve the transient performance of the system and avoid static errors; 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 the expression is:

[0110]

[0111] Among them, I d is the current reference value result, k p is the proportionality coefficient, k i is the integration coefficient, k p ′, k p ″ are the first adaptive correction coefficient and the second adaptive correction coefficient of the proportional coefficient, respectively, i ′, k i″ are 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.

[0112] Furthermore, the model predictive control current loop model is designed to be based on the offline single-step cycle model predictive control using tracking triangle wave PWM modulation, the carrier is an isosceles triangle wave, and i is set L (k) and i L (k+1) are the inductor current at the current moment and the predicted value of the inductor current at the next moment, such as Figure 2 As shown;

[0113] According to formula (1), combined with the duty cycle μ of the isosceles triangle wave = 1 or 0, 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, v o (k) is the output voltage of the boost converter at the current moment;

[0116] According to the inductor current i at the current moment L (k) and opening time t 1 =t 3 , get the predicted value of the inductor current at the next moment i L (k+1) is expressed as:

[0117]

[0118] Among them, i S1 is the first inductor current extreme point, i S2 is the second inductor current extreme point, i S3 It is the third inductor current extreme point;

[0119] When the predictive current control algorithm is used to track the reference current, there are usually three modes of tracking the current reference value: current waveform peak tracking, current waveform trough tracking and current waveform average value tracking. However, both the peak and trough tracking modes will have a certain error from the current reference value, while the current predictive control using the average value tracking mode is not affected by the switching duty cycle and can achieve error-free tracking of the reference current.

[0120] The reference value of the inductor current is set to track using the average tracking mode. The 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 equation (6) for the inductor current extreme point into equation (7), we get the expression:

[0123] J(k)=(I d -i S0 -h 1 t 1 ) 2 +(I d -i S0 -h 1 t 1 -h 2 t 2 ) 2 +(I d -i S0 -2h 1 t 1 -h 2 t 2 ) 2 (8)

[0124] Considering a switching cycle T in equation (8) s =t 1 +t 2 +t 3 =2t 1 +t 2 , so we regard formula (8) as 1 A quadratic equation with J(k) as the independent variable and J(k) as the dependent variable; by taking the derivative and finding the corresponding t when the derivative is zero 1 The corresponding time of different actions of the switch in one cycle is as follows when the tracking reference current is optimal:

[0125]

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

[0127] μ=2t 1 / T s (10).

[0128] Furthermore, a nonlinear disturbance observer model is designed, and a feedforward loop based on the nonlinear disturbance observer is introduced to transform equation (1) into a nonlinear system form, which is expressed as follows:

[0129]

[0130] Where d is the total disturbance in the system;

[0131] 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:

[0132]

[0133] Among them, R 0 and P CPL0 They are the rated resistance load value and the constant power load rated power respectively;

[0134] According to the nonlinear system form of equation (11), the basic nonlinear disturbance observer model is expressed as follows:

[0135]

[0136] Where λ represents the nonlinear disturbance observer gain coefficient, and p(Z) represents the nonlinear function to be designed;

[0137] Define the estimation error e of the nonlinear disturbance observer d As shown below:

[0138]

[0139] By taking the derivative of equation (14) and bringing the general equation of the nonlinear system and the basic nonlinear disturbance observer model represented by equation (13) into the derivative error estimation derivative equation, we can obtain:

[0140]

[0141] in, is the derivative of the estimation error of the nonlinear disturbance observer;

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

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

[0144]

[0145] Combining the adaptive proportional-integral voltage controller (4), model predictive control (5), (9) and (10) and the nonlinear disturbance observer (16), we can obtain the proposed boost converter adaptive composite model predictive control. The detailed control block diagram is shown in Figure 3When selecting the disturbance observer parameters, it is necessary to balance the convergence speed and 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 implemented based on an adaptive composite model predictive control method for a DC microgrid with a constant power load described in Example 1. Based on the hybrid potential function theorem and Lyapunov's theorem, combined with the large signal equivalent circuit structure of a boost converter, a hybrid potential function is constructed, and a large signal stability criterion is derived, thereby judging the stability of the system;

[0148] 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.

[0149] Considering that small signal stability analysis is only applicable to system parameter analysis and stability estimation under small disturbances, and is not applicable to DC microgrids under large disturbance conditions such as source-load step changes, plug-and-play, and high-penetration constant power loads, it is necessary to perform large signal stability analysis on the proposed controller. Compared with other large signal stability analysis methods, the hybrid potential function theorem is based on Lyapunov's theorem, combines the characteristics of the circuit structure, constructs a hybrid 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. It is a powerful tool for large signal analysis of power electronic systems. There are three theorems in the hybrid 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 of 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 object.

[0150] Further, the specific steps include:

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

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

[0153] 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;

[0154] S2. Use the third theorem to analyze the large signal stability of the object under study;

[0155] set up μ 1 With μ 2 L -1 / 2 A ii (i)L -1 / 2 and C -1 / 2 B vv (v)C -1 / 2 The minimum eigenvalue of ;

[0156] If the conditions are met

[0157] μ 1 +μ 2 ≥δδ>0 (18)

[0158] And when i+v→∞, there exists

[0159]

[0160] 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;

[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. Figure 4 As shown:

[0162] 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:

[0163]

[0164] To facilitate large signal stability analysis, equation (20) is rewritten as a unified expression of the mixed potential function as follows:

[0165]

[0166] S3. Based on the model predictive control current loop model, the reference current is quickly tracked. Let i in (21) L =I d ; Combined with the adaptive proportional integral control voltage loop model in formula (4), we get μ 1 , μ 2 The expression is:

[0167]

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

[0169]

[0170] When the constant power load and resistive load in the system change, the large signal stability boundary of the system is as follows Figure 5 As shown. Figure 5 It can be seen that the upper part of the three-dimensional surface is the large signal stable area. 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 coefficient k of the proportional link and the integral link is finally selected. p =0.5, k i =35, k p ′=1.5,k p ″=0.5,k i ′=1,k i = 0.5 and β = 10. Combining the large signal stability criterion of formula (23) and Figure 5 As shown in the large signal stability boundary diagram, 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 characteristics of the constant power load and improve the transient performance of the system during source-load side disturbances in the DC microgrid. The 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 cycle is designed to reduce the computational burden and improve the dynamic performance. In addition, the large signal stability analysis based on the mixed potential theory shows that when the controlled object deviates from the rated operating state due to uncertainty and has a constant power load with high penetration, the proposed control algorithm can still ensure the stability of the controlled object when the obtained large signal stability criterion is met.

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

[0173] Table 1 System parameter configuration

[0174]

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

[0176] This case investigates the robustness of the invented method in the face of input voltage step disturbances to verify the superiority of the proposed controller. Figure 8 The experimental waveform comparison between adaptive composite model predictive control and traditional proportional integral predictive control under input voltage step disturbance is shown. The input voltage changes from 50V to 80V and returns to 50V after a period of time. 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 3.5V and 25ms respectively, while the maximum overshoot and recovery time of the output voltage of the traditional proportional integral predictive control are 6.5V and 60ms respectively.

[0177] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0178] Although the present application has been described above with reference to specific embodiments, various modifications may be made thereto and parts thereof may be replaced with equivalents without departing from the scope of the present application. In particular, as long as there is no structural conflict, the various features in the specific embodiments disclosed in the present application may be used in combination with each other in any manner, and the fact that these combinations are not exhaustively described in this specification is only for the sake of omitting space and saving 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. A DC microgrid adaptive composite model predictive control method with 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 collected reference voltage value and the boost converter output voltage data collected by the voltage signal sensor, and outputs the current reference value result to the model prediction control current loop model; The model predictive control current loop model outputs the boost converter duty cycle signal to the nonlinear disturbance observer model by inputting the current reference value result obtained by the adaptive proportional integral control voltage loop model and the boost converter inductor current data collected by the current signal sensor; The nonlinear disturbance observer model outputs a concentrated disturbance estimate through the boost converter output voltage data collected by the input voltage signal sensor, the boost converter inductor current data collected by the current signal sensor, and the boost converter duty cycle signal obtained by the model predictive control current loop model. The nonlinear disturbance observer model then feed-forwards the concentrated disturbance estimate to the adaptive proportional-integral control voltage loop model.

2. The method for adaptive composite model predictive control of a DC microgrid with a constant power load according to claim 1, characterized in that: The control method is based on operating the boost converter in continuous conduction mode with a parallel resistive load and a constant power load; First, the average dynamic model of the boost converter is constructed, and the expression is: Among them, L, C, v s , v o ,i L , μ, R and P CPL They 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; According to formula (1), the open-loop transfer function G(s) with resistive load and constant power load is constructed, and the expression is: in, Represents the small signal disturbance of the output voltage steady-state operating point, Represents a small signal perturbation at the steady-state operating point of the duty cycle.

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

4. The method for adaptive composite model predictive control of a DC microgrid with a constant power load according to claim 3, characterized in that: Design model predictive control The current loop model is based on offline single-step cycle model predictive control using tracking triangle wave PWM modulation, the carrier is an isosceles triangle wave, and set i L (k) and i L (k+1) is the inductor current at the current moment and the predicted value of the inductor current at the next moment; According to formula (1), combined with the duty cycle μ of the isosceles triangle wave = 1 or 0, the current slope h is calculated as follows: Where 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; According to the inductor current i at the current moment L (k) and the opening time t1 = t3, the predicted value of the inductor current at the next moment is obtained L (k+1) is expressed as: Among them, i S1 is the first inductor current extreme point, i S2 is the second inductor current extreme point, i S3 It is the third inductor current extreme point; The reference value of the inductor current is set to track using the average tracking mode. The 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 equation (6) for the inductor current extreme point into equation (7), we get the expression: 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 cycle T in equation (8) s =t1+t2+t3=2t1+t2, so the formula (8) is regarded as a quadratic equation with t1 as the independent variable and J(k) as the dependent variable; by taking the derivative and finding the corresponding t1 value when the derivative is zero, the corresponding time of different actions of the switch in one cycle under the optimal tracking reference current effect is obtained as follows: According to formula (9), the duty cycle of the boost converter in working mode is expressed as: μ=2t1 / T s (10)。 5. The method for adaptive composite model predictive control of a DC microgrid with a constant power load according to claim 4, characterized in that: A nonlinear disturbance observer model is designed, and a feedforward loop based on the nonlinear disturbance observer is introduced to transform equation (1) into a nonlinear system form, which is expressed as follows: Where d is the total 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: Among them, R0 and P CPL0 They are the rated resistance load value and the constant power load rated power 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 shown below: By taking the derivative of equation (14) and bringing the general equation of the nonlinear system and the basic nonlinear disturbance observer model represented by equation (13) into the derivative error estimation derivative equation, we can obtain: in, is the derivative of the estimation error of the nonlinear disturbance observer; By selecting the disturbance observer gain λ, the estimation error of the disturbance observer will eventually 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 a constant power load, based on the adaptive composite model predictive control method for a DC microgrid with a constant power load according to any one of claims 1 to 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, a hybrid potential function is constructed to derive the large signal stability criterion, thereby judging 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. The large signal stability analysis method of a DC microgrid with a constant power load according to claim 6 is 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; set up μ1 and μ2 are L -1 / 2 A ii (i)L -1 / 2 and C -1 / 2 B vv (v)C -1 / 2 The minimum eigenvalue of ; 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, the reference current is quickly tracked. Let i in (21) L =I d ; Combined with the adaptive proportional integral control voltage loop model in formula (4), the expressions of μ1 and μ2 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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