Island ac microgrid control method resistant to actuator faults and saturation

Abstract

The application provides an islanded AC microgrid anti-actuator fault and saturation control method, comprising: establishing an islanded AC microgrid system model; establishing an actuator fault model; establishing an actuator saturation model; establishing an islanded microgrid model under actuator fault and saturation; establishing an actuator saturation compensation system model; establishing a frequency and predetermined time disturbance observer; establishing a distributed predetermined time voltage observer; establishing a voltage and predetermined time disturbance observer; and establishing a distributed predetermined time fault-tolerant controller based on the disturbance observer. The application solves the problem of inaccurate frequency / voltage regulation and power distribution under actuator fault and saturation in the islanded AC microgrid, and realizes effective regulation of the microgrid frequency / voltage and accurate power distribution within a predetermined time.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of fault-tolerant control of actuators under the effects of actuator faults and saturation in islanded AC microgrids, in particular, to an anti-actuator fault and saturation control method for islanded AC microgrids. Especially, to an anti-actuator fault and saturation control method for islanded AC microgrids based on a distributed pre-determined time disturbance observer. BACKGROUND

[0002] Due to the high concern for environmental problems, the development of renewable energy is promoted. A large number of renewable energy is integrated into the power system through power electronic devices. Microgrid (MG) is a key operation mode of using renewable energy / distributed generator (DG) output power. However, due to the randomness of renewable energy and the low inertia of microgrid, the microgrid in islanded mode may have problems of stability and power quality decline. In addition, it is necessary to ensure the accurate power distribution of all DGs to maintain the safety and reliability of the islanded microgrid. Therefore, it is essential to design an efficient control method for the islanded microgrid, which helps to promote the penetration of renewable energy.

[0003] In order to improve the dynamic performance of islanded microgrid, a hierarchical control strategy including primary and secondary control is proposed. The primary control should provide the fastest response when the system is disturbed, but the steady-state error is large, and it is difficult to achieve accurate power distribution. Therefore, the secondary control is designed to overcome the shortcomings of the primary control. Distributed control can meet the minimum communication requirements, reduce communication and computing burden, thereby improving the reliability of the controller and simplifying the "plug and play" function of DG. Therefore, distributed control is usually used as a secondary controller for performance improvement.

[0004] Different distributed control methods have been proposed to improve the performance of islanded microgrids. For example, power distribution and voltage adjustment are achieved through distributed consensus, inertia of microgrid is compensated by limiting the change of frequency and voltage, or distributed predictive control is adopted, etc. However, these methods mainly guarantee the asymptotic stability of the islanded microgrid, while in the face of intermittency and randomness of renewable energy / load, the control strategy needs to have stronger robustness and faster convergence speed.

[0005] The finite-time consensus method has strong robustness and high precision, and can stabilize the island micro-grid in a limited time. However, the convergence time of the finite-time consensus method depends on the initial state of the system, which is difficult to monitor in real time in practical applications. The fixed-time consensus method can keep the system stable in a fixed time without considering the initial state of the system, but it is conservative and computationally complex. The pre-defined time consensus method can ensure the convergence of the system within a pre-defined time, and has lower conservatism, so it is proposed as a secondary controller for islanded AC microgrids to ensure frequency / voltage recovery and accurate power distribution.

[0006] However, the above control method does not consider actuator faults, including bias faults and partial effectiveness loss faults. Actuator faults are a serious threat in the actual operation of islanded AC microgrids, which can cause system performance degradation or critical events, thereby worsening the operating characteristics of islanded microgrids. Therefore, it is necessary to study fault-tolerant operation considering actuator faults. In addition, due to the actual physical limitations of islanded AC microgrids, the actuator output will experience saturation, and the control input amplitude cannot exceed the limit set by the digital controller, which poses a challenge to the control algorithm. Therefore, a control method considering actuator saturation is particularly important. At present, there are still limited methods for pre-defined convergence time stability of islanded microgrids under actuator faults and saturation. SUMMARY

[0007] In view of the defects in the prior art, the purpose of the present application is to provide an islanded AC microgrid control method resistant to actuator faults and saturation.

[0008] The islanded AC microgrid control method resistant to actuator faults and saturation provided by the present application comprises:

[0009] Step 1: Establish an islanded AC microgrid system model to achieve preliminary regulation of frequency and voltage;

[0010] Step 2: Establish an actuator fault model to describe and predict the dynamic behavior of the actuator when it fails;

[0011] Step 3: Establish an actuator saturation model to help the controller cope with the physical limitations of the actuator output and ensure that the system remains stable and performance-optimized under saturation conditions;

[0012] Step 4: Establish an islanded microgrid model under actuator faults and saturation to accurately describe the dynamic behavior of the system, enabling the controller to implement fault tolerance and saturation compensation;

[0013] Step 5: Establish a system model for actuator saturation compensation to enable the controller to handle the output limitations of the actuator and mitigate the impact of saturation effects on system performance;

[0014] Step 6: Establishing a predetermined time disturbance observer of frequency and, accurately estimating the deviation caused by external disturbance or actuator failure, and realizing error convergence within a predetermined time to enhance the response speed and accuracy of the controller;

[0015] Step 7: Establishing a distributed predetermined time voltage observer, accurately estimating the voltage deviation of each distributed generator, and realizing error convergence within a predetermined time;

[0016] Step 8: Establishing a predetermined time disturbance observer of voltage and, accurately estimating the deviation caused by external disturbance or actuator failure, and realizing error convergence within a predetermined time to enhance the response speed and accuracy of the controller;

[0017] Step 9: Establishing a distributed predetermined time fault-tolerant controller based on disturbance observer, realizing the regulation of frequency and voltage and accurate sharing of active power and reactive power within a predetermined time.

[0018] Preferably, the step 1 comprises:

[0019] The islanded AC microgrid system model contains multiple inverter-based distributed generators DG, each DG consisting of an LCL filter, a DC voltage source and a voltage source inverter, and the control framework of the microgrid includes power, current and voltage control loops;

[0020] The droop control based on ω-P and U-Q relationship is described as:

[0021] ω i = ω ni -m i P i (1)

[0022] U i = U ni -n i Q i (2)

[0023] Where U i and ω i represent the output voltage amplitude and angular frequency of the i-th DG; U ni and ω ni are the rated values of droop control; n i and m i are the droop coefficients; P i and Q i represent the active power and reactive power of the i-th DG, respectively.

[0024] Preferably, the step 2 comprises:

[0025] The actuator failure includes bias failure and partial effectiveness loss failure, and the actuator failure model of the i-th device is represented as:

[0026] u 0i = (1 - p i )u i + φ i (3)

[0027] where u 0i and u i represent the output and input control signals of the ith device, respectively; p i is a continuous time-varying function reflecting the severity of partial effectiveness loss faults, ranging from 0 < p i < 1; and φ i is a bias fault.

[0028] Preferably, the step 3 comprises:

[0029] The saturation controller is described as:

[0030]

[0031] where y i is the actual output of the controller; u max and -u max are the maximum and minimum values of the controller output, respectively.

[0032] Preferably, the step 4 comprises:

[0033] First, based on equation (1), the dynamic characteristics of the frequency ω i are represented as:

[0034]

[0035] where u fi represents the dynamic characteristics of the frequency ω i ; and are the first-order derivatives of ω i , ω ni , and P i , respectively; m i is a coefficient, which is a constant;

[0036] Second, the derivative of m i P i is taken to obtain the auxiliary controller u pi for active power distribution as:

[0037]

[0038] Considering the actuator faults and saturation, equations (3) and (4) are substituted into equations (5) and (6) to obtain the dynamic characteristics of the frequency as:

[0039]

[0040] where γ fi represents the actual output of the frequency controller; u f0i represents the output control signal of the frequency considering the actuator fault; φ fi represents the bias fault of the frequency actuator; γ pi represents the actual output of the active power controller; u p0i represents the output control signal of the active power considering the actuator fault; φ pi represents the bias fault of the active power actuator; Δu fi = γ fi - u f0i , Δu pi = γ pi - u p0i ;

[0041] Then, the control input ω ni for frequency restoration and accurate active power distribution is obtained as:

[0042] ω ni = ∫(γ fi + γ pi )dt (9)

[0043] Similarly, the dynamic characteristic of voltage u vi is obtained based on equation (2) as:

[0044]

[0045] where are the first derivatives of U i , U ni , and Q i , respectively;

[0046] The reactive power auxiliary controller u qi is:

[0047]

[0048] Considering the actuator fault and saturation, the dynamic characteristic of voltage is obtained as:

[0049]

[0050] where γ vi represents the actual output of the voltage controller; u v0i represents the output control signal of the voltage considering the actuator fault; φ vi represents the bias fault of the voltage actuator; γ qi represents the actual output of the reactive power controller; u q0irepresents the output control signal considering the reactive power under actuator fault; φ qi represents the bias fault of the reactive power actuator; Δu vi = γ vi - u v0i , Δu qi = γ qi - u q0i ;

[0051] Then, the control input U ni for voltage restoration and accurate reactive power distribution is obtained:

[0052] U ni = ∫(γ vi + γ qi )dt (14).

[0053] Preferably, the step 5 comprises:

[0054] The saturation compensators are designed for frequency and mP, voltage and nQ respectively, and the expressions are:

[0055]

[0056] where h i represents a ij represents the i-th row and j-th column element of the weighted adjacent matrix A = (a ij ) of the islanded AC microgrid communication topology, a ij = 1 if the i-th distributed generator can receive information from the j-th distributed generator, otherwise a ij = 0; j represents the sum symbol except the i-th node itself; N i represents the node set of all distributed generators; k1, k2, k3 and k4 are positive numbers; and are state variables of the compensation system; N represents the number of distributed generators; b i represents the gain coefficient, b i = 1 if the i-th distributed generator can obtain reference value information, otherwise b i = 0.

[0057] Preferably, the step 6 comprises:

[0058] Firstly, the consistency error is defined:

[0059]

[0060] where e 1i and e 2irespectively, represent the consistency error based on the frequency and active power information of the neighboring nodes; ω0is the nominal value of the virtual leader; b i represents the communication coefficient between the follower and the leader, where b i = 1 or b i = 0;

[0061] Then, the derivatives of e 1i and e 2i are obtained as follows:

[0062]

[0063] where,

[0064] Substituting equations (7), (8) and (15), (16) into equation (20) gives:

[0065]

[0066] where Δ 1i = h i (φ fi - ρ i u fi ),

[0067] A predetermined time observer is designed to evaluate Δ 1i , which is expressed as:

[0068]

[0069] where ε 1i represents the deviation between the frequency state variable and the frequency consistency error; θ1represents the gain coefficient of the predetermined time observer; V1represents V1= ε 1i 2 ; τ1is a positive parameter; χ1represents a gain coefficient greater than Υ, where Υ is a positive constant greater than zero; 0 < θ1< 1, χ1> Υ; is the observed value of Δ 1i , T s represents a positive constant;

[0070] The predetermined time observer in equation (23) can observe the disturbance Δ 1i within a predetermined time , where κ > 1;

[0071] Similarly, a predetermined time observer is designed to evaluate Δ 2i , which is expressed as:

[0072]

[0073] where ε 2i represents the deviation between the active power state quantity and the active power consistency error; θ2represents a gain coefficient of the predefined time observer; V2represents V2= ε 2i 2 ; χ2represents a gain coefficient greater than Y, Y is a positive constant greater than zero; τ2is a positive parameter; 0 < θ2< 1, χ2> γ; is the observation value of Δ 2i , T s represents a positive constant;

[0074] The predefined time observer in formula (24) can observe the disturbance Δ 2i within a predefined time .

[0075] Preferably, the step 7 comprises:

[0076] The distributed predefined time voltage observer is designed to obtain the average voltage bus voltage, and the expression is:

[0077]

[0078] where β1and β2are positive odd numbers and β1< β2; w1and w2are positive numbers.

[0079] Preferably, the step 8 comprises:

[0080] First, the consistency error is defined as follows:

[0081]

[0082] where e 3i represents the consistency error based on the average voltage information of adjacent nodes; e 4i represents the consistency error based on the reactive power information of adjacent nodes;

[0083] Derivation of formula (26) is as follows:

[0084]

[0085] Bringing formula (10)-formula (11) and formula (17)-formula (18) into formula (27) is as follows:

[0086]

[0087] where Δ 3i = h i (φ fi - p i u vi ),

[0088] Then, the predefined time observer is designed to observe Δ 3i and Δ 4i , whose expressions are as follows:

[0089]

[0090] Similarly, the predefined time observer in formula (30) and formula (31) observes the disturbance Δ s3 and Δ s4 within the predefined time T 3i and T 4i .

[0091] Preferably, the step 9 comprises:

[0092] Based on the predefined time observer formula (23)-formula (24) and formula (30)-formula (31), the distributed predefined time fault-tolerant controller based on the disturbance observer is designed as:

[0093]

[0094]

[0095] Wherein, b f represents the gain coefficient of the distributed predefined time frequency fault-tolerant controller in the saturation state; b p represents the gain coefficient of the distributed predefined time active power fault-tolerant controller in the saturation state; b v represents the gain coefficient of the distributed predefined time voltage fault-tolerant controller in the saturation state; b q represents the gain coefficient of the distributed predefined time active power fault-tolerant controller in the saturation state; μ1, μ2, μ3, μ4 respectively represent the gain coefficients of the frequency, active power, voltage and reactive power controllers, 0<μ1, μ2, μ3, μ4<1; T di is the upper bound of the consistency error convergence;

[0096] Through the distributed predefined time fault-tolerant controller based on the disturbance observer, the frequency and voltage regulation and the accurate sharing of active power and reactive power can be realized within the predefined time T=T si +T di .

[0097] Compared with the prior art, the present application has the following beneficial effects:

[0098] The distributed predefined time fault-tolerant controller based on the disturbance observer of the present application solves the problem of inaccurate frequency / voltage regulation and power distribution under the actuator fault and saturation condition in the islanded AC microgrid, and realizes the effective regulation of the microgrid frequency / voltage and the accurate power distribution within the predefined time. BRIEF DESCRIPTION OF DRAWINGS

[0099] Other features, objects, and advantages of the application will become more apparent from the following detailed description of non-limiting embodiments thereof, when read in connection with the following drawings:

[0100] Figure 1 A simplified system model of islanded AC microgrid under actuator faults and saturation for the present application;

[0101] Figure 2 A distributed communication topology for the present application;

[0102] Figure 3 A distributed pre-scheduled time fault-tolerant control framework based on disturbance observer for the present application;

[0103] Figure 4 A simulation case result graph for the present application. DETAILED DESCRIPTION

[0104] The present application will be described in detail below with specific embodiments. The following embodiments will help those skilled in the art to further understand the present application, but do not limit the present application in any form. It should be noted that for those skilled in the art, without departing from the concept of the present application, a number of changes and improvements can be made. These are within the scope of the present application.

[0105] EMBODIMENT

[0106] The present application provides a control method for islanded AC microgrid against actuator faults and saturation based on distributed pre-scheduled time disturbance observer, comprising the following steps:

[0107] 1) Establish the islanded AC microgrid system model, the detailed content is as follows:

[0108] The simplified system model of islanded AC microgrid under actuator faults and saturation is shown in Figure 1 , which contains multiple inverter-based distributed generators (DGs). Each DG is composed of an LCL filter, a DC voltage source and a voltage source inverter. The control framework of the microgrid includes power, current and voltage control loops to ensure power quality, reliability and safety.

[0109] Primary control is used in islanded microgrid to achieve preliminary regulation of frequency and voltage, ensuring stable operation of the system without external grid support. The primary droop control based on ω-P and U-Q relationship can be described as:

[0110] ω i = ω ni -m i P i (36)

[0111] U i = U ni -n i Q i (37)

[0112] where U i and ω i represent the output voltage amplitude and angular frequency of the ith DG, respectively; U ni and ω ni are the rated values of droop control; n i and m i are droop coefficients. In addition, P i and Q i represent the active and reactive power of the ith DG, respectively.

[0113] 2) Establish the actuator fault model, the details are as follows:

[0114] In order to accurately describe and predict the dynamic behavior of the actuator when it fails, so as to help design a fault-tolerant control algorithm, ensure that the system can still maintain stability and normal operation when the fault occurs, and reduce the impact of the fault on the performance of the system. Considering the actuator fault, including bias fault and partial effectiveness loss fault. Therefore, the actuator fault model of the ith device can be expressed as:

[0115] u 0i = (1-ρ i )u i +φ i (38)

[0116] where u 0i and u i represent the output and input control signals of the ith device, respectively. ρ i is a continuous time-varying function, reflecting the severity of partial effectiveness loss fault, ranging from 0≤ρ i <1. φ i is the bias fault. Therefore, we can classify the actuator fault into different fault types, as shown in Table I.

[0117] Table I Fault classification

[0118] Fault type i ]]> ​ i ]]> ​ Normal condition i = 0 ​ i = 0 ​ Bias fault condition i = 0 ​ <![CDATA[φ i ≠0]]> Partial performance loss condition 0 < p i <1]]> i = 0]]> ​ Bias fault and partial performance loss condition 0 < p i <1]]> <![CDATA[φ i ≠0]]>

[0119] 3) Establish the actuator saturation model, the details are as follows:

[0120] In order to help the controller cope with the physical limitations of the actuator output, ensure that the system still maintains stability and performance optimization under saturation conditions. When the state of the system changes and the input is not properly constrained, the output of the actuator may produce a significant impact response. The saturation controller can be described as:

[0121]

[0122] Among them, γ i is the actual output of the controller, u max and -u max are the maximum and minimum values ​​of the controller output respectively.

[0123] 4) Establish an island microgrid model under actuator failure and saturation. The details are as follows:

[0124] In order to accurately describe the dynamic behavior of the system, enable the controller to achieve fault tolerance and saturation compensation, and ensure system stability and performance optimization, it is necessary to design the controller based on the island microgrid model under actuator faults and saturation.

[0125] First, based on (1), the frequency ω i The dynamic characteristics can be expressed as:

[0126]

[0127] Among them, u fi Indicates frequency ω i Dynamic characteristics of are ω i 、ω ni 、P i The first derivative of m i is the coefficient, which is a constant;

[0128] Secondly, for m i P i Take the derivative and get the auxiliary controller u for active power distribution pi for:

[0129]

[0130] Taking into account actuator failure and saturation, substituting (3) and (4) into (5) and (6), the dynamic characteristics of the frequency are obtained as follows:

[0131]

[0132] Among them, γ fi Indicates the actual output of the frequency controller; u f0i represents the output control signal of the frequency under the consideration of actuator failure; φ fi Indicates the bias fault of the frequency actuator; γ pi Indicates the actual output of the active power controller; u p0i Indicates the output control signal of active power considering actuator failure; φ pi Indicates the bias fault of the active power actuator; Δufi = γ fi - u f0i , Δu pi = γ pi - u p0i .

[0133] Then, the control input ω ni for frequency recovery and accurate active power allocation is obtained as:

[0134] ω ni = ∫(γ fi + γ pi )dt (44)

[0135] Similarly, the dynamic behavior of the voltage u vi is obtained based on (2) as:

[0136]

[0137] are the first derivatives of U i , U ni , Q i , respectively;

[0138] The reactive power auxiliary controller u qi is:

[0139]

[0140] Considering actuator faults and saturation, the dynamic behavior of the voltage is obtained as:

[0141]

[0142] where γ vi is the actual output of the voltage controller; u v0i is the output control signal of the voltage considering actuator faults; φ vi is the bias fault of the voltage actuator; γ qi is the actual output of the reactive power controller; u q0i is the output control signal of the reactive power considering actuator faults; φ qi is the bias fault of the reactive power actuator; Δu vi = γ vi - u v0i , Δu qi = γ qi - u q0i .

[0143] Then, the control input U ni for voltage recovery and accurate reactive power allocation is obtained as:

[0144] Uni = ∫(γ vi + γ qi )dt (49)

[0145] 5) The system model of actuator saturation compensation is established, and the details are as follows:

[0146] In order to make the controller effectively deal with the output limit of the actuator and reduce the influence of saturation effect on the system performance, compensation is needed for saturation. Based on the adaptive auxiliary system, saturation compensators are designed for frequency and mP, voltage and nQ respectively, as follows:

[0147]

[0148] Where, h i represents a ij represents the i-th row and j-th column element of the weighted adjacency matrix A=(a ij ) of the communication topology of the islanded AC microgrid, a ij = 1 if the i-th distributed generator can receive information from the j-th distributed generator, otherwise a ij = 0; j represents the sum symbol except itself i node; N i represents the node set of all distributed generators; k1, k2, k3 and k4 are positive numbers; and are state variables of the compensation system; N represents the number of distributed generators; b i represents the gain coefficient, b i = 1 if the i-th distributed generator can obtain reference value information, otherwise b i = 0;

[0149] 6) The predetermined time disturbance observer of frequency and mP is established, and the details are as follows:

[0150] In order to accurately estimate the deviation caused by external disturbance or actuator fault, and realize error convergence within a predetermined time, in order to enhance the response speed and accuracy of the controller, a disturbance observer based on predetermined time is needed.

[0151] Firstly, the consistency error is defined:

[0152]

[0153] Where, e 1i and e 2i represent the consistency error based on the frequency and active power information of adjacent nodes respectively; ω0 is the nominal value of the virtual leader; b i represents the communication coefficient between the follower and the leader, where bi = 1 or b i = 0.

[0154] Then, the derivative of e 1i and e 2i is obtained:

[0155]

[0156] where, Substituting (7)-(8) and (15)-(16) into (20) gives:

[0157]

[0158] where, Δ 1i = h i (φ fi - p i u fi ),

[0159] A predefined time observer is designed to evaluate Δ 1i , which is expressed as:

[0160]

[0161] where, ε 1i represents the deviation between the frequency state variable and the frequency consistency error; θ1represents the gain coefficient of the predefined time observer; V1represents V1= ε 1i 2 ; τ1represents a positive parameter that can be set; χ1represents a gain coefficient greater than γ, and γ is a positive constant greater than zero; 0 < θ1< 1, χ1> γ; is the observation value of Δ 1i , and T s represents a positive constant.

[0162] The predefined time observer in formula (23) can accurately observe the disturbance Δ 1i within a predefined time , where κ > 1.

[0163] Similarly, a predefined time observer is designed to evaluate Δ 2i , which is expressed as:

[0164]

[0165] where, ε 2i represents the deviation between the active power state variable and the active power consistency error; θ2represents the gain coefficient of the predefined time observer; V2represents V2= ε 2i 2; χ2 represents a gain coefficient greater than γ, γ is a positive constant greater than zero; τ2 represents a positive parameter that can be set; 0 < θ2 < 1, χ2 > γ; is Δ 2i , T s represents a positive constant.

[0166] The predefined time observer in formula (24) can accurately observe the disturbance Δ 2i within a predefined time .

[0167] 7) Establish a distributed predetermined time voltage observer, the details are as follows:

[0168] In order to quickly and accurately estimate the voltage deviation of each distributed generator, and realize error convergence within a predetermined time, ensure the coordination and stability of system voltage regulation. Design a distributed predetermined time voltage observer to obtain the average voltage bus voltage, its expression is:

[0169]

[0170] Where, β1 and β2 are positive odd numbers and β1 < β2; w1 and w2 are positive numbers.

[0171] 8) Establish a predetermined time disturbance observer of voltage and nQ, the details are as follows:

[0172] In order to accurately estimate the deviation caused by external disturbance or actuator failure, and realize error convergence within a predetermined time, in order to enhance the response speed and accuracy of the controller, it is necessary to design a disturbance observer based on predetermined time.

[0173] First, define the consistency error as follows:

[0174]

[0175] Where, e 3i represents the consistency error based on the average voltage information of adjacent nodes; e 4i represents the consistency error based on the adjacent node reactive power information;

[0176] Taking the derivative of formula (26) can obtain:

[0177]

[0178] (10)-(11) and (17)-(18) into (27) to obtain:

[0179]

[0180] Where, Δ 3i = h i (φfi - p i u vi ,

[0181] Then, the pre-defined time observers are designed to observe the values of Δ 3i and Δ 4i , whose expressions are:

[0182]

[0183] Similarly, the pre-defined time observers (30) and (31) can estimate the values of Δ s3 and Δ s4 within the pre-defined time T 3i and T 4i .

[0184] 9) The distributed pre-defined time fault-tolerant controller based on disturbance observer is established, and the details are as follows:

[0185] Based on the pre-defined time observers (23)-(24) and (30)-(31), a new type of distributed pre-defined time fault-tolerant controller based on disturbance observer is designed as follows:

[0186]

[0187]

[0188] where b f represents the gain coefficient of the distributed pre-defined time frequency fault-tolerant controller in the saturation state; b p represents the gain coefficient of the distributed pre-defined time active power fault-tolerant controller in the saturation state; b v represents the gain coefficient of the distributed pre-defined time voltage fault-tolerant controller in the saturation state; b q represents the gain coefficient of the distributed pre-defined time active power fault-tolerant controller in the saturation state; μ1, μ2, μ3, μ4 represent the gain coefficients of the frequency, active power, voltage and reactive power controllers respectively, and 0 < μ1, μ2, μ3, μ4 < 1; T di is the upper bound of the convergence of the consistency error.

[0189] Therefore, the distributed pre-defined time fault-tolerant controller based on disturbance observer can realize the regulation of frequency and voltage and the accurate sharing of active power and reactive power within the pre-defined time T = T si + T di .

[0190] The distributed communication topology is shown in Figure 2 The distributed pre-defined time fault-tolerant control framework based on disturbance observer is shown inFigure 3 .

[0191] 10) Simulation results,

[0192] Table II Island AC microgrid system model parameters

[0193]

[0194] According to the scheduled time theory and pre-selected parameters, the scheduled time is determined as The relevant parameters are set as θ1=θ2=θ3=θ4=0.9, χ1=χ2=χ3=χ4=0.1, τ1=τ2=τ3=τ4=0.1, k1=k2=k3=k4=11.5, T s =2,μ1=μ2=μ3=μ4=0.9,T di =0.5.

[0195] Simulation Example: Actuator Failure

[0196] The bias fault is set to φ i =0.1sin(t), the severity of partial efficiency loss failure ρ i Set to ρ i =0.2sin(t). Load 6 is connected to the microgrid at t=2 seconds, while load 5 is disconnected from the microgrid at t=5 seconds. The simulation results show that the control method proposed in this invention can achieve average voltage and frequency recovery and accurate power sharing when the actuator fails. Figure 4 .

[0197] Those skilled in the art will appreciate that, in addition to implementing the system, device, and various modules provided by the present invention in purely computer-readable program code, it is entirely possible to implement the same program in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, embedded microcontrollers, and the like by logically programming the method steps. Therefore, the system, device, and various modules provided by the present invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; the modules for implementing various functions can also be considered both software programs for implementing the method and structures within the hardware component.

[0198] The above describes specific embodiments of the present invention. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. The embodiments of this application and the features in the embodiments may be combined with each other in any manner unless there is a conflict.

Claims

1. A control method for islanded AC microgrid against actuator faults and saturation, characterized in that, The application relates to a method for designing a fault-tolerant and saturation-compensated controller for an islanded AC microgrid system. Step 1: establishing an islanded AC microgrid system model to realize preliminary regulation of frequency and voltage; Step 2: establishing an actuator fault model to describe and predict the dynamic behavior of the actuator when a fault occurs; Step 3: establishing an actuator saturation model to help the controller cope with the physical limitations of the actuator output and ensure that the system remains stable and performance-optimized under saturation conditions; Step 4: establishing an islanded microgrid model under actuator fault and saturation to accurately describe the dynamic behavior of the system, so that the controller realizes fault tolerance and saturation compensation; Step 5: establishing a system model for actuator saturation compensation to enable the controller to handle the output limitations of the actuator and reduce the impact of saturation effects on system performance; Step 6: establishing a predetermined time disturbance observer for frequency saturation to accurately estimate the deviation caused by external disturbances or actuator faults and realize error convergence within a predetermined time, thereby enhancing the response speed and accuracy of the controller; Step 7: establishing a distributed predetermined time voltage observer to accurately estimate the voltage deviation of each distributed generator and realize error convergence within a predetermined time; Step 8: establishing a predetermined time disturbance observer for voltage saturation to accurately estimate the deviation caused by external disturbances or actuator faults and realize error convergence within a predetermined time, thereby enhancing the response speed and accuracy of the controller; Step 9: establishing a distributed predetermined time fault-tolerant controller based on the disturbance observer to realize regulation of frequency and voltage and accurate sharing of active power and reactive power within a predetermined time; The step 1 comprises: The islanded AC microgrid system model comprises a plurality of inverter-based distributed generators DG, each DG being composed of an LCL filter, a direct-current voltage source and a voltage source inverter, and the control framework of the microgrid comprises power, current and voltage control loops; The droop control based on the relationship between omega-P and U-Q is described as: ω i = ω ni -m i P i (1) U i = U ni - n i Q i (2) wherein, U i and ω i represent the output voltage amplitude and angular frequency of the i-th DG, respectively; U ni and ω ni are the rated values of droop control; n i and m i are the droop coefficients; P i and Q i represent the active power and reactive power of the i-th DG, respectively; The step 2 comprises: The actuator fault comprises a bias fault and a partial performance loss fault, and the actuator fault model of the i-th device is expressed as: u 0i = (1 - p i )u i + φ i (3) where u 0i and u i are the output and input control signals of the ith device, respectively; p i is a continuous time-varying function reflecting the severity of the partial performance loss fault, ranging from 0 i < 1; and f i is the bias fault. The step 3 comprises: The saturation controller is described as: where γ i is the actual output of the controller; u max and -u max are the maximum and minimum values of the controller output, respectively; The step 4 comprises: First, based on equation (1), the dynamic characteristic of the frequency ω i is expressed as: where u fi represents the frequency ω i of the dynamic characteristics; are the first derivatives of ω i , ω ni , P i , respectively; m i is the droop coefficient, which is a constant; Second, m i P i Taking the derivative, we get the auxiliary controller u pi is: Considering the actuator fault and saturation, the formula (3) and the formula (4) are substituted into the formula (5) and the formula (6), and the dynamic characteristics of the frequency are obtained as: where γ fi denotes the actual output of the frequency controller; u f0i denotes the output control signal of the frequency considering actuator faults; φ fi denotes the bias fault of the frequency actuator; γ pi denotes the actual output of the active power controller; u p0i denotes the output control signal of the active power considering actuator faults; φ pi denotes the bias fault of the active power actuator; Δu fi = γ fi - u f0i , Δu pi = γ pi - u p0i ; Then, the control input ω for frequency restoration and accurate active power distribution is obtained ni : ω ni = ∫(γ fi + γ pi ) dt (9) By the same token, the dynamic characteristic of the voltage u based on equation (2) is vi is represented as: wherein U i , U ni , Q i the first derivative of Reactive power assist controller u qi is: Considering the actuator fault and saturation, the dynamic characteristics of the voltage are obtained as: where γ vi represents the actual output of the voltage controller; u v0i represents the output control signal of the voltage under consideration of actuator faults; φ vi represents the bias fault of the voltage actuator; γ qi represents the actual output of the reactive power controller; u q0i represents the output control signal of the reactive power under consideration of actuator faults; φ qi represents the bias fault of the reactive power actuator; Δu vi = γ vi - u v0i , Δu qi = γ qi - u q0i ; Then, the control input U for voltage restoration and accurate reactive power distribution is obtained ni :

2. The control method of islanded AC microgrid against actuator faults and saturation according to claim 1, characterized in that, The step 5 comprises: Saturation compensators are designed for the frequency saturation mP and the voltage saturation nQ respectively, and the expression is: Among them, h i express a ij The weighted adjacency matrix A represents the communication topology of the isolated AC microgrid = (a ij ), if the i-th distributed generator can receive information from the j-th distributed generator, then a ij =1, otherwise a ij = 0; j represents the rest of the nodes in the summation symbol except the i node itself; N i represents the set of nodes of all distributed generators; k1, k2, k3 and k4 are positive numbers; and is the state variable of the compensation system; N represents the number of distributed generators; b i Represents the gain coefficient. If the i-th distributed generator can obtain the reference value information, then b i =1, otherwise b i =0.

3. The control method of islanded AC microgrid against actuator faults and saturation according to claim 2, characterized in that, The step 6 comprises: Firstly, the consistency error is defined as: where e 1i and e 2i denote the consistency error based on the neighboring nodes' frequency and active power information, respectively; ω0is the nominal value of the virtual leader; b i denotes the communication coefficient between the follower and the leader, where b i = 1 or b i = 0; Then, we get e 1i and the derivative of e 2i is wherein, The formula (7), the formula (8) and the formula (15), the formula (16) are substituted into the formula (20), and the formula (21) is obtained as: where Δ 1i = h i (φ fi - p i u fi ), A scheduled time observer is designed to evaluate Δ 1i whose expression is where ε 1i represents the deviation between the frequency state quantity and the frequency consistency error; represents the gain coefficient of the predetermined time observer; V1 represents V1 = ε 1i 2 ; τ1 is a positive parameter; χ1 represents a gain coefficient greater than Y, Y being a positive constant greater than zero; χ1 > Y; is the observation value of Δ 1i ; T s represents a positive constant; The predefined time observer in equation (23) is able to observe the disturbance Δ 1i where κ > 1;​ Similarly, a predetermined time observer is designed to evaluate Delta2i, and the expression is: where ε 2i represents a deviation between the active power state quantity and the active power consistency error; represents a gain coefficient of the predetermined time observer; V2represents V2= ε 2i 2 ; χ2represents a gain coefficient greater than Y, Y being a positive constant greater than zero; τ2is a positive parameter; χ2> Y; is an observation value of Δ 2i T s represents a positive constant; The predefined time observer in equation (24) is able to observe the disturbance Δ within a predefined time 2i .

4. The control method of islanded AC microgrid against actuator faults and saturation according to claim 3, characterized in that, The step 7 comprises: A distributed predetermined time voltage observer is designed to obtain the average voltage bus voltage, and the expression is: Wherein, beta1 and beta2 are positive odd numbers and beta1 < beta2; w1 and w2 are positive numbers.

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