Adaptive fault-tolerant control method for islanded microgrid based on extended state observer

Abstract

The invention proposes an adaptive fault-tolerant control method for an island microgrid under an extended state observer. The method uses a third-order extended state observer and a power generation cost optimization method to construct a feedback linearization model of an AC microgrid, reveals the equivalence of sensor failure and actuator failure from a new control perspective, proposes a unified sensor and actuator failure model based on the microgrid physical system, and proposes an adaptive fault-tolerant control method using a modified distributed consistency protocol to maintain system voltage quality and optimal economic dispatch in the case of unknown sensor and actuator failures. The method utilizes information from local and neighboring distributed generators to improve the reliability, efficiency, and fault tolerance of the microgrid system.

Description

Technical Field

[0001] The present invention belongs to the field of fault-tolerant control of AC microgrids, and in particular to an adaptive fault-tolerant control method for isolated island microgrids under an extended state observer. Background Art

[0002] The islanded AC microgrid is considered to be the most effective structure to promote the widespread integration of renewable energy distributed generators (DGs). Without the support of the main grid, the frequency and voltage stability, power balance, operation optimization, fault diagnosis and protection of the islanded AC microgrid are completely determined by the control strategy of the distributed power source. Distributed control has been widely used due to the reduced communication and power generation costs, improved fault tolerance, and enhanced voltage and frequency quality. In practical applications, microgrids are susceptible to the failure of electrical components such as sensors and signal processors. In order to minimize the impact of sensor and actuator failures on the microgrid and ensure its reliability and stability under fault or abnormal conditions, it is crucial to establish a good fault-tolerant mechanism.

[0003] Commonly used fault-tolerant control methods include sliding mode control, robust H∞ control and adaptive control. The sliding mode controller can achieve voltage and frequency recovery, but the inevitable jitter phenomenon may be detrimental to the dynamic response of the system and increase the system's sensitivity to noise. Robust H∞ control can reflect the negative impact of faults to a certain extent, but this method focuses on minimizing the gain in the worst case and is highly conservative. In addition, most of the existing microgrid fault-tolerant control methods only target single sensor faults or actuator faults, which increases the complexity of the control system; and the control objectives are mostly concentrated on voltage and frequency recovery, power sharing, and improving system robustness, which cannot guarantee the minimization of the system's power generation cost.

[0004] The patents that have been applied for are as follows:

[0005] Patent number: CN202410499239.1, patent name: Distributed fault-tolerant secondary control method for isolated microgrids based on event triggering. The method uses a model that takes into account both partial failure of the actuator and bias fault droop control to study the fault-tolerant control of the distributed microgrid; analyzes the rationality of the triggering conditions of the event-triggered distributed fault-tolerant secondary control strategy, as well as the controller's suppression mechanism for unknown faults; and provides a complete proof process of the convergence of the system under the control of the event-triggered distributed fault-tolerant secondary control strategy. This method simultaneously considers the situation of partial failure and bias failure in the system, and can restore the system to normal frequency and voltage in the event of a fault, and accurately distribute power according to the capacity of each power supply in the system. The invention establishes the triggering conditions for event triggering, and each distributed power source only needs to exchange information at the time of event triggering, reducing the communication pressure between distributed power sources.

[0006] The inventive method mainly aims at improving the fault tolerance capability of the microgrid system under actuator failure, without considering potential sensor failures; the event trigger mechanism adopted by the inventive method may have time error problems, and the setting of the event trigger time may affect the fault-tolerant control effect; in addition, the inventive method mainly achieves the control goals of power sharing, voltage and frequency recovery, and lacks constraints on the economic cost of power generation.

[0007] The distributed adaptive control strategy adopted in the present invention can realize real-time fault tolerance of the microgrid system under sensor and actuator failures, effectively reduce communication costs, improve voltage and frequency recovery, and achieve power sharing and optimal power generation costs.

[0008] Patent number: CN202011309721.2, patent name: Microgrid sensor fault-tolerant control method based on PD-type learning observer. According to the state space model of the microgrid inverter-type distributed power supply, a system closed-loop output feedback controller is established; a microgrid system sensor fault model is established, and the sensor fault model is converted into an actuator fault model form; a sensor fault-tolerant PD-type learning observer is established to obtain the reconstructed fault signal, and the output after the reconstructed signal compensation is fed back to the output feedback controller to ensure stable tracking of the output power. Real-time monitoring of faults is achieved, and finally the sensor fault is accurately reconstructed, and the reconstructed fault signal is used to correct the measurement error of the sensor; the safe and reliable operation of IIDG is ensured when the microgrid system is connected to the grid for power transmission, and it has a wide range of adaptability to various faults in microgrid sensors.

[0009] The inventive method converts the sensor fault model into the actuator fault model form through a fault conversion filter, without considering the actual occurrence of actuator failures; the PD-type learning observer adopted by the inventive method requires estimation and reconstruction of sensor faults, which increases the complexity of system design; in addition, the inventive method mainly achieves the control objectives of power tracking, voltage and frequency recovery, and lacks constraints on the economic feasibility of power generation costs.

[0010] The distributed adaptive control strategy adopted in the present invention can achieve fault tolerance of the microgrid system under sensor and actuator failures, without the need to design a fault observer, effectively reducing system design and communication costs, improving voltage and frequency recovery, and achieving optimal power sharing and power generation costs.

[0011] Patent number: CN202011309721.2, patent name: A distributed adaptive control method for AC microgrids under non-ideal communication, which establishes a multi-period economic dispatch problem. Under the premise that each power generation unit meets the upper and lower limits of output power, slope constraints and supply and demand balance constraints, the power generation cost of the microgrid is optimized by dispatching the power generation of each power generation unit. The microgrid distributed control method proposed in this invention realizes the restoration of the frequency and voltage of the microgrid to the rated value, ensuring the quality of power; at the same time, it realizes the tracking of the active power output value to the optimal solution of the economic dispatch problem and the reactive power equalization control, reducing the power generation cost of the microgrid.

[0012] The distributed adaptive control method proposed in the inventive method only considers communication failures, but does not consider the impact of sensor and actuator failures on the isolated AC microgrid.

[0013] The present invention designs an adaptive fault-tolerant control law based on a distributed consistency protocol, so that the isolated AC microgrid can achieve voltage and frequency recovery, power sharing and optimal power generation cost in the event of sensor failure, actuator failure and communication failure, thereby improving the robustness and economy of the microgrid system. Summary of the invention

[0014] In order to solve the above problems, the present invention proposes an adaptive fault-tolerant control method for an island microgrid under an extended state observer. This method can improve the voltage quality and robustness of the island microgrid system under sensor failure and actuator failure by relying solely on neighbor information, and through improved droop control, the economy of the microgrid system is improved, achieving optimization of power generation cost.

[0015] To achieve the above object, the technical solution adopted by the present invention is:

[0016] The adaptive fault-tolerant control method of an island microgrid under an extended state observer comprises the following steps:

[0017] Step 1) Based on the large signal state space model and improved droop control, a feedback linearization model of the island AC microgrid is established;

[0018] First consider the power generation cost to improve droop control:

[0019]

[0020] In the formula, ω ni and V ni are the reference values ​​of angular frequency and output voltage amplitude, V odi * and V oqi * V o * The components on the d-axis and q-axis, nQi is the voltage droop coefficient, parameter k λ and k p Related to economic optimal control, λ i c is the cost increment rate, χ(·) is a step function, if P i <P mi , then χ(P mi -P i )=1, otherwise χ(P mi -P i )=0, that is

[0021]

[0022] Where n i is the number of neighbors of the ith DG, α i and β i Related to the cost function of the microgrid system, considering the constraints of power balance and power limitation, the optimal control problem of power generation cost is solved by the equal incremental cost criterion, that is, λ1 c =λ2 c =L=λ n c ;

[0023] Subsequently, to simplify the modeling and analysis process, the large signal state space model of each DG unit is described as

[0024]

[0025] Where x i =[δ i ,λ i ,Q i ,φ di ,φ qi ,γ di ,γ qi ,i fdi ,i fqi ,v odi ,v oqi ,i odi ,i oqi ] T is the state vector, D i is the disturbance vector, and the control input is u i =V ni , the output is y i =v odi ;

[0026] Then, using the feedback linearization method, the auxiliary control law is defined:

[0027]

[0028] Where F i (x) = f i (x i )+k i (x i )D i ,

[0029] Finally, the input-output feedback linearization model is established:

[0030]

[0031] In the formula B=

[01] T ;

[0032] Step 2) Establish a third-order extended state observer:

[0033] Step 3) Analyze the equivalence of sensor failure and actuator failure and establish a unified fault model;

[0034] Step 4) According to the error between the observed value and the reference value, an adaptive fault-tolerant control law is designed based on a distributed consensus protocol to achieve optimal voltage and frequency recovery, power sharing, and power generation cost.

[0035] As a further improvement of the present invention, the specific steps of step 2) are as follows:

[0036] Establish a third-order extended state observer:

[0037]

[0038] In the formula is the observed value, and is defined Gain G i1 ,G i2 ,G i3 are all positive numbers, and there are;

[0039]

[0040] As a further improvement of the present invention, the specific steps of step 3) are as follows:

[0041] The measured value of the system output when the sensor fails is defined as:

[0042]

[0043] In the formula Indicates a signal containing a fault, unknown additive fault It may be caused by accuracy degradation, measurement noise or external data injection. Equation (9) can be rewritten as:

[0044]

[0045] In the formula Function f i s1 (·) and f i s2 (·) and unknown faults related;

[0046] When there is an actuator fault, the auxiliary control law is expressed as:

[0047]

[0048] Where v i a Defined as an unknown bias fault, parameter Used to indicate partial failure;

[0049] Combined with formula (10), a unified model of sensor and actuator failure is established as follows:

[0050]

[0051] Where f i a (·) is defined as f i s1 ,f i s2 , The new actuator fault, f i a It contains information about sensor faults, so additive sensor faults are analytically considered as actuator bias faults;

[0052] The linearized large signal model based on the extended state observer considering sensor and actuator failures is expressed as:

[0053]

[0054] In the formula

[0055] As a further improvement of the present invention, the specific steps of step 4) are as follows:

[0056] The voltage tracking error based on the consistency protocol is described as:

[0057]

[0058] Using Kronecker product Re-describe formula (14);

[0059]

[0060] Where γi =[γ i1 γ i2 ] T ,γ=[γ1…γ N ] T ;

[0061] According to the optimal control theory, the Riccati equation is used to design a suitable feedback control. Let P be the solution of the Riccati equation:

[0062] A T P+PA-PBB T P+Q=0 (16)

[0063] Where Q is a positive definite matrix, and the feedback control matrix is ​​K = B T P;

[0064] definition Design the feedback control law:

[0065]

[0066] Where σ is a positive control parameter, and Represents the adaptive control law:

[0067]

[0068] In the formula κ i,1 and κ i,2 is a positive constant to be designed, and

[0069] Defining Voltage Tracking Error Its derivative is The global error is then expressed as:

[0070]

[0071] Therefore, the distributed voltage tracking problem is transformed into the asymptotic stability problem of the global tracking error. If γ>0 exists, then the global error system (19) of the adaptive fault-tolerant control scheme expressed by equations (17) and (18) will be asymptotically stable. In addition, the steady-state tracking error of the global voltage can be constrained in the residual set:

[0072]

[0073] Adjustment time limit:

[0074]

[0075] Beneficial effects:

[0076] The adaptive fault-tolerant control method for an island microgrid under an extended state observer proposed in the present invention proves through theoretical derivation that additive sensor failure can be equivalent to actuator bias failure in analytical form, and establishes a unified model of sensor and actuator failures; it improves the voltage quality and robustness of the island microgrid system under sensor failure and actuator failure by relying only on neighbor information; it improves the droop control by considering the system power generation cost, so that the invented method has advantages in the reliability and economy of the microgrid system. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 is a flow chart of the present invention;

[0078] Figure 2 A single distributed power supply control block diagram of the present invention;

[0079] Figure 3 The structure diagram of the three-phase AC microgrid including four distributed power sources of the present invention;

[0080] Figure 4 A communication topology diagram including four distributed power sources of the present invention;

[0081] Figure 5 A schematic diagram of performance evaluation results of actual values ​​and estimated values ​​of output voltages of the present invention;

[0082] Figure 6 It is a schematic diagram of the performance evaluation results of the output power, cost increment rate and frequency of the present invention;

[0083] Figure 7 It is a schematic diagram of the output voltage amplitude and the cost increase rate under communication failure of the present invention. DETAILED DESCRIPTION

[0084] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0085] The invention proposes an island microgrid adaptive fault-tolerant control method under an extended state observer, and the flowchart of the invention is as follows: Figure 1 As shown, the single distributed power supply control block diagram of the present invention is as follows Figure 2 As shown in the figure, firstly, based on the large signal state space model and the improved droop control, the feedback linearization model of the isolated AC microgrid is established; secondly, a third-order extended state observer is established; thirdly, the equivalence of sensor fault and actuator fault is analyzed, and a unified fault model is established; then, according to the error between the observed value and the reference value, an adaptive fault-tolerant control law is designed based on the distributed consistency protocol, and the stability is proved by the Lyapunov method; finally, the simulation results verify the effectiveness of the control strategy proposed in this invention. The specific steps are as follows:

[0086] 1. Feedback linearization model of isolated AC microgrid

[0087] First consider the power generation cost to improve droop control:

[0088]

[0089] In the formula, ω ni and V ni are the reference values ​​of angular frequency and output voltage amplitude, V odi * and V oqi * V o * The components on the d-axis and q-axis, n Qi is the voltage droop coefficient, parameter k λ and k p Related to economic optimal control, λ i c is the cost increment rate, χ(·) is a step function, if P i <P mi , then χ(P mi -P i )=1, otherwise χ(P mi -P i )=0, that is

[0090]

[0091] Where n i is the number of neighbors of the ith DG. i and β i It is related to the cost function of the microgrid system. Considering the constraints of power balance and power limitation, the optimal control problem of power generation cost can be solved by the equal incremental cost criterion, that is, λ1 c =λ2 c =L=λ n c .

[0092] Subsequently, to simplify the modeling and analysis process, the large signal state space model of each DG unit can be described as

[0093]

[0094] Where x i =[δ i ,λ i ,Q i ,φ di ,φ qi ,γ di ,γ qi ,i fdi,i fqi ,v odi ,v oqi ,i odi ,i oqi ] T is the state vector, D i is the disturbance vector, and the control input is u i =V ni , the output is y i =v odi .

[0095] Then, using the feedback linearization method, the auxiliary control law is defined:

[0096]

[0097] Where F i (x) = f i (x i )+k i (x i )D i ,

[0098] Finally, the input-output feedback linearization model is established:

[0099]

[0100] In the formula B=

[01] T ;

[0101] 2. Establish a third-order extended state observer

[0102] Establish a third-order extended state observer:

[0103]

[0104] In the formula is the observed value. Definition Gain G i1 ,G i2 ,G i3 are all positive numbers, and there is

[0105]

[0106] 3. Establish a unified fault model

[0107] The measured value of the system output when the sensor fails is defined as:

[0108]

[0109] In the formula Indicates a signal containing a fault, unknown additive fault It may be caused by accuracy degradation, measurement noise or external data injection. In order to describe the fault more generally and simplify the derivation, equation (9) can be rewritten as:

[0110]

[0111] In the formula Function f i s1 (·) and f i s2 (·) and unknown faults related.

[0112] When there is an actuator fault, the auxiliary control law is expressed as:

[0113]

[0114] In the formula Defined as an unknown bias fault, parameter Used to indicate a partial loss of efficiency (PLOE) fault.

[0115] Combined with formula (10), a unified model of sensor and actuator failure is established as follows:

[0116]

[0117] Where f i a (·) is defined as f i s1 ,f i s2 , The new actuator fault, f i a It contains information about sensor failure. Therefore, additive sensor failure can be analytically regarded as actuator bias failure.

[0118] The linearized large signal model based on the extended state observer considering sensor and actuator failures is expressed as:

[0119]

[0120] In the formula

[0121] 4. Design adaptive fault-tolerant control law and prove stability

[0122] The voltage tracking error based on the consistency protocol is described as:

[0123]

[0124] Using Kronecker product Re-describe formula (14);

[0125]

[0126] Where γ i =[γ i1 γ i2 ] T ,γ=[γ1…γ N ] T .

[0127] According to the optimal control theory, the Riccati equation is used to design a suitable feedback control. Let P be the solution of the Riccati equation:

[0128] A T P+PA-PBB T P+Q=0 (16)

[0129] Where Q is a positive definite matrix. The feedback control matrix is ​​selected as K = B T P.

[0130] definition Design the feedback control law:

[0131]

[0132] Where σ is a positive control parameter, and Represents the adaptive control law:

[0133]

[0134] In the formula κ i,1 and κ i,2 is a positive constant to be designed, and

[0135] Defining Voltage Tracking Error Its derivative is Then the global error can be expressed as:

[0136]

[0137] Thus, the distributed voltage tracking problem is transformed into the asymptotic stability problem of the global tracking error. If γ>0 exists, then the global error system (19) of the adaptive fault-tolerant control scheme expressed by equations (17) and (18) will be asymptotically stable. In addition, the steady-state tracking error of the global voltage can be constrained in the residual set:

[0138]

[0139] Adjustment time limit:

[0140]

[0141] Considering the adaptive law (18) and the error system (19), the Lyapunov function is constructed:

[0142]

[0143] In the formula j=1,2,τ i,1 and τ i,2 is a constant to be defined.

[0144] Derivative of formula (23):

[0145]

[0146] Select τ i,1 =1 / (2λ1μ i )and Considering bounded conditions for failure It can be deduced that:

[0147]

[0148] Therefore, it can be proved that the error system (19) is asymptotically stable, thus ensuring the accuracy of voltage tracking.

[0149] 5. Simulation verification

[0150] In order to verify the effectiveness of the distributed adaptive fault-tolerant control method for islanded AC microgrid based on extended state observer proposed in this paper, a parallel three-phase AC microgrid with four distributed power sources is built in MATLAB / Simulink, with a voltage level of 220V, a frequency of 50Hz, and a maximum active power value of 25kW. Figure 3 The distributed communication structure is shown in Figure 4 The present invention verifies the effectiveness of the proposed algorithm under two embodiments, as follows:

[0151] Example 1: Evaluating the performance of the proposed control scheme considering load switching, sensor and actuator failures

[0152] The power generation cost ratio of each distributed generation unit is set to be 1:2:1.8:1.8, and the bias fault and partial failure fault are and Sensor failure oabci Generate using random function. The simulation scenario is as follows:

[0153] 1) At t0 = 0s, the microgrid operates normally in island mode;

[0154] 2) At t1 = 4s, the switch of load 2 is closed and a sensor failure occurs.

[0155] 3) At t2 = 8s, the switch of load 2 is turned on, and an actuator bias fault occurs.

[0156] 4) When t3=12s, the sensor fails Eliminate, the actuator has a partial failure at the same time and bias faults

[0157] 5) At t4=16s, the switch of load 3 is closed.

[0158] like Figure 5 As shown in Figure 2, the AC microgrid exhibits a stable operating state from t = 0 to 4s, and the output phase voltage amplitude always remains at the reference value. At t = 4s, load 2 is connected, and the output voltage quickly stabilizes at 311V. Figure 5 The results in (b) further demonstrate that the extended state observer can effectively track the output voltage, verifying the effectiveness of the large signal model based on the extended state observer.

[0159] Although sensor failure, partial failure and bias failure occurred during 4≤t≤20s, Figure 5 and Figure 6 The waveform diagram in FIG. 1 verifies the system's strong resistance to faults and its ability to quickly recover voltage and frequency, thereby confirming the feasibility of the control scheme proposed in the present invention. After adding load 3 at t≥16s, Figure 6 (a) It can be seen that the distributed power source #1 with the lowest cost reaches the maximum power output first and is subject to the maximum power limit of 25kW. Figure 6 (b) represents the cost increase rate λ of each distributed power source in the AC microgrid under different scenarios. c can be synchronized efficiently, thus achieving the goal of optimizing power generation costs. Figure 6 In (c), the frequency of each distributed generation can be adjusted within the range of 50 ± 0.03 Hz, which shows that the frequency control algorithm considering the optimal cost is still effective in the presence of a faulty voltage controller.

[0160] Example 2: Performance evaluation under communication delay and topology switching

[0161] The simulation scenario is as follows:

[0162] 1) When t0=0, the microgrid operates normally without communication delay.

[0163] 2) At t1 = 2s, the switch of load 2 is closed. The communication link from DG#1 to DG#2 is disconnected, and the entire system experiences a communication delay of 10 milliseconds.

[0164] 3) At t2 = 4s, the switch of load 2 is turned off. The communication link from DG#4 to DG#1 is disconnected, and the entire system experiences a communication delay of 20 milliseconds.

[0165] 4) At t3 = 6s, the switch of load 2 is closed. The communication link from DG#3 to DG#4 is disconnected, and the entire system experiences a communication delay of 40 milliseconds.

[0166] 5) At t4 = 8s, the switch of load 2 is turned off. The voltage controller has a communication delay of 60 milliseconds, while the frequency controller has a delay of 80 milliseconds.

[0167] 6) At t5 = 10 s, the switch of load 2 is closed. The voltage controller has a communication delay of 80 milliseconds, while the frequency controller has a delay of 120 milliseconds.

[0168] exist Figure 7 In (a), the voltage overshoot controlled by the distributed tracking algorithm increases due to the variation in communication delay between the voltage and frequency controllers. Nevertheless, it still tracks the reference accurately. In addition, a communication link failure prolongs the transient process of distributed consensus and slows down the tracking speed. Figure 7 The results in (b) show that communication delay and changes in network topology can affect the cost increment λ c However, the control scheme proposed in the present invention is still robust to the delay of 80 milliseconds.

[0169] The above description is only a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent change made based on the technical essence of the present invention still falls within the scope of protection required by the present invention.

Claims

1. An adaptive fault-tolerant control method for an island microgrid under an extended state observer is characterized in that: The following steps are involved: Step 1) Based on the large signal state space model and improved droop control, a feedback linearization model of the island AC microgrid is established; First consider the power generation cost to improve droop control: In the formula, ω ni and V ni are the reference values ​​of angular frequency and output voltage amplitude, V odi * and V oqi * V o * The components on the d-axis and q-axis, n Qi is the voltage droop coefficient, parameter k λ and k p Related to economic optimal control, λ i c is the cost increment rate, χ(·) is a step function, if P i <P mi , then χ(P mi -P i )=1, otherwise χ(P mi -P i )=0, that is Where n i is the number of neighbors of the ith DG, α i and β i Related to the cost function of the microgrid system, considering the constraints of power balance and power limitation, the optimal control problem of power generation cost is solved by the equal incremental cost criterion, that is, λ1 c =λ2 c =L=λ n c ; Subsequently, to simplify the modeling and analysis process, the large signal state space model of each DG unit is described as Where x i =[δ i ,λ i ,Q i ,φ di ,φ qi ,γ di ,γ qi ,i fdi ,i fqi ,v odi ,v oqi ,i odi ,i oqi ] T is the state vector, D i is the disturbance vector, and the control input is u i =V ni , the output is y i =v odi ; Then, using the feedback linearization method, the auxiliary control law is defined: Where F i (x) = f i (x i )+k i (x i )D i , Finally, the input-output feedback linearization model is established: In the formula B=[01] T ; Step 2) Establish a third-order extended state observer: Step 3) Analyze the equivalence of sensor failure and actuator failure and establish a unified fault model; Step 4) According to the error between the observed value and the reference value, an adaptive fault-tolerant control law is designed based on a distributed consensus protocol to achieve voltage and frequency recovery, power sharing, and optimal power generation cost.

2. The island microgrid adaptive fault-tolerant control method under the extended state observer according to claim 1 is characterized in that: Step 2) The specific steps are as follows: Establish a third-order extended state observer: In the formula is the observed value, and is defined Gain G i1 ,G i2 ,G i3 are all positive numbers, and there are; 3. The island microgrid adaptive fault-tolerant control method under the extended state observer according to claim 1 is characterized in that: Step 3) The specific steps are as follows: The measured value of the system output when the sensor fails is defined as: In the formula Signal indicating fault inclusion, unknown additive fault It may be caused by decreased accuracy, measurement noise or external data injection. Equation (9) can be rewritten as: In the formula function and With unknown fault related; When there is an actuator fault, the auxiliary control law is expressed as: In the formula Defined as an unknown bias fault, parameter Used to indicate partial failure; Combined with formula (10), a unified model of sensor and actuator failure is established as follows: In the formula is defined as The new actuator fault, It contains information about sensor faults, so additive sensor faults are analytically considered as actuator bias faults; The linearized large signal model based on the extended state observer considering sensor and actuator failures is expressed as: In the formula 4. The island microgrid adaptive fault-tolerant control method under the extended state observer according to claim 1 is characterized in that: Step 4) The specific steps are as follows: The voltage tracking error based on the consistency protocol is described as: Using Kronecker product Re-describe formula (14); where γ i = [γ i1 γ i2 T , γ = [γ1…γ N T ;​​ According to the optimal control theory, the Riccati equation is used to design a suitable feedback control. Let P be the solution of the Riccati equation: A T P+PA-PBB T P+Q=0 (16) Where Q is a positive definite matrix, and the feedback control matrix is ​​K = B T P; definition Design the feedback control law: Where σ is a positive control parameter, and Represents the adaptive control law: In the formula κ i,1 and κ i,2 is a positive constant to be designed, and Defining Voltage Tracking Error Its derivative is The global error is then expressed as: Therefore, the distributed voltage tracking problem is transformed into the asymptotic stability problem of the global tracking error. If γ>0 exists, the global error system (19) of the adaptive fault-tolerant control scheme expressed by equations (17) and (18) will be asymptotically stable. In addition, the steady-state tracking error of the global voltage can be constrained in the residual set: Adjustment time limit:

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