A data-driven based fault detection method for dc microgrid

Abstract

The application provides a kind of data-driven DC microgrid fault detection method, it is related to the fault detection and safety control technical field of DC microgrid.The application obtains input and output data by system operation under the condition that the parameters of microgrid system are unknown, and constructs unknown input observer to carry out fault detection.Compared with single system, the application estimates the interconnection item that cannot be measured in the data-driven framework, and identifies the system matrix.In addition, on the basis of designing unknown input observer, the design of observer is converted into solving linear matrix inequality, and the robust performance index and sensitive performance index are considered, and finally the fault detection of each DC motor is realized.The detector designed by the application can still complete the detection task under the condition that only input and output data are obtained.In addition, the method proposed by the application uses a large amount of system operation data, and can be put into use online by programming directly on the computer, and the cost is very low.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of fault detection and safety control of direct current microgrids, and particularly relates to a data-driven fault detection method for a direct current microgrid. BACKGROUND

[0002] With the rapid development of renewable energy and the application of smart grid technology, direct current microgrids (DC Microgrid) as an important power system mode have gradually become an important part of modern power systems. A direct current microgrid is composed of multiple distributed generation units (DGU), energy storage devices, load devices, etc., and its main feature is to transmit and distribute power through direct current. The direct current microgrid not only realizes localized power production and consumption, but also enhances the reliability and flexibility of the system, reduces energy loss, and improves energy utilization efficiency. Due to its flexibility and efficiency, the direct current microgrid faces many challenges in actual operation, especially in fault detection, fault isolation and fault recovery, which directly affects the stability and safety of the power system. In a direct current microgrid system, due to its complex structure, diverse devices and dynamic operating environment, the probability of fault occurrence is high. Therefore, it is particularly important to study the fault detection method of the direct current microgrid to ensure the stability and safety of the system.

[0003] Chinese patent "CN118501614A A fault analysis method for a direct current microgrid based on Pearson" provides a method for analyzing the fault of a direct current microgrid based on a Pearson correlation coefficient optimization model. According to the fault detection analysis result, the fault line set and the fault type corresponding to each fault line in the fault line set are determined, and the Pearson correlation coefficient optimization model and the fault information combination scheme set of the direct current microgrid are combined to analyze the fault positioning of each fault line in the fault line set and the corresponding sampling current. The technical solution described in Chinese patent "CN118501614A A fault analysis method for a direct current microgrid based on Pearson" needs to be fully known when the microgrid system model is researched, but in general cases, system model parameters may be difficult to obtain, and when only system input and output data can be obtained, this method cannot be used and fault detection cannot be achieved. SUMMARY

[0004] In view of the deficiencies of the prior art, the present application proposes a data-driven fault detection method for a direct current microgrid in the case where the parameters of the existing direct current microgrid system are unknown. By collecting data on the operation of the direct current microgrid, a subspace identification technology is used to construct an unknown input observer based on the identification result to detect fault signals.

[0005] A data-driven fault detection method for a direct current microgrid, comprising the following steps:

[0006] Step 1: Constructing the state space model of the distributed generation units in the direct current micro-grid, and collecting the input and output data tuples of each distributed generation unit;

[0007] Step 1.1: Constructing the state space model of the distributed generation units in the direct current micro-grid, including the state space model of the distributed generation units in the fault and non-fault state; the fault is the actuator fault;

[0008] The state space model of the i-th distributed generation unit in the non-fault state is:

[0009]

[0010] Wherein, x i (k)∈R n is the state of the i-th distributed generation unit at the current time, i is the number of the distributed generation unit, N represents the number of the distributed generation units, k is the transient time of the current operation, n is the dimension of the state of the distributed generation unit, x i (k)=[V i (k)I i (k)] T , V i (k) is the voltage at the load of the i-th distributed generation unit at the current time; I i (k) is the current generated by the i-th distributed generation unit at the current time; N i is the set of distributed generation units adjacent to the i-th distributed generation unit, |N i | represents the number of distributed generation units adjacent to the i-th distributed generation unit, j is the number of the distributed generation unit adjacent to the i-th distributed generation unit, x j (k) is the state of the distributed generation unit adjacent to the i-th distributed generation unit, which is recorded as the state of the coupled single distributed generation unit; u i (k)∈R m is the input vector of the i-th distributed generation unit, m is the dimension of the input vector of the i-th distributed generation unit, u i (k)=[V ti (k)I Li (k)] T , V ti (k) is the control command of the converter of the i-th distributed generation unit at the current time, I Li (k) is the required current of the i-th distributed generation unit at the current time; y i (k)∈R n is the output vector of the i-th distributed generation unit, v i (k)∈R ndenotes the measurement noise of the ith distributed generation unit, C i = I is an identity matrix; and denotes the unknown system matrix of the ith distributed generation unit, representing the interaction between the ith distributed generation unit and its neighboring distributed generation units; C ti is the shunt capacitance of the ith distributed generation unit, R ij is the power line conductance, L ti is the inductance of the filter of the ith distributed generation unit, R ti is the resistance of the filter of the ith distributed generation unit;

[0011] The state space model of the ith distributed generation unit with actuator faults is:

[0012]

[0013] where f i (k) ∈ R m is the actuator fault vector of the ith distributed generation unit;

[0014] Step 1.2: Run each distributed generation unit in the direct current microgrid, and collect input-output data tuples of each distributed generation unit under a set of excitation conditions; the input-output data tuples include output vectors and input vectors of all distributed generation units at different times;

[0015] Step 2: Use the row subspace method to identify the state of coupling a single distributed generation unit, respectively, to obtain the estimated value of the state of coupling a single distributed generation unit; the coupling single distributed generation unit is the neighboring distributed generation unit of the distributed generation unit to be detected;

[0016] Step 2.1: Establish two local network systems and construct state space models of the two local network systems, respectively;

[0017] The two local network systems are both sub-networks of the direct current microgrid, each local network system includes a plurality of distributed generation units, and a plurality of neighboring distributed generation units exist externally, the intersection of the two local network systems is the coupling single distributed generation unit to be solved; the two local network systems are respectively called left local network system and right local network system, and the left and right local network systems are denoted as Σ left and Σ right , respectively, the state space models are:

[0018]

[0019] wherein the superscripts l and r respectively denote the left local network system and the right local network system, and are the states of the left local network system at time k and k+1, respectively, and are the states of the right local network system at time k and k+1, respectively, and are the inputs of the left and right local network systems, respectively, and are the outputs of the left and right local network systems, respectively, and are the measurement noises of the left and right local network systems, respectively, and are the output and measurement noise of the distributed generation unit connected to the left local network system, respectively, and are the output and measurement noise of the distributed generation unit connected to the right local network system, respectively, and are block matrices;

[0020] Step 2.2: Iterating the state-space model of the left and right local network systems at each time, respectively, to establish the input-output data equations of the left and right local network systems;

[0021] For the left and right local network systems, the input-output data equations are:

[0022]

[0023] where the subscripts f and p denote the future and past time windows at time k, respectively, and l and r are the observability matrices of the left and right local network systems, respectively, and denote the state sequences of the left and right local network systems, respectively, and are the Toeplitz matrices of the left local network system, and are the Toeplitz matrices of the right local network system, and denote the future Hankel matrices composed of the outputs and of the left and right local network systems, respectively, and denote the history Hankel matrices composed of the outputs and of the left and right local network systems, respectively, and denote the future and historical Hankel matrices composed of the left local network system input, and denote the future and historical Hankel matrices composed of the right local network system input, and denote the future and historical Hankel matrices composed of the output of the adjacent distributed generation units in the left local network system; and denote the future and historical Hankel matrices composed of the noise of the adjacent distributed generation units in the left local network system, and denote the future and historical Hankel matrices composed of the measurement noise in the left local network system, and denote the future and historical Hankel matrices composed of the output of the adjacent distributed generation units in the right local network system, and denote the future and historical Hankel matrices composed of the noise of the adjacent distributed generation units in the right local network system, and denote the future and historical Hankel matrices composed of the measurement noise in the right local network system;

[0024] Step 2.3: The Hankel matrices in the constructed input-output data equation are sorted out, and the data Hankel matrix sets of the left local network system and the right local network system are constructed respectively;

[0025] The data Hankel matrix sets of the left local network system and the right local network system are:

[0026]

[0027] Step 2.4: Based on the constructed data Hankel matrix set, the estimated values of the state sequences of the left local network system and the right local network system are obtained by using the row subspace method;

[0028] Γ l and Γ r are column full rank, so the row subspaces of the state sequences and are and where Row[] represents the row subspace of a matrix; define the noise term:

[0029] Define the matrix:

[0030]

[0031]

[0032] The second part of (7) and (8) is the noise term, which is derived from the collected Hankel matrix data set. and Calculated;

[0033] For Φ l and Φ r Perform singular value decomposition:

[0034]

[0035] in, For matrix Φ l The first part of the left singular value matrix, For matrix Φ l The second part of the left singular value matrix; Known as Φ l The left null space; and It is a diagonal matrix; It is matrix Φ l The first part of the right singular value matrix, It is matrix Φ l The second part of the right singular value matrix; For matrix Φ r The first part of the left singular value matrix, For matrix Φ r The second part of the left singular value matrix, Known as Φ r The left null space; and It is a diagonal matrix; It is matrix Φ r The first part of the right singular value matrix, It is matrix Φ r The second part of the right singular value matrix;

[0036] The row space of the state sequence of the left local network system is The state sequence of the left local network system is then:

[0037]

[0038] in, and It is a block matrix, and satisfies F is a non-singular matrix; and because... Since it is unknown, the estimated value of the state sequence of the left local network system is: Multiply both sides of (10) by F -1 Then the estimated value of the state sequence of the left local network system is Similarly, the state sequence of the right local network system is: in It is a block matrix;

[0039] Step 2.5: Based on the intersection of the estimated values ​​of the state sequences of the left local network system and the right local network system, estimate the state of the coupled single distributed generation unit to obtain the estimated value of the state of the coupled single distributed generation unit;

[0040] Because the intersection of the state sequences of two local network systems is the state sequence x coupled to a single distributed generation unit. j =[x j (k) x j (k+1) ... x j (k+a)]∈R an Therefore, the state sequence x of a single distributed generation unit is coupled. j The row subspace is

[0041] Define matrix:

[0042]

[0043] The second part of (11) is the noise term, which is derived from the collected Hankel matrix data set. and Calculated, and then applied to Φ j Perform singular value decomposition:

[0044]

[0045] in, For matrix Φ j The first part of the left singular value matrix, For matrix Φ j The second part of the left singular value matrix; Known as Φ j The left null space; and It is a diagonal matrix; It is matrix Φ j The first part of the right singular value matrix, It is matrix Φ j The second part of the right singular value matrix;

[0046] The row space of the state sequence coupled to a single distributed generation unit is then: in, and For a block matrix, satisfying Then the state sequence of a single distributed generation unit is coupled:

[0047]

[0048] Among them, F j It is a non-singular matrix; and because Since it is unknown, the estimated value of the state sequence coupled to a single distributed generation unit is: Multiply both sides of (13) by have This leads to the estimated state of the coupled individual distributed generation unit. Where e j (k) represents the noise term, from... Take the value from, e j (k) is The first column;

[0049] Step 3: Repeat step 2 to obtain the estimated state of all coupled individual distributed generation units corresponding to the distributed generation unit to be detected;

[0050] The estimated value of the state sequence of all coupled individual distributed generation units corresponding to the distributed generation unit to be detected is denoted as: For the i-th distributed generation unit, the number of adjacent coupled single distributed generation units is |N i | Then step 2 needs to be repeated for a total of |N. i |times;

[0051] Step 4: Based on the input and output data tuples and the estimated values ​​of the states of all coupled individual distributed generation units corresponding to the distributed generation unit to be detected, identify the system matrix in the state space model of the distributed generation unit to be detected when there is no fault.

[0052] Step 4.1: Substitute the estimated state of the coupled single distributed generation unit into the state space model of the distributed generation unit established in Step 1 under fault-free conditions to obtain the new state space model of the distributed generation unit under fault-free conditions and its corresponding input-output equations.

[0053] By substituting the estimated state of a single distributed generation unit into the state-space model of the distributed generation unit under fault-free conditions, a new state-space model of the distributed generation unit under fault-free conditions is obtained:

[0054] x i (k+1)=A i x i (k)+D i (h i (k)-ε i (k)) (14)

[0055] y i (k)=Ci x i (k)+v i (k)

[0056] in, in This represents the noise term coupled to a single distributed generation unit. Therefore, the corresponding input-output equation is:

[0057] y i,h (k)=Γ i,h x i (k)+H zi,h (h i,h (k)-ε i,h (k))+v i,h (k) (15)

[0058] Among them, y i,h (k), v i,h (k), h i,h and ε i,h (k) represents y from time k to time k+h. i v i h i and ε i The sequence formed, Γ i,h It is the observability matrix, H i,h The Toplitz matrix;

[0059] Step 4.2: Based on the input-output equations obtained in Step 4.1, construct the equations relating the output to the data in future time periods;

[0060] Suppose there exists a constant matrix ψ i This makes the state x at time k+h... i (k+h) is represented as:

[0061]

[0062] For some future time k+h+L, there exists a future time output y. i Equation relating (k+h+L) to data:

[0063]

[0064] Where L is the time length, x i (k+h+L), y i (k+h+L) and v i (k+h+L) represent the state, output vector, and measurement noise at time k+h+L, respectively. Let be the Markov parameter vector. It is a coefficient matrix. h represents the time from k+h to k+h+L-1. i The sequence formed ε from time k+h to time k+h+L-1 i The sequence formed;

[0065] Step 4.3: Based on the input and output data tuples obtained in Step 1.2, use the instrumental variable method to estimate the Markov parameter vector in the equation relating the output and data at future times, and obtain the estimated value of the Markov parameter vector;

[0066] Based on the input and output data tuples obtained in step 1.2, define instrumental variables. and noise variables in, h represents the time from time k to time k+h-1. i The sequence formed ε represents the time from k to k+h-1. i The sequence is formed by multiplying both sides of (17) by (ξ). i (k)) T ,but:

[0067]

[0068] Simplifying the above formula, we get:

[0069]

[0070] Among them, T ξ,a T yi,ξ,a and They are defined as Applying least squares estimation to equation (19), the Markov parameter vector The estimated value is In this invention, the pseudo-inverse of a matrix is ​​represented.

[0071] Step 4.4: Based on the estimated values ​​of the Markov parameter vectors, use the HoKalman method to identify the system matrix A in the state-space model of the distributed generation unit under fault-free conditions. i A ij and B i ;

[0072] Based on the structure of the Markov parameter vector, the estimated values ​​of the Markov parameter vector are... Divide into L blocks, Let l1 + l2 = L-1 be the τ-th block term of the Markov parameter vector estimate, where τ is the block term number and τ = 0, 1, ..., L-1. Then, let l1 + l2 = L-1. From the block terms of the Markov parameter vector... The constructed Hankel matrix for

[0073] Hankel matrix Perform singular value decomposition:

[0074]

[0075] in, Hankel matrix The first part of the left singular value matrix, Hankel matrix The second part of the left singular value matrix, and It is a diagonal matrix. Hankel matrix The first part of the right singular value matrix, Hankel matrix The second part of the right singular value matrix;

[0076] According to the Ho-Kalman method, the system matrix estimate in the state-space model of the distributed generation unit under fault-free conditions is:

[0077]

[0078] in, For system matrix A i The estimated value, For matrix D i The estimated value, based on The system matrix A is obtained. ij and B i The estimated value, For matrix The pseudo-inverse matrix, For matrix From row (n+1) to row (l1+1)n, Representation matrix The (l2n+1)th column to the ((l2+1)n)th column, Representation matrix Lines 1 to l1n;

[0079] Step 5: Based on the system matrix in the state-space model of the distributed generation unit to be detected when there are no faults, design an unknown input observer;

[0080] Step 5.1: Based on the system matrix in the state-space model of the distributed generation unit to be detected when there are no faults, construct the expression for the unknown input observer;

[0081] First, the state sequences of all coupled individual distributed generation units are treated as unknown input d. i (k), and then the system matrix identified in step 4 is substituted into the state space model (2) of the distributed generation unit under fault conditions to obtain:

[0082]

[0083] in, It is the state of coupling a single distributed generation unit. For the system matrix;

[0084] Design an unknown input observer of the following form for distributed generation units:

[0085]

[0086] Among them, z i (k+1) and z i (k) represent the states of the unknown input observer of the i-th distributed generation unit at time k+1 and time k, respectively, T i ,F i ,K i and H i Let be the observer parameter matrix to be designed, and satisfy the following equation:

[0087]

[0088] Among them, H i,1 and H i,2 It is the coefficient matrix in the unknown input observer;

[0089] Step 5.2: Solve for the parameter matrix in the unknown input observer so that the designed unknown input observer satisfies the sensitivity performance H_ and robustness performance H_. ∞ ;

[0090] Based on the unknown input observer (23), the estimation error equation and residual equation can be obtained as follows:

[0091] e i (k+1)=T i e i (k)+F i B i f i (k)-(K i +H i,1 )v i (k) (25)

[0092] r i (k)=C i e i (k)+v i (k)

[0093] Where, r i (k) represents the residual. Let e ​​be the estimation error at time k+1. i (k) represents the estimation error at time k. Let H_k be the estimated state at time k+1. By introducing sensitivity performance and robustness performance indices, the designed unknown input observer satisfies the sensitivity performance H_k and robustness performance H_k. ∞ ;

[0094] When the initial state of the estimation error is zero, the residual r i (k) For the fault signal f i (k) It has sensitivity, that is, it satisfies the sensitivity energy: Where β i For sensitivity performance indicators;

[0095] When the initial state of the estimation error is zero, the residual r i (k) Measurement noise v i (k) It is robust, that is, it satisfies the robustness property H. ∞ : Where, λ i Robust performance metrics;

[0096] First, given the robustness performance index λ i Solving for the parameter matrix of an unknown input observer can be transformed into solving the following optimization problem:

[0097]

[0098] Where V i U i Z i P i,1 P i,2 and Q i Let * represent the matrix to be solved, i.e., the decision variables in the optimization problem. The asterisk (*) indicates a symmetric term in the matrix. He{X} denotes matrix X plus the transpose of matrix X, ξ i,1 and θ l It is a constant given in advance. I represents the identity matrix. L i It is a pre-given matrix. ξ i,2 It is a constant given in advance.

[0099] Then Q is obtained by solving the linear matrix inequality (26). i V i U i ,because The parameter matrix of the unknown input observer is then calculated as follows: H i,2 =T i K i H i =H i,1 +H i,2 ;

[0100] Step 6: Based on the unknown input observer obtained in Step 5, design a residual generator and use the residual generator to obtain the residual signal;

[0101] Based on (24), the residual generator is obtained:

[0102]

[0103] Step 7: Calculate the average energy of the residual signal over a period of time and compare it with the set detection threshold to achieve fault detection;

[0104] The residual signal in (k0, k η The average energy J over the time period r,i (η) is:

[0105]

[0106] Where k0 represents the initial evaluation time, k η Indicates the evaluation termination time, where η is the time length between the evaluation termination time and the initial evaluation time; the detection threshold is defined as: Here, sup represents the supremum; therefore, the alarm rule is:

[0107]

[0108] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0109] First, for microgrid systems with unknown parameters, this invention proposes a data-driven method for fault detection. This method does not require prior knowledge of system model parameters; it only acquires input and output data during system operation and constructs an unknown input observer for fault detection. Second, compared to single systems, fault detection in microgrids is challenging because the interconnection signals formed by the states of adjacent subsystems are unmeasurable. To overcome this difficulty, this invention estimates the unmeasurable interconnection terms within a data-driven framework, identifying the system matrix. Furthermore, based on the design of the unknown input observer, the observer design is transformed into solving linear matrix inequalities, considering robustness and sensitivity performance indicators, ultimately achieving fault detection for individual DC motors. This invention's detector can still complete the detection task even with only input and output data. Moreover, the proposed method utilizes a large amount of system operation data and can be directly programmed on a computer for online deployment at a very low cost. Attached Figure Description

[0110] Figure 1 A schematic diagram of a DC microgrid structure consisting of five distributed generation units in an embodiment of the present invention;

[0111] Figure 2 This is a flowchart of a data-driven DC microgrid fault detection method according to an embodiment of the present invention;

[0112] Figure 3 In the case of a failure of the actuator of the second distributed generation unit in this embodiment of the invention, the evaluation function curve generated by the proposed method is shown. Detailed Implementation

[0113] The main objective of this embodiment is to utilize the described method to promptly detect faults in a DC microgrid, such as... Figure 1 The diagram shows the interconnected structure of the five distributed generation units involved in this invention, illustrating the connections between the components. The following example uses a failure in the second distributed generation unit (DGU) to illustrate the fault detection method of this invention.

[0114] Table 1 Electrical Parameters of DGU

[0115]

[0116] Table 2 DGU Line Parameters R ij (Ω)

[0117]

[0118] A data-driven fault detection method for DC microgrids, such as Figure 2 As shown, it includes the following steps:

[0119] Step 1: Based on the physical principles of DC microgrids, construct the state-space model of distributed generation units (DGUs) in DC microgrids, and collect the input and output data tuples of each distributed generation unit (DGU);

[0120] Step 1.1: Construct the state-space model of the distributed generation unit in the DC microgrid, including the state-space model of the distributed generation unit under fault conditions and without fault conditions; the fault is an actuator fault;

[0121] The state-space model of the i-th distributed generation unit when there are no faults is as follows:

[0122]

[0123] Where, x i (k)∈R n Let x represent the state of the i-th distributed generation unit at the current moment, where i is the unit number, N represents the number of distributed generation units, k is the current transient time, n is the dimension of the distributed generation unit's state, and x... i (k)=[V i (k) I i (k)] T V i (k) represents the voltage at the load of the i-th distributed generation unit at the current time; I i (k) represents the current generated by the i-th distributed generation unit at the current moment; x i (k+1) represents the state of the i-th distributed generation unit at the next time step, and N i Let |N| be the set of distributed generation units adjacent to the i-th distributed generation unit. i | represents the number of distributed generation units adjacent to the i-th distributed generation unit, j is the number of the distributed generation unit adjacent to the i-th distributed generation unit, x j (k) represents the state of the distributed generation unit adjacent to the i-th distributed generation unit, denoted as the state coupled to a single distributed generation unit; u i (k)∈R m Let u be the input vector of the i-th distributed generation unit, m be the dimension of the input vector of the i-th distributed generation unit, and u be the input vector of the i-th distributed generation unit. i (k)=[V ti (k)I Li (k)] T V ti (k) represents the control command for the converter of the i-th distributed generation unit at the current time, I Li (k) represents the current required by the i-th distributed generation unit at the current moment; y i(k)∈R n Let v be the output vector of the i-th distributed generation unit. i (k)∈R n The measured noise of the i-th distributed generation unit is Gaussian white noise, and the output is set to be observable by the output sensor; A i A ij and B i Let C be the unknown system matrix of the i-th distributed generation unit. Assume the state can be observed through the output sensor, then... i =I is the identity matrix; and Let C be the system matrix, representing the interaction between the i-th distributed generation unit and its neighboring distributed generation units; ti R is the parallel capacitor of the i-th distributed generation unit. ij Let L be the cross-line resistance between the i-th distributed generation unit and its adjacent distributed generation unit, i.e., the power line conductance. ti Let R be the inductance of the filter for the i-th distributed generation unit. ti Let be the resistance of the filter in the i-th distributed generation unit;

[0124] The state-space model of the i-th distributed generation unit when there is an actuator failure is as follows:

[0125]

[0126] Where f i (k)∈R m Let be the actuator fault vector of the i-th distributed generation unit;

[0127] In this embodiment, under fault-free conditions, the state-space models of the five distributed generation units are calculated based on the parameters as follows:

[0128]

[0129] In this embodiment It is an identity matrix, and the relevant matrix calculation is as follows:

[0130] If a fault occurs, regardless of the type, it may lead to the paralysis of the distributed generation unit or even more serious consequences. Therefore, fault detection is always a critical and important task. In this example, we consider that the second distributed generation unit is affected by an actuator fault. The state space model of the second distributed generation unit with the fault is as follows:

[0131] x2(k+1)=A2x2(k)+A 23 x3(k)+A24 x4(k)+B2(u2(k)+f2(k)) (37)

[0132] y2(k)=Cx2(k)+v2(k)

[0133] Where f2(k) is the fault signal of the second distributed generation unit at time k.

[0134] Step 1.2: Based on the physical principles of DC microgrids, operate each distributed generation unit (32)-(36) in the DC microgrid, under the set excitation conditions (input signal u) i (k) (i = 1, 2, 3, 4, 5) is set as a sinusoidal signal with an amplitude of 1, and the noise v is measured. i (k)(i=1,2,3,4,5) is set as a random signal with an amplitude of 0.1), and the input and output data tuples of each distributed generation unit are collected; the input and output data tuples include the output vector and input vector of all distributed generation units at different times;

[0135] The input and output data tuples are represented as {y i (k),u i (k)}(i=1,2,3,4,5), where i represents the i-th distributed source unit, k represents the current time, and different values ​​of k represent data tuples at different times. In this example, 500 sets of input and output data are collected for each distributed source unit to construct the Hankel matrix used in the following steps.

[0136] Step 2: Using the row subspace method, identify the states of the coupled individual distributed generation units, namely x3(k) and x4(k), and obtain the estimated values ​​of the states of the coupled individual distributed generation units. and The coupled single distributed generation unit is the distributed generation unit adjacent to the distributed generation unit to be detected;

[0137] Step 2.1: Establish two local network systems and construct state-space models for each system.

[0138] Both local network systems are sub-networks of a DC microgrid. Each local network system includes several distributed generation units (DG units), and there are also several adjacent DG units externally. The intersection of the two local network systems is the desired coupled single DG unit. The two local network systems are referred to as the left local network system and the right local network system, respectively. The left local network system is denoted as Σ. left Its interior includes K l A distributed generation unit, with J outside. lLet Σ be an adjacent distributed generation unit, and denote the local network system on the right as Σ. right Its interior includes K r A distributed generation unit, with J outside. r There are three adjacent distributed generation units, where the superscripts l and r correspond to the left and right local network systems, respectively. The state-space models of these two local network systems are as follows:

[0139]

[0140] in, and Let represent the states of the left and right local network systems at time k, respectively, and T denote the transpose of the vector. and These represent the states of the local network system around time k+1. and For the input, output, and measurement noise of the left local network system, and These are the output vector and measurement noise of the distributed generation unit connected to the left local network system, respectively. and These represent the input, output, and measurement noise of the right local network system, respectively. and These are the output vector and measurement noise of the distributed generation unit connected to the right local network system, respectively. and It is a diagonal array. and It is a block matrix;

[0141] In this embodiment, the state x3(k) of the coupled single distributed generation unit is first estimated. In this embodiment, two local network systems are constructed, where the left local network system contains the 1st and 3rd DGUs, and the right local network system contains the 3rd and 4th DGUs. The intersection of these two local network systems is the 3rd DGU. The state space expressions of these two local network systems are given below.

[0142]

[0143] Step 2.2: Iterate the state space models of the left and right local network systems at each time step, and establish the input-output data equations of the left and right local network systems respectively;

[0144] For a left-side local network system, its input-output data equations, composed of data, are as follows:

[0145]

[0146] in, It is the left local network observability matrix. This represents the state sequence of the left local network system from time k to time k+a, where 'a' represents the horizontal length of the data. and It is the Topulitz matrix of the left local network. This represents the output vector of the left local network. The constructed future Hankel matrix, where f represents the future time window at time k, and p represents the past time window at time k. This represents the output vector y from the left local network. l The historical Hankel matrix is ​​constructed, where h represents the vertical dimension. and respectively with and Isomorphic and composed of the inputs of the left local network system at each time step Composition, that is, putting the corresponding Change to This represents the future and historical Hankel matrices formed by the input vectors of the left local network; and respectively with and Isomorphic and composed of the left local network system at each time step Composition, representing the future and historical Hankel matrices formed by the outputs of adjacent distributed generation units in the left local network; and and and Isomorphic and composed of the left local network system at each time step Composition, that is, putting the corresponding Change to This represents the future and historical Hankel matrices, which are composed of noise from adjacent distributed generation units in the left local network. and and and Isomorphic and composed of the left local network system at each time step Composition, representing the future and historical Hankel matrices formed by measurement noise in the left local network;

[0147] Similarly, for a right local network system, its input-output data equations, composed of data, are as follows:

[0148]

[0149] in, It is the observability matrix of the right local network system. This represents the state sequence of the right local network system from time k to time k+a. and It is the Topulitz matrix of the right local network system. This represents the future Hankel matrix, which is composed of the output vectors of the local network system on the right. This represents the historical Hankel matrix, which is composed of the output vectors of the right local network system. and respectively with and Isomorphic and composed of the input vectors of the right local network system at each time step Composition, representing the future and historical Hankel matrices formed by the input vectors of the right local network system. and respectively with and Isomorphic and composed of the right local network system at various time points Composition, representing the future and historical Hankel matrices formed by the output vectors of adjacent distributed generation units in the right local network system. and and and Isomorphic and composed of the right local network system at various time points Composition, representing the future and historical Hankel matrices of noise composition of adjacent distributed generation units in the right local network system. and Represents the future and historical Hankel matrices formed by measurement noise in the right local network;

[0150] In this embodiment, for the left local network system: k = 4, h = 3, a = 20. and in

[0151] For the local network system on the right: take k=4, h=3, a=20. and in

[0152] Step 2.3: Organize the Hankel matrices in the constructed input-output data equations to construct the data Hankel matrix sets for the left and right local network systems respectively;

[0153] The data Hankel matrix set is and

[0154] Step 2.4: Based on the constructed Hankel matrix set, the state sequences of the left and right local network systems are estimated using the row subspace method;

[0155] Consider a left-hand local system, keeping the first term in the input-output data equations on one side and moving the remaining terms to the other side:

[0156]

[0157] Γ l and Γ r It is full rank, therefore the state sequence The row subspace is Where Row[] represents the row subspace of the matrix; similarly, the state sequence line space Define the noise term: To obtain the state sequence In the row subspace, we need to compute the matrix. and In the left null space, define the matrix:

[0158]

[0159] And for Φ l Noise item in Part 2 Since it is unknown, the calculation in the second part can be based on the output and input corresponding to the noise term. The result is:

[0160]

[0161] Therefore, the data Hankel matrix set is constructed from the collected input and output data. Φ can be obtained l and Φ r In order to calculate and The left null space, for Φ l and Φ r Perform singular value decomposition:

[0162]

[0163] in, For matrix Φ l The first part of the left singular value matrix, For matrix Φ l The second part of the left singular value matrix contains the matrix Φ l K l The left singular vectors corresponding to the n smallest singular values, K l n is number of rows; Known as Φ l The left null space; It is a diagonal matrix; It is matrix Φ l The first part of the right singular value matrix, It is matrix Φ l The second part of the right singular value matrix; For matrix Φ r The first part of the left singular value matrix, For matrix Φ r The second part of the left singular value matrix contains the matrix Φ r K r The left singular vectors corresponding to the n smallest singular values, K r n is the number of rows, Known as Φ r The left null space; and It is a diagonal matrix; It is matrix Φ r The first part of the right singular value matrix, It is matrix Φ r The second part of the right singular value matrix;

[0164] The row space of the state sequence of the left local network system is The state sequence of the left local network system is then:

[0165]

[0166] in, and It is a block matrix, and satisfies F is a non-singular matrix F;

[0167] And because Since it is unknown, the estimated value of the state sequence of the left local network system is: Multiply both sides of (54) by F -1 Then the estimated value of the state sequence of the left local network system is Similarly, the state sequence of the right local network system is: in It is a block matrix;

[0168] In this implementation, a matrix is ​​defined as follows:

[0169]

[0170] Then, for the local data matrix Φ l and Φ rPerforming singular value decomposition, we obtain: and

[0171] Therefore, estimates of the state sequences of the two local network systems can be obtained. and

[0172] Step 2.5: Based on the intersection of the estimated values ​​of the state sequences of the left local network system and the right local network system, estimate the state of the coupled single distributed generation unit to obtain the estimated value of the state of the coupled single distributed generation unit;

[0173] Because the intersection of the state sequences of two local network systems is the state sequence x coupled to a single distributed generation unit. j =[x j (k)x j (k+1)...x j (k+a)]∈R an Therefore, the state sequence x of a single distributed generation unit is coupled. j The row subspace is Therefore, the following calculations are performed. In the left null space, define the matrix:

[0174]

[0175] in, Therefore Φ j The collected Hankel matrix can be used to calculate Φ. j Perform singular value decomposition:

[0176]

[0177] in, For matrix Φ j The first part of the left singular value matrix, For matrix Φ j The second part of the left singular value matrix contains the matrix Φ j The left singular vectors corresponding to the n smallest singular values; Known as Φ j The left null space; and It is a diagonal matrix; It is matrix Φ j The first part of the right singular value matrix, It is matrix Φ j The second part of the right singular value matrix;

[0178] The row space of the state sequence coupled to a single distributed generation unit is then: in, and For a block matrix, satisfying Then the state sequence of a single distributed generation unit is coupled:

[0179]

[0180] Among them, F j It is a non-singular matrix;

[0181] And because Since it is unknown, the estimated value of the state sequence coupled to a single distributed generation unit is: Multiply both sides of (59) by have This leads to the estimated state of the coupled individual distributed generation unit.

[0182] This implementation method is based on the Hankel matrix collected earlier and the results obtained in step 2.4. and Calculate Φ3;

[0183]

[0184] And by performing singular value decomposition on it, we can calculate Estimating the state sequence coupled to a single distributed generation unit Considering the impact of noise, satisfy in It consists of a noise sequence and is unknown. It is a non-singular matrix;

[0185] The estimated state of a single distributed generation unit coupled at time k is: for The first column, similarly, at time k+1. The estimated value is The second column, and so on. Where e3(k) is the noise term, from The value is taken from the middle, e3(k) is The first column, e3(k+1) is In the second column, e3(k+2) is The third column, and so on.

[0186] Step 3: Repeat step 2 to obtain the estimated state of all coupled individual distributed generation units corresponding to the distributed generation unit to be detected;

[0187] In this embodiment, for the second distributed generation unit, the number of adjacent coupled single distributed generation units is 2. Therefore, step 2 needs to be repeated to obtain the estimated state of the coupled single distributed generation unit.

[0188] Step 4: Based on the input and output data tuples and the estimated values ​​of the states of all coupled individual distributed generation units corresponding to the distributed generation unit to be detected, identify the system matrix in the state space model of the distributed generation unit to be detected.

[0189] Step 4.1: Substitute the estimated state of the coupled single distributed generation unit into the state space model of the distributed generation unit established in Step 1 under fault-free conditions to obtain the new state space model of the distributed generation unit under fault-free conditions and its corresponding input-output equations.

[0190] By substituting the estimated state of a single distributed generation unit into the state-space model of the distributed generation unit under fault-free conditions, a new state-space model of the distributed generation unit under fault-free conditions is obtained:

[0191] x i (k+1)=A i x i (k)+D i (h i (k)-ε i (k)) (61)

[0192] y i (k)=C i x i (k)+v i (k)

[0193] in, in This represents the noise term coupled to a single distributed generation unit.

[0194]

[0195] The corresponding input-output equations are:

[0196] y i,h (k)=Γ i,h x i (k)+H zi,h (h i,h (k)-ε i,h (k))+v i,h (k) (62)

[0197] in, This represents the sequence of output vectors from time k to time k+h. It is the observability matrix. For Topelitz matrix, This represents the time from time k to time k+h, where h is the value of time h. i The sequence formed This represents the change from time k to time k+h due to ε. i The sequence formed This represents the sequence of measurement noise from distributed generation units from time k to time k+h;

[0198] In this embodiment, the estimated value of the state of a single distributed generation unit is coupled. and Substitute the state space model of the distributed generation unit under fault-free conditions established in step 1 to obtain the new state space model of the distributed generation unit under fault-free conditions and its corresponding input-output equations.

[0199] x2(k+1)=A2x2(k)+D3(h2(k)-ε2(k)) (63)

[0200] y2(k)=Cx2(k)+v2(k)

[0201] in, in D2 represents the noise term coupled to a single distributed generation unit, where D2 = [B2 A] 21 A 23 ];

[0202] Step 4.2: Based on the input-output equations obtained in Step 4.1, construct the equations relating the output to the data in future time periods;

[0203] Suppose there exists a constant matrix ψ i So that the state at time k+h can be represented as:

[0204]

[0205] Where, x i (k+h) represents the state of the i-th distributed generation unit at time k+h;

[0206] For some future time k+h+L, there exists a future time output y. i Equation relating (k+h+L) to data:

[0207]

[0208] Where L is the time length, y i (k+h+L) is the output vector at time k+h+L, v i (k+h+L) represents the measurement noise at time k+h+L, x i(k+h+L) represents the state at time k+h+L. Let be the Markov parameter vector. It is a coefficient matrix. h represents the time from k+h to k+h+L-1. i The sequence formed ε from time k+h to time k+h+L-1 i The sequence formed;

[0209] Step 4.3: Based on the input and output data tuples obtained in Step 1.2, use the instrumental variable method to estimate the Markov parameter vector in the equation relating the output and data at future times, and obtain the estimated value of the Markov parameter vector;

[0210] Based on the input and output data tuples obtained in step 1.2, define instrumental variables. and noise variables in, h represents the time from time k to time k+h-1. i The sequence formed ε represents the time from k to k+h-1. i The resulting sequence, multiplied by (ξ) on both sides of (65) i (k)) T ,but:

[0211]

[0212] Simplifying the above formula, we get:

[0213]

[0214] Among them, T ξ,a T yi,ξ,a and They are defined as They can be calculated from the input-output vectors collected in step 1.2; using least squares estimation on equation (67), the Markov parameter vectors The estimated value is This is the pseudo-inverse of the matrix;

[0215] In this embodiment, h = 3, a = 20, L = 5, and the calculation is performed. and

[0216] in, and noise variables and Let z2 and ε2 represent the sequences formed by z2 and ε2 from time k to time k+h-1, respectively; in this invention, Tξ,a and All of these can be calculated using the input and output data collected in step 1.2, while the noise term... The calculation can also be converted into corresponding input and output data for calculation, similar to Φ. l ,Φ r The calculation of the second term in Φ2. Therefore, the Markov parameter vector. The estimated value is I is the identity matrix. This is the pseudo-inverse of the matrix;

[0217] Step 4.4: Based on the estimated values ​​of the Markov parameter vectors, use the HoKalman method to identify the system matrix A in the state-space model of the distributed generation unit under fault-free conditions. i A ij and B i ;

[0218] Based on the structure of the Markov parameter vector, the estimated values ​​of the Markov parameter vector are... Divide into L blocks, Let l1 + l2 = L-1 (l1 and l2 take values ​​in τ), which is the τ-th block term of the estimated value of the Markov parameter vector. Let τ be the block term number and τ = 0, 1, ..., L-1. The constructed Hankel matrix for Then, regarding the Hankel matrix... Perform singular value decomposition:

[0219]

[0220] in, Hankel matrix The first part of the left singular value matrix, Hankel matrix The second part of the left singular value matrix, It is a diagonal matrix. Hankel matrix The first part of the right singular value matrix, Hankel matrix The second part of the right singular value matrix;

[0221] According to the Ho-Kalman method, the system matrix estimate in the state-space model of the distributed generation unit under fault conditions is:

[0222]

[0223] in, For system matrix A iThe estimated value, For matrix D i The estimated value, based on The system matrix A is obtained. ij and B i The estimated value, For matrix The pseudo-inverse matrix, For matrix From row (n+1) to row (l1+1)n, Representation matrix The (l2n+1)th column to the ((l2+1)n)th column, Representation matrix Lines 1 to l1n;

[0224] In this embodiment, the estimated value of the Markov parameter vector is used. The HoKalman method is used to identify the system matrix A2,A in the state-space model of the distributed generation unit under fault-free conditions. 23 A 24 B2;

[0225] The estimated Markov parameter vector Divided into 5 parts, respectively in Represented by matrix The matrix formed by columns 25 to 30, Represented by matrix The matrix formed by columns 19 to 24 is similar. Also by The matrix is ​​constructed from the corresponding column numbers in the matrix, and then these five matrices are combined to form... Then, singular value decomposition is performed on it to obtain

[0226] Step 5: Based on the system matrix in the state-space model of the distributed generation unit to be detected when there are no faults, design an unknown input observer;

[0227] Step 5.1: Based on the system matrix in the state-space model of the distributed generation unit to be detected when there are no faults, construct the expression for the unknown input observer;

[0228] First, the state sequences of all coupled individual distributed generation units are treated as unknown input d. i (k), and then the system matrix identified in step 4 is substituted into the state space model (2) of the distributed generation unit under fault conditions to obtain:

[0229]

[0230] in, It is a state sequence coupled with a single distributed generation unit. For the system matrix;

[0231] To achieve fault detection, an unknown input observer of the distributed generation unit is designed in the following form:

[0232]

[0233] Among them, z i (k+1) and z i (k) represent the states of the unknown input observer of the i-th distributed generation unit at time k+1 and time k, respectively, T i ,F i ,K i and H i Here is the observer parameter matrix to be designed, and it satisfies the following equation:

[0234]

[0235] Among them, H i,1 and H i,2 It is the coefficient matrix in the unknown input observer;

[0236] In this embodiment, to achieve fault detection of the second distributed generation unit, an unknown input observer is designed for fault detection. First, all unknown states coupled to a single distributed generation unit are regarded as unknown inputs d. i (k), and then the system matrix identified in step 4 is substituted into the state-space model of the fault-prone distributed generation unit (DGU). Then the state-space model of the fault-prone distributed generation unit (DGU) is equivalent to the following state equation:

[0237]

[0238] in, The states of the 3rd and 4th distributed generation units are considered as unknown inputs. The system matrix has been estimated in the previous step. In this example, the fault signal is considered to be designed as follows: And it occurs between 200 and 400 seconds.

[0239] Step 5.2: Solve for the parameter matrix in the unknown input observer so that the designed unknown input observer satisfies the sensitivity performance H_ and robustness performance H_. ∞ ;

[0240] Based on the unknown input observer (71), the estimation error equation and residual equation can be obtained as follows:

[0241]

[0242] Where, r i (k) represents the residual. Let e ​​be the estimation error at time k+1. i (k) represents the estimation error at time k. Let H_k be the estimated state at time k+1. By introducing sensitivity performance and robustness performance indices, the designed unknown input observer satisfies the sensitivity performance H_k and robustness performance H_k. ∞ ;

[0243] When the initial state of the estimation error is zero, the residual r i (k) For the fault signal f i (k) It has sensitivity, that is, it satisfies the sensitivity energy: Where, β i For sensitivity performance indicators;

[0244] When the initial state of the estimation error is zero, the residual r i (k) Measurement noise v i (k) It is robust, that is, it satisfies the robustness property H. ∞ : Where, λ i Robust performance metrics;

[0245] First, given the robustness performance index λ i Solving for the parameter matrix of an unknown input observer can be transformed into solving the following optimization problem:

[0246]

[0247] Where V i U i Z i P i,1 P i,2 and Q i Let I be the matrix to be solved, i.e., the decision variable in the optimization problem. * denotes a symmetric term in the matrix, and I is the identity matrix. He{X} denotes matrix X plus the transpose of matrix X, ξ i,1 and θ l It is a constant given in advance. It is the pseudo-inverse of the matrix. L i It is a pre-given matrix. ξ i,2 It is a constant given in advance.

[0248] Then Q is obtained by solving the linear matrix inequality (72). i V i U i ,because The parameter matrix of the unknown input observer is then calculated as follows:

[0249] In this embodiment, the robust performance index λ2 = 2.2 is given, and ξ is taken as... 2,1 =ξ 2,2 =0.12, θ l =π and Solve the following linear matrix inequalities:

[0250]

[0251] Where V2, U2, Z2, P 2,1 P 2,2 Q2 and I are the matrices to be solved, where I is the identity matrix. The solution is obtained from the linear matrix inequality. The sensitivity performance index β² = 4.3855, therefore the parameter matrix of the unknown input observer is calculated as follows:

[0252] Step 6: Based on the unknown input observer obtained in Step 5, design a residual generator and use the residual generator to obtain the residual signal;

[0253] Residual generator:

[0254]

[0255] The residual generator in this embodiment:

[0256]

[0257] in, It is the state of the second distributed generation unit estimated by the unknown input observer;

[0258] Step 7: Calculate the average energy of the residual signal over a period of time and compare it with the set detection threshold to achieve fault detection;

[0259] The residual signal in (k0, k η Average energy over the time period:

[0260]

[0261] Where k0 represents the initial evaluation time, kη Indicates the evaluation termination time, where η is the time length between the evaluation termination time and the initial evaluation time; the detection threshold is calculated as follows: The alarm rules are as follows:

[0262]

[0263] Figure 3 The fault signal is designed as In the event of a failure in the actuator of the second distributed generation unit, the evaluation function curve generated by the proposed method shows that the fault signal, being artificially designed, may be very weak. However, the detector designed in this invention, which considers both sensitivity and robustness performance indicators, can still successfully detect the fault signal when a fault occurs.

Claims

1. A data-driven fault detection method for DC microgrids, characterized in that, Includes the following steps: Step 1: Construct the state-space model of the distributed generation unit in the DC microgrid and collect the input and output data tuples of each distributed generation unit; Step 2: Using the row subspace method, identify the state of each coupled individual distributed generation unit and obtain an estimate of the state of each coupled individual distributed generation unit; the coupled individual distributed generation unit is the distributed generation unit adjacent to the distributed generation unit to be detected. Step 3: Repeat step 2 to obtain the estimated state of all coupled individual distributed generation units corresponding to the distributed generation unit to be detected; Step 4: Based on the input and output data tuples and the estimated values ​​of the states of all coupled individual distributed generation units corresponding to the distributed generation unit to be detected, identify the system matrix in the state space model of the distributed generation unit to be detected when there is no fault. Step 5: Based on the system matrix in the state-space model of the distributed generation unit to be detected when there are no faults, design an unknown input observer; Step 5 specifically includes: Step 5.1: Based on the system matrix in the state-space model of the distributed generation unit to be detected when there are no faults, construct the expression for the unknown input observer; First, the state sequences of all coupled individual distributed generation units are treated as unknown input d. i (k), and then the system matrix identified in step 4 is substituted into the state-space model of the distributed generation unit under fault conditions to obtain: y i (k)=C i x i (k)+v i (k), Where, x i (k)∈R n Let x represent the state of the i-th distributed generation unit at the current moment, where i is the unit number, k is the current transient time, n is the dimension of the distributed generation unit's state, and x is the number of distributed generation units. i (k)=[V i (k) I i (k)] T V i (k) represents the voltage at the load of the i-th distributed generation unit at the current time; I i (k) represents the current generated by the i-th distributed generation unit at the current moment; and Let C be the unknown system matrix of the i-th distributed generation unit, representing the interaction between the i-th distributed generation unit and its neighboring distributed generation units; ti R is the parallel capacitor of the i-th distributed generation unit. ij For the power line conductivity, L ti Let R be the inductance of the filter for the i-th distributed generation unit. ti Let C be the resistance of the filter in the i-th distributed generation unit, and j be the number of the distributed generation unit adjacent to the i-th distributed generation unit; i =I is the identity matrix, For system matrix A i The estimated value; f i (k)∈R m Let y be the actuator fault vector of the i-th distributed generation unit, m be the dimension of the input vector of the i-th distributed generation unit, and y be the value of the input vector of the i-th distributed generation unit. i (k)∈R n Let v be the output vector of the i-th distributed generation unit. i (k)∈R n Let represent the measured noise of the i-th distributed generation unit. It is a state sequence coupled with a single distributed generation unit. Let N be the system matrix. i It is the set of distributed generation units adjacent to the i-th distributed generation unit; Design an unknown input observer of the following form for distributed generation units: Among them, z i (k+1) and z i (k) represents the state of the unknown input observer of the i-th distributed generation unit at time k+1 and time k, respectively. i (k)∈R m Let u be the input vector of the i-th distributed generation unit. i (k)=[V ti (k)I Li (k)] T V ti (k) represents the control command for the converter of the i-th distributed generation unit at the current time, I Li (k) represents the current required by the i-th distributed generation unit at the current moment; T is the estimated state at time k. i ,F i ,K i and H i Let be the observer parameter matrix to be designed, and satisfy the following equation: Where I is the identity matrix, H i,1 and H i,2 It is the coefficient matrix in the unknown input observer; Step 5.2: Solve for the parameter matrix in the unknown input observer so that the designed unknown input observer satisfies the sensitivity performance H_ and robustness performance H_. ∞ ; Based on the unknown input observer (23), the estimation error equation and residual equation can be obtained as follows: e i (k+1)=T i e i (k)+F i B i f i (k)-(K i +H i,1 )v i (k) (25) r i (k)=C i e i (k)+v i (k) Where, r i (k) represents the residual. Let e ​​be the estimation error at time k+1. i (k) represents the estimation error at time k. Let H_k be the estimated state at time k+1. By introducing sensitivity performance and robustness performance indices, the designed unknown input observer satisfies the sensitivity performance H_k and robustness performance H_k. ∞ ; When the initial state of the estimation error is zero, the residual r i (k) For the fault signal f i (k) It has sensitivity, that is, it satisfies the sensitivity energy: Where β i For sensitivity performance indicators; When the initial state of the estimation error is zero, the residual r i (k) Measurement noise v i (k) It is robust, that is, it satisfies the robustness property H. ∞ : Where, λ i Robust performance metrics; First, given the robustness performance index λ i Solving for the parameter matrix of an unknown input observer can be transformed into solving the following optimization problem: Where V i U i Z i P i,1 P i,2 and Q i Let * represent the matrix to be solved, i.e., the decision variables in the optimization problem. The asterisk (*) indicates a symmetric term in the matrix. ξ represents matrix X plus the transpose of matrix X. i,1 and θ l It is a constant given in advance. This is the pseudo-inverse of the matrix; L i It is a pre-given matrix. ξ i,2 It is a constant given in advance. Then Q is obtained by solving the linear matrix inequality (26). i V i U i ,because The parameter matrix of the unknown input observer is then calculated as follows: H i,2 =T i K i H i =H i,1 +H i,2 ; Step 6: Based on the unknown input observer obtained in Step 5, design a residual generator and use the residual generator to obtain the residual signal; Step 7: Calculate the average energy of the residual signal over a period of time and compare it with the set detection threshold to achieve fault detection.

2. The data-driven DC microgrid fault detection method according to claim 1, characterized in that, Step 1 specifically includes: Step 1.1: Construct the state-space model of the distributed generation unit in the DC microgrid, including the state-space model of the distributed generation unit under fault conditions and without fault conditions; the fault is an actuator fault; The state-space model of the i-th distributed generation unit when there are no faults is as follows: Where N represents the number of distributed generation units, |N i | represents the number of distributed generation units adjacent to the i-th distributed generation unit, x j (k) represents the state of the distributed generation unit adjacent to the i-th distributed generation unit, denoted as the state of a single coupled distributed generation unit; The state-space model of the i-th distributed generation unit when there is an actuator failure is as follows: Step 1.2: Run each distributed generation unit in the DC microgrid, and under the set excitation conditions, collect the input and output data tuples of each distributed generation unit; the input and output data tuples include the output vectors and input vectors of all distributed generation units at different times.

3. The data-driven DC microgrid fault detection method according to claim 2, characterized in that, Step 2 specifically includes: Step 2.1: Establish two local network systems and construct state-space models for each system. Both local network systems are sub-networks of a DC microgrid. Each local network system includes several distributed generation units (DG units), and there are also several adjacent DG units externally. The intersection of the two local network systems is the desired coupled single DG unit. The two local network systems are referred to as the left local network system and the right local network system, respectively, and are denoted as Σ. left and Σ right Their state-space models are as follows: In this context, the superscripts l and r refer to the left local network system and the right local network system, respectively. and These represent the states of the left local network system at times k and k+1, respectively. and Let K and K+1 represent the states of the right local network system, respectively. and These are the inputs for the left and right local network systems, respectively. and These are the outputs of the left and right local network systems, respectively. and The measurement noise of the left and right local network systems are respectively. and These are the output and measured noise of the distributed generation unit connected to the left local network system, respectively. and These are the output and measured noise of the distributed generation unit connected to the right local network system, respectively. and It is a block matrix; Step 2.2: Iterate the state space models of the left local network system and the right local network system at each time step, and establish the input-output data equations of the left local network system and the right local network system respectively; For the left local network system and the right local network system, their input-output data equations are as follows: Where the subscripts f and p refer to the future and past time windows at time k, respectively, and Γ l and Γ r These are the observability matrices of the left and right local network systems, respectively. and These represent the state sequences of the left and right local network systems, respectively. and It is the Topulitz matrix of the left local network system. and It is the Topulitz matrix of the right local network system. and These represent the outputs of the left and right local network systems, respectively. and The future Hankel matrix is ​​constructed. and These represent the outputs of the left and right local network systems, respectively. and The historical Hankel matrix is ​​constructed. and This represents the future and historical Hankel matrices formed by the inputs of the left local network system. and This represents the future and historical Hankel matrices constructed from the inputs of the right local network system. and This represents the future and historical Hankel matrix, which consists of the outputs of adjacent distributed generation units in the left local network system. and This represents the future and historical Hankel matrices, which are composed of noise from adjacent distributed generation units in the left local network system. and This represents the future and historical Hankel matrices formed by measurement noise in the left local network system. and This represents the future and historical Hankel matrices formed by the outputs of adjacent distributed generation units in the right local network system. and This represents the future and historical Hankel matrices representing the noise composition of adjacent distributed generation units in a right-hand local network system. and Represents the future and historical Hankel matrices formed by measurement noise in the right local network system; Step 2.3: Organize the Hankel matrices in the constructed input-output data equations to construct the data Hankel matrix sets for the left local network system and the right local network system, respectively; The data Hankel matrix sets of the left and right local network systems are as follows: and Step 2.4: Based on the constructed Hankel matrix set, the state sequences of the left and right local network systems are estimated using the row subspace method; Γ l and Γ r It is full rank, therefore the state sequence and The row subspaces are respectively and Where Row[] represents the row subspace of the matrix; define the noise term: Define matrix: The second part of (7) and (8) is the noise term, which is derived from the collected Hankel matrix data set. and Calculated; For Φ l and Φ r Perform singular value decomposition: in, For matrix Φ l The first part of the left singular value matrix, For matrix Φ l The second part of the left singular value matrix, and It is a block matrix; Known as Φ l The left null space; and It is a diagonal matrix; (V1) l ) T It is matrix Φ l The first part of the right singular value matrix, It is matrix Φ l The second part of the right singular value matrix; For matrix Φ r The first part of the left singular value matrix, For matrix Φ r The second part of the left singular value matrix, Known as Φ r The left null space; and It is a diagonal matrix; (V1) r ) T It is matrix Φ r The first part of the right singular value matrix, It is matrix Φ r The second part of the right singular value matrix; The row space of the state sequence of the left local network system is The state sequence of the left local network system is then: Where F is a non-singular matrix; and because Since it is unknown, the estimated value of the state sequence of the left local network system is: Multiply both sides of (10) by F -1 Then the estimated value of the state sequence of the left local network system is Similarly, the state sequence of the right local network system is: in It is a block matrix; Step 2.5: Based on the intersection of the estimated values ​​of the state sequences of the left local network system and the right local network system, estimate the state of the coupled single distributed generation unit to obtain the estimated value of the state of the coupled single distributed generation unit; Because the intersection of the state sequences of two local network systems is the state sequence x coupled to a single distributed generation unit. j =[x j (k)x j (k+1)...x j (k+a)]∈R an Therefore, the state sequence x of a single distributed generation unit is coupled. j The row subspace is Define matrix: The second part of (11) is the noise term, which is derived from the collected Hankel matrix data set. and Calculated, and then applied to Φ j Perform singular value decomposition: in, For matrix Φ j The first part of the left singular value matrix, For matrix Φ j The second part of the left singular value matrix; Known as Φ j The left null space; and It is a diagonal matrix; (V1) j ) T It is matrix Φ j The first part of the right singular value matrix, It is matrix Φ j The second part of the right singular value matrix; The row space of the state sequence coupled to a single distributed generation unit is then: in, and If it is a block matrix, then the state sequence of a single distributed generation unit is coupled as follows: Among them, F j It is a non-singular matrix; and because Since it is unknown, the estimated value of the state sequence coupled to a single distributed generation unit is: Multiply both sides of (13) by have This leads to the estimated state of the coupled individual distributed generation unit. Where e j (k) represents the noise term, from... Take the value from, e j (k) is The first column.

4. The data-driven DC microgrid fault detection method according to claim 3, characterized in that, Step 3 specifically includes: The estimated value of the state sequence of all coupled individual distributed generation units corresponding to the distributed generation unit to be detected is denoted as: For the i-th distributed generation unit, the number of adjacent coupled single distributed generation units is |N i | Then step 2 needs to be repeated for a total of |N. i |times.

5. The data-driven DC microgrid fault detection method according to claim 4, characterized in that, Step 4 specifically includes: Step 4.1: Substitute the estimated state of the coupled single distributed generation unit into the state space model of the distributed generation unit established in Step 1 under fault-free conditions to obtain the new state space model of the distributed generation unit under fault-free conditions and its corresponding input-output equations. By substituting the estimated state of a single distributed generation unit into the state-space model of the distributed generation unit under fault-free conditions, a new state-space model of the distributed generation unit under fault-free conditions is obtained: x i (k+1)=A i x i (k)+D i (h i (k)-ε i (k)) (14) y i (k)=C i x i (k)+v i (k) in, in This represents the noise term coupled to a single distributed generation unit. Therefore, the corresponding input-output equation is: Among them, y i,h (k), v i,h (k), h i,h (k) and ε i,h (k) represents y from time k to time k+h. i v i h i and ε i The sequence formed, Γ i,h It is the observability matrix, H zi,h The Toplitz matrix; Step 4.2: Based on the input-output equations obtained in Step 4.1, construct the equations relating the output to the data in future time periods; Suppose there exists a constant matrix ψ i This makes the state x at time k+h... i (k+h) is represented as: For some future time k+h+L, there exists a future time output y. i Equation relating (k+h+L) to data: Where L is the time length, x i (k+h+L), y i (k+h+L) and v i (k+h+L) represent the state, output vector, and measurement noise at time k+h+L, respectively. Let be the Markov parameter vector. It is a coefficient matrix. h represents the time from k+h to k+h+L-1. i The sequence formed ε from time k+h to time k+h+L-1 i The sequence formed; Step 4.3: Based on the input and output data tuples obtained in Step 1.2, use the instrumental variable method to estimate the Markov parameter vector in the equation relating the output and data at future times, and obtain the estimated value of the Markov parameter vector; Based on the input and output data tuples obtained in step 1.2, define instrumental variables. and noise variables in, h represents the time from time k to time k+h-1. i The sequence formed ε represents the time from k to k+h-1. i The sequence is formed by multiplying both sides of (17) by (ξ). i (k)) T ,but: Simplifying the above formula, we get: Among them, T ξ,a , and They are defined as Applying least squares estimation to equation (19), the Markov parameter vector The estimated value is Step 4.4: Based on the estimated values ​​of the Markov parameter vectors, use the HoKalman method to identify the system matrix A in the state-space model of the distributed generation unit under fault-free conditions. i A ij and B i ; Based on the structure of the Markov parameter vector, the estimated values ​​of the Markov parameter vector are... Divide into L blocks, Let l1 + l2 = L-1 be the τ-th block term of the Markov parameter vector estimate, where τ is the block term number and τ = 0, 1, ..., L-1. Then, let l1 + l2 = L-1. From the block terms of the Markov parameter vector... The constructed Hankel matrix for Hankel matrix Perform singular value decomposition: in, Hankel matrix The first part of the left singular value matrix, Hankel matrix The second part of the left singular value matrix, and It is a diagonal matrix. Hankel matrix The first part of the right singular value matrix, Hankel matrix The second part of the right singular value matrix; According to the Ho-Kalman method, the system matrix estimate in the state-space model of the distributed generation unit under fault-free conditions is: in, For matrix D i The estimated value, based on The system matrix A is obtained. ij and B i The estimated value, For matrix The pseudo-inverse matrix, For matrix From row (n+1) to row (l1+1)n, Representation matrix The (l2n+1)th column to the ((l2+1)n)th column, Representation matrix Lines 1 to l1n.

6. The data-driven DC microgrid fault detection method according to claim 1, characterized in that, Step 6 specifically includes: Based on (24), the residual generator is obtained:

7. The data-driven DC microgrid fault detection method according to claim 6, characterized in that, Step 7 specifically includes: The residual signal in (k0, k η The average energy J over the time period r,i (η) is: Where k0 represents the initial evaluation time, k η Indicates the evaluation termination time, where η is the time length between the evaluation termination time and the initial evaluation time; the detection threshold is defined as: Here, sup represents the supremum; therefore, the alarm rule is:

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