Direct-current micro-grid fault diagnosis method based on reduced-order unknown input observer

Abstract

The invention discloses a DC micro-grid fault diagnosis method based on a reduced-order unknown input observer. The method comprises the following steps: S1, calculating a state transition matrix, a control matrix, an observation matrix and a control input observation matrix of a state space model of each converter and line; s2, voltage and current of the alternating current side and the direct current side of each converter and interelectrode voltage and current at the two ends of a line are collected, and input quantity and output quantity of the state space model of each converter and the line are calculated; s3, calculating a state transition matrix, a control matrix, an observation matrix and a control input observation matrix of the state space model during steady-state operation of the direct-current micro-grid system; s4, calculating a direct current micro-grid system fault component matrix; s5, designing a sensitivity matrix; s6, stabilizing the reduced-order unknown input observer; s7, calculating a normalized residual error output by the observer; and S8, calculating a fault reconstruction error, and judging a fault sequence number. According to the method, whether the fault occurs in the DC micro-grid can be rapidly detected, and the method has important practical significance on rapid isolation of the fault and guarantee of safe and stable operation of the system.

Description

Technical Field

[0001] The present invention belongs to the field of power systems, relates to the technical field of relay protection of direct current microgrids, and specifically to a direct current microgrid fault diagnosis method based on linear variable parameters and reduced-order unknown input observers. Background Art

[0002] DC microgrids have been developing continuously in recent years, breaking through their technical bottlenecks and being widely used in industrial parks, data centers, ship systems and other fields. DC microgrids have introduced a new power system structure, and the access of a large number of distributed power sources, energy storage and loads has given them new operating characteristics. As one of the effective means to solve the problems of new energy grid connection and consumption, DC microgrids are of great significance to promoting energy conservation and emission reduction and achieving sustainable energy development.

[0003] However, since DC microgrids contain more power electronic commutation links, the topology and fault types are relatively complex, the system inertia is low, the fault current develops rapidly, and the equipment has poor overcurrent tolerance, etc., these factors have put forward higher requirements for fault diagnosis of DC microgrids and restricted the further development of DC microgrids. Therefore, it is of great practical application value to study advanced, efficient, reliable and economical protection schemes.

[0004] Since the distance between nodes in a DC microgrid is short, usually only hundreds of meters to thousands of meters, the fault characteristics are complex and easily affected by measurement errors and disturbances. In this application scenario, the communication cost of the DC microgrid is greatly reduced. The longitudinal or centralized protection based on multi-point measurement information avoids the separate design of multiple protection functions in different protection zones, can cover various faults in the DC microgrid, and reduces the measurement and calculation costs. It has greater advantages than the traditional distributed local protection method. Among them, the observer-based method is one of the most effective methods. However, for the more complex DC microgrid in reality, the model order of the system is higher. The increase in the order of the system will greatly increase the computational complexity and pose a challenge to the speed of protection. In addition, for the case where the state space model contains variable parameters due to the action of the controller, the traditional observer-based method cannot be directly applied. Therefore, it is urgent to propose a DC microgrid protection principle that can reduce the order of the system and is applicable to the variable parameter system. Summary of the invention

[0005] In order to solve the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a DC microgrid fault diagnosis method based on a reduced-order unknown input observer, which uses less measurement volume and saves a lot of measurement costs; for the problem that the traditional observer method is not applicable due to the presence of variable parameters, a linear variable parameter model is adopted to realize fast and accurate diagnosis of faults; a reduced-order unknown input observer method is adopted to decouple the unknown input while reducing the order of the model, thereby realizing the distinction of faults.

[0006] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] The DC microgrid fault diagnosis method based on reduced-order unknown input observer includes the following steps:

[0008] Step 1: Calculate the state transfer matrix, control matrix, observation matrix and control input observation matrix of the state space model of each converter and line;

[0009] Determine the number of converters in the DC microgrid system as N vsc , the number of buses is N bus ; The number of bipolar lines is N cable ;

[0010] Collect the amplitude and phase shift angle of the modulation wave of each converter, and calculate the d-axis control quantity of each converter according to formula (1): and q-axis control amount

[0011]

[0012] In the formula, k vsc is the inverter serial number, is the amplitude of the modulated wave, is the phase shift angle of the modulated wave;

[0013] According to formula (2), calculate the kth vsc The state transfer matrix of the converter Control Matrix Observation Matrix and the control input observation matrix

[0014]

[0015] Where ω is the angular frequency of the DC microgrid system, For the kth vsc The equivalent resistance of the transformer and line loss at the AC outlet side of each converter, For the kth vsc The commutation reactance on the AC outlet side of each converter is: For the kth vsc The DC output side capacitor of the converter, is the equivalent resistance of the busbar short circuit at the DC outlet side of the converter, I is the unit matrix, and O is the zero matrix;

[0016] According to formula (3), calculate the kth cable The state transition matrix of the lines Control Matrix Observation Matrix and the control input observation matrix

[0017]

[0018] In the formula, k cable is the line number, a represents the first section of the line, b represents the last section of the line, is the short-circuit resistance of a bipolar short-circuit fault somewhere in the line, They represent the resistance and inductance of the single-pole line from the first section of the line to the short-circuit fault point, They represent the resistance and inductance of the single-pole line from the point where the short-circuit fault occurs to the end of the line;

[0019] Step 2: Collect the voltage and current on the AC side and DC side of each converter and the pole-to-pole voltage and current at both ends of the line, and calculate the input and output of the state space model of each converter and line;

[0020] According to formula (4), the d-axis and q-axis voltages and d-axis and q-axis currents on the AC outlet side of the converter are calculated:

[0021]

[0022] Among them, Z a,b,c Represent the three-phase voltage u and three-phase current i, Z d,q,0 represents the d, q, and 0-axis voltages and currents after Parker transformation;

[0023] According to formula (5), calculate the kth vsc Input quantity of each converter and output

[0024]

[0025] In the formula, is the current at the DC output side of the converter, For the kth vsc The DC side voltage of each converter;

[0026] According to formula (6), calculate the kth cable Input quantity of lines and output

[0027]

[0028] In the formula, and Represents the kth cable The line voltage at the beginning and end of the DC line, and Represents the kthcable The current flowing into and out of the first section of the line;

[0029] Step 3: Calculate the state transfer matrix, control matrix, observation matrix and control input observation matrix of the state space model of the DC microgrid system during steady-state operation;

[0030] According to formula (7), the state quantity x, input quantity u and output quantity y of the DC microgrid system are defined as:

[0031]

[0032] According to formula (8), define the input quantity set u a , output set y b ,

[0033]

[0034] According to formula (9), combined with the topological node relationship of the DC microgrid system, symbolic operations are performed to calculate the connection matrix L 11 , L 12 , L 21 and L 22 :

[0035]

[0036] According to formula (10), the block diagonal state transfer matrix A of the DC microgrid system is calculated: diag , block diagonal control matrix B diag , block diagonal observation matrix C diag and block diagonal control input observation matrix D diag :

[0037]

[0038] According to formula (11), the state transfer matrix A, control matrix B, observation matrix C and control input observation matrix D of the state space model of the DC microgrid system in steady-state operation are calculated.

[0039]

[0040] Step 4: Calculate the fault component matrix of the DC microgrid system;

[0041] According to formula (12), the total number of possible faults n in the DC microgrid system is calculated;

[0042] n=N vsc +N cable +N bus (12)

[0043] According to formula (13), calculate the kthvsc The fault component matrix of the converter with internal fault

[0044]

[0045] According to formula (14), calculate k cable Fault component matrix of a line with a bipolar short circuit fault

[0046]

[0047] According to formula (15), calculate k bus Fault component matrix of a busbar with bipolar short circuit fault

[0048]

[0049] According to formula (16), the fault component matrix E of the DC microgrid system is calculated f ,

[0050]

[0051] Step 5: Design sensitivity matrix;

[0052] According to formula (17), the required number of observers m is calculated:

[0053]

[0054] in, Indicates rounding down;

[0055] The sensitivity matrix S has an order of n×m, and each row is designed to be a different m-bit binary number that cannot be zero and must satisfy the nNth sensitivity matrix. vsc +k vsc Row equals k vsc At least one 1 in the row is changed to a 0 value;

[0056] According to formula (18), according to the row number of 1 in each column of the sensitivity matrix S, the fault component matrix E is selected f The corresponding columns of the block matrix are composed of matrix Depend on Linearly independent columns are constructed as follows:

[0057]

[0058] Among them, k m represents the observer number, is a reversible matrix, not unique;

[0059] Step 6: Stabilize the reduced-order unknown input observer;

[0060] According to formula (19), the variable d-axis control quantity in the state transfer matrix A is and q-axis control amount Substitute the maximum value of the corresponding variable or minimum value Calculate the polytope vertex matrix A k ,

[0061]

[0062] Among them, k is the serial number of the polytope vertex matrix, is the total number of polytope vertex matrices, and The parameters are The upper and lower limits of and Respective parameters The upper and lower limits of

[0063] According to formula (20), calculate the polytope vertex matrix A k The corresponding weight μ k :

[0064]

[0065] According to formula (21), define the kth m The state estimator of a reduced-order observer and the output estimator

[0066]

[0067] Where k represents the number of the polytope vertex. Superscript + denotes Moore-Penrose pseudoinverse, with superscript ⊥ represents orthogonality, For the kth m The gain matrix of the k-th polytope vertex of the observer needs to be designed with a negative eigenvalue real part using the pole placement method;

[0068] Step 7: Calculate the normalized residual of the observer output;

[0069] According to formula (22), the residual error of the observer is calculated

[0070]

[0071] According to formula (23), the residual modulus of the observer output is calculated

[0072]

[0073] The protection activation criterion of the DC microgrid system is shown in formula (24):

[0074]

[0075] in, is the upper limit of the residual threshold of each observer in the case of no fault;

[0076] According to formula (25), the normalized residual of the observer output is calculated

[0077]

[0078] Step 8: Calculate the fault reconstruction error and identify the fault sequence number that occurred;

[0079] According to formula (26), the reconstruction error of each fault is calculated

[0080]

[0081] Among them, k n Indicates the fault sequence number. Represents the kth value in the sensitivity matrix n Row k m Column data;

[0082] Reconstruction error at all faults Find the minimum value k in n,min , k n,min Corresponding to the fault sequence number, the DC microgrid fault diagnosis is realized.

[0083] Variable d-axis control quantity in the state transfer matrix A and q-axis control amount The maximum or minimum value of is:

[0084]

[0085] Compared with the prior art, the present invention has the following advantages:

[0086] (1) The present invention avoids the separate design of each protection section in the DC microgrid through the unified design of the fault diagnosis method, uses less measurement quantity, and saves a lot of measurement cost compared with the distributed observer method;

[0087] (2) For the more complex DC microgrid in practice, the model order of the system is relatively high. The increase of the system order will greatly increase the computational complexity. By adopting the method of reduced-order unknown input observer, the system order can be significantly reduced, saving a lot of computational cost.

[0088] (3) The reconstruction error is generated by the normalized residual output of each observer to diagnose multiple faults. The unknown input observer method is used to decouple the unknown input, so that the observer shows different sensitivities to different faults, thus achieving fault differentiation.

[0089] (4) The method of the present invention does not rely on specific components or structures to perform fault diagnosis and has good versatility.

[0090] In summary, the present invention can quickly isolate various faults occurring in a DC microgrid, which has important practical significance for ensuring the safe and stable operation of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 The present invention is a topological diagram of a DC microgrid system suitable for the method of the present invention.

[0092] Figure 2 is a flow chart of the method of the present invention.

[0093] FIG. 3( a ) is a waveform of a modulation wave amplitude M1 of the inverter 1 .

[0094] FIG3( b ) is a waveform of the modulation wave amplitude M2 ​​of the inverter 2 .

[0095] FIG3( c ) is a waveform of the modulation phase shift angle δ1 of the inverter 1 .

[0096] FIG3(d) is a waveform of the modulation phase shift angle δ2 of the inverter 2. ...

[0097] FIG. 4( a ) is a diagram showing the d-axis control variable d of the converter 1. d1 waveform.

[0098] FIG. 4( b ) is a diagram showing the d-axis control amount d of the converter 2. d2 waveform.

[0099] FIG. 4( c ) is a diagram showing the q-axis control amount d of the converter 1. q1 waveform.

[0100] FIG. 4( d ) is a graph showing the q-axis control amount d of the converter 2. q2 waveform.

[0101] Figure 5(a) is the input quantity u of converter 1 VSC,1 Medium weight d1 waveform.

[0102] Figure 5(b) is the input quantity u of converter 1 VSC,1 Medium weight q1 waveform.

[0103] Figure 5(c) is the input quantity u of converter 1 VSC,1 Medium weight dc1 waveform.

[0104] Figure 5(d) is the output y of converter 1 VSC,1 Medium weight d1 waveform.

[0105] Figure 5(e) is the output y of converter 1 VSC,1 Medium weight q1 Figure 5(f) is the waveform of the output y of converter 1. VSC,1 Medium weight dc1 waveform.

[0106] Figure 5(g) is the input quantity u of converter 2 VSC,2 Medium weight d2 waveform.

[0107] Figure 5(h) is the input quantity u of converter 2 VSC,2 Medium weight q2 waveform.

[0108] Figure 5(i) is the input quantity u of converter 2 VSC,2 Medium weight dc2 waveform.

[0109] Figure 5(j) is the output y of converter 2 VSC,2 Medium weight d2 waveform.

[0110] Figure 5(k) is the output y of converter 2 VSC,2 Medium weight q2 waveform.

[0111] Figure 5(l) is the output y of converter 2 VSC,2 Medium weight dc2 waveform.

[0112] Figure 6(a) is the input quantity u of line 1 cable,1 Medium weight a1 Figure 6(b) is the input quantity u of line 1 cable,1 Medium weight b1 Figure 6(c) is the output y of line 1 cable,1 Medium weight a1 Waveform.

[0113] Figure 6(d) is the output y of line 1 cable,1 Medium weight b1Waveform.

[0114] FIG7( a ) is the output waveform of the weight μ1 corresponding to the vertex 1 of the polytope.

[0115] FIG7( b ) is the output waveform of the weight μ2 corresponding to the vertex 2 of the polytope.

[0116] FIG7( c ) is the output waveform of weight μ3 corresponding to vertex 3 of the polytope.

[0117] FIG7( d ) is the output waveform of the weight μ4 corresponding to the vertex 4 of the polyhedron.

[0118] FIG7( e ) is the output waveform of weight μ5 corresponding to vertex 5 of the polytope.

[0119] FIG7( f ) is the output waveform of weight μ6 corresponding to polytope vertex 6. ...

[0120] FIG7( g ) is the output waveform of weight μ7 corresponding to polytope vertex 7 .

[0121] FIG7( h ) is the output waveform of the weight μ8 corresponding to the vertex 8 of the polyhedron.

[0122] FIG7( i ) is the output waveform of the weight μ9 corresponding to the polytope vertex 9 .

[0123] Figure 7(j) shows the weight μ corresponding to the polytope vertex 10 10 Output waveform.

[0124] Figure 7(k) is the weight μ corresponding to the polytope vertex 11 11 Output waveform.

[0125] Figure 7(l) is the weight μ corresponding to the polytope vertex 12 12 Output waveform.

[0126] Figure 7(m) is the weight μ corresponding to the polytope vertex 13 13 Output waveform.

[0127] Figure 7(n) is the weight μ corresponding to the polytope vertex 14 14 Output waveform.

[0128] Figure 7(o) shows the weight μ corresponding to the polytope vertex 15 15 Output waveform.

[0129] Figure 7(p) shows the weight μ corresponding to the polytope vertex 16 16 Output waveform.

[0130] Figure 8(a) is the normalized result of the output residual of observer 1.

[0131] FIG8( b ) is the normalized result of the output residual of observer 2.

[0132] FIG8( c ) is the normalized result of the residual output of observer 3. DETAILED DESCRIPTION

[0134] The present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0135] like Figure 1 As shown, at 0.2ms, an IGBT open circuit fault (represented as fault F) occurs inside the converter VSC1.

[0136] The DC microgrid fault diagnosis method based on reduced-order unknown input observer is as follows: Figure 2 As shown, the following steps are included:

[0137] Step 1: Determine the number of voltage source converters N in the DC microgrid system vsc , the number of lines is N cable , the number of buses is N bus , the results are 2, 1, and 2 respectively.

[0138] The amplitudes M1 and M2 of the modulation waves of each converter and the phase shift angles δ1 and δ2 of the modulation waves are collected, and the waveforms are shown in Figure 3(a), Figure 3(b), Figure 3(c), and Figure 3(d), respectively.

[0139] According to formula (1), the d-axis control quantity d of each converter is calculated d1 d d2 and q-axis control quantity d q1 d q2 , the waveforms are shown in Figure 4(a), Figure 4(b), Figure 4(c), and Figure 4(d) respectively.

[0140] According to equations (2) and (3), the expressions of each converter and line are obtained as follows:

[0141]

[0142]

[0143] C VSC,1 =I 3×3

[0144] D VSC,1 =O 3×3

[0145]

[0146]

[0147] C VSC,2 =I 3×3

[0148] D VSC,2 =O 3×3

[0149]

[0150]

[0151] C cable,1 =I 2×2

[0152] D cable,1 =O 2×2

[0153] Step 2: Collect the voltage and current on the AC side and DC side of each converter and the pole voltage and current at both ends of the line. Perform Park transformation on the AC side voltage and current according to formula (4).

[0154] According to formula (5), the input quantity u of converter 1 is obtained VSC,1 Each component u d1 、u q1 、i dc1 As shown in Figure 5(a), Figure 5(b), and Figure 5(c), the output y VSC,1 Each component i d1 、i q1 、u dc1 As shown in Figure 5(d), Figure 5(e), and Figure 5(f), the input quantity u of the converter 2 is VSC,2 Each component u d2 、u q2 、i dc2 As shown in Figure 5(g), Figure 5(h), and Figure 5(i), the output y VSC,2 Each component i d2 、i q2 、u dc2 As shown in Figure 5(j), Figure 5(k) and Figure 5(l) respectively.

[0155] According to formula (6), the input quantity u of line 1 is obtained cable,1 Each component u a1 、u b1 As shown in Figure 6(a) and Figure 6(b) respectively, the output y cable,1 Each component i a1 、i b1 The waveforms are shown in Figure 6(c) and Figure 6(d) respectively.

[0156] Step 3: According to formula (7), find the state quantity and output quantity expression of the DC microgrid system, and the result is:

[0157]

[0158] According to formula (8), determine the input quantity set u a , output set y b , the results are:

[0159]

[0160] According to formula (9), calculate the contact matrix L 11 , L 12 , L 21 and L 22 , the result is:

[0161]

[0162]

[0163] L 21 =I 8×8

[0164] L 22 =O 8×4

[0165] According to formula (10), the block diagonal state transfer matrix A of the DC microgrid system is calculated: diag , block diagonal control matrix B diag , block diagonal observation matrix C diag and block diagonal control input observation matrix D diag :

[0166]

[0167]

[0168] C diag =I 8×8

[0169] D diag =O 8×8

[0170] According to formula (11), the state space model state transfer matrix A, control matrix B, observation matrix C and control input observation matrix D of the DC microgrid system during steady-state operation are calculated as follows:

[0171]

[0172]

[0173] C=I 8×8

[0174] D=O 8×4

[0175] Step 4: Determine the total number of faults n in the DC microgrid system, the result is 5. According to formula (16), calculate the fault component matrix E f , the result is:

[0176]

[0177] Step 5: Calculate the number of observers m that need to be designed, and the result is 3. Design the sensitivity matrix, and the result is:

[0178]

[0179] Calculating the Matrix The result is:

[0180]

[0181]

[0182]

[0183] Step 6: Calculate the polytope vertex matrix A k , the result is:

[0184]

[0185] Calculate the polytope vertex matrix A1-A 16 The corresponding weights are as follows Figure 7(a)-Figure 7(p) As shown:

[0186] According to formula (21), solve the parameter matrix in each observer Given k m The result of k=1 and k=1 is:

[0187]

[0188]

[0189] C 1,1 =I 5×5

[0190]

[0191]

[0192] Step 7: Calculate the normalized observer output residual;

[0193] The normalized residual results of each observer output are calculated according to formula (25). The normalized residuals of observer 1, observer 2, and observer 3 are shown in Figure 8(a), Figure 8(b), and Figure 8(c), respectively.

[0194] Calculate the reconstruction error of each fault and find the number k of its minimum value n,min , the result is 1, indicating that the converter VSC1 fails.

Claims

1. A DC microgrid fault diagnosis method based on a reduced-order unknown input observer, characterized in that: The steps include: Step 1: Calculate the state transfer matrix, control matrix, observation matrix and control input observation matrix of the state space model of each converter and line; Determine the number of converters in the DC microgrid system as N vsc , the number of buses is N bus ; The number of bipolar lines is N cable ; Collect the amplitude and phase shift angle of the modulation wave of each converter, and calculate the d-axis control quantity of each converter according to formula (1): and q-axis control amount In the formula, k vsc is the inverter serial number, is the amplitude of the modulated wave, is the phase shift angle of the modulated wave; According to formula (2), calculate the kth vsc The state transfer matrix of the converter Control Matrix Observation Matrix and the control input observation matrix Where ω is the angular frequency of the DC microgrid system, For the kth vsc The equivalent resistance of the transformer and line loss connected to the AC outlet side of each converter, For the kth vsc The commutation reactance on the AC outlet side of each converter is: For the kth vsc The DC output side capacitor of the converter, is the equivalent resistance of the busbar short circuit at the DC outlet side of the converter, I is the unit matrix, and O is the zero matrix; According to formula (3), calculate the kth cable The state transition matrix of the lines Control Matrix Observation Matrix and the control input observation matrix In the formula, k cable is the line number, a represents the first section of the line, b represents the last section of the line, is the short-circuit resistance of a bipolar short-circuit fault somewhere in the line, They represent the resistance and inductance of the single-pole line from the first section of the line to the short-circuit fault point, They represent the resistance and inductance of the single-pole line from the point where the short-circuit fault occurs to the end of the line; Step 2: Collect the voltage and current on the AC side and DC side of each converter and the pole-to-pole voltage and current at both ends of the line, and calculate the input and output of the state space model of each converter and line; According to formula (4), the d-axis and q-axis voltages and d-axis and q-axis currents on the AC outlet side of the converter are calculated: Among them, Z a,b,c Represent the three-phase voltage u and three-phase current i, Z d,q,0 represents the d, q, and 0-axis voltages and currents after Parker transformation; According to formula (5), calculate the kth vsc Input quantity of each converter and output In the formula, is the current at the DC output side of the converter, For the kth vsc The DC side voltage of each converter; According to formula (6), calculate the kth cable Input quantity of lines and output In the formula, and Represents the kth cable The line voltage at the beginning and end of the DC line, and Represents the kth cable The current flowing into and out of the first section of the line; Step 3: Calculate the state transfer matrix, control matrix, observation matrix and control input observation matrix of the state space model of the DC microgrid system during steady-state operation; According to formula (7), the state quantity x, input quantity u and output quantity y of the DC microgrid system are defined as: According to formula (8), define the input quantity set u a , output set y b , According to formula (9), combined with the topological node relationship of the DC microgrid system, symbolic operations are performed to calculate the connection matrix L 11 , L 12 , L 21 and L 22 : According to formula (10), the block diagonal state transfer matrix A of the DC microgrid system is calculated: diag , block diagonal control matrix B diag , block diagonal observation matrix C diag and block diagonal control input observation matrix D diag : According to formula (11), the state transfer matrix A, control matrix B, observation matrix C and control input observation matrix D of the state space model of the DC microgrid system in steady-state operation are calculated. Step 4: Calculate the fault component matrix of the DC microgrid system; According to formula (12), the total number of possible faults n in the DC microgrid system is calculated; n=N vsc +N cable +N bus (12) According to formula (13), calculate the kth vsc The fault component matrix of the converter with internal fault According to formula (14), calculate k cable Fault component matrix of a line with a bipolar short circuit fault According to formula (15), calculate k bus Fault component matrix of a busbar with bipolar short circuit fault According to formula (16), the fault component matrix E of the DC microgrid system is calculated f , Step 5: Design sensitivity matrix; According to formula (17), the required number of observers m is calculated: in, Indicates rounding down; The sensitivity matrix S has an order of n×m, and each row is designed to be a different m-bit binary number that cannot be zero and must satisfy the nNth sensitivity matrix. vsc +k vsc Row equals k vsc At least one 1 in the row is changed to a 0 value; According to formula (18), according to the row number of 1 in each column of the sensitivity matrix S, the fault component matrix E is selected f The corresponding columns of the block matrix are composed of matrix Depend on Linearly independent columns are constructed as follows: Among them, k m represents the observer number, is a reversible matrix, not unique; Step 6: Stabilize the reduced-order unknown input observer; According to formula (19), the variable d-axis control quantity in the state transfer matrix A is and q-axis control amount Substitute the maximum value of the corresponding variable or minimum value Calculate the polytope vertex matrix A k , Among them, k is the serial number of the polytope vertex matrix, is the total number of polytope vertex matrices, and The parameters are The upper and lower limits of and Respective parameters The upper and lower limits of According to formula (20), calculate the polytope vertex matrix A k The corresponding weight μ k : According to formula (21), define the kth m The state estimator of a reduced-order observer and the output estimator Where k represents the number of the polytope vertex. Superscript + denotes Moore-Penrose pseudoinverse, with superscript ⊥ represents orthogonality, For the kth m The gain matrix of the k-th polytope vertex of the observer needs to be designed with a negative eigenvalue real part using the pole placement method; Step 7: Calculate the normalized residual of the observer output; According to formula (22), the residual error of the observer is calculated According to formula (23), the residual modulus of the observer output is calculated The protection activation criterion of the DC microgrid system is shown in formula (24): in, is the upper limit of the residual threshold of each observer in the case of no fault; According to formula (25), the normalized residual of the observer output is calculated Step 8: Calculate the fault reconstruction error and identify the fault sequence number that occurred; According to formula (26), the reconstruction error of each fault is calculated Among them, k n Indicates the fault number. Represents the kth value in the sensitivity matrix n Row k m Column data; Reconstruction error at all faults Find the minimum value k in n,min , k n,min Corresponding to the fault sequence number, the DC microgrid fault diagnosis is realized.

2. The DC microgrid fault diagnosis method based on reduced-order unknown input observer according to claim 1 is characterized in that: Variable d-axis control quantity in the state transfer matrix A and q-axis control amount The maximum or minimum value of is:

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