Unified mathematical modeling method for open-circuit fault of three-level photovoltaic inverter

Abstract

The present invention discloses a unified mathematical modeling method for an open-circuit fault of a three-level photovoltaic inverter, and the steps include: 1. according to the characteristics of the DC side voltage fluctuation when the three-level photovoltaic inverter is in maximum power point tracking operation, a mathematical expression of the DC side voltage of the three-level photovoltaic inverter is obtained; 2. according to different working conditions and current paths of the main circuit power switch device of the three-level photovoltaic inverter, a switch function expression under the corresponding fault condition is obtained, and finally a unified open-circuit fault switch function expression and an expression of the output phase voltage of the three-level photovoltaic inverter are obtained. The present invention can quickly establish a correct unified mathematical model of the open-circuit fault of the three-level photovoltaic inverter through the switch function modeling method, thereby solving the problems of the large number of modules, large amount of calculation, poor flexibility of switching simulation of different types of faults, etc. in the existing three-level photovoltaic inverter fault simulation circuit modeling method, and reducing the workload of modeling and its simulation working time.

Description

Technical Field

[0001] The invention relates to a unified mathematical modeling method for an open-circuit fault of a three-level photovoltaic inverter, and belongs to the technical field of photovoltaic operation and maintenance fault diagnosis. Background Art

[0002] Photovoltaic inverters are key power conversion equipment in distributed photovoltaic power generation systems. Distributed photovoltaic power generation is geographically dispersed, has a harsh operating environment, and has variable operating conditions, which can easily lead to photovoltaic inverter failures, posing a hazard to the reliable operation of photovoltaic power generation and system safety. Photovoltaic inverter failures are generally divided into structural failures and parametric failures. Structural failures are open circuit or short circuit failures of power devices, which cause changes in system structure. Parametric failures are parameter drifts of components, such as changes in the characteristics of capacitors, inductors, transformers, and other components. Parametric failures reduce the operating characteristics and safety margins of the system. If they are not diagnosed and handled in a timely manner, they often cause structural failures, resulting in photovoltaic inverters being de-gridified. According to statistics, the probability of open circuit failures of inverter switch power devices is relatively high.

[0003] At present, most of the open circuit faults studied in the literature are based on two-level photovoltaic inverters. However, most of the photovoltaic string inverters in distributed photovoltaic power stations now use three-level photovoltaic inverters, which have the advantages of less ripple and harmonic content and reduced switching loss. Due to the increase in the number of internal switching devices of the three-level photovoltaic inverter, nine situations and up to 78 types of open circuit faults occur when it fails, resulting in increased complexity of the three-level photovoltaic inverter fault. Most of the existing three-level photovoltaic inverter switch fault models are built using MATLAB / Simulink simulation software, but the simulation module provided by Simulink is not suitable for the simulation of three-level photovoltaic inverter switch faults. In order to solve this problem, most of them use self-built modules, but the self-built modules have problems such as long time consumption and poor flexibility in simulation of different types of fault switching. Therefore, it can be seen that it is necessary to establish a mathematical model of the open circuit fault of the power switch tube of the actual three-level photovoltaic inverter. Summary of the invention

[0004] The present invention aims to solve the deficiencies of the above-mentioned prior art and proposes a unified mathematical modeling method for open-circuit faults of three-level photovoltaic inverters, in order to establish a relatively simple unified mathematical model of switch faults of three-level photovoltaic inverters through fault mechanism modeling, so as to better identify and judge open-circuit faults of three-level photovoltaic inverters and improve the rapidity of open-circuit fault diagnosis, so as to solve the problems of large number of modules, large amount of calculation, poor flexibility of switching simulation of different types of faults, etc. in the existing three-level photovoltaic inverter fault simulation circuit modeling method.

[0005] In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme:

[0006] The unified mathematical modeling method for an open circuit fault of a three-level photovoltaic inverter of the present invention is characterized in that it comprises the following steps:

[0007] Step 1: According to the characteristics of DC side voltage fluctuation when the three-level photovoltaic inverter is in maximum power point tracking operation, a mathematical expression of the DC side voltage of the three-level photovoltaic inverter is obtained;

[0008] Step 2: according to the commutation conditions of the main circuit power switch devices of the three-level photovoltaic inverter under normal working conditions, a mathematical expression of the AC side output phase voltage under normal conditions is obtained;

[0009] Step 3: According to the fault physical model, the topological structure and current path when an open circuit fault occurs are obtained;

[0010] Step 4: construct a unified mathematical model expression of the switching function under different open circuit faults, thereby obtaining an expression of the output phase voltage of the three-level photovoltaic inverter.

[0011] The unified mathematical modeling method for the open circuit fault of the three-level photovoltaic inverter described in the present invention is also characterized in that, in step 1, the mathematical expression of the DC side voltage of the three-level photovoltaic inverter is obtained by using formula (1):

[0012]

[0013] In formula (1): U dc Represents the DC side voltage of the three-level photovoltaic inverter; U mpp represents the DC side steady-state voltage when the three-level photovoltaic inverter is in maximum power point tracking operation; Δu represents the DC side voltage fluctuation when the three-level photovoltaic inverter is in maximum power point tracking operation; T m Represents the control sampling period of MPPT; C dc Represents the capacitance of the DC link capacitor C1 or C2, and C1=C2=C dc ;I in Represents the DC side input current of the three-level photovoltaic inverter; S k ′ represents the unified switching function of the k-phase three-level photovoltaic inverter; I k Represents the output current of the three-level photovoltaic inverter with phase k, k = A, B, C.

[0014] The step 2 comprises:

[0015] Step 2.1: Use formula (2) to obtain the mathematical expression of the switching function of the three-level photovoltaic inverter under normal conditions:

[0016] S′ k(0) =S k =S k1-S k2 (2)

[0017] In formula (2): S′ k(0) represents the switching function of phase k under normal working condition; S k represents the theoretical equivalent switching function of the three-level photovoltaic inverter; S k1 and S k2 It is used to represent S k Two custom switches, and S k =S k1 -S k2 ; k = A, B, C;

[0018] Step 2.2: Use formula (3) to obtain the mathematical expression of the output phase voltage of the three-level photovoltaic inverter:

[0019]

[0020] In formula (3), U kO Represents the output phase voltage of phase k of the three-level photovoltaic inverter; U kN Represents the voltage between the k-phase output terminal of the three-level photovoltaic inverter and the midpoint N of the DC side capacitor; U NO Represents the voltage between the midpoint N of the DC capacitor and the midpoint O of the power grid; S′ k(0) represents the switching function of phase k under normal working condition; S′ m(0) represents the switching function of the m-phase under normal working condition; S′ n(0) Represents the switching function under normal working conditions of n phases, k = A, B, C; m = A, B, C and m≠k; n = A, B, C and n≠k≠m.

[0021] The open circuit failure in step 3 includes: an open circuit failure of a single switch tube and an open circuit failure of two switch tubes at the same time.

[0022] In step 4, the formula (3) is used to construct a unified mathematical model expression of the switch function of the open circuit fault, so as to obtain the output phase voltage U of the three-level photovoltaic inverter using formula (4): kO The expression is:

[0023]

[0024]

[0025] In formulas (3) and (4): k A logical quantity indicating whether the output current of a three-level photovoltaic inverter is flowing in or out; δ k =1, indicating that the current direction is from the three-level photovoltaic inverter to the grid; δ k=0, indicating that the current direction is from the grid to the three-level photovoltaic inverter; D is a 3×3 unit matrix representing the working state of the three-level photovoltaic inverter; E is Q k1 3×3 matrix with open circuit fault; F represents Q k2 3×3 matrix with open circuit fault; G represents Q k3 3×3 matrix with open circuit fault; H represents Q k4 3×3 matrix with open circuit fault; in matrices E, F, G, and H, when an open circuit fault occurs, the corresponding matrix diagonal elements are 1; when no open circuit fault occurs, the corresponding matrix diagonal elements are 0.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] 1. The present invention takes the LCL type grid-connected three-level photovoltaic inverter as the object, takes the mathematical model of the three-level photovoltaic inverter under normal working state as the basis, and obtains the mathematical expression of the DC side voltage of the three-level photovoltaic inverter according to the characteristics of the DC side voltage fluctuation when the three-level photovoltaic inverter is in maximum power point tracking operation. Starting from the fault mechanism, according to the topological diagram of the switch tube of the three-level photovoltaic inverter when the switch fails and the current path of the actual current, the mathematical model of the switch failure of the three-level photovoltaic inverter with different open circuit faults and the unified mathematical model are derived, so that the model can quickly describe the correct output current characteristics of the three-level photovoltaic inverter when the switch fails.

[0028] 2. Compared with several existing three-level photovoltaic inverter switch function modeling methods, the present invention provides a unified mathematical modeling for the open-circuit fault of the three-level photovoltaic inverter. The model intuitively describes the impact of the open-circuit fault of the switch tube on the output parameters of the three-level photovoltaic inverter and obtains the output parameters of the three-level photovoltaic inverter under different open-circuit faults through a unified mathematical model, which reduces the amount of calculation and ensures the modeling accuracy. The present invention only relies on the theoretical equivalent switch function S of the three-level photovoltaic inverter. k 、The direction of the actual output current of the three-level photovoltaic inverterδ k , DC side voltage U dc Three inverter parameters are used to establish a unified model of three-level photovoltaic inverter switch faults, which reduces the modeling workload and working time, and has strong flexibility in switching simulation for different types of faults. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a flow chart of the unified modeling method of three-level photovoltaic inverter switch fault in the present invention;

[0030] Figure 2 This is a physical model diagram of the LCL type grid-connected three-level photovoltaic inverter in the present invention (the input stage boost circuit is omitted);

[0031] Figure 3 is a current path diagram (P state) of phase k in a normal working state of a three-level photovoltaic inverter in the present invention;

[0032] Figure 4 is a current path diagram (O state) of phase k of the three-level photovoltaic inverter in the normal working state in the present invention;

[0033] Figure 5 is a current path diagram (N state) of phase k in a normal working state of a three-level photovoltaic inverter in the present invention;

[0034] Figure 6a Q in the present invention k1 The current path (P state) diagram of phase k when an open circuit fault occurs;

[0035] Figure 6b Q in the present invention A1 Comparison chart of the physical model simulation results and mathematical model results when an open circuit fault occurs;

[0036] Figure 7a Q in the present invention k2 The current path (P and O states) of phase k when an open circuit fault occurs;

[0037] Figure 7b Q in the present invention A2 Comparison chart of the physical model simulation results and mathematical model results when an open circuit fault occurs;

[0038] Figure 8 Q in the present invention k3 The current path (O and N states) of phase k when an open circuit fault occurs;

[0039] Fig. 9 Q in the present invention k4 The current path (N state) diagram of phase k when an open circuit fault occurs;

[0040] Fig.10 Q in the present invention A1 and Q B1 Comparison chart of the physical model simulation results and the mathematical model results when an open circuit fault occurs. DETAILED DESCRIPTION

[0041] In this embodiment, a unified modeling method for open-circuit faults of three-level photovoltaic inverters is based on the mathematical model of the three-level photovoltaic inverter under normal working conditions, and according to the characteristics of DC side voltage fluctuations when the three-level photovoltaic inverter is in maximum power point tracking operation, a mathematical expression of the DC side voltage of the three-level photovoltaic inverter is obtained. Starting from the fault mechanism, according to the topological diagram of the switch tube of the three-level photovoltaic inverter when the switch fails and the current path of the actual current, the mathematical models of the switch faults of the three-level photovoltaic inverter with different open-circuit faults and a unified mathematical model are derived, so that the model can quickly describe the correct output current characteristics of the three-level photovoltaic inverter when the switch fails. Specifically, if Figure 1 As shown, the modeling method includes the following steps:

[0042] Step 1: According to the characteristics of DC side voltage fluctuation when the three-level photovoltaic inverter is in maximum power point tracking operation, the mathematical expression of the DC side voltage of the three-level photovoltaic inverter is obtained:

[0043] The physical model of LCL grid-connected three-level photovoltaic inverter is shown in the figure below: Figure 2 As shown, according to Kirchhoff's current theorem:

[0044]

[0045]

[0046] In formula (1) and formula (2), I in Represents the DC side input current of the three-level photovoltaic inverter; I dc1 Represents the positive input current of the three-level photovoltaic inverter (I in After being shunted by capacitor C1); I dc2 Represents the negative input current of the three-level photovoltaic inverter (I in After being shunted by capacitor C2); U C1 Represents the voltage across capacitor C1 on the input side; U C2 Represents the voltage across capacitor C2 on the input side; I C1 Represents the current flowing through the capacitor C1 on the input side; I C2 Represents the current flowing through capacitor C2 on the input side.

[0047] Assume that the capacitance of the DC side capacitors C1 and C2 of the three-level photovoltaic inverter is C dc , then C1=C2=C dc , then according to formula (1) and formula (2), we can get:

[0048]

[0049] According to I dc1 -Idc2 =S′ A I A +S′ B I B +S′ C I C Formula (3) can be transformed into:

[0050]

[0051] In formula (4): S′ k I represents the unified switching function of the k-phase three-level photovoltaic inverter; k Represents the output current of the three-level photovoltaic inverter with phase k, k = A, B, C.

[0052] When the three-level photovoltaic inverter is in maximum power point tracking operation, the DC side voltage of the three-level photovoltaic inverter will fluctuate. Finally, according to formula (4), the DC side voltage fluctuation Δu of the three-level photovoltaic inverter in maximum power point tracking operation can be written as:

[0053]

[0054] In formula (5), Δu represents the DC side voltage fluctuation of the three-level photovoltaic inverter in maximum power point tracking operation; T m Represents the control sampling period of MPPT.

[0055] Therefore, the DC side voltage expression of the three-level photovoltaic inverter is:

[0056]

[0057] In formula (6): U dc Represents the DC side voltage of the three-level photovoltaic inverter; U mpp Represents the DC side steady-state voltage of the three-level PV inverter when it is in maximum power point tracking operation.

[0058] Step 2: According to the commutation conditions of the power switch devices in the main circuit of the three-level photovoltaic inverter under normal working conditions, the mathematical expression of the AC side output phase voltage under normal conditions is obtained:

[0059] Define switch quantity S k1 and S k2 To express the theoretical equivalent switching function S k , that is, S k =S k1 -S k2 The three-level photovoltaic inverter has three working states: P, O and N. The switching function S kIt can be used to represent the three working states of the three-level photovoltaic inverter, which are described as follows: In the normal working state, P state (S k =1), the switch quantity defined at this time satisfies S k1 =1, S k2 =0; O state (S k =0), the switch quantity defined at this time satisfies S k1 =0, S k2 =0; N state (S k =-1), the switch quantity defined at this time satisfies S k1 =0, S k2 =1. The current paths in the three states of PON are as follows Figure 3 , Figure 4 and Figure 5 The voltage U between the k-phase output terminal of the three-level photovoltaic inverter and the midpoint N of the DC side capacitor is shown in kN You can use the expression To express.

[0060] The equivalent open-circuit fault of the three-level photovoltaic inverter is defined as S k ′, then when the three-level photovoltaic inverter is in normal working state, there is S′ k =S k The actual output current direction of the three-level photovoltaic inverter is defined as positive when it flows from the three-level photovoltaic inverter to the grid, and negative when it flows from the grid to the three-level photovoltaic inverter. Its logical variable is defined as δ k (k=A, B, C, the same below). k Represents the current direction of the k-phase current. k =1, indicating that the current direction is positive (flowing from the three-level PV inverter to the grid); δ k =0, indicating that the current direction is negative (flowing from the grid to the three-level PV inverter).

[0061] When the three-level photovoltaic inverter is in normal working state, the voltage U between the output end of the three-level photovoltaic inverter and the midpoint of the DC side capacitor kN The truth table is shown in Table 1:

[0062] Table 1 Voltage U under normal working condition of three-level photovoltaic inverter kN Truth Table

[0063] <![CDATA[S k ]]> <![CDATA[S k ′]]> <![CDATA[S k1 ]]> <![CDATA[S k2 ]]> <![CDATA[δ k ]]> <![CDATA[U kN ]]> 1 1 1 0 1,0 <![CDATA[U dc / 2]]> 0 0 0 0 1,0 0 -1 -1 0 1 1,0 <![CDATA[-U dc / 2]]>

[0064] According to Table 1, the voltage U between point K and point N of the three-level photovoltaic inverter is kN The mathematical description is:

[0065]

[0066] According to formula (7), the switching function S′ k can be written as:

[0067] S′ k(0) =S k =S k1 -S k2 (8)

[0068] At this time, the mathematical expression of the output phase voltage of the three-level photovoltaic inverter is:

[0069]

[0070] Among them, U kO Represents the output phase voltage of phase k of the three-level photovoltaic inverter; U kN Represents the voltage between the k-phase output terminal of the three-level photovoltaic inverter and the midpoint N of the DC side capacitor; U NO Represents the voltage between the midpoint N of the DC capacitor and the midpoint O of the power grid; S′ k(0) represents the switching function of phase k under normal working condition; S′ m(0) represents the switching function of the m-phase under normal working condition; S′ n(0) Represents the switching function under normal working conditions of n phases, k = A, B, C; m = A, B, C and m≠k; n = A, B, C and n≠k≠m.

[0071] Step 3: Based on the fault physical model, obtain the topological structure and current path when an open circuit fault occurs:

[0072] When an open-circuit fault occurs in the switch tube, the topology and output current path of the three-level photovoltaic inverter are different. At this time, the output phase voltage of the three-level photovoltaic inverter is not only related to the switch state of the switch tube, but also to the current direction of the output current. Generally, in the actual operation of the inverter, it is rare for three or more switch tubes to fail at the same time, so only single-tube and double-tube open-circuit faults are considered below.

[0073] When the switch tube Q k1 When an open circuit fault occurs, the P state is affected, while the O and N states are not affected. In the P state, the current path is shown in Figure 6:

[0074] according to Figure 6a and Figure 6b It can be seen that the current path is different from that in normal working state. k1 An open circuit fault occurs, so that when the current I k >0, the current I k Through the diode D k5 And the switch tube Q k2 Flowing to the grid, it is no longer Q in normal working statek1 and Q k2 The current path. At this time, the working state of the three-level photovoltaic inverter changes from P state to O state. At this time, the voltage U from point k to point N of the three-level photovoltaic inverter kN The relationship between the current direction and the working state is shown in Table 2:

[0075] Table 2 Q k1 In case of an open circuit fault, the voltage U kN Truth Table

[0076]

[0077] When Q k2 When an open circuit fault occurs, it affects the P and O states of the three-level photovoltaic inverter, but has no effect on the N state.

[0078] according to Figure 7a and Figure 7b Know Q k2 An open circuit fault occurs. In the P state, when the current I k >0, the current I k Through the diode D k3 And diode D k4 Flowing to the grid, it is no longer Q in normal working state k1 and Q k2 The current path. At this time, the working state of the three-level photovoltaic inverter changes from P state to N state. In the O state, when the current I k >0, the current I k Through the diode D k3 And diode D k4 Flowing to the grid, no longer in normal working state D k5 and Q k2 The current path. At this time, the working state of the three-level photovoltaic inverter changes from O state to N state. Analysis shows that Q k2 When an open circuit fault occurs, the voltage U from point K to point N of the three-level photovoltaic inverter is kN The relationship between the current direction and the working state is shown in Table 3:

[0079] Table 3 Q k2 In case of an open circuit fault, the voltage U kN Truth Table

[0080]

[0081] When Q k3 If an open circuit fault occurs, it will affect the three-level photovoltaic inverter states O and N, but will not affect the P state.

[0082] according to Figure 8 Know Qk3 An open circuit fault occurs. In the O state, when the current I k When <0, the current I k Through the diode D k1 And diode D k2 flows to the inverter, and is no longer Q k3 and D k6 The current path. At this time, the working state of the three-level photovoltaic inverter changes from O state to P state. In N state, when the current I k When <0, the current I k Through the diode D k1 And diode D k2 flows to the inverter, and is no longer Q k3 and Q k4 At this time, the working state of the three-level photovoltaic inverter changes from N state to P state. k3 When an open circuit fault occurs, the voltage U from point K to point N of the three-level photovoltaic inverter is kN The relationship between the current direction and the working state is shown in Table 4:

[0083] Table 4 Q k3 In case of an open circuit fault, the voltage U kN Truth Table

[0084]

[0085] When Q k4 When an open circuit fault occurs, it affects the state N of the three-level photovoltaic inverter, but has no effect on the P and O states.

[0086] according to Fig. 9 It can be seen that due to Q k4 An open circuit fault occurs, so that when the current I k When <0, the current I k Through the diode Q k3 And switch tube D k6 Flows to the three-level photovoltaic inverter, and is no longer Q k3 and Q k4 The current path. Analysis shows that when Q k4 When an open circuit fault occurs, the voltage U from point K to point N of the three-level photovoltaic inverter is kN The relationship between the current direction and the working state is shown in Table 5:

[0087] Table 5 Q k4 Terminal voltage U in case of open circuit fault kN Truth Table

[0088]

[0089] When a double-tube open-circuit fault occurs, it can be regarded as a combination of two single-tube open-circuit faults. The switching function S k The change of ′ can also be regarded as the sum of the switching functions of the two single-tube switch tubes with open circuit faults.

[0090] Step 4: Construct a unified mathematical model expression of the switch function under different open circuit faults, thereby obtaining the expression of the output phase voltage of the three-level photovoltaic inverter:

[0091] According to Table 2, when Q k1 When an open circuit fault occurs, the switching function will change. The switching function S after the open circuit fault k ′ satisfies formula (10):

[0092]

[0093] According to Table 3, when Q k2 When an open circuit fault occurs, the switching function will change. The switching function S after the open circuit fault k ' satisfies formula (11):

[0094]

[0095] According to Table 4, when Q k3 When an open circuit fault occurs, the switching function will change. The switching function S after the open circuit fault k ′ satisfies formula (12):

[0096]

[0097] According to Table 5, it can be concluded that when Q k4 When an open circuit fault occurs, the switching function will change. The switching function S after the open circuit fault k ' satisfies formula (13):

[0098]

[0099] According to equations (8), (10), (11), (12) and (13), it can be concluded that the unified switching function S for open circuit fault is k The expression of ′ is:

[0100]

[0101] In formula (14), S k =S k1 -S k2 ; D is the 3×3 unit matrix representing the working state of the three-level photovoltaic inverter; E is the unit matrix representing Qk1 3×3 matrix with open circuit fault; F represents Q k2 3×3 matrix with open circuit fault; G represents Q k3 3×3 matrix with open circuit fault; H represents Q k4 A 3×3 matrix with an open circuit fault. In the matrix EFGH, when an open circuit fault occurs, the corresponding matrix diagonal element is 1; when no open circuit fault occurs, the corresponding matrix diagonal element is 0.

[0102] If Q B1 If an open circuit fault occurs, the matrix EFGH satisfies:

[0103] If Q B1 and Q B3 If an open circuit fault occurs, the matrix EFGH satisfies:

[0104] If Q A1 and Q B1 If an open circuit fault occurs, the matrix EFGH satisfies:

[0105] In summary: The voltage U from the k-phase output terminal of the three-level photovoltaic inverter to the midpoint N of the DC side capacitor is kN The expression can be written as:

[0106]

[0107] According to the symmetry of the three-phase system:

[0108]

[0109] According to equations (15) and (16), the output phase voltage U of the three-level photovoltaic inverter can be obtained: kO expression:

[0110]

[0111] in,

[0112] Finally, according to Kirchhoff's law, the electrical parameter expression corresponding to the LCL type grid-connected three-level photovoltaic inverter is obtained:

[0113]

[0114] Among them, I gk Represents the k-phase grid-connected current; U ck is the voltage across the filter capacitor in the k-phase LCL filter; E k is the grid voltage; UkO is the k-phase output voltage of the three-level photovoltaic inverter; C f is the capacitance of the filter capacitor in the LCL filter.

[0115] To verify the accuracy of the mathematical model, we first built a physical model of the three-level photovoltaic inverter switch fault in Simulink, and then used the unified mathematical model of the three-level photovoltaic inverter switch fault obtained above to build a mathematical model. Finally, by comparing the output current of the physical model and the mathematical model, we can know the correctness of the open circuit fault mathematical model. The details are as follows:

[0116] (1) Let Q A1 An open circuit fault occurs, and a single-tube open circuit fault occurs at 0.2s in the physical model and the mathematical model respectively; the three-level photovoltaic inverter is still in the maximum power tracking stage before 0.1s, and Q A1 The comparison between the physical model simulation results and the mathematical model results of an open circuit fault is shown in the figure below. Figure 6b As shown in the figure, the currents before and after the fault are basically the same.

[0117] (2) Let Q A2 An open circuit fault occurs, and a single-tube open circuit fault occurs at 0.2s in the physical model and the mathematical model respectively; the three-level photovoltaic inverter is still in the maximum power tracking stage before 0.1s, and Q A2 The comparison between the physical model simulation results and the mathematical model results of an open circuit fault is shown in the figure below. Figure 7b As shown in the figure, the currents before and after the fault are basically the same.

[0118] (3) Let Q A1 and Q B1 An open circuit fault occurs, and a double-tube open circuit fault occurs at 0.2s in the physical model and the mathematical model respectively; the three-level photovoltaic inverter is still in the maximum power tracking stage before 0.1s, and Q A1 and Q B1 The comparison between the physical model simulation results and the mathematical model results of an open circuit fault is shown in the figure below. Fig.10 As shown in the figure, the currents before and after the fault are basically the same.

[0119] Figure 6b , Figure 7b and Fig.10 The results show that the mathematical model of open-circuit fault of three-level photovoltaic inverter obtained by the unified mathematical model construction method of three-level photovoltaic inverter switch fault proposed in the present invention has the characteristics of high accuracy and the like.

Claims

1. A unified mathematical modeling method for open-circuit faults of three-level photovoltaic inverters, characterized in that: The following steps are involved: Step 1: According to the characteristics of DC side voltage fluctuation when the three-level photovoltaic inverter is in maximum power point tracking operation, a mathematical expression of the DC side voltage of the three-level photovoltaic inverter is obtained; Step 2: according to the commutation conditions of the main circuit power switch devices of the three-level photovoltaic inverter under normal working conditions, a mathematical expression of the AC side output phase voltage under normal conditions is obtained; Step 3: According to the fault physical model, the topological structure and current path when an open circuit fault occurs are obtained; Step 4: Use formula (4) to construct a unified mathematical model expression of the open circuit fault switch function expressed by the switch function under different open circuit faults, so as to obtain the output phase voltage of the three-level photovoltaic inverter using formula (5): Expression of (4) (5) In formula (4) and formula (5): Represents the DC side voltage of the three-level photovoltaic inverter, represents the unified switching function of the three-level photovoltaic inverter with phase k; represents the theoretical equivalent switching function of a three-level photovoltaic inverter with k phases; and It is used to indicate Two custom switches, and ; Represents the output phase voltage of phase k of the three-level photovoltaic inverter; Represents the voltage between the k-phase output terminal of the three-level photovoltaic inverter and the midpoint N of the DC side capacitor; k=A, B, C; Represents the voltage between the midpoint N of the DC side capacitor and the midpoint O of the grid; A logical quantity indicating whether the output current of a three-level photovoltaic inverter is flowing in or out; , which means the current direction is from the three-level photovoltaic inverter to the grid; , represents the current direction is from the grid to the three-level photovoltaic inverter; D is the 3×3 unit matrix representing the working state of the three-level photovoltaic inverter; E is the A 3×3 matrix with an open circuit fault; F represents A 3×3 matrix with an open circuit fault; G represents A 3×3 matrix with an open circuit fault; H represents 3×3 matrix with open circuit fault; in matrices E, F, G, and H, when an open circuit fault occurs, the corresponding matrix diagonal elements are 1; when no open circuit fault occurs, the corresponding matrix diagonal elements are 0.

2. The unified mathematical modeling method for open circuit fault of three-level photovoltaic inverter according to claim 1, characterized in that: In step 1, the mathematical expression of the DC side voltage of the three-level photovoltaic inverter is obtained by using formula (1): (1) In formula (1): Represents the DC side voltage of the three-level photovoltaic inverter; Represents the DC side steady-state voltage of the three-level photovoltaic inverter when it is in maximum power point tracking operation; Represents the DC side voltage fluctuation of the three-level photovoltaic inverter when it is in maximum power point tracking operation; Represents the control sampling period of MPPT; Represents the DC link capacitance or The capacitance value of ; Represents the DC side input current of the three-level photovoltaic inverter; represents the unified switching function of the three-level photovoltaic inverter with phase k; Represents the output current of the three-level photovoltaic inverter with phase k, k=A,B,C.

3. The unified mathematical modeling method for open circuit fault of three-level photovoltaic inverter according to claim 2, characterized in that: The step 2 comprises: Step 2.1: Use formula (2) to obtain the mathematical expression of the switching function of the three-level photovoltaic inverter under normal conditions: (2) In formula (2): represents the switching function of phase k under normal working condition; represents the theoretical equivalent switching function of a three-level photovoltaic inverter; and It is used to indicate Two custom switches, and ; k = A, B, C; Step 2.2: Use formula (3) to obtain the mathematical expression of the output phase voltage of the three-level photovoltaic inverter: (3) In formula (3), Represents the output phase voltage of phase k of the three-level photovoltaic inverter; Represents the voltage between the k-phase output terminal of the three-level photovoltaic inverter and the midpoint N of the DC side capacitor; Represents the voltage between the midpoint N of the DC side capacitor and the midpoint O of the grid; represents the switching function of phase k under normal working condition; Represents the switching function of the m-phase under normal working condition; Represents the switching function under normal working conditions of n phases, k=A, B, C; m=A, B, C and m≠k; n=A, B, C and n≠k≠m.

4. The unified mathematical modeling method for open circuit fault of three-level photovoltaic inverter according to claim 3, characterized in that: The open circuit failure in step 3 includes: an open circuit failure of a single switch tube and an open circuit failure of two switch tubes at the same time.

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