Duty ratio optimization voltage prediction control method for four-leg inverter

Abstract

The application provides a four-bridge-arm inverter duty cycle optimization voltage prediction control method, which improves the traditional modulation type model prediction control C-M 2 The steady-state performance of the PC, such as reducing the output ripple amplitude, etc.; while inheriting the fast dynamic response and over-modulation capability of the limited set model prediction control FCS-MPC, the fixed switching frequency is maintained; the virtual vector is constructed through the angle error between vectors, which divides the space tetrahedron into finer subspaces and performs iterative operations, thereby improving the prediction accuracy; in addition, the Lagrange function with the Karush-Kuhn-Tucker (KKT) condition is constructed and solved to obtain the output voltage boundary of the inverter in the direction of the current reference vector, which is used as the basis for determining the over-modulation region; compared with the FCS-MPC and C-M 2 The comparative experiments of the PC under different working conditions show that the application has the best steady-state performance and the dynamic performance close to the FCS-MPC, and has the over-modulation capability.

Description

Technical Field

[0001] This invention belongs to the field of power electronics technology, specifically relating to a method for optimizing the duty cycle and predicting voltage control of a four-arm inverter. Background Technology

[0002] Four-arm voltage source inverters (VSIs) offer greater control flexibility than three-arm inverters due to the additional degree of freedom they possess, and they are highly adaptable to diverse power demands, making them widely used in three-phase four-wire power electronic systems. Currently, the main applications of four-arm inverters include: distributed generation; power quality improvement; active power filters (APF); static var compensator (SVC); fault-tolerant control of permanent magnet synchronous motors (PMSMs); and uninterruptible power supplies (UPS).

[0003] In recent years, Finite Control Set Model Predictive Control (FCS-MPC) has been widely applied to four-arm inverters due to its simple control method, excellent dynamic performance, and ability to achieve multiple control objectives. However, because only one voltage vector is applied in a single sampling period, the switching frequency of FCS-MPC is variable, increasing the design difficulty of the filter and reducing steady-state performance. To address these inherent problems of FCS-MPC, a control method combining FCS-MPC with three-dimensional space vector modulation (3D-SVM) has been applied to both three-arm and four-arm inverters, namely, conventional modulation model predictive control (CM). 2 PC). Although CM 2 The PC method achieves a constant switching frequency, but has low DC voltage utilization and its steady-state performance needs improvement.

[0004] In order to improve CM 2 Regarding PC performance, some studies have proposed a three-arm inverter CM with duty cycle optimization as its objective. 2PC method. Zhang Yongchang et al. proposed a model predictive torque control method for permanent magnet synchronous motors (PMSMs). Based on the deadbeat torque control principle, the duty cycle of each voltage vector is obtained, and the voltage vector and duty cycle are optimized simultaneously in the cost function, thus avoiding separate processing of voltage vector selection and duty cycle. Yan Yan et al. proposed a hybrid control set model predictive control method for field-oriented control of PMSMs. They established a hybrid control set containing virtual vectors and selected the optimal vector and its duty cycle through finite enumeration and error evaluation, thereby more accurately adjusting the magnitude and angle of the output vector. Similarly, Zhou Zhanqing et al. proposed a variable control set model predictive direct duty cycle control method for PMSMs. By changing the prediction model and control set, multiple switching modes are used to adjust torque and flux linkage, thereby maximizing the control freedom of the virtual vector. Dan Xiao et al. and Xing Xiangyang et al. respectively proposed an improved modulation model predictive control method for grid-connected inverters and an adaptive model predictive control method for three-level inverters. They constructed intermediate virtual vectors on the angle bisectors of equilateral triangular sectors to refine the sectors. Different active vectors were applied in each refined region, reducing the current ripple amplitude. Chen Junshuo et al. proposed a dual-vector model predictive current control method for permanent magnet synchronous motors (PMSMs). This method utilizes the projection of the current error vector onto the active voltage vector to solve for the duty cycle of the active vector, thereby minimizing the prediction error and improving the output current quality. Sun Xiaodong et al. proposed an improved model predictive torque control method for PMSMs based on duty cycle optimization. In this method, due to the influence of torque inertia delay, the duty cycle is obtained from the average torque control principle. Experimental results demonstrate that this method can reduce torque and flux linkage fluctuations.

[0005] The duty cycle optimization methods described above have been applied to the control of three-arm inverters with significant results. However, due to the irregular three-dimensional spatial vector structure of four-arm inverters, these methods are difficult to apply to this inverter topology. Recently, a mathematical analysis framework for determining the duty cycle was proposed by Dan Xiao et al., which constructs a mathematical expression between the cost function and the duty cycle and obtains the optimal duty cycle through an extremum problem. This method has been applied to model predictive control of both three-arm and four-arm inverters, improving steady-state performance, reducing current ripple amplitude, and enhancing overmodulation capability. However, the optimal duty cycle obtained through the extremum problem cannot remain constant between 0 and 1, leading to undesirable control effects outside the modulation limit.

[0006] Duty cycle optimization improves DC bus voltage utilization and overmodulation capability. The extremum method proposed by Dan Xiao et al. struggles to completely disable zero vectors, limiting overmodulation capability. To disable zero vectors in overmodulation mode, Cristian F. Garcia et al. proposed a modulation model predictive control method to optimize overmodulation. This method divides the hexagonal vector space into different operating regions, applying different numbers of vectors in each region, but is limited to overmodulation in three-arm inverters. Zhang Xiaoguang et al. proposed a CM based on time-varying control cycles. 2 The PC method changes the control cycle according to the duration of the optimal vector, thereby enhancing the overmodulation capability. However, increasing the control cycle will increase the amplitude and phase distortion of the controller output, thus affecting the control effect. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention presents a voltage prediction control method for optimizing the duty cycle of a four-arm inverter.

[0008] The duty cycle optimization voltage prediction control method for four-arm inverters includes the following:

[0009] Step 1: Establish a decoupling model of a four-arm inverter with an LC filter in the αβγ coordinate system and define its cost function;

[0010] To eliminate the coupling relationship between the neutral arm and the three-phase arm, a decoupling model of a four-arm inverter with an LC filter is established in the αβγ coordinate system.

[0011] For the α component, the discrete dynamic equation of the four-arm inverter is written as:

[0012]

[0013] Where i α i αo v αn v αo L, C and T s These are the inverter output current, load current, inverter output voltage, load voltage, filter inductor, filter capacitor, and sampling period, respectively. To compensate for the controller's calculation delay, equation (1) is updated to the next time step, resulting in:

[0014]

[0015] When the sampling frequency is much greater than the fundamental frequency (f s When >>20f), v in equation (2) αn (k+2) is linearly approximated by v αn (k+1), therefore, combining equations (1) and (2) yields:

[0016] v αo (k+2)=x1v αo (k)+x2[i α (k)-i αo (k)]+x3v αn (k+1) (3)

[0017] in,

[0018] Based on the above derivation process of the α component, the β component and γ component are obtained;

[0019] Considering the ability to track the reference voltage, the cost function is defined as follows:

[0020]

[0021] in The y-axis component represents the reference voltage;

[0022] Step 2: Perform a formal transformation on the reference voltage vector of the four-arm inverter and the cost function obtained in Step 1 to obtain the inverter output reference voltage, the corresponding cost function, and the optimal tetrahedron containing the optimal vector and the zero vector;

[0023] The formal transformation of the reference voltage vector and cost function is specifically as follows:

[0024] The two-level four-bridge inverter has 16 switching states, corresponding to 16 voltage vectors, including 14 active vectors and two zero vectors; as shown in equation (3), the α component v of the inverter output voltage at the next moment is... αn (k+1) only accounts for a portion of the load voltage v αo Part of (k+2), namely equation (3), can be rewritten as:

[0025] v αo (k+2)=v αs (k)+x3v αn (k+1) (5)

[0026] Where v αs (k) is v αo A portion of (k+2), specifically:

[0027] v αs (k)=x1v αo (k)+x2[i α (k)-i αo (k)] (6)

[0028] As can be seen from equation (5), the load voltage vector and the inverter output voltage vector will always differ by v. αs (k), therefore eliminate vαs (k) and the coefficient x3 in equation (5); construct a new form of the reference voltage vector:

[0029]

[0030] in Load reference voltage vector The new form; finally, equation (4) is rewritten as:

[0031]

[0032] in The inverter output voltage at the next moment; in the αβγ coordinate system, the active vector and zero vector Forming a tetrahedron Zero vector and active vector Co-synthesis Through the formal transformation in equation (7), Converted to and yes The reference vector and cost function are respectively derived from equations (7) and (8);

[0033] The four-arm inverter outputs 16 switching states, corresponding to 16 active vectors. The zero vector and three adjacent active vectors form a spatial tetrahedron. The vector space of the four-arm inverter is divided into 24 spatial tetrahedrons by 14 active vectors. By evaluating the cost function of the voltage vectors in each tetrahedron, the tetrahedron with the smallest sum of the cost function values ​​of the contained voltage vectors is selected as the optimal tetrahedron. The optimal tetrahedron is Tetradron. opt The selection method is as follows:

[0034]

[0035] The three active vectors contained in the optimal tetrahedron are called the optimal vectors, denoted as . and Commonly synthesized reference vector;

[0036] Step 3: Based on the optimal vector and reference vector in Step 2, obtain a variable control set containing virtual vectors. Then, iteratively partition the optimal tetrahedron using virtual vectors to obtain the optimal second-order sub-tetrahedron. Finally, obtain the optimized duty cycle of the optimal vector and the zero vector.

[0037] Step 3.1: Construct a virtual vector based on the angle error between the optimal vector and the reference vector to obtain a variable control set containing the virtual vector;

[0038] The degree of approximation between any vector and another vector sharing the same origin is called the fitting level, denoted by F; considering the use of addition and multiplication operations instead of angle operations, the optimal vector is defined. The fitting level for the reference vector is:

[0039]

[0040] Where v iproj For the optimal vector The projection onto the reference vector direction; to improve prediction accuracy, the virtual vector should approximate the reference vector more closely than the optimal vector; therefore, the virtual vector is synthesized from three optimal vectors, and the duty cycle of the optimal vector is proportional to its fitting level F, let them be d... v1 d v2 and d v3 The result is obtained by calculation using the following formula:

[0041]

[0042] d vi and Multiplying them together, we get:

[0043]

[0044] in Let be the component of the virtual vector in the optimal vector direction; finally, define the virtual vector as:

[0045]

[0046] The virtual vectors generated by equations (10) to (12) are synthesized from them. It is the optimal geometric solution of the optimal vector synthesis reference vector; Equations (10) to (13) allow the generation of corresponding virtual vectors for any reference vector in the entire three-dimensional vector space, indicating that the control set will change with the change of the reference vector to adapt to the new reference vector;

[0047] Step 3.2: Use the virtual vector obtained in Step 3.1 to divide the optimal tetrahedron and perform iterative operations to obtain the optimal second-order sub-tetrahedron containing the reference vector;

[0048] The tetrahedron partitioning and iteration operations are specifically as follows:

[0049] The virtual vector adds additional degrees of freedom to the control set, and the optimal tetrahedron in which the reference vector lies... Divided into three sub-tetrahedrons and To reduce tracking error, and Filter to include reference vectors The space is reduced; based on F, the selection of the optimal subtetrahedron is defined as:

[0050]

[0051] Among them, Tetrasub opt The sub-tetrahedron that is closer to the reference vector than the other two sub-tetrahedrons is called the optimal sub-tetrahedron; assuming and The angle error is largest between them, which is manifested in F1 being smaller than F2 and F3, i.e., selecting It is the optimal subtetrahedron; Shrink the space where the reference vector is located, and use a ratio A more accurate spatial approximation reference vector, overcoming The inherent angular error;

[0052] Based on the iterative approach, using the optimal subtetrahedron Replace the optimal tetrahedron And repeat equations (10) to (14) to obtain a tetrahedron that more closely approximates the reference vector; For example, second-order virtual vector Generated by the following formula:

[0053]

[0054] Where d v ′ i and d vir They are respectively and Duty cycle, F vir for The level of fit; Because in The largest angular error is found in equation (15). Instead, equation (14) becomes:

[0055]

[0056] Tetrasub o ′ pt It is the optimal second-order subtetrahedron; in middle, Because in vector combination and The one with the largest angular error between itself and the reference vector is excluded; therefore, Selected as the optimal second-order subtetrahedron, it further reduces the prediction angle error of the reference vector, using Replace the optimal tetrahedron This will significantly improve the tracking performance of the reference vector;

[0057] Step 3.3: Based on the optimal second-order subtetrahedron obtained in Step 3.2, the optimized duty cycle of the active vector and the zero vector is derived, and finally the optimized duty cycle of the active vector and the zero vector is obtained.

[0058] exist In the case of the optimal second-order subtetrahedron, They are respectively represented as and To minimize the tracking error, the solution for the optimal duty cycle is transformed into an extremum problem, and the root mean square of the weighted tracking error is defined. for:

[0059]

[0060] Where, e opts ,d opts and g opts They are respectively The tracking error, duty cycle, and cost function value; combined with equations (8), (10)~(13) and (15), g opt1 and g opt2 Calculated as:

[0061]

[0062] The duty cycle that minimizes equation (17) is solved using the Lagrange multiplier method, with the constraint that the duty cycle is between 0 and 1 added; therefore, the solution function is:

[0063]

[0064] d can be obtained by solving for the extreme value of equation (19). opts ;final, The optimized duty cycle is derived as follows:

[0065]

[0066] After obtaining the optimized duty cycle of other second-order sub-tetrahedrons through steps 3.1 to 3.3 above, and obtaining the optimized duty cycle of the optimal vector and the zero vector, a 9-segment switching sequence is generated.

[0067] Step 4: Based on the projection of the optimal vector in the optimal tetrahedron onto the reference vector direction, construct and solve the Lagrange equation with KKT conditions to obtain the inverter output voltage limit under the current reference vector direction in real time, which serves as the criterion for the overmodulation region.

[0068] To determine the inverter operating region where the reference vector is located, the maximum length reached by the optimal vector along the reference vector direction at the current moment is calculated in real time, which represents the inverter output voltage limit under the current reference. If the amplitude of the reference vector is greater than this maximum length, it is determined that it is in the overmodulation region; otherwise, it is in the linear modulation region.

[0069] For the optimal tetrahedron, the optimal vector exist The maximum effective lengths achievable in each direction are respectively in Projection v in the direction 1proj ~v 3proj ; Assuming that The duty cycles that reach maximum length in the current reference direction are d. 1m ,d 2m and d 3m This includes d 1m ~d 3m The maximum length is represented as:

[0070] v m (d 1m ,d 2m ,d 3m )=d 1m v 1proj +d 2m v 2proj +d 3m v 3proj (twenty one)

[0071] To find the maximum value of equation (21), the Lagrangian function containing the Karush-Kuhn-Tucker conditions is constructed as follows:

[0072]

[0073] The constraint terms are:

[0074]

[0075] Solving equation (22), we get:

[0076]

[0077] Therefore, when the magnitude of the reference vector is greater than v m When the inverter is in the overmodulation region, only the active vector is used to synthesize the reference vector, i.e., d is used in equation (19). opt0 Set to zero; based on step 3, the optimized duty cycle in the multi-vector voltage prediction control of the four-arm inverter is obtained using a geometric method; step 4 provides the criterion for the overmodulation region of the four-arm inverter, and adjusts the optimized duty cycle obtained in step 3 in the overmodulation mode.

[0078] Beneficial technical effects of the present invention:

[0079] This invention proposes a duty cycle optimized voltage predictive control method (DCO-VPC) for four-arm inverters, which improves CM 2 While maintaining the performance of PC, it inherits the fast dynamic response and overmodulation capability of FCS-MPC. An equivalent form of the reference voltage and cost function of the four-arm inverter in the αβγ coordinate system is constructed for intuitive comparative analysis. First, a virtual vector is constructed based on the angular error between the active voltage vector and the reference voltage vector. Second, existing vector combinations are filtered, and the optimal tetrahedron is divided into sub-tetrahedrons and iteratively refined to further refine the space in which the reference vector resides. Finally, the reference vector is synthesized in a more optimal vector space. Therefore, the proposed method significantly improves the tracking capability of the reference vector. Furthermore, a Lagrange equation containing Karush-Kuhn-Tucker (KKT) conditions is constructed using the projection of the active voltage vector onto the direction of the reference vector. This equation is used to solve the output voltage limit of the inverter in the current reference vector direction, overcoming the problem of difficulty in geometrically dividing the overmodulation region due to the irregular vector space of the four-arm inverter. Attached Figure Description

[0080] Figure 1 A schematic diagram of a four-arm inverter topology with an LC filter according to an embodiment of the present invention;

[0081] Figure 2 The space voltage vector of a two-level four-bridge inverter in the αβγ coordinate system of this invention;

[0082] Figure 3 Transformation of the reference voltage vector in embodiments of the present invention

[0083] Figure 4 A schematic diagram illustrating the synthesis of virtual vectors in an optimal tetrahedron according to an embodiment of the present invention;

[0084] Figure 5 A schematic diagram of the division of the sub-tetrahedron in an embodiment of the present invention;

[0085] Figure 6 A schematic diagram of the optimal second-order subtetrahedron partitioning in an embodiment of the present invention;

[0086] Figure 7 A schematic diagram of a 9-segment switch sequence according to an embodiment of the present invention;

[0087] Figure 8 The control strategy block diagram of the duty cycle optimization voltage prediction control method for the fourth-arm inverter of this invention is shown below.

[0088] Figure 9A schematic diagram of a nonlinear load consisting of a single-phase rectifier bridge according to an embodiment of the present invention;

[0089] Figure 10 Load current under linear load conditions in embodiments of the present invention; wherein Figure a is FCS-MPC, Figure b is CM 2 PC Figure c, the DCO-VPC method proposed in this invention;

[0090] Figure 11 Load current under nonlinear load conditions in embodiments of the present invention; wherein Figure a is FCS-MPC, Figure b is CM 2 PC Figure c, the DCO-VPC method proposed in this invention;

[0091] Figure 12 The FFT spectrum of the c-phase load voltage under nonlinear load conditions in this embodiment of the invention; wherein Figure a is FCS-MPC, Figure b is CM 2 PC Figure c, the DCO-VPC method proposed in this invention;

[0092] Figure 13 A schematic diagram of the load voltage dynamic response of the FCS-MPC according to an embodiment of the present invention;

[0093] Figure 14 Embodiment CM of the present invention 2 A schematic diagram of the dynamic response of the PC's load voltage;

[0094] Figure 15 A schematic diagram of the load voltage dynamic response of the DCO-VPC method proposed in this invention;

[0095] Figure 16 A schematic diagram of the steady-state experimental waveforms of load voltage and line voltage under overmodulation mode in an embodiment of the present invention;

[0096] Figure 17 A schematic diagram of the dynamic experimental waveforms of load voltage and line voltage under overmodulation mode in an embodiment of the present invention. Detailed Implementation

[0097] The present invention will be further described below with reference to the accompanying drawings and embodiments;

[0098] A duty cycle optimization voltage prediction control method for four-arm inverters is attached. Figure 8 As shown, it specifically includes the following:

[0099] Step 1: Establish a decoupling model of a four-arm inverter with an LC filter in the αβγ coordinate system and define its cost function;

[0100] To eliminate the coupling between the neutral arm and the three-phase arms, a decoupling model of a four-arm inverter with an LC filter is established in the αβγ coordinate system; a schematic diagram of the four-arm inverter topology with an LC filter is attached. Figure 1 As shown;

[0101] For the α component, the discrete dynamic equation of the four-arm inverter is written as:

[0102]

[0103] Where i α i αo v αn v αo L, C and T s These are the inverter output current, load current, inverter output voltage, load voltage, filter inductor, filter capacitor, and sampling period, respectively. To compensate for the controller's calculation delay, equation (25) is updated to the next time step, resulting in:

[0104]

[0105] When the sampling frequency is much greater than the fundamental frequency (f s When >>20f), v in equation (26) αn (k+2) is linearly approximated by v αn (k+1), therefore, combining equations (25) and (26) yields:

[0106] v αo (k+2)=x1v αo (k)+x2[i α (k)-i αo (k)]+x3v αn (k+1) (27)

[0107] in,

[0108] Based on the above derivation process of the α component, the β component and γ component are obtained;

[0109] Considering the ability to track the reference voltage, the cost function is defined as follows:

[0110]

[0111] in The y-axis component represents the reference voltage;

[0112] Step 2: Perform a formal transformation on the reference voltage vector of the four-arm inverter and the cost function obtained in Step 1 to obtain the inverter output reference voltage, the corresponding cost function, and the optimal tetrahedron containing the active vector;

[0113] The formal transformation of the reference voltage vector and cost function is specifically as follows:

[0114] A two-level four-arm inverter has 16 switching states, corresponding to 16 voltage vectors, including 14 active vectors and two zero vectors, distributed in the αβγ coordinate system as follows: Figure 2 As shown; from equation (27), it can be seen that the α component v of the inverter output voltage at the next moment αn (k+1) only accounts for a portion of the load voltage v αo Part of (k+2), namely equation (27), can be rewritten as:

[0115] v αo (k+2)=v αs (k)+x3v αn (k+1) (29)

[0116] Where v αs (k) is v αo A portion of (k+2), specifically:

[0117] v αs (k)=x1v αo (k)+x2[i α (k)-i αo (k)] (30)

[0118] As can be seen from equation (29), the load voltage vector and the inverter output voltage vector will always differ by v. αs (k), which makes it difficult to analyze the relationship between them in a spatial coordinate system; in order to make the inverter output voltage a predicted value of the reference voltage, it is necessary to eliminate v. αs (k) and the coefficient x3 in equation (29); construct a new form of the reference voltage vector:

[0119]

[0120] in Load reference voltage vector The new form; finally, equation (28) is rewritten as:

[0121]

[0122] in The inverter output voltage at the next moment; such as Figure 3 As shown, in the αβγ coordinate system, the source vector and zero vector Forming a tetrahedron Zero vector and active vector Co-synthesis Through the formal transformation in equation (31), Converted to and yes The reference voltage form is adopted to perform geometric analysis in three-dimensional vector space more intuitively; the subsequent reference vector and cost function adopt equations (31) and (32) respectively;

[0123] like Figure 2 As shown, the four-arm inverter outputs 16 switching states, corresponding to 16 active vectors. The zero vector and three adjacent active vectors form a spatial tetrahedron. The vector space of the four-arm inverter is divided into 24 spatial tetrahedrons by 14 active vectors. By evaluating the cost function of the voltage vectors in each tetrahedron, the tetrahedron with the smallest sum of the cost function values ​​of the contained voltage vectors is selected as the optimal tetrahedron. The optimal tetrahedron is Tetradron. opt The selection method is as follows:

[0124]

[0125] The three active vectors contained in the optimal tetrahedron are called the optimal vectors, denoted as . and Commonly synthesized reference vector;

[0126] Step 3: Based on the optimal vector and reference vector in Step 2, obtain a variable control set containing virtual vectors. Then, iteratively partition the optimal tetrahedron using virtual vectors to obtain the optimal second-order sub-tetrahedron. Finally, obtain the optimized duty cycle of the optimal vector and the zero vector.

[0127] Step 3.1: Construct a virtual vector based on the angle error between the optimal vector and the reference vector to obtain a variable control set containing the virtual vector;

[0128] Generating virtual vectors within the optimal tetrahedron expands the control set and improves prediction accuracy. For two vectors with the same origin, their approximation is determined by the angle between them. In this invention, the approximation between any vector and another vector sharing the same origin is called the fitting level, denoted as F. Considering the use of addition and multiplication operations instead of angle operations, an optimal vector is defined. The fitting level for the reference vector is:

[0129]

[0130] Where v iproj For the optimal vector The projection onto the reference vector direction; to improve prediction accuracy, the virtual vector should approximate the reference vector more closely than the optimal vector; therefore, the virtual vector is synthesized from three optimal vectors, and the duty cycle of the optimal vector is proportional to its fitting level F, let them be d... v1 d v2 and d v3 The result is obtained by calculation using the following formula:

[0131]

[0132] d vi With V i Multiplying them together, we get:

[0133]

[0134] in Let be the component of the virtual vector in the optimal vector direction; finally, define the virtual vector as:

[0135]

[0136] The synthesis of virtual vectors, as follows Figure 4 As shown, The virtual vectors generated by equations (34) to (36) are synthesized from them. It is the optimized geometric solution of the optimal vector synthesis reference vector; because compared to the three optimal vectors, It has a smaller angular error with the reference vector. The synthesis is equivalent to correcting the direction of the optimal vector toward the direction of the reference vector; Equations (34) to (37) allow the generation of corresponding virtual vectors for any reference vector in the entire three-dimensional vector space, indicating that the control set will change with the change of the reference vector to adapt to the new reference vector;

[0137] Step 3.2: Use the virtual vector obtained in Step 3.1 to divide the optimal tetrahedron and perform iterative operations to obtain the optimal second-order sub-tetrahedron containing the reference vector;

[0138] The tetrahedron partitioning and iteration operations are specifically as follows:

[0139] like Figure 5 As shown, the virtual vector adds additional degrees of freedom to the control set, and the optimal tetrahedron where the reference vector is located... Divided into three sub-tetrahedrons and To reduce tracking error, and Filter to include reference vectors The space is reduced; based on F, the selection of the optimal subtetrahedron is defined as:

[0140]

[0141] Among them, Tetrasub opt The sub-tetrahedron that is closer to the reference vector than the other two sub-tetrahedrons is called the optimal sub-tetrahedron, such as... Figure 5 In As shown. Assume and The angle error is largest between them, which is manifested in F1 being smaller than F2 and F3, i.e., selecting It is the optimal subtetrahedron; Shrink the space where the reference vector is located, and use a ratio A more accurate spatial approximation reference vector overcomes, to some extent, the limitations of... The inherent angular error;

[0142] Based on the iterative approach, using the optimal subtetrahedron Replace the optimal tetrahedron And repeat equations (34) to (38) to obtain a tetrahedron that more closely approximates the reference vector; For example, second-order virtual vector Generated by the following formula:

[0143]

[0144] Where d v ′ i and d vir They are respectively and Duty cycle, F vir for The level of fit; Because in The largest angular error is found in equation (39). Instead, equation (38) becomes:

[0145]

[0146] Tetrasub o ′ pt It is the optimal second-order subtetrahedron; such as Figure 6 As shown, in middle, Because in vector combination and The one with the largest angular error between itself and the reference vector is excluded; therefore, Selected as the optimal second-order subtetrahedron, it further reduces the prediction angle error of the reference vector, using Replace the optimal tetrahedron This will significantly improve the tracking performance of the reference vector;

[0147] Step 3.3: Based on the optimal second-order subtetrahedron obtained in Step 3.2, the optimized duty cycle of the optimal vector and the zero vector is derived, and finally the optimized duty cycle of the optimal vector and the zero vector is obtained.

[0148] exist In the case of the optimal second-order subtetrahedron, They are respectively represented as and To minimize the tracking error, the solution for the optimal duty cycle is transformed into an extremum problem, and the root mean square of the weighted tracking error is defined. for:

[0149]

[0150] Where, e opts ,d opts and g opts They are respectively The tracking error, duty cycle, and cost function value; combined with equations (32), (34)~(37) and (39), g opt1 and g opt2 Calculated as:

[0151]

[0152] The duty cycle that minimizes equation (41) is solved using the Lagrange multiplier method, with the constraint that the duty cycle is between 0 and 1 added; therefore, the solution function is:

[0153]

[0154] The extreme value of equation (43) is used to obtain d. opts ;final, The optimized duty cycle is derived as follows:

[0155]

[0156] After obtaining the optimized duty cycles in other second-order sub-tetrahedrons through steps 3.1-3.3 above, and then obtaining the optimized duty cycles of the optimal vector and the zero vector, a 9-segment switching sequence is generated, as follows: Figure 7 As shown.

[0157] Step 4: Based on the projection of the optimal vector in the optimal tetrahedron onto the reference vector direction, construct and solve the Lagrange equation with KKT conditions to obtain the inverter output voltage limit under the current reference vector direction in real time, which serves as the criterion for the overmodulation region.

[0158] To determine the inverter operating region where the reference vector is located, the maximum length reached by the optimal vector along the reference vector direction at the current moment is calculated in real time, which represents the inverter output voltage limit under the current reference. If the amplitude of the reference vector is greater than this maximum length, it is determined that it is in the overmodulation region; otherwise, it is in the linear modulation region.

[0159] for Figure 4 The optimal tetrahedron and optimal vector shown exist The maximum effective lengths achievable in each direction are respectively in Projection v in the direction 1proj ~v 3proj ; Assuming that The duty cycles that reach maximum length in the current reference direction are d. 1m ,d 2m and d 3m This includes d 1m ~d 3m The maximum length is represented as:

[0160] v m (d 1m ,d 2m ,d 3m )=d 1m v 1proj +d 2m v 2proj +d 3m v 3proj (45)

[0161] To find the maximum value of equation (45), the Lagrangian function containing the Karush-Kuhn-Tucker conditions is constructed as follows:

[0162]

[0163] The constraint terms are:

[0164]

[0165] Solving equation (46), we get:

[0166]

[0167] Therefore, when the magnitude of the reference vector is greater than v m When the inverter is in the overmodulation region, only the active vector is used to synthesize the reference vector, i.e., d is used in equation (43). opt0Set to zero; based on step 3, the optimized duty cycle in the multi-vector voltage prediction control of the four-arm inverter is obtained using a geometric method; step 4 provides the criterion for the overmodulation region of the four-arm inverter, and adjusts the optimized duty cycle obtained in step 3 in the overmodulation mode.

[0168] To verify the effectiveness of the DCO-VPC method proposed in this invention, FCS-MPC and CM were compared. 2 The PC method and the proposed DCO-VPC method were experimentally verified, and the main experimental parameters are shown in Table 1.

[0169] High-power resistors are used to construct linear / nonlinear loads, with resistance values ​​of 10Ω and 20Ω selected. The nonlinear load used in the experiment is as follows: Figure 9 As shown, a single-phase rectifier bridge is connected between the three-phase bridge arm and the neutral bridge arm. The DC output terminal of the rectifier bridge is connected to a purely resistive load (connecting a 10Ω symmetrical resistor is type A, and connecting a 20Ω symmetrical resistor is type B).

[0170] Table 1. Main experimental parameters;

[0171]

[0172]

[0173] Steady-state performance verification;

[0174] The three-phase reference voltage amplitude is set to 30V, FCS-MPC, CM 2 The load currents of PC and the proposed DCO-VPC method under a 10Ω symmetrical linear load condition are as follows: Figure 10 As shown in (a) to (c), it can be seen that under the same load conditions, FCS-MPC and CM... 2 The load current fluctuations of the PC and the proposed DCO-VPC method decrease sequentially, indicating that the reference tracking capability of the three methods improves sequentially. The three methods exhibit similar steady-state performance differences under nonlinear load conditions (Type A) and linear load conditions, such as... Figure 11 As shown in (a) to (c).

[0175] Fast Fourier Transform (FFT) was performed on the c-phase load voltage under nonlinear load conditions for the three methods, and the resulting spectra are shown below. Figure 12 As shown in (a) to (c), the FCS-MPC exhibits the worst steady-state performance (THD = 7.78%), with a diffused harmonic spectrum and high-order harmonics distributed across all frequency points. In contrast, the CM... 2 PC and the proposed DCO-VPC method achieve a fixed switching frequency, with higher harmonics concentrated near integer multiples of the switching frequency. Compared to FCS-MPC, CM 2The PC method has lower output waveform distortion (THD = 4.23%). The proposed DCO-VPC method inherits the CM... 2 While maintaining advantages such as fixed PC switching frequency, the steady-state performance is further improved, and the harmonic content is minimized (THD = 2.83%).

[0176] Dynamic performance verification;

[0177] To simulate the actual operation of the inverter, a three-phase reference voltage with an amplitude of 30V is first tracked under a 10Ω symmetrical linear load condition. Then, the amplitude of the three-phase reference voltage is suddenly changed to 20V, and a nonlinear load (Type B) is connected in parallel. Figures 13-15 FCS-MPC and CM were showcased respectively. 2 Dynamic responses of PC and the proposed DCO-VPC method. The figure shows that FCS-MPC has the fastest settling time (1.28 ms), followed by the proposed DCO-VPC method (1.48 ms) and CM. 2 PC (2.08ms).

[0178] Overmodulation capability verification;

[0179] To verify the overmodulation capability of the proposed DCO-VPC method under conditions such as nonlinear load and transient changes in the operating conditions of a four-arm inverter, steady-state and dynamic experiments were conducted under overmodulation conditions. Under nonlinear load conditions (Type A), the reference voltage amplitude was set to 40V, and the load voltage and line voltage were... ac The waveform is as follows Figure 16 As shown. In addition, the four-arm inverter is operated in linear modulation mode with a reference voltage amplitude of 30V and a 10Ω symmetrical linear load, and the reference voltage amplitude is suddenly increased to 40V while a nonlinear load (type B) is connected in parallel. Figure 17 It shows the changes in load voltage and line voltage.

[0180] Depend on Figure 16 It can be seen that when the four-arm inverter operates in overmodulation mode under nonlinear load conditions, the maximum three-phase load voltage can reach 40V and the modulation ratio can reach 0.667.

[0181] When reference and load conditions change abruptly, the reference vector jumps from the linear modulation region to the overmodulation region. Accordingly, the proposed DCO-VPC method successfully switches from linear modulation mode to overmodulation mode and continuously tracks the reference voltage under deep overmodulation conditions, such as... Figure 17 As shown, when the operating conditions change abruptly, the load voltage waveform exhibits a smooth transition. The line voltage waveform reflects the process of the zero vector being shielded before and after the modulation mode switching.

[0182] This invention proposes a duty cycle optimized voltage predictive control method for two-level four-arm inverters with LC filters. The proposed DCO-VPC method improves CM 2 The PC inherits the overmodulation capability of FCS-MPC while maintaining stable and dynamic performance, and keeps the switching frequency constant. A virtual vector is constructed by utilizing the angular error between the active vector and the reference vector. A better vector combination is used to approximate the reference vector through iterative operations, significantly improving the reference tracking capability. A Lagrangian function with KKT conditions is constructed and solved to obtain the inverter output voltage limit corresponding to the current reference vector, serving as the basis for defining the overmodulation region of the four-arm inverter. The proposed DCO-VPC method is simultaneously applied to both FCS-MPC and CM. 2 The experimental results under different operating conditions, compared with PC, proved the effectiveness of the proposed DCO-VPC method.

Claims

1. A duty cycle optimization voltage prediction control method for a four-arm inverter, characterized in that, Specifically, it includes the following: Step 1: Establish A decoupling model of a four-arm inverter with an LC filter in a coordinate system is presented, and its cost function is defined. To eliminate the coupling between the neutral arm and the three-phase arm, establish Decoupling model of a four-arm inverter with LC filter in coordinate system; Among them, targeting The discrete dynamic equations of the four-arm inverter are written as follows: in , , , , , and These are the inverter output current, load current, inverter output voltage, load voltage, filter inductor, filter capacitor, and sampling period, respectively. To compensate for the controller's calculation delay, equation (1) is updated to the next time step, resulting in: When the sampling frequency f s When the frequency is greater than 20 times the fundamental frequency f, the value in equation (2) is... Approximated by linearity Therefore, combining equations (1) and (2) yields: in, , , ; According to the above The derivation process of the components is obtained Components and Quantity; Considering the ability to track the reference voltage, the cost function is defined as follows: in The y-axis component represents the reference voltage; Step 2: Perform a formal transformation on the reference voltage vector of the four-arm inverter and the cost function obtained in Step 1 to obtain the inverter output reference voltage, the corresponding cost function, and the optimal tetrahedron containing the optimal vector and the zero vector; Step 3: Based on the optimal vector and reference vector in Step 2, obtain a variable control set containing virtual vectors. Then, iteratively partition the optimal tetrahedron using virtual vectors to obtain the optimal second-order sub-tetrahedron. Finally, obtain the optimized duty cycle of the optimal vector and the zero vector. Step 4: Based on the projection of the optimal vector in the optimal tetrahedron onto the reference vector direction, construct and solve the Lagrange equation with KKT conditions to obtain the inverter output voltage limit under the current reference vector direction in real time, which serves as the criterion for the overmodulation region, and adjust the optimized duty cycle obtained in step 3 in the overmodulation mode.

2. The duty cycle optimization voltage prediction control method for a four-arm inverter according to claim 1, characterized in that, Step 2 is as follows: The formal transformation of the reference voltage vector and cost function is specifically as follows: The two-level four-bridge inverter has 16 switching states, corresponding to 16 voltage vectors, including 14 active vectors and two zero vectors; as shown in equation (3), the inverter output voltage at the next moment is Quantity Only accounts for the load voltage Part of it, namely equation (3), can be rewritten as: in yes Part of it, specifically: As can be seen from equation (5), the load voltage vector and the inverter output voltage vector will always be out of phase. Therefore, eliminate The coefficients in equation (5) Constructing a new form of the reference voltage vector: in Load reference voltage vector The new form; finally, equation (4) is rewritten as: in The inverter output voltage at the next moment; In a coordinate system, the source vector ~ and zero vector Forming a tetrahedron ; Zero vector and active vector ~ Co-synthesis Through formal transformations in equation (7), Converted to ,and yes The reference vector and cost function are respectively derived from equations (7) and (8); The four-arm inverter outputs 16 switching states, corresponding to 16 active vectors. The zero vector and three adjacent active vectors form a spatial tetrahedron. The vector space of the four-arm inverter is divided into 24 spatial tetrahedrons by 14 active vectors. By evaluating the cost function of the voltage vectors in each tetrahedron, the tetrahedron with the smallest sum of the cost function values ​​of the contained voltage vectors is selected as the optimal tetrahedron. The selection method is as follows: The three active vectors contained in the optimal tetrahedron are called the optimal vectors, denoted as . , and , ~ A common composite reference vector.

3. The duty cycle optimization voltage prediction control method for a four-arm inverter according to claim 1, characterized in that, Step 3 specifically involves: Step 3.1: Construct a virtual vector based on the angle error between the optimal vector and the reference vector to obtain a variable control set containing the virtual vector; The degree of approximation between any vector and another vector sharing the same origin is called the fitting level, denoted by F; considering the use of addition and multiplication operations instead of angle operations, the optimal vector is defined. ~ The fitting level for the reference vector is: in For the optimal vector The projection along the direction of the reference vector; to improve prediction accuracy, the virtual vector should be closer to the reference vector than the optimal vector; Therefore, the virtual vector is synthesized from three optimal vectors, and the duty cycle of the optimal vector is proportional to its fitting level F, let them be respectively... , and The result is obtained by calculation using the following formula: Will and Multiplying them together, we get: in Let be the component of the virtual vector in the optimal vector direction; finally, define the virtual vector as: ~ The virtual vectors generated by equations (10) to (12) are synthesized from them. It is the optimal geometric solution of the optimal vector synthesis reference vector; Equations (10) ~ (13) allow the generation of corresponding virtual vectors for any reference vector in the entire three-dimensional vector space, indicating that the control set will change with the change of the reference vector to adapt to the new reference vector; Step 3.2: Use the virtual vector obtained in Step 3.1 to divide the optimal tetrahedron and perform iterative operations to obtain the optimal second-order sub-tetrahedron containing the reference vector; The tetrahedron partitioning and iteration operations are specifically as follows: The virtual vector adds additional degrees of freedom to the control set, and the optimal tetrahedron in which the reference vector lies... Divided into three sub-tetrahedrons , and To reduce tracking errors, ~ and Filter to include reference vectors The space is reduced; based on F, the selection of the optimal subtetrahedron is defined as: in, The sub-tetrahedron that is closer to the reference vector than the other two sub-tetrahedrons is called the optimal sub-tetrahedron; assuming and The angle error between them is the largest, which is manifested as Compare and Smaller, i.e., select It is the optimal subtetrahedron; Shrink the space where the reference vector is located, and use a ratio A more accurate spatial approximation reference vector, overcoming ~ The inherent angular error; Based on the iterative approach, using the optimal subtetrahedron Replace the optimal tetrahedron And repeat equations (10) ~ (14) to obtain a tetrahedron that more closely approximates the reference vector; For example, second-order virtual vector Generated by the following formula: in and They are respectively and duty cycle, for The level of fit; Because in ~ The largest angular error is found in equation (15). Instead, equation (14) becomes: in It is the optimal second-order subtetrahedron; in middle, Because in vector combination , and The one with the largest angular error between itself and the reference vector is excluded; therefore, Selected as the optimal second-order subtetrahedron, it further reduces the prediction angle error of the reference vector, using Replace the optimal tetrahedron This will significantly improve the tracking performance of the reference vector; Step 3.3: Based on the optimal second-order subtetrahedron obtained in Step 3.2, the optimized duty cycle of the active vector and the zero vector is derived, and finally the optimized duty cycle of the active vector and the zero vector is obtained. exist In the case of the optimal second-order subtetrahedron, , , , They are respectively represented as , , and To minimize the tracking error, the solution for the optimal duty cycle is transformed into an extremum problem, and the root mean square of the weighted tracking error is defined. for: in, , and They are respectively The tracking error, duty cycle, and cost function value; combined with equations (8), (10) ~ (13) and (15), and Calculated as: The duty cycle that minimizes equation (17) is solved using the Lagrange multiplier method, with the constraint that the duty cycle is between 0 and 1 added; therefore, the solution function is: The result is obtained by solving for the extreme value of equation (19). ;final, ~ The optimized duty cycle is derived as follows: After obtaining the optimized duty cycle of other second-order sub-tetrahedrons through steps 3.1 to 3.3 above, and obtaining the optimized duty cycle of the optimal vector and the zero vector, a 9-segment switching sequence is generated.

4. The duty cycle optimization voltage prediction control method for a four-arm inverter according to claim 1, characterized in that, Step 4 is as follows: In order to determine the inverter operating region where the reference vector is located, the maximum length that the optimal vector reaches along the reference vector direction at the current moment is obtained in real time, which represents the inverter output voltage limit under the current reference. If the magnitude of the reference vector is greater than the maximum length, it is determined that it is in the overmodulation region; otherwise, it is in the linear modulation region. For the optimal tetrahedron, the optimal vector ~ exist The maximum effective lengths achievable in each direction are respectively in Projection in direction ~ ; Assuming that ~ The duty cycles that reach maximum length in the current reference direction are respectively , and This includes ~ The maximum length is represented as: To find the maximum value of equation (21), the Lagrangian function containing the Karush–Kuhn–Tucker conditions is constructed as follows: The constraint terms are: Solving equation (22), we get: Therefore, when the magnitude of the reference vector is greater than When it is determined that the inverter is currently operating in the overmodulation region, only the active vector is used to synthesize the reference vector, that is, in equation (19) the reference vector is... Set to zero; based on step 3, the optimized duty cycle in the multi-vector voltage prediction control of the four-arm inverter is obtained using a geometric method; step 4 provides the criterion for the overmodulation region of the four-arm inverter, and adjusts the optimized duty cycle obtained in step 3 in the overmodulation mode.

Images