Multi-level converter predictive control method and device based on multi-objective optimization and spherical decoding

Abstract

This invention discloses a predictive control method and apparatus for multilevel converters based on multi-objective optimization and spherical decoding. This method considers the relationship between redundant switches and capacitor voltage balance in the multilevel converter, incorporating capacitor voltage constraints into the search process of the spherical decoding algorithm. While maintaining good output current quality, it effectively controls the voltage balance of the DC-side capacitor and the flying capacitor. The method employs a branch-and-bound approach, continuously updating the hypersphere radius during the search process to find the optimal switching sequence, significantly reducing computational complexity. Furthermore, this invention proposes a method for calculating the upper bound of the number of search nodes in the spherical decoding algorithm, allowing for a more intuitive evaluation of the method's computational advantages. The feasibility and superiority of this method are verified using a three-phase five-level active neutral-point clamp converter as an example. It is also applicable to multilevel converters with other phase numbers, level numbers, and topologies, demonstrating a very broad application prospect.

Description

Technical Field

[0001] This invention relates to the field of three-phase multilevel converter control technology, and in particular to a predictive control method and apparatus for multilevel converters based on multi-objective optimization and spherical decoding. Background Technology

[0002] With the increasing severity of the global energy crisis and environmental pollution, improving the efficiency of motor systems has become crucial for solving these problems. In the field of high-voltage frequency converters and their control systems, traditional diode-clamped three-level converters cannot meet the demands of high-voltage frequency conversion due to the limitations of power device voltage levels. Therefore, five-level and higher-level converters have attracted attention due to their advantages such as low switching transistor stress and low total harmonic distortion (THD), and their applications are increasingly growing, especially in new energy power generation, harmonic control, and electric drives.

[0003] Control methods for multilevel converters include hysteresis control, PI control, sliding mode control, and model predictive control. Multilevel converter control typically requires achieving multi-objective optimization control, such as output waveform quality, midpoint potential balance, flying capacitor voltage balance, and switching losses. Model predictive control has gained widespread attention because it does not require complex parameter tuning, can achieve multi-objective optimization control, and has good dynamic performance. However, as the number of levels in a multilevel converter increases, the number of control objectives and computational complexity of model predictive control also increase dramatically. Taking a three-phase five-level active midpoint clamp converter as an example, its voltage vectors can reach as many as 125, and the three-phase bridge arm switching state combinations can reach as many as 512. This causes the computational complexity of traditional model predictive control methods to increase exponentially and the computation time to be long when making multi-step predictions. Furthermore, existing spherical decoding model predictive control, due to its limitations in the number of control objectives and hard constraint control of capacitor voltage, is only suitable for three-level converters and cannot effectively control converters with higher levels.

[0004] Therefore, solving the problems of multi-objective optimization control and large computational load is particularly important in model predictive control of multilevel converters. Summary of the Invention

[0005] The purpose of this invention is to propose a predictive control method and apparatus for multi-level converters based on multi-objective optimization and spherical decoding, in order to solve the above-mentioned technical problems.

[0006] To achieve the above objectives, the present invention is implemented according to the following technical solution:

[0007] This invention provides a predictive control method for a multilevel converter based on multi-objective optimization and spherical decoding, the method comprising:

[0008] A quadratic programming model is established for the prediction algorithm of a multi-step finite control set model that only considers reference current tracking and switching frequency constraints.

[0009] The cost function in matrix form is derived from the quadratic programming model and simplified into an unconstrained optimal solution problem. The unconstrained optimal solution of the switch sequence is then obtained.

[0010] The unconstrained optimal solution problem is described as an integer least squares problem;

[0011] Based on the mathematical relationship between the switching state combination of the multilevel converter and the voltage of the three-phase flying capacitor and the DC-side capacitor, the balance constraint of the DC-side capacitor and the flying capacitor voltage is derived.

[0012] Based on the unconstrained optimal solution problem, the voltage balance constraints of the DC-side capacitor and the flying capacitor are added to the search process of the spherical decoding algorithm, and the cost function of multi-level converter prediction based on multi-objective optimization and spherical decoding is obtained, that is, the distance between the center of the sphere obtained by the switching sequence without level jump.

[0013] The initial radius of the hypersphere is set, and the single-phase switching state of a single prediction step is taken as a node. The nodes in each dimension are searched sequentially. When a switching sequence is found in the hypersphere, the hypersphere radius is updated. After multiple searches and updates, until there is one and only one switching sequence in the hypersphere, which is the optimal switching sequence. The updated hypersphere radius is the sum of the squares of the distance from the node of the switching sequence to the unconstrained optimal switching sequence and the capacitor voltage error conversion distance.

[0014] In one implementation, the quadratic programming model for establishing a multi-step finite control set model prediction algorithm that only considers reference current tracking and switching frequency constraints includes:

[0015] Based on the state variable coefficient matrix and input variable coefficient matrix of the current-voltage space state system predicted by single step, a traditional single step model is established to predict the current-space state system.

[0016] A mathematical model for predicting the current-space state system using a traditional single-step model is derived by extending the prediction model to a multi-step model.

[0017] Based on the mathematical model of multi-step model prediction, a quadratic programming model is established for the multi-step finite control set model prediction algorithm that only considers reference current tracking and switching frequency constraints.

[0018] In one implementation, the quadratic programming model is expressed as:

[0019]

[0020] Where, N p To predict the step size, i sx (k+n)(x=a,b,c) represents the three-phase currents at time k+n, and λ sThese are the weighting coefficients for the switching frequency constraint term. Let Δu(k+n) be the three-phase output reference phase current at time k+n, and let Δu(k+n) be the total number of three-phase phase voltage level jumps per unit control cycle at time k+n.

[0021] In one implementation, the unconstrained optimal solution problem is expressed as:

[0022]

[0023] The unconstrained optimal solution for the switching sequence is:

[0024] U unc (k)=-H -1 Θ(k)

[0025] The Cholesky decomposition of the symmetric positive definite matrix H is: H = VV T U(k) is the multi-step three-phase switching sequence or multi-step three-phase voltage vector being searched at time k, and H -1 Θ(k) is the derived multi-step three-phase optimal switching sequence or multi-step three-phase voltage vector.

[0026] In one implementation, describing the unconstrained optimal solution problem as an integer least squares problem specifically involves:

[0027]

[0028] Among them, J sda (k) represents the naked sphere center distance of the current searched switch sequence, U unc (k) is the unconstrained optimal switching sequence derived at time k. This is the transformed unconstrained optimal solution.

[0029] In one embodiment, the voltage balance constraint between the DC-side capacitor and the flying capacitor is:

[0030]

[0031] Among them, U dc-upper (k+n) represents the DC-side upper bus capacitor voltage at time k+n, U dc-lower (k+n) represents the DC-side lower bus capacitor voltage at time k+n, U fx (k+n)(x=a,b,c) represents the three-phase flying capacitor voltage at time k+n, λ dc U is the weighting coefficient for the DC-side capacitor voltage constraint term. dc λ is the DC bus voltage. fc J is the weighting coefficient for the three-phase flying capacitor voltage constraint term. xfc(k+n)(x=a,b,c) represents the equivalent sphere center distance converted from the voltage error of the flying capacitor in one of the three phases at time k+n. J dc (k+n) is the equivalent sphere center distance converted from the DC-side capacitor voltage error at time k+n, U dc This is the DC bus voltage.

[0032] In one implementation, the cost function for multi-level converter prediction based on multi-objective optimization and spherical decoding is expressed as:

[0033]

[0034] Among them, J xfc (k+n)(x=a,b,c) represents the equivalent sphere center distance converted from the voltage error of the flying capacitor in one of the three phases at time k+n. J dc (k+n) is the equivalent sphere center distance converted from the DC-side capacitor voltage error at time k+n, J fc (k) represents the equivalent sphere center distance converted from the three-phase flying capacitor voltage error at time k, J sda (k) represents the naked sphere center distance of the switch sequence being searched at time k, J sda-5LANPC (k) represents the total center distance of the sphere corresponding to the switch sequence searched at time k.

[0035] In one implementation, at the beginning of each sampling period, the initial radius of the hypersphere is set, and the square of the initial radius R is... 2 init The optimal switching sequence U at time k-1 opt (k-1) The sum of the squares of the distance from the unconstrained optimal switching sequence shifted by one time step and the weighted distance of the capacitor voltage error at time k, plus the square of the initial hypersphere radius:

[0036]

[0037] Among them, J optdc (k) and J optfc (k) represents the weighted transformation distance of the capacitor voltage error at time k, VU ini (k) is the initial switching sequence for a unit control cycle after processing with a lower triangular matrix. This is the unconstrained optimal switch sequence transformation form derived from the derivation.

[0038] In one implementation, based on the principle that switches cannot jump across level boundaries, a formula for calculating the upper bound of the search node number in the spherical decoding algorithm for a three-phase multilevel converter is derived. The formula for calculating the upper bound of the search node number is expressed as:

[0039]

[0040] Among them, S x-statenum (k+n) represents the vector of the number of switching nodes in the search tree dimension of the multi-level converter predictive control method based on multi-objective optimization and spherical decoding corresponding to the x-phase bridge arm at time k+n, where N is the number of switching nodes. p To predict the step size.

[0041] The present invention also provides a multi-level converter predictive control device based on multi-objective optimization and spherical decoding, the device comprising:

[0042] The quadratic programming model building module is used to establish a quadratic programming model for a multi-step finite control set model prediction algorithm that only considers reference current tracking and switching frequency constraints.

[0043] The unconstrained optimal solution module is used to derive the cost function in matrix form from the quadratic programming model, simplify it into an unconstrained optimal solution problem, and find the unconstrained optimal solution of the switch sequence.

[0044] The least squares module is used to describe an unconstrained optimal solution problem as an integer least squares problem;

[0045] The DC-side capacitor and flying capacitor voltage balance constraint module is used to derive the DC-side capacitor and flying capacitor voltage balance constraint based on the mathematical relationship between the switching state combination of the multilevel converter and the three-phase flying capacitor voltage and DC-side capacitor voltage.

[0046] The cost function module is used to incorporate the voltage balance constraints of the DC-side capacitor and the flying capacitor into the search process of the spherical decoding algorithm based on the unconstrained optimal solution problem, and to obtain the cost function of the multi-level converter prediction based on multi-objective optimization and spherical decoding, that is, the distance between the center of the sphere obtained by the switching sequence without level jumps.

[0047] The search module is used to set the initial radius of the hypersphere. Taking the single-phase switch state of a single prediction step as a node, the module searches for nodes in each dimension sequentially. When a switch sequence is found within the hypersphere, the hypersphere radius is updated. After multiple searches and updates, until there is exactly one switch sequence within the hypersphere, which is the optimal switch sequence. The updated hypersphere radius is the sum of the squares of the distance from the node of the switch sequence to the unconstrained optimal switch sequence and the capacitor voltage error conversion distance.

[0048] Beneficial effects of this invention:

[0049] (1) This invention significantly reduces the computation time of the control algorithm while maintaining better output current waveform quality than the traditional multi-step finite control set model prediction algorithm. Its computational load does not increase exponentially with the increase of the prediction step size. In fact, as the prediction step size increases, the output current quality of the method in this invention is better, the total harmonic distortion of the output current is lower, and the robustness of the control algorithm is stronger. This invention is not limited to three-phase five-level active neutral-point clamp converters; it is also applicable to multilevel converters with other phase numbers, level numbers, and topologies.

[0050] (2) The method of this invention takes into account the multi-objective control requirements of the midpoint voltage and flying capacitor voltage of the multilevel converter. The search node of each dimension will include all switching states of the converter, and the DC-side capacitor and flying capacitor voltage control will be added to the calculation of the node center distance and the update of the hypersphere radius of each dimension according to an appropriate ratio (which can be adjusted to an appropriate weighting coefficient through simulation). This can maintain a superior capacitor voltage balance effect under good output current control. This capacitor voltage balancing method is not limited to three-phase five-level active midpoint clamp converters, but is also applicable to other converter topologies with capacitor voltage balance control requirements.

[0051] (3) Based on the principle that the output level cannot cross levels, this invention can calculate the upper bound of the number of search nodes for the spherical decoding algorithm with different prediction step sizes, which is effective in reducing the amount of computation. This method for calculating the upper bound of the number of search nodes is not limited to three-phase five-level active neutral point clamping converters. By changing the number of switch states (or the number of levels), it is also applicable to converters with other phase numbers, number of levels, and topology types. Attached Figure Description

[0052] The accompanying drawings, as part of this invention, are provided to further illustrate the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention, but do not constitute an undue limitation thereof. Clearly, the drawings described below are merely some embodiments, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0053] Figure 1 This is a flowchart of a multi-level converter predictive control method based on multi-objective optimization and spherical decoding provided in an embodiment of the present invention;

[0054] Figure 2 The topology diagram of a three-phase five-level active neutral-point clamp converter;

[0055] Figure 3 A flowchart of a search method for a three-phase five-level active neutral point clamp converter provided in an embodiment of the present invention;

[0056] Figure 4A vector diagram of all voltages in a three-phase five-level active neutral-point clamping converter;

[0057] Figure 5 This refers to all branch nodes of the spherical decoding search tree for a three-phase five-level active neutral-point clamping converter provided in one embodiment of the present invention.

[0058] Figure 6 This is a search tree of search nodes within the initial radius of a hypersphere that satisfies constraints, provided in one embodiment of the present invention.

[0059] Figure 7 The line voltage, phase voltage and phase current (from top to bottom) of the traditional single-step finite control set model are predicted and controlled for a three-phase five-level active neutral point clamp converter.

[0060] Figure 8 The single-step predictive control (of which one phase, from top to bottom, represents the line voltage, phase voltage, and phase current) of a three-phase five-level active neutral point clamp converter based on multi-objective optimization and spherical decoding.

[0061] Figure 9 The two-step predictive control (one phase, from top to bottom) of a three-phase five-level active neutral point clamp converter is based on multi-objective optimization and spherical decoding to measure the line voltage, phase voltage and phase current of one phase.

[0062] Figure 10 The three-step predictive control (from top to bottom) of a three-phase five-level active neutral point clamping converter is based on multi-objective optimization and spherical decoding to measure the line voltage, phase voltage and phase current of the three phases.

[0063] Figure 11 The traditional single-step finite control set model is used to predict and control the DC-side capacitor voltage for a three-phase five-level active neutral-point clamping converter.

[0064] Figure 12 A single-step predictive control of the DC-side capacitor voltage based on multi-objective optimization and spherical decoding is proposed for a three-phase five-level active neutral-point clamping converter.

[0065] Figure 13 A two-step predictive control of the DC-side capacitor voltage based on multi-objective optimization and spherical decoding is proposed for a three-phase five-level active neutral point clamp converter.

[0066] Figure 14 A three-step predictive control of the DC-side capacitor voltage based on multi-objective optimization and spherical decoding is proposed for a three-phase five-level active neutral point clamp converter.

[0067] Figure 15 The traditional single-step finite control set model is used to predict and control the three-phase flying capacitor voltage for a three-phase five-level active neutral point clamping converter.

[0068] Figure 16 A single-step predictive control method for three-phase flying capacitor voltage based on multi-objective optimization and spherical decoding is proposed for a three-phase five-level active neutral point clamp converter.

[0069] Figure 17 A two-step predictive control method for three-phase flying capacitor voltage based on multi-objective optimization and spherical decoding is proposed for a three-phase five-level active neutral point clamping converter.

[0070] Figure 18 This is a three-step long predictive control method for three-phase flying capacitor voltage based on multi-objective optimization and spherical decoding for a three-phase five-level active neutral point clamping converter.

[0071] It should be noted that these accompanying drawings and textual descriptions are not intended to limit the scope of the invention in any way, but rather to illustrate the concept of the invention to those skilled in the art by referring to specific embodiments. Detailed Implementation

[0072] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0073] This disclosure provides a predictive control method for a multilevel converter based on multi-objective optimization and spherical decoding, referring to... Figure 1 As shown, the method specifically includes the following steps:

[0074] Step S100: Establish a quadratic programming model for the multi-step finite control set model prediction algorithm that only considers reference current tracking and switching frequency constraints.

[0075] In this embodiment, a quadratic programming model is established for the prediction algorithm of a multi-step finite control set model that only considers reference current tracking and switching frequency constraints, including:

[0076] Step S110: Based on the state variable coefficient matrix and input variable coefficient matrix of the current-voltage space state system predicted by the single-step model, establish the traditional single-step model for predicting the current-space state system.

[0077] The traditional single-step model for predicting the current-space state system can be represented as:

[0078] i s (k+1)=Ai s (k)+Bu(k) (1)

[0079]

[0080] In the formula, i α (k+1) and i β (k+1) represents the three-phase output phase current at time k+1 in a two-dimensional rotating coordinate system, u(k) represents the three-phase output phase voltage level, Δu(k) represents the sum of the number of three-phase level transitions per unit control cycle, R represents the load resistance, L represents the load inductance, and T represents the load voltage level. s For the sampling period, U dc This is the DC bus voltage.

[0081] Step S120: The mathematical model for predicting the current space state system by the traditional single-step model is extended to obtain the mathematical model for prediction by the multi-step model.

[0082] Traditional single-step models for predicting current-space state systems can be extended to multi-step models for prediction:

[0083] I s (k+1)=DI s (k)+γU(k) (5)

[0084]

[0085] I s (k+1)=[i s (k+1) i s (k+2)…i s (k+N p (7)

[0086] U(k)=[u(k) u(k+1)…u(k+N p -1)] (8)

[0087] Step S130: Based on the mathematical model predicted by the multi-step model, establish a quadratic programming model for the multi-step finite control set model prediction algorithm that only considers reference current tracking and switching frequency constraints.

[0088] The quadratic programming model considering only reference current tracking and switching frequency constraints can be expressed as:

[0089]

[0090] In the formula, N p To predict the step size, i sx (k+n)(x=a,b,c) represents the three-phase currents at time k+n, and λ s These are the weighting coefficients for the switching frequency constraint term. Let Δu(k+n) be the three-phase output reference phase current at time k+n, and let Δu(k+n) be the total number of three-phase phase voltage level jumps per unit control cycle at time k+n.

[0091] Step S200: Based on the matrix form of the cost function derived from the quadratic programming model, simplify it into an unconstrained optimal solution problem, and find the unconstrained optimal solution of the switch sequence.

[0092] J SDA =U T (k)HU(k)+2Θ T (k)U(k)+θ(k) (10)

[0093]

[0094] Right now,

[0095]

[0096] This can be further simplified to an unconstrained optimal solution problem:

[0097]

[0098] The unconstrained optimal solution for the switching sequence is:

[0099] U unc (k)=-H -1 Θ(k) (15)

[0100] The Cholesky decomposition of the symmetric positive definite matrix H is: H = VV T U(k) is the multi-step three-phase switching sequence or multi-step three-phase voltage vector being searched at time k, and H -1 Θ(k) is the derived multi-step three-phase optimal switching sequence or multi-step three-phase voltage vector.

[0101] Step S300: Describe the unconstrained optimal solution problem as an integer least squares problem.

[0102] The cost function of the multi-step predictive control method for multi-level converters based on multi-objective optimization and spherical decoding can be described as an integer least squares problem:

[0103]

[0104] Right now,

[0105]

[0106] Among them, J sda (k) represents the naked sphere center distance of the current searched switch sequence, U unc(k) is the unconstrained optimal switching sequence derived at time k. This is the transformed unconstrained optimal solution.

[0107] Step S400: Based on the mathematical relationship between the switching state combination of the multilevel converter and the voltage of the three-phase flying capacitor and the DC-side capacitor, the balance constraint of the DC-side capacitor and the flying capacitor voltage is obtained.

[0108] The mathematical relationship between the switching state combination and the DC-side capacitor voltage of a three-phase five-level active neutral-point clamping converter can be expressed as:

[0109] U dc-upper (k+n)=U dc-upper (k+n-1)+(|S a1 (k+n-1)-S a3 (k+n-1)|*i sa (k+n-1)+|S b1 (k+n-1)-S b3 (k+n-1)|*i sb (k+n-1)+|S c1 (k+n-1)-S c3 (k+n-1)|*i sc (k+n-1))*T s / C dc / 2 (19)

[0110] U dc-lower (k+n)=U dc -U dc-upper (k+n) (20)

[0111] Among them U dc-upper U dc-lower S is the DC-side capacitor voltage; xy (x = a, b, c; y = 1, 3) represents the switching state of the three-phase bridge arm, i sx (x = a, b, c) represents the three-phase current, T s For the sampling period, C dc U is the DC-side capacitance value. dc This is the DC bus voltage.

[0112] The mathematical relationship between the switching state combination of a three-phase five-level active neutral-point clamping converter and the voltage of the three-phase flying capacitor can be expressed as:

[0113]

[0114] Among them U fx (x = a, b, c) represents the three-phase flying capacitor voltage; S xy(x = a, b, c; y = 3, 4) represents the switching state of the three-phase bridge arm, i sx (x = a, b, c) represents the three-phase current, T s For the sampling period, C fx (x=a,b,c) represents the three-phase flying capacitor values.

[0115] The cost functions for the DC-side capacitor voltage and the flying capacitor voltage can be expressed as:

[0116]

[0117] Among them, U dc-upper (k+n) represents the DC-side upper bus capacitor voltage, U dc-lower (k+n) represents the DC-side lower bus capacitor voltage, U fx (k+n)(x=a,b,c) represents the three-phase flying capacitor voltage, λ dc U is the weighting coefficient for the DC-side capacitor voltage constraint term. dc λ is the DC bus voltage. fc J is the weighting coefficient for the three-phase flying capacitor voltage constraint term. xfc (k+n)(x=a,b,c) represents the equivalent sphere center distance converted from the voltage error of the flying capacitor in one of the three phases at time k+n. J dc (k+n) is the equivalent sphere center distance converted from the DC side capacitor voltage error at time k+n.

[0118] Step S500: Based on the unconstrained optimal solution problem, the voltage balance constraints of the DC side capacitor and the flying capacitor are added to the search process of the spherical decoding algorithm to obtain the cost function of the multi-level converter prediction based on multi-objective optimization and spherical decoding, that is, the distance between the center of the sphere obtained by the switching sequence without level jump.

[0119] Furthermore, the cost function of the multi-level converter predictive control method based on multi-objective optimization and spherical decoding, i.e., the formula for calculating the distance between the center of the sphere, can be derived from the switching sequence without level transitions:

[0120]

[0121] Among them, J xfc (k+n)(x=a,b,c) represents the equivalent sphere center distance converted from the voltage error of the flying capacitor in one of the three phases at time k+n. J dc (k+n) is the equivalent sphere center distance converted from the DC-side capacitor voltage error at time k+n, J fc (k) represents the equivalent sphere center distance converted from the three-phase flying capacitor voltage error at time k, J sda (k) represents the naked sphere center distance of the switch sequence being searched at time k, J sda-5LANPC(k) represents the total center distance of the sphere corresponding to the switch sequence searched at time k.

[0122] Step S600: Set the initial radius of the hypersphere. Taking the single-phase switch state of a single prediction step as a node, search for nodes in each dimension in turn. When a switch sequence is found within the hypersphere, update the hypersphere radius. After multiple searches and updates, until there is one and only one switch sequence within the hypersphere, which is the optimal switch sequence. The updated hypersphere radius is the sum of the squares of the distance from the node of the switch sequence to the unconstrained optimal switch sequence and the capacitor voltage error conversion distance.

[0123] The following example uses a three-step three-phase five-level active neutral-point clamp converter. The topology of the three-phase five-level active neutral-point clamp converter is as follows: Figure 2 As shown. Figure 3 A flowchart of the search method for a three-phase five-level active neutral-point clamping converter is presented. The voltage vector diagram of the three-phase five-level active neutral-point clamping converter is shown below. Figure 4 As shown.

[0124] Considering the impact of redundant switching in the multilevel converter on control performance, a single-phase switch state in a single prediction step is considered as a node. The system sequentially searches and determines whether the sum of the squares of the distances from nodes in the switch sequence to the unconstrained optimal switch sequence and the capacitor voltage error conversion distance is less than the hypersphere radius. Whenever all nodes in a branch have been searched and the condition is met, the hypersphere radius is updated to the distance from the switch sequence to the center of the hypersphere, and the locally optimal switch sequence is updated. When all branches and nodes have been searched, the current locally optimal switch sequence is output as the globally optimal switch sequence.

[0125] The nodes in each dimension are filtered sequentially. When a switch sequence is found within the hypersphere, the hypersphere radius is updated. At the beginning of each sampling period, the initial radius of the hypersphere needs to be set, and the square of the initial radius R... 2 init The optimal switching sequence U at time k-1 opt (k-1) is the sum of the squares of the distance between the unconstrained optimal switching sequence shifted by one time step and the distance transformed by the capacitor voltage error weight at time k.

[0126] Therefore, the square of the initial hypersphere radius can be calculated:

[0127]

[0128] Among them, J optdc (k) and J optfc (k) represents the weighted transformation distance of the capacitor voltage error at time k, VU ini (k) is the initial switching sequence for a unit control cycle after processing with a lower triangular matrix. This is the unconstrained optimal switch sequence transformation form derived from the derivation.

[0129]

[0130] Without crossing level transitions, the distance to the center of the sphere can be calculated using equation (25) to determine whether the sphere is inside the hypersphere.

[0131] J sda-5LANPC (k)≤r 2 (k) (28)

[0132] Where, r 2 (k) represents the center-to-center distance of the currently searched optimal switch sequence, which is also the radius of the currently updated hypersphere. J sda-5LANPC (k) represents the total center-to-center distance of the current search sequence of switches.

[0133] By leveraging the properties of the lower triangular matrix V, multidimensional problems can be transformed into one-dimensional problems requiring successive computations, which also facilitates the software design of the algorithm.

[0134]

[0135] like Figure 5 and 6 As shown, this method sequentially determines whether the sum of the squares of the distances from each dimension of the switching sequence to the unconstrained optimal switching sequence and the capacitor voltage error conversion distance is less than the hypersphere radius. If it is greater than the hypersphere radius, the search for the dimensional branches below the current node in the current dimension is stopped, and the process jumps to the next node in the same dimension for further judgment. If the switching sequence is determined to be within the hypersphere, the square of the hypersphere radius is updated to the sum of the squares of the distances from the switching sequence to the unconstrained optimal switching sequence and the capacitor voltage error conversion distance. Then, the process continues to judge the next node in the current dimension. If all nodes in the same dimension have been filtered, the process jumps to the next node in the parent node's dimension to continue the search.

[0136] It should be noted that, in order to improve the readability of the search process, Figure 6 The search nodes that do not satisfy the level transition constraints and those that satisfy the constraints but are outside the initial radius of the hypersphere are omitted. Only the search nodes within the initial radius of the hypersphere that satisfy the constraints are retained. The curves with arrows represent the node search order of the spherical decoding algorithm. It can be seen that whenever all nodes of a branch have been searched and satisfy the conditions, i.e., the hypersphere radius is updated to the distance from the switch sequence to the center of the sphere, the local optimal switch sequence is updated.

[0137] When all branches and nodes have been searched, the current locally optimal switch sequence is output as the globally optimal switch sequence.

[0138] Furthermore, based on the principle that switches cannot jump across levels, the formula for calculating the upper bound of the search node number in the spherical decoding algorithm for three-phase multilevel converters is derived. The formula for calculating the upper bound of the search node number in SDA-LH-FCS-MPC based on 3P5LANPC can be expressed as:

[0139]

[0140] Among them, S x-statenum (k+n) represents the vector of the number of switching nodes in the search tree dimension of the multi-level converter predictive control method based on multi-objective optimization and spherical decoding corresponding to the x-phase bridge arm at time k+n, where N is the number of switching nodes. p To predict the step size. (S here) x-statenum (k+n-1) will be further explained below, where x represents one of the three phases a, b, and c.

[0141]

[0142] The eight switching states (x = a, b, c) of each phase arm of the three-phase five-level active neutral point clamping converter are shown in Table 1.

[0143] Table 1

[0144]

[0145] Furthermore, the nodes in each dimension are filtered sequentially. When a switch sequence is found within the hypersphere, the hypersphere radius is updated. After multiple searches and updates, until there is exactly one switch sequence within the hypersphere, which is the optimal switch sequence.

[0146] Table 2 shows the switching vector switching table of each bridge arm of the three-phase five-level active neutral point clamp converter based on level transition constraints.

[0147] Table 2

[0148]

[0149] The switching state transition matrix of the three-phase five-level active neutral-point clamping converter based on level constraints is:

[0150]

[0151] in

[0152]

[0153] S x-statenum (k+n) represents the vector of the number of switching nodes in the search tree dimension of the multi-level converter predictive control method based on multi-objective optimization and spherical decoding corresponding to the x-phase bridge arm at time k+n. num(k+n)(X=1,2,…,8) represents the number of nodes corresponding to each of the eight switch states.

[0154] By adjusting the level-constrained switching state switching matrix M and the number of switching states, this method for calculating the upper bound of the search node can be applied to multilevel converters with other phase numbers, level numbers, and topologies.

[0155] The multi-level converter predictive control method based on multi-objective optimization and spherical decoding proposed in this invention is a highly efficient and time-saving method. It adopts the branch and bound approach, sequentially filtering nodes in each dimension. When a switch sequence is found within the hypersphere, the hypersphere radius is updated until there is exactly one switch sequence within the hypersphere, which is the optimal switch sequence.

[0156] If all nodes in the same dimension (as shown in Table 2, 3P5LANPC has 8 switch states, meaning a maximum of 8 nodes in one dimension) have been filtered, then return to the next node in the previous dimension and repeat the above operation until all nodes in the search tree have been filtered. Finally, the current locally optimal switch sequence is output as the globally optimal switch sequence.

[0157] Figures 7 to 18 The simulation results of the traditional single-step FCS-MPC based on a three-phase five-level active neutral point clamp converter and the multi-level converter predictive control method based on multi-objective optimization and spherical decoding are compared and analyzed to verify the feasibility and superiority of the present invention.

[0158] Table 3 shows an example of calculating the upper bound of the number of search nodes for a multi-level converter predictive control method based on multi-objective optimization and spherical decoding for a three-phase five-level active neutral point clamp converter.

[0159] Table 3

[0160]

[0161] Table 3 shows the upper bounds of the number of search nodes for step sizes of 1, 2, 3, 5, and 10 calculated by this method based on a three-phase five-level active neutral-point clamp converter. Compared with the simulation results of the multi-level converter predictive control method based on multi-objective optimization and spherical decoding for the three-phase five-level active neutral-point clamp converter, it can be seen that this invention is significantly effective in reducing the computational load. This algorithm is not limited to three-phase five-level active neutral-point clamp converters; by changing the number of switching states (or the number of levels), it is also applicable to converters with other phase numbers, level numbers, and topology types.

[0162] Table 3 shows an example of calculating the upper bound of the search node number for a multi-level converter predictive control method based on multi-objective optimization and spherical decoding for a three-phase five-level active neutral-point clamp converter. The upper bound of the search node number is the total number of nodes that satisfy the level transition constraint. The search node number is the number of nodes that satisfy the level transition constraint and are inside the constantly updating radius of the hypersphere. Table 3 shows that the spherical decoding algorithm reduces computational complexity more significantly with increasing prediction step size.

[0163] In one embodiment, the present invention provides a multi-level converter predictive control device based on multi-objective optimization and spherical decoding, the device comprising:

[0164] The quadratic programming model building module is used to establish a quadratic programming model for a multi-step finite control set model prediction algorithm that only considers reference current tracking and switching frequency constraints.

[0165] The unconstrained optimal solution module is used to derive the cost function in matrix form from the quadratic programming model, simplify it into an unconstrained optimal solution problem, and find the unconstrained optimal solution of the switch sequence.

[0166] The least squares module is used to describe an unconstrained optimal solution problem as an integer least squares problem;

[0167] The DC-side capacitor and flying capacitor voltage balance constraint module is used to derive the DC-side capacitor and flying capacitor voltage balance constraint based on the mathematical relationship between the switching state combination of the multilevel converter and the three-phase flying capacitor voltage and DC-side capacitor voltage.

[0168] The cost function module is used to incorporate the voltage balance constraints of the DC-side capacitor and the flying capacitor into the search process of the spherical decoding algorithm based on the unconstrained optimal solution problem, and to obtain the cost function of the multi-level converter prediction based on multi-objective optimization and spherical decoding, that is, the distance between the center of the sphere obtained by the switching sequence without level jumps.

[0169] The search module is used to set the initial radius of the hypersphere. Taking the single-phase switch state of a single prediction step as a node, the module searches for nodes in each dimension sequentially. When a switch sequence is found within the hypersphere, the hypersphere radius is updated. After multiple searches and updates, until there is exactly one switch sequence within the hypersphere, which is the optimal switch sequence. The updated hypersphere radius is the sum of the squares of the distance from the node of the switch sequence to the unconstrained optimal switch sequence and the capacitor voltage error conversion distance.

[0170] It should be noted that the multi-level converter predictive control device based on multi-objective optimization and spherical decoding provided in the above embodiments is only illustrated by the division of the above functional modules when executing the multi-level converter predictive control method based on multi-objective optimization and spherical decoding. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. In addition, the multi-level converter predictive control device based on multi-objective optimization and spherical decoding provided in the above embodiments and the multi-level converter predictive control method embodiment based on multi-objective optimization and spherical decoding belong to the same concept. The implementation process is detailed in the multi-level converter predictive control method embodiment based on multi-objective optimization and spherical decoding, and will not be repeated here.

[0171] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0172] Furthermore, those skilled in the art will understand that although some embodiments described herein include certain features found in other embodiments but not others, combinations of features from different embodiments are also within the scope of protection of this invention and form different embodiments. For example, in the embodiments described above, those skilled in the art can use them in combination based on known technical solutions and the technical problems to be solved by this application.

Claims

1. A predictive control method for a multi-level converter based on multi-objective optimization and spherical decoding, characterized in that, The method includes: A quadratic programming model is established for the prediction algorithm of a multi-step finite control set model that only considers reference current tracking and switching frequency constraints. The cost function in matrix form is derived from the quadratic programming model and simplified into an unconstrained optimal solution problem. The unconstrained optimal solution of the switch sequence is then obtained. The unconstrained optimal solution problem is described as an integer least squares problem; Based on the mathematical relationship between the switching state combination of the multilevel converter and the voltage of the three-phase flying capacitor and the DC-side capacitor, the balance constraint of the DC-side capacitor and the flying capacitor voltage is derived. Based on the unconstrained optimal solution problem, the voltage balance constraints of the DC-side capacitor and the flying capacitor are added to the search process of the spherical decoding algorithm, and the cost function of multi-level converter prediction based on multi-objective optimization and spherical decoding is obtained, that is, the distance between the center of the sphere obtained by the switching sequence without level jump. The initial radius of the hypersphere is set, and the single-phase switching state of a single prediction step is taken as a node. The nodes in each dimension are searched sequentially. When a switching sequence is found in the hypersphere, the hypersphere radius is updated. After multiple searches and updates, until there is one and only one switching sequence in the hypersphere, which is the optimal switching sequence. The updated hypersphere radius is the sum of the squares of the distance from the node of the switching sequence to the unconstrained optimal switching sequence and the capacitor voltage error conversion distance.

2. The multi-level converter predictive control method based on multi-objective optimization and spherical decoding according to claim 1, characterized in that, The quadratic programming model for establishing a multi-step finite control set model prediction algorithm that only considers reference current tracking and switching frequency constraints includes: Based on the state variable coefficient matrix and input variable coefficient matrix of the current-voltage space state system predicted by single step, a traditional single step model is established to predict the current-space state system. A mathematical model for predicting the current-space state system using a traditional single-step model is derived by extending the prediction model to a multi-step model. Based on the mathematical model of multi-step model prediction, a quadratic programming model is established for the multi-step finite control set model prediction algorithm that only considers reference current tracking and switching frequency constraints.

3. The multi-level converter predictive control method based on multi-objective optimization and spherical decoding according to claim 1 or 2, characterized in that, The quadratic programming model is expressed as: Where, N p To predict the step size, i sx (k+n)(x=a,b,c) represents the three-phase currents at time k+n, and λ s These are the weighting coefficients for the switching frequency constraint term. Let Δu(k+n) be the three-phase output reference phase current at time k+n, and let Δu(k+n) be the total number of three-phase phase voltage level jumps per unit control cycle at time k+n.

4. The multi-level converter predictive control method based on multi-objective optimization and spherical decoding according to claim 3, characterized in that, The unconstrained optimal solution problem is expressed as: The unconstrained optimal solution for the switching sequence is: U unc (k)=-H -1 Θ(k) The Cholesky decomposition of the symmetric positive definite matrix H is: H = VV T U(k) is the multi-step three-phase switching sequence or multi-step three-phase voltage vector being searched at time k, and H -1 Θ(k) is the derived multi-step three-phase optimal switching sequence or multi-step three-phase voltage vector.

5. The multi-level converter predictive control method based on multi-objective optimization and spherical decoding according to claim 4, characterized in that, The description of the unconstrained optimal solution problem as an integer least squares problem is as follows: Among them, J sda (k) represents the naked sphere center distance of the current searched switch sequence, U unc (k) is the unconstrained optimal switching sequence derived at time k. This is the transformed unconstrained optimal solution.

6. The multi-level converter predictive control method based on multi-objective optimization and spherical decoding according to claim 1 or 5, characterized in that, The voltage balance constraint for the DC-side capacitor and the flying capacitor is: Among them, U dc-upper (k+n) represents the DC-side upper bus capacitor voltage at time k+n, U dc-lower (k+n) represents the DC-side lower bus capacitor voltage at time k+n, U fx (k+n)(x=a,b,c) represents the three-phase flying capacitor voltage at time k+n, λ dc U is the weighting coefficient for the DC-side capacitor voltage constraint term. dc λ is the DC bus voltage. fc J is the weighting coefficient for the three-phase flying capacitor voltage constraint term. xfc (k+n)(x=a,b,c) represents the equivalent sphere center distance converted from the voltage error of the flying capacitor in one of the three phases at time k+n. J dc (k+n) is the equivalent sphere center distance converted from the DC-side capacitor voltage error at time k+n, U dc This is the DC bus voltage.

7. The multi-level converter predictive control method based on multi-objective optimization and spherical decoding according to claim 6, characterized in that, The cost function for multi-level converter prediction based on multi-objective optimization and spherical decoding is expressed as: Among them, J xfc (k+n)(x=a,b,c) represents the equivalent sphere center distance converted from the voltage error of the flying capacitor in one of the three phases at time k+n. J dc (k+n) is the equivalent sphere center distance converted from the DC-side capacitor voltage error at time k+n, J fc (k) represents the equivalent sphere center distance converted from the three-phase flying capacitor voltage error at time k, J sda (k) represents the naked sphere center distance of the switch sequence being searched at time k, J sda-5LANPC (k) represents the total center distance of the sphere corresponding to the switch sequence being searched at time k.

8. The multi-level converter predictive control method based on multi-objective optimization and spherical decoding according to claim 1, characterized in that, At the beginning of each sampling period, the initial radius of the hypersphere is set, and the square of the initial radius R is... 2 init The optimal switching sequence U at time k-1 opt (k-1) The sum of the squares of the distance from the unconstrained optimal switching sequence shifted by one time step and the weighted distance of the capacitor voltage error at time k, plus the square of the initial hypersphere radius: Among them, J optdc (k) and J optfc (k) represents the weighted transformation distance of the capacitor voltage error at time k, VU ini (k) is the initial switching sequence for a unit control cycle after processing with a lower triangular matrix. This is the unconstrained optimal switch sequence transformation form derived from the derivation.

9. The multi-level converter predictive control method based on multi-objective optimization and spherical decoding according to claim 1, characterized in that, Based on the principle that switches cannot jump across levels, a formula for calculating the upper bound of the search node number in the spherical decoding algorithm for three-phase multilevel converters is derived. The formula for calculating the upper bound of the number of search nodes is expressed as follows: Among them, S x-statenum (k+n) represents the vector of the number of switching nodes in the search tree dimension of the multi-level converter predictive control method based on multi-objective optimization and spherical decoding corresponding to the x-phase bridge arm at time k+n, where N is the number of switching nodes. p To predict the step size.

10. A predictive control device for a multi-level converter based on multi-objective optimization and spherical decoding, characterized in that, The device includes: The quadratic programming model building module is used to establish a quadratic programming model for a multi-step finite control set model prediction algorithm that only considers reference current tracking and switching frequency constraints. The unconstrained optimal solution module is used to derive the cost function in matrix form from the quadratic programming model, simplify it into an unconstrained optimal solution problem, and find the unconstrained optimal solution of the switch sequence. The least squares module is used to describe an unconstrained optimal solution problem as an integer least squares problem; The DC-side capacitor and flying capacitor voltage balance constraint module is used to derive the DC-side capacitor and flying capacitor voltage balance constraint based on the mathematical relationship between the switching state combination of the multilevel converter and the three-phase flying capacitor voltage and DC-side capacitor voltage. The cost function module is used to incorporate the voltage balance constraints of the DC-side capacitor and the flying capacitor into the search process of the spherical decoding algorithm based on the unconstrained optimal solution problem, and to obtain the cost function of the multi-level converter prediction based on multi-objective optimization and spherical decoding, that is, the distance between the center of the sphere obtained by the switching sequence without level jumps. The search module is used to set the initial radius of the hypersphere. Taking the single-phase switch state of a single prediction step as a node, the module searches for nodes in each dimension sequentially. When a switch sequence is found within the hypersphere, the hypersphere radius is updated. After multiple searches and updates, until there is exactly one switch sequence within the hypersphere, which is the optimal switch sequence. The updated hypersphere radius is the sum of the squares of the distance from the node of the switch sequence to the unconstrained optimal switch sequence and the capacitor voltage error conversion distance.

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