Three-dimensional vector space model predictive control method based on quadratic cost function

Abstract

The application discloses a three-dimensional vector space model predictive control method based on a quadratic cost function, and belongs to the field of power electronic control. The method maps the switching state of a three-phase three-level inverter to a three-dimensional vector space, and divides the three-dimensional vector space into sub-cubes. The reference vector coordinates containing current tracking and midpoint potential balance information are calculated through the deadbeat principle. According to the coordinate symbol and size relationship, the sub-cubes and tetrahedron sectors are located in sequence, so that the selected switching sequence is quickly determined without global traversal. On this basis, a quadratic cost function about the output current and the midpoint potential deviation is constructed, and the optimal action time of each vector is obtained by analytically solving the gradient equation, so that multi-objective collaborative optimization is realized. The application greatly reduces the online calculation amount, realizes fixed switching frequency, significantly improves the steady-state current quality and dynamic response speed, and has strong robustness to parameter changes.

Description

Technical Field

[0001] This invention relates to the field of power electronic system control technology, specifically to a model predictive control method applied to a three-phase three-level voltage source inverter. Background Technology

[0002] Multilevel inverter topologies have been widely used in new energy power generation and energy storage systems due to their advantages such as low device withstand voltage and low voltage stress. Currently, typical multilevel inverter topologies mainly include neutral-point clamped (NPC) inverters, flying capacitor inverters, and T-type inverters. Among them, the three-phase three-level T-type inverter has a simpler structure and higher power conversion efficiency, exhibiting superior overall performance compared to traditional NPC inverters.

[0003] Control strategy is a core technical challenge for three-phase three-level inverters. Currently, commonly used inverter control methods include proportional-integral control, sliding mode control, proportional-resonant control, and repetitive control. Model predictive control (MPC), due to its strong anti-interference capability, fast dynamic response, and ability to flexibly achieve multi-objective optimization, has become a highly promising alternative.

[0004] Traditional finite set model predictive control (FCS-MPC) selects only one optimal voltage vector in each sampling period. Although it has a simple structure and fast dynamic response, it has a large computational burden, and single-vector operation will lead to large output current ripple and unstable switching frequency.

[0005] Optimal Switching Sequence MPC (OSS-MPC) achieves a constant switching frequency by optimizing the switching sequence and the duration of each state, effectively suppressing current ripple and improving steady-state performance. However, calculating the optimal duty cycle incurs a heavy computational burden, and some improved methods still suffer from implementation complexity. For multilevel inverters with numerous switching states, the synchronous determination of the switching sequence and duty cycle limits the real-time implementation of the aforementioned methods.

[0006] Therefore, there is an urgent need for a model predictive control method suitable for T-type three-level inverters, which can ensure high-quality output voltage tracking, balance the midpoint voltage, and reduce the complexity of online calculations.

[0007] Existing technologies have several drawbacks: Traditional FCS-MPC requires traversing 27 switching states, and online prediction and full cost function evaluation result in extremely high computational costs, making real-time implementation difficult. Single-vector action leads to large output current ripple, inconsistent switching frequency, and poor steady-state power quality. Most methods do not collaboratively handle current tracking and midpoint potential balance within a unified framework, limiting multi-objective control capabilities. While multi-vector MPCs such as OSS-MPC can fix the switching frequency, full-sector vector traversal and duty cycle calculation are complex, resulting in a heavy computational burden. Summary of the Invention

[0008] The objective of this invention is achieved through the following technical solutions.

[0009] This invention aims to propose a predictive control method for a three-dimensional vector space model based on a quadratic cost function, thereby addressing the shortcomings of existing technologies.

[0010] (1) A three-dimensional vector space zero-difference vector screening method is proposed, which can quickly locate the region where the optimal vector is located and determine the sequence of candidate vectors accordingly, significantly reducing the amount of online computation.

[0011] (2) Simultaneously consider the dynamics of output current and midpoint potential to establish a more accurate prediction model; combine the output current tracking error and midpoint potential offset to form a cost function, and realize multi-objective coordinated control of current quality and midpoint potential balance.

[0012] (3) Reconstruct the cost function into a quadratic form to optimize the action time of the selected vector sequence; obtain the optimal action time of each vector by solving the gradient equation to minimize the cost function.

[0013] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps: A three-dimensional vector space model predictive control method based on a quadratic cost function, applied to a three-phase three-level T-type inverter, includes the following steps: Step 1: Map the 27 switching states of the three-phase three-level inverter to a three-dimensional vector space composed of the switching states of phases a, b, and c, and divide the three-dimensional vector space into multiple sub-cubes as the basic spatial region for vector selection.

[0014] Step 2: Based on the deadbeat principle, derive and calculate the coordinates (X, Y, Z) of the equivalent reference voltage vector in the three-dimensional vector space, which includes output current tracking and DC side midpoint potential balance information.

[0015] Step 3: Based on the sign of the coordinates (X,Y,Z), quickly determine the sub-cube where the reference vector is located, thereby narrowing the search range from the global 27 vectors to a single sub-cube.

[0016] Step 4: Within the identified sub-cube, based on the magnitude relationship of the components in the coordinates (X, Y, Z), the sub-cube is further divided into six congruent tetrahedral sectors, and the tetrahedral sector where the reference vector is located is determined. The switch vectors corresponding to the four vertices of this tetrahedral sector are directly selected as the candidate switch vector sequence, achieving fast and accurate positioning of the candidate vectors without the need for traversal enumeration.

[0017] Step 5: Construct a high-precision prediction model that includes the deviation between output current and midpoint potential. Substitute this model into a cost function with output current tracking error and midpoint potential offset as control objectives, and reconstruct it into a quadratic cost function with respect to the action time (duty cycle) of the four selected vectors.

[0018] Step Six: By calculating the gradient of the quadratic cost function and setting it to zero, the optimal operating time of each vector in the candidate switch vector sequence is obtained. To address the potential singularity of the coefficient matrix during the solution process, a block-based, order-reduction solution method is used to obtain all optimal duty cycles.

[0019] Step 7: Based on the optimal operating time, generate a symmetrically arranged switch sequence that starts and ends with a zero vector, which is used to generate a pulse width modulation signal to control the inverter, thereby achieving a fixed switching frequency and optimal steady-state performance.

[0020] The advantages of this invention are: (1) By using the two-level geometric positioning method of three-dimensional vector space and sub-cube-tetrahedron, the minimum candidate switch sequence containing the reference vector can be quickly screened out, completely avoiding the traversal prediction and cost function evaluation of the global 27 vectors. The execution time of the core algorithm is shortened by about 53% compared with the traditional FCS-MPC, significantly reducing the online computing burden.

[0021] (2) Integrating current tracking and midpoint potential balance into a unified three-dimensional deadbeat reference vector calculation framework realizes multi-objective collaborative control and ensures excellent control performance.

[0022] (3) By constructing a quadratic cost function and analytically solving for the optimal duty cycle, the system performance under multi-vector action is optimized. While maintaining a fixed switching frequency, the steady-state current quality is significantly improved, and the total harmonic distortion (THD) of the output voltage and current is far superior to that of traditional methods. Experiments show that under the same operating conditions, its current THD can be as low as 1.42%, while that of traditional FCS-MPC is 10.20%.

[0023] (4) The method proposed in this invention has strong robustness to changes in model parameters. It can still maintain a low current THD within the range of -40% to 40% of inductance parameter mismatch, ensuring stable operation under complex working conditions. Attached Figure Description

[0024] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1This is a topology diagram of a T-type three-phase three-level inverter. Figure 2 It is a voltage vector distribution diagram in the traditional α-β coordinate system. Figure 3 This is a schematic diagram of the distribution of the 27 vectors in the three-dimensional vector space in this invention. Figure 4 This is a schematic diagram of the tetrahedral division of a sub-cube, taking Cube0 as an example in this invention.

[0025] Figure 5 This is a schematic diagram showing the changes in output current and NP voltage deviation under the action of a symmetrical vector sequence within one control cycle in this invention.

[0026] Figure 6 This is a block diagram of the overall control structure of the TDVS-MPC method proposed in this invention. Figure 7 This is a comparison chart of the execution times of different MPC algorithms. Figure 8 This is a comparison of steady-state experimental waveforms when the reference current amplitude is 2A. Figure 9 This is a comparison of steady-state experimental waveforms when the reference current amplitude is 4A. Figure 10 This is a comparison diagram of dynamic experimental waveforms when the reference current amplitude jumps from 2A to 4A. Figure 11 This is a comparison diagram of waveforms from a midpoint potential equilibrium experiment. Figure 12 This is a graph showing the robustness test results when the inductor parameters are misaligned. Detailed Implementation

[0027] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0028] Terminology Explanation: Three-phase three-level voltage source inverter (3P-3L-VSI): An advanced power conversion device in the field of power electronics, the three-level inverter topology offers a good trade-off between topology complexity, conversion efficiency, and output voltage quality, making it a preferred solution for medium- and low-voltage, high-power applications. Compared to traditional two-level or three-level topologies, it has advantages such as lower output harmonic content, less electromagnetic interference, and lower filtering requirements.

[0029] Finite Control Set Model Predictive Control (FCS-MPC) is an advanced control strategy applicable to power electronic converters. Its core lies in leveraging the finite number of converter switching states. Within each control cycle, it predicts the future system behavior under all possible combinations of switching states using a discrete model of the system, and directly selects the optimal switching state for application to the converter based on a predefined cost function. This method is characterized by its conceptual simplicity and fast dynamic response.

[0030] Optimal Switching Sequence Model Predictive Control (OSS-MPC): Achieves a fixed switching frequency by optimizing the switching sequence and the action time, which can suppress current ripple, but the duty cycle is complex to solve.

[0031] Midpoint potential (NP voltage) balance: The voltages of the upper and lower capacitors on the DC side of a three-level inverter remain balanced. If the charging and discharging of the upper and lower capacitors are inconsistent, a midpoint voltage shift will occur, which will affect the output voltage quality and device safety.

[0032] A. System Model The topology of a T-type three-phase three-level inverter is as follows: Figure 1 As shown. The DC-side input voltage is expressed as... And the voltages of the upper and lower capacitors are respectively and The currents flowing through the upper and lower capacitors are respectively... and ,and This represents the current flowing through the midpoint potential. The inverter uses an output-side filter inductor. Connected to a three-phase linear resistor The phase output current is represented by , and the phase current is represented by . ,in .

[0033] like Figure 1 As shown, each phase of the T-type three-phase three-level inverter contains four controllable switching components: , , and By combining these switches appropriately, each phase branch can generate three voltage levels. Therefore, the state of each phase switch can be represented as follows: , defined as “1”, “0” and “-1”, corresponding to “P”, “O” and “N” respectively. Formula (1) represents the switching state and the output phase voltage. The relationships are summarized in Table 1.

[0034] Table 1 Three-phase switch status Since each phase arm has three switching states, a total of 3 can be obtained. 3 =27 switching combinations. Based on the voltage amplitude, these voltage vectors can be divided into four categories: zero voltage vector, small voltage vector, medium voltage vector, and large voltage vector. Figure 2 The output voltage vector distribution of a three-phase three-level T-type inverter in the traditional α-β coordinate system is shown.

[0035] The output current in the α-β coordinate system is as follows As shown: in It is expressed as the voltage difference between the DC side midpoint O and the load neutral point n.

[0036] Will The Clark transformation yields the following... : in and These represent the output voltages in the α-β coordinate system, respectively.

[0037] Using the forward Euler method Discretization yields the predicted output current in the α-β coordinate system: This represents the sampling and control period. When the DC bus voltage is considered constant, the capacitive current flowing through the upper and lower capacitors on the DC side can be expressed as: This represents the upper and lower capacitances. Similarly, the forward Euler method is used to represent the equation. Discretization yields the predicted values ​​of the upper and lower capacitor voltages: Combined And introduce the equilibrium current condition. The predicted NP voltage deviation can be obtained. for: B. Three-dimensional vector space distribution Traditional α-β plane representation compresses the switching information of each phase. To preserve this information, 27 voltage vectors are mapped to a three-dimensional vector space, with the three axes corresponding to the switching states of phases a, b, and c, respectively. Each switching state can be directly represented by spatial coordinates, such as... Figure 3 As shown.

[0038] The entire switch state space is divided into eight sub-cubes, each bounded by eight adjacent switch state vectors, serving as the basic spatial region for vector selection. For ease of analysis, these sub-cubes are numbered sequentially from 0 to 7. This division provides a geometric basis for candidate vector simplification; the target switch sequence can be searched only within the sub-cubes containing the reference vector.

[0039] C. Vector sequence sector filtering In traditional sector selection methods based on deadbeat detection, the reference vector is fixed in the α-β plane, which cannot uniquely determine the switching sequence. For example... Figure 2 In sector S1, the same α-β vector region can correspond to multiple multi-vector switching sequences, each with a different path. If candidate sequences are filtered one by one using a cost function, the computational load on the processor will increase significantly.

[0040] To address this, this invention proposes a direct basis vector sector selection strategy in a three-dimensional vector space. By mapping the three-phase switch states to three-dimensional space, the optimal switch sequence can be directly determined, significantly reducing the number of candidates and improving computational efficiency.

[0041] Step 1: The reference voltage is from Derivation: in and These are the reference voltages in the α-β coordinate system at the current moment. , These are the reference currents in the α-β coordinate system at the current moment.

[0042] Step 2: The output voltage in the α-β coordinate system can be derived from the phase voltage through Clarke transformation: Will Substitute Based on the deadbeat principle, the reference voltage vector formula is as follows: in , and Represents the equivalent switch state coordinates in three-dimensional vector space.

[0043] For discrete NP voltage models Using the deadbeat principle, the NP voltage balance condition can be derived: in This indicates voltage deviation. Combined with... , and NP voltage balance condition ,definition The coordinates of a reference vector in three-dimensional vector space can be represented by the following formula: in . This indicates capacitance deviation.

[0044] Step 3: Based on The coordinates (X, Y, Z) in the coordinate plane determine the sub-cube containing the reference vector. The coordinate planes X=0, Y=0, and Z=0 divide the three-dimensional vector space into 8 sub-cubes. Therefore, the sub-cube to which the reference vector belongs can be determined based on the signs of X, Y, and Z. The specific determination rules are summarized in Table 2.

[0045] Table 2 Sub-cube determination Step 4: To determine the switch vector sequence, the identified sub-cubes need to be further decomposed into six congruent tetrahedrons, denoted as S0–S5. Each sub-cube shares a zero vector and its corresponding larger vector as two common vertices, meaning the body diagonal connecting these two vectors is shared by all six tetrahedrons.

[0046] Taking Cube0 as an example, the body diagonal formed by OOO and PPP serves as a common edge, dividing Cube0 into six tetrahedrons with identical geometric shapes, such as... Figure 4 As shown.

[0047] After obtaining the reference vector coordinates (X, Y, Z), the tetrahedron containing these coordinates is further determined, and the four switch vectors at each vertex of the tetrahedron are selected as the corresponding switch vector sequence. For example... Figure 1 As shown, when the reference coordinates are located in sector S0 of Cube0, the corresponding four vertex vectors are OOO, POO, PPO and PPP, respectively.

[0048] The tetrahedral region where the reference vector is located can be determined based on the magnitude relationship between X, Y, and Z. Specifically, by comparing the maximum and minimum values ​​of X, Y, and Z, the sector to which the reference vector belongs can be determined, and the determination rules are shown in Table 3. Table 3 Sector identification based on coordinate comparison To simplify the implementation process, this invention maps the reference vectors in the identified sub-cubes back to Cube0 through rotation and mirror transformations, thereby unifying the sector identification process for all sub-cubes. Therefore, the tetrahedral partitioning rules established for Cube0 can be extended to all sub-cubes. The rotation and mirror matrices are defined as follows: in Let be the rotation matrix about the Z-axis, where It is the index of the rotation. Matrix H represents the mirror transformation relative to the XY plane.

[0049] make This represents the index of the identified sub-cube. A sub-cube located above the XY plane is defined as... The lower sub-cube located below the XY plane is defined as Accordingly, the composite transformation matrix for Cubej is designed as follows: Furthermore, each switch sequence is arranged symmetrically, with the zero vector OOO shared by all sub-cubes serving as the start and end vectors. This arrangement can identify changes in the sub-cubes within continuous sampling periods, avoiding unnecessary switch transitions, while also helping to achieve a fixed switching frequency and improve output current quality.

[0050] After coordinate transformation, all sub-cubes can be identified using a unified sector recognition rule. Subsequently, the switch vector sequence can be determined through geometric positioning without the need for global enumeration. Compared to traditional FCS-MPC, this method reduces the real-time computational burden on the controller.

[0051] D. Predictive Model Construction For each acting vector, the components of the output current in the α-β coordinate system and the NP voltage deviation can be obtained from... and Derivation: in , and They represent vectors respectively Caused by the action , and The change in quantity. and Representing vectors respectively The corresponding output voltage in the α-β coordinate system.

[0052] The predicted values ​​of output current and NP voltage deviation are as follows: As shown: in , , and This represents the duty cycle allocated to the four selected vectors within one sampling period. It satisfies the following constraints: Figure 5 The variations of the α-β axis current components and NP voltage deviation within one control cycle under the action of a symmetrical vector sequence are presented. The applied vector sequence is arranged as V0-V1-V2-V3-V3-V2-V1-V0, and the corresponding vector application times are symmetrically distributed within one control cycle.

[0053] E. Optimal duty cycle calculation The cost function of the proposed TDVS-MPC strategy is as follows: As shown: in This represents the weighting factor.

[0054] Will Substituting the prediction model into the cost function, we obtain the quadratic expression: in Elements in A can be defined as: in .

[0055] right The gradient function for differentiating d in the given form is: in .

[0056] The optimal duty cycle can be obtained through the command expression. The gradient is zero, which is obtained as follows: Let Q represent the optimal duty cycle. If the voltage reference vector is located in Cube0 or Cube6, then the first column of A is zero. Therefore, Q is a singular matrix with its first row and first column both being zero. For the other cubes, the first column of A is non-zero, and Q is a non-singular matrix. Therefore, the solution for the duty cycle is discussed in two cases.

[0057] Case 1: The reference vector is located in a cube outside of Cube0 and Cube6, in which case A is a non-singular matrix. Therefore, Q is also a non-singular matrix, and and (A) T ) -1 Both exist. The optimal duty cycle can be obtained from the formula... The derivation is as follows: Case 2: When the reference vector is located within Cube0 or Cube6, the first and fourth vectors in the selected vector sequence are both zero-voltage vectors. Therefore, they do not cause any increments in the output current component or NP voltage deviation. Accordingly, the first column of A is zero, resulting in a singular matrix Q. Therefore, Q, d, and q can be represented in blocks as follows: in Q ij Let q represent the element in the i-th row and j-th column of matrix Q. i Let represent the i-th element of q.

[0058] Will Substitution We can obtain: Due to the singularity of Q, the first row of the linear equation system degenerates into the trivial identity 0 = 0, indicating that the variable It is not constrained by the quadratic cost function. The remaining variables can be obtained by solving the reduced-order system: Since the other two effective column vectors of A are linearly independent in this case, Q r It is a positive definite and non-singular matrix. Therefore, Q r -1 There exists a reduced-order solution, which can be expressed as: In obtaining and Then, the remaining duty cycle is allocated to and Since the first and fourth vectors in Cube0 and Cube6 have no effect on the controlled variables, their duty cycles are symmetrically distributed as follows: F. Overall Control Diagram The control structure of TDVS-MPC is as follows: Figure 6 As shown, it includes the following steps: Step 1: Map the 27 switching states of the three-phase three-level inverter to a three-dimensional vector space composed of the switching states of phases a, b, and c, and divide the three-dimensional vector space into multiple sub-cubes; Step 2: Based on the deadbeat principle, calculate the coordinates (X, Y, Z) of the equivalent reference voltage vector in the three-dimensional vector space, which includes output current tracking and DC side midpoint potential balance information; Step 3: Determine the sub-cube containing the equivalent reference voltage vector based on the signs of the coordinates (X, Y, Z); Step 4: Within the identified sub-cube, based on the magnitude relationship of each component in the coordinates (X,Y,Z), the sub-cube is further divided into multiple tetrahedral sectors, and the tetrahedral sector where the equivalent reference voltage vector is located is determined. The switch vectors corresponding to each vertex of the tetrahedral sector are selected as the candidate switch vector sequence. Step 5: Construct a prediction model that includes the deviation between output current and midpoint potential. Use the action time of each vector in the candidate switch vector sequence as the optimization variable, and establish a quadratic cost function that includes the output current tracking error and the midpoint potential offset. Step 6: By calculating the gradient of the quadratic cost function and setting it to zero, the optimal action time of each vector in the candidate switch vector sequence is obtained; Step 7: Generate a symmetrically arranged switch sequence based on the optimal operating time to control the inverter.

[0059] Table 4 System Parameters This invention establishes an experimental platform for a three-phase, three-level T-type inverter controlled by a DSP-TMS320F28374S to evaluate the performance of the TDVS-MPC method. In the experimental platform, the output current is measured using a Hall effect current sensor, and the NP voltage is measured using a LEM voltage sensor. Both sampling and control algorithm execution are performed by the DSP-TMS320F28374S. Table 4 summarizes the main experimental parameters.

[0060] On the same experimental platform, the traditional FCS-MPC, OSS-MPC, and the TDVS-MPC algorithm proposed in this invention were tested. To ensure fair comparison, all three algorithms used the same dead time, sampling frequency, and control frequency. After steady-state and dynamic experimental debugging, the weight factor of the three MPC methods was uniformly set to 1.0 in subsequent experiments, thereby further ensuring the fairness of the comparison.

[0061] The experimental verification was conducted under the following operating conditions: Condition A: Compare the execution time of the three algorithms.

[0062] Condition B1: The reference current amplitude is set to 2A.

[0063] Condition B2: The reference current amplitude is set to 4A.

[0064] Condition C: Apply a dynamic current step from condition B1 to condition B2.

[0065] Condition D: Apply a 40V midpoint voltage offset to examine the voltage balance capability.

[0066] Condition E: Under condition B2, test the robustness of TDVS-MPC to changes in inductance parameters.

[0067] Experimental results of the present invention A. Calculation time The runtime of each control task is evaluated using the clock cycles recorded by the CCS built-in clock function. Accordingly, the time consumed by ADC conversion, protection procedures, MPC algorithm execution, and PWM updates within each control cycle can be obtained.

[0068] like Figure 7 As shown, the execution time of FCS-MPC is 28.54 μs, that of OSS-MPC is 30.53 μs, while that of TDVS-MPC is only 13.29 μs. Compared with FCS-MPC, TDVS-MPC reduces the execution time by approximately 53%; compared with OSS-MPC, it reduces it by approximately 56%.

[0069] The above results demonstrate that TDVS-MPC significantly reduces the amount of online computation.

[0070] B. Steady-state performance test To evaluate the steady-state performance of TDVS-MPC, two sets of comparative experiments were conducted under conditions B1 and B2. Figure 8 The experimental results under condition B1 are given. Figure 9 The corresponding experimental results under condition B2 are presented. These figures show the upper capacitor voltage under conventional FCS-MPC, OSS-MPC, and the TDVS-MPC proposed in this invention, respectively. Line voltage The FFT spectra of the output currents of phase A and phase B, and the current of phase A.

[0071] Experimental results show that under conditions B1 and B2, all three algorithms can track the current reference value and maintain NP voltage balance.

[0072] However, the steady-state current quality of the three algorithms differs significantly. According to FFT results, the THD of the A-phase current obtained by the traditional FCS-MPC under conditions B1 and B2 are 19.28% and 10.20%, respectively. When using OSS-MPC, the corresponding THDs are reduced to 6.87% and 4.20%, respectively. In contrast, TDVS-MPC achieves the lowest THD under the same operating conditions, at 3.56% and 1.42%, respectively, indicating that it has superior steady-state current quality.

[0073] Furthermore, FCS-MPC applies only a single vector in each control cycle, resulting in a variable switching frequency, which is detrimental to filter design. In contrast, OSS-MPC and TDVS-MPC both employ multi-vector modulation to maintain a fixed switching frequency. Therefore, TDVS-MPC not only improves output current quality but also exhibits superior switching frequency characteristics in practical applications.

[0074] C. Dynamic Performance Testing To evaluate the dynamic performance of TDVS-MPC, experiments were conducted under condition C. Figure 10 The upper capacitor voltages are given for conventional FCS-MPC, OSS-MPC, and the TDVS-MPC proposed in this invention. Line voltage And the A-phase current waveform.

[0075] The measured waveforms show that when the current reference value increases from 2A to 4A, all three algorithms can track the updated command and maintain stable current regulation. However, there are differences in their transient response speeds. FCS-MPC requires 3.7ms to reach the new steady state, while OSS-MPC reduces the response time to 1.0ms. In contrast, the TDVS-MPC proposed in this invention achieves the fastest response, with a settling time of only 0.4ms.

[0076] Regarding NP voltage regulation, the NP voltage differences of FCS-MPC, OSS-MPC, and TDVS-MPC after a current step are approximately 5.6V, 6.0V, and 5.8V, respectively, indicating that the three algorithms have similar NP voltage fluctuation suppression capabilities during transient processes.

[0077] D. Midpoint potential self-balancing For a three-phase three-level T-type inverter, NP voltage balance is a critical control objective. Under condition D, an initial 40V deviation is applied between the upper and lower capacitor voltages to compare the voltage balance capabilities of three algorithms. Figure 11 The lower capacitor voltages for conventional FCS-MPC, OSS-MPC, and TDVS-MPC are given respectively. upper capacitor voltage and line voltage .

[0078] Experimental results show that all three algorithms can suppress the initial NP voltage deviation and restore the balance between the upper and lower capacitor voltages. However, there are significant differences in their balancing speeds. FCS-MPC requires approximately 1162 ms to eliminate the NP voltage imbalance, while OSS-MPC can achieve voltage balance within 38 ms. TDVS-MPC requires approximately 108 ms, which is longer than OSS-MPC but still significantly shorter than FCS-MPC.

[0079] Once the NP voltage stabilizes, the voltage ripple of FCS-MPC, OSS-MPC, and TDVS-MPC are 3V, 2V, and 1.2V, respectively. Despite slight differences, the three algorithms generally perform similarly in terms of NP voltage balancing.

[0080] E. Parameter Misalignment Test In practical applications, model parameter mismatch is unavoidable and can be caused by temperature variations and changes in operating conditions. To examine parameter robustness, the inductance value used in the control algorithm is varied relative to the actual inductance value within a range of -40% to 40%. The corresponding inductance mismatch is defined as: in, This indicates the inductance parameters used by the controller. This represents the actual inductance value in the experimental platform. Except for the inductance parameter mismatch, the other experimental conditions are consistent with condition B2.

[0081] Figure 12 The THD of the current under different inductance mismatches is presented. When the inductance mismatch varies within the range of -40% to 40%, the THD values ​​of the traditional FCS-MPC and OSS-MPC change significantly, indicating that they are highly sensitive to changes in inductance parameters. In contrast, the TDVS-MPC proposed in this invention can maintain the THD within a narrow range of approximately 1.4%–2.9% throughout the entire mismatch range, demonstrating superior harmonic suppression capability and stronger robustness to inductance parameter mismatch.

[0082] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A three-dimensional vector space model predictive control method based on a quadratic cost function, applied to a three-phase three-level T-type inverter, characterized in that, Includes the following steps: Step 1: Map the 27 switching states of the three-phase three-level inverter to a three-dimensional vector space composed of the switching states of phases a, b, and c, and divide the three-dimensional vector space into multiple sub-cubes; Step 2: Based on the deadbeat principle, calculate the coordinates (X, Y, Z) of the equivalent reference voltage vector in the three-dimensional vector space, which includes output current tracking and DC side midpoint potential balance information; Step 3: Determine the sub-cube containing the equivalent reference voltage vector based on the signs of the coordinates (X, Y, Z); Step 4: Within the identified sub-cube, based on the magnitude relationship of each component in the coordinates (X,Y,Z), the sub-cube is further divided into multiple tetrahedral sectors, and the tetrahedral sector where the equivalent reference voltage vector is located is determined. The switch vectors corresponding to each vertex of the tetrahedral sector are selected as the candidate switch vector sequence. Step 5: Construct a prediction model that includes the deviation between output current and midpoint potential. Use the action time of each vector in the candidate switch vector sequence as the optimization variable, and establish a quadratic cost function that includes the output current tracking error and the midpoint potential offset. Step 6: By calculating the gradient of the quadratic cost function and setting it to zero, the optimal action time of each vector in the candidate switch vector sequence is obtained; Step 7: Generate a symmetrically arranged switch sequence based on the optimal operating time to control the inverter.

2. The method according to claim 1, characterized in that, In step two, the calculation of the coordinates (X,Y,Z) of the equivalent reference voltage vector in the three-dimensional vector space combines deadbeat current prediction based on the system discrete model and deadbeat condition of DC side midpoint potential balance.

3. The method according to claim 1, characterized in that, In step three, determining the sub-cube based on the signs of the coordinates (X,Y,Z) specifically involves: based on the positive and negative signs of the coordinates X, Y, and Z, and according to a pre-defined correspondence, positioning the reference vector to one of the eight sub-cubes.

4. The method according to claim 1, characterized in that, In step four, determining the tetrahedral sector where the equivalent reference voltage vector is located further includes: when the identified sub-cube is not the reference sub-cube, mapping the reference vector coordinates within the sub-cube back to the reference sub-cube through rotation transformation and / or mirror transformation, so as to adopt a unified sector identification rule.

5. The method according to claim 1, characterized in that, Step five, specifically, involves constructing the quadratic cost function: Substituting the prediction model of output current and DC side midpoint potential deviation into the initial cost function, we obtain a quadratic function expression with the duty cycle of each vector as the independent variable.

6. The method according to claim 1, characterized in that, Step six, specifically, involves determining the optimal action time: Determine whether the coefficient matrix of the quadratic cost function is singular; When the coefficient matrix is ​​non-singular, the optimal duty cycle can be obtained directly by matrix inversion. When the coefficient matrix is ​​singular, the variables to be solved are divided into blocks. First, the non-singular reduced-order subsystem is solved to obtain a portion of the effective duty cycle. Then, the remaining duty cycle is symmetrically distributed to redundant vectors that have no effect on the control objective.

7. The method according to claim 1, characterized in that, In step seven, the symmetrically arranged switch sequence uses the zero vector as the start and end vectors, and the switch sequence is symmetrically distributed within one control cycle to achieve a fixed switching frequency.

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