Equivalent two-level fast double-vector model predictive control method applied to three-level inverter

Abstract

The invention relates to an equivalent two-level fast double-vector model predictive control method applied to a three-level inverter. The method specifically comprises the following steps: sampling output current and direct current side upper and lower capacitor voltages at a k moment; predicting an expected voltage according to the mathematical model of the three-level inverter and the expected current; performing first value function calculation according to an equivalent two-level vector set composed of positive and negative small vectors to obtain an optimal small vector; calculating a second value function according to the equivalent two-level vector set where the optimal small vector is located to obtain a suboptimal vector; according to the characteristic that the vector action time is inversely proportional to a value function, the action time of an optimal small vector and the action time of a suboptimal vector are calculated; and applying a switching signal under the combined action of the optimal small vector and the suboptimal vector to a three-level inverter. According to the method, the vector set equivalent to two levels is established, so that the vector optimization process is simplified, and the model calculation time is greatly shortened; a value function of a single control target is established, and the tedious design process of weight factors is omitted; and a double-vector model predictive control method is adopted, so that output current harmonics are reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of three-level inverter control, and in particular to an equivalent two-level fast dual-vector model predictive control method applied to a three-level inverter. Background Art

[0002] With the continuous advancement of power electronic devices and control technology, multi-level inverters have become a major development direction for power conversion systems. Traditional two-level inverters have problems such as switching losses and large electromagnetic interference in high-power applications. By increasing the voltage level, three-level inverters can effectively reduce switching stress and improve power density and conversion efficiency. In the fields of renewable energy, industrial drive, grid interconnection, etc., there is an urgent need for high-quality and high-efficiency power conversion equipment. Three-level inverters have received extensive attention and research due to their excellent performance.

[0003] The model predictive control strategy based on optimization theory has received extensive attention and research in the field of industrial control in recent years. Compared with the traditional space vector pulse width modulation strategy, the model predictive control strategy has better dynamic response and anti-interference ability, and does not require complex modulation wave generation links, and the control structure is simpler. The three-level inverter adopts the model predictive control strategy to give full play to the advantages of its multi-level topology and achieve better dynamic response performance, output power quality and system robustness. For the traditional model predictive control, its essence is an enumeration method, that is, all the switch states of the next cycle are evaluated, and the optimal switch state is selected from them for application to the actual circuit topology. For the three-level inverter, it contains 27 different voltage vectors. If these voltage vectors are traversed one by one according to the traditional model predictive control, a lot of calculations are required, which puts high demands on the computing power of the processor. At the same time, the traditional model predictive control only outputs a single voltage vector in each control cycle, which may cause the same voltage vector output to be maintained in several consecutive control cycles, reducing the average switching frequency of the switch tube, resulting in large output current harmonics.

[0004] For the midpoint potential imbalance problem of three-level inverters, traditional model predictive control has the advantage of easy multi-target tracking. It introduces the midpoint potential constraint term in the value function to achieve midpoint potential balance control. However, in actual application scenarios, there is no clear linear relationship between the weight factor and the control quantity, and it usually needs to be repeatedly adjusted in experiments. If the weight factor is introduced into the value function, that is, the value function contains two control objectives, current control and midpoint potential balance control, the two will inevitably affect each other, which to a certain extent affects the accurate prediction of the current control target, and ultimately leads to the problem of increased output current harmonics.

[0005] Therefore, the present invention proposes an equivalent two-level fast dual-vector model predictive control method applied to a three-level inverter. By establishing an equivalent two-level vector set, the vector optimization process is simplified and the model calculation time is greatly reduced; a value function of a single control target is established, eliminating the tedious design process of the weight factor; and the dual-vector model predictive control method is adopted to reduce the output current harmonics. Summary of the invention

[0006] The technical problem to be solved by the present invention is to overcome the deficiencies in the prior art and provide an equivalent two-level fast dual-vector model predictive control method applied to a three-level inverter to solve the problems of large amount of calculation, difficulty in setting weight factors, and large output current harmonics in the existing model predictive control.

[0007] To achieve the above object, the present invention is implemented through the following technical solutions:

[0008] Step 1: Sample and calculate the output current i at time k αβ (k) and the DC side upper and lower capacitor voltage u 1 、u 2 ;

[0009] Step 2: Predict the expected voltage u based on the three-level inverter mathematical model and the expected current αβ * (k):

[0010]

[0011] Where L is the filter inductance, T s is the sampling period, R is the load resistance, and the expected current i at time k+1 is αβ * (k+1) is obtained by Lagrange interpolation method:

[0012]

[0013] Step 3: Construct an equivalent two-level vector set based on the positive and negative small vectors around the zero vector, and substitute the coordinates of the six voltage vectors representing the positive and negative small vectors into the value function g 1 :

[0014]

[0015] Where u αβ (k) is the voltage vector coordinate of the positive and negative small vectors under the αβ coordinate axis. Compare the value function values ​​under the 6 different voltage vector coordinates and select the value that makes g 1 The minimum voltage vector coordinates are taken as the optimal small vector v 1 .

[0016] Step 4: Set the expected voltage uαβ * (k) Subtract the optimal small vector v1 to obtain the modified expected voltage vector u in the equivalent two-level region where the optimal small vector is located αβ ′(k):

[0017]

[0018] Step 5: Substitute the coordinates of the six voltage vectors representing the positive and negative small vectors into the value function g 2 :

[0019] g 2 =|u′ αβ (k)-u aβ (k)|

[0020] Compare the value function values ​​under 6 different voltage vector coordinates and select g 2 The minimum voltage vector coordinate is taken as the suboptimal vector v2.

[0021] Step 6: Calculate the optimal small vector v based on the characteristic that the vector action time is inversely proportional to the value function 1 and the suboptimal vector v 2 Duration of action:.

[0022]

[0023] Where t 1 ,t 2 are the optimal small vector v 1 and the suboptimal vector v 2 The action time, and t 1 +t 2 =T s .

[0024] Step 7: According to the DC side upper and lower capacitor voltage u 1 、u 2 The relationship between selects the type of small vector, so as to obtain the optimal small vector v 1 and the suboptimal vector v 2 It represents the actual switching status of the twelve-way switching tubes.

[0025] Step 8: According to the optimal small vector v 1 and the suboptimal vector v 2 Switching state and action time t 1 ,t 2 , in a control cycle, when T s <t 1 / 2, the output v 1 represents the switch state; when t 1 / 2≤T s <t 1 / 2+t 2 When t 1 / 2+t 2 ≤T s When the output is v 1 Represents the switch state.

[0026] The above switching states are applied to the three-level inverter topology to achieve current prediction control and midpoint potential balance control.

[0027] The beneficial technical effects of the present invention are:

[0028] 1) The present invention simplifies the vector optimization process by establishing an equivalent two-level vector set, reduces the number of predictions from 27 times per cycle to 12 times, and greatly reduces the model calculation time.

[0029] 2) The present invention establishes a value function of a single control objective, omitting weight factors and avoiding the cumbersome design process.

[0030] 3) The present invention adopts a dual-vector model predictive control method, and the synthesized voltage vector is closer to the desired voltage, which can reduce the output current harmonics. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to make the technical solutions of the prior art clearer and the specific implementation methods easier to understand, the accompanying drawings are introduced.

[0032] Figure 1 It is a three-level inverter circuit topology;

[0033] Figure 2 This is the three-level space voltage vector distribution diagram:

[0034] Figure 3 is an equivalent two-level vector diagram;

[0035] Figure 4 A modified expected voltage vector diagram in the first region;

[0036] Figure 5 The implementation steps of the control method involved in the present invention;

[0037] FIG6( a ) is a waveform diagram of the output current under the action of the traditional model predictive control;

[0038] FIG6( b ) is a waveform diagram of the output current under the control method of the present invention;

[0039] FIG7( a ) is a waveform diagram of the DC bus capacitor voltage under the traditional model predictive control;

[0040] FIG7( b ) is a waveform diagram of the DC bus capacitor voltage under the control method of the present invention. DETAILED DESCRIPTION

[0041] The technical solution is described below in conjunction with the accompanying drawings to make the objects and advantages of the present invention clearer and easier to understand for those skilled in the art. However, the present invention is not limited to the scope of the specific implementation methods. For those of ordinary skill in the art, as long as the changes are obvious within the scope and spirit of the claims, they are all protected by the present invention.

[0042] The implementation steps of the equivalent two-level fast dual-vector model predictive control method applied to a three-level inverter according to the present invention are as follows: Figure 5 As shown, the following steps are included:

[0043] Step 1: Sample and calculate the output current i at time k αβ (k) and the DC side upper and lower capacitor voltage u 1 、u 2 ;

[0044] Step 2: Predict the expected voltage u based on the three-level inverter mathematical model and the expected current αβ * (k):

[0045] The mathematical model of the inverter in the αβ two-phase stationary coordinate system is:

[0046]

[0047] where u αβ is the αβ component of the inverter output voltage, i αβ is the αβ component of the output current, L is the filter inductor, and R is the load resistance. Since the sampling period is very small, the output current can be discretized forward Euler, where k is the time index, T s is the sampling period, as follows:

[0048]

[0049] Substituting into the inverter mathematical model, we get the corresponding discrete prediction model:

[0050]

[0051] Where i αβ (k+1) represents the predicted output current value at time k+1. Based on the deadbeat principle, the expected voltage u is obtained αβ * (k):

[0052]

[0053] The expected current i at time k+1 is ɑβ *(k+1) is obtained through linear interpolation:

[0054]

[0055] Step 3: Construct an equivalent two-level vector set based on the positive and negative small vectors around the zero vector, and substitute the coordinates of the six voltage vectors representing the positive and negative small vectors into the value function g based on the expected voltage. 1 :

[0056]

[0057] Where u αβ (k) is the voltage vector coordinate of the positive and negative small vectors under the αβ coordinate axis, Figure 1 is its vector position. Table 1 is the vector table:

[0058] Table 1 Positive and negative small vector voltage vector coordinates

[0059] Compare the value function values ​​under 6 different voltage vector coordinates and choose the value that makes g 1 The minimum voltage vector coordinate is the optimal small vector v 1 .

[0060] Step 4: Set the expected voltage u αβ * (k) Subtract the optimal small vector to obtain the modified expected voltage vector u′ in the equivalent two-level region where the optimal small vector is located αβ (k):

[0061]

[0062] The expected voltage vector is composed of the optimal small vector and the modified expected voltage vector. The purpose of predicting the modified expected voltage vector is to select the suboptimal vector, such as Figure 2 The calculation of the modified desired voltage vector is to convert the three-level space vector set coordinate system into an equivalent two-level vector set coordinate system. The purpose is to reduce the number of candidate voltage vector coordinates. In the equivalent two-level vector set, only 6 different voltage vector coordinates are involved in the calculation, and there is no need to list all 18 voltage vector coordinates.

[0063] Step 5: Substitute the coordinates of the six different voltage vectors into the value function g established based on the modified expected voltage vector 2 :

[0064] g 2 =|u′ αβ (k)-u αβ (k)|

[0065] Choose the value function g 2 The minimum voltage vector coordinate is taken as the suboptimal vector v 2 Because this optimization process can only determine the suboptimal vector v 2 The vector coordinate position in the equivalent two-level vector set, so it is also necessary to select the optimal small vector v 1 With the suboptimal vector v 2 The position relationship and the DC side upper and lower capacitor voltage u 1 、u 2 The relationship between the suboptimal vector v 2 Represents the actual switch state.

[0066] Step 6: According to the characteristic that the vector action time is inversely proportional to the value function, the optimal small vector v is obtained using the following formula: 1 With the suboptimal vector v 2 Action time:

[0067]

[0068] Where t 1 ,t 2 are the optimal small vector v 1 and the suboptimal vector v 2 The action time, and t 1 +t 2 =T s .

[0069] Because a vector coordinate represents two positive and negative small vectors, according to the upper and lower capacitor voltages u on the DC side 1 、u 2 The relationship between selects the type of small vector in Table 1, thereby determining the optimal small vector v 1 Determines the switch state.

[0070] Step 7: According to the DC side upper and lower capacitor voltage u 1 、u 2 The relationship between selects the type of small vector, so as to obtain the optimal small vector v 1 With the suboptimal vector v 2 The actual switch state of the twelve-way switch tube represented by 1 >u 2 , then select a small P-type vector that increases the midpoint voltage. If u 1 <u 2 , then select the N-type small vector that reduces the midpoint voltage. The classification of positive and negative small vectors is shown in Table 2:

[0071] Table 2 Classification of positive and negative small vectors

[0072] Step 8: According to the optimal small vector v1 and the suboptimal vector v 2 Switching state and action time t 1 ,t 2 , in a control cycle, when T s <t 1 / 2, the output v 1 represents the switch state; when t 1 / 2≤7 s <t 1 / 2+t 2 When the output is v 2 The switch state represented by t 1 / 2+t 2 ≤T s When the output is v 1 Represents the switch state.

[0073] Based on Matlab / Simulink software, a three-level inverter simulation model based on the traditional model predictive control method and an equivalent two-level fast dual-vector model predictive control method applied to the three-level inverter was built. The system parameters are shown in Table 3:

[0074] Table 3 System parameters

[0075] First, in order to prove the effectiveness of the proposed equivalent two-level fast dual-vector model predictive control method applied to three-level inverters, the steady-state control performance was tested and compared with the traditional single-vector model predictive control method. Figure 6(a) and Figure 6(b) are the current waveforms of the above two control methods when the reference current amplitude is 10A. It can be seen from Figure 6(a) and Figure 6(b) that compared with the traditional single-vector model predictive control, the proposed method reduces the THD and ripple of the output current, which reflects the advantages of the proposed method.

[0076] In addition, a comparative analysis of the DC side midpoint potential balance control is conducted. Figure 7(a) and Figure 7(b) respectively show the midpoint potential balance process of the above two methods when the voltage difference between the upper and lower capacitors on the DC side is 20 V. It can be seen from Figure 7(a) and Figure 7(b) that both methods have the ability to control the midpoint potential balance, and the balance speed is similar, but the proposed method eliminates the design process of the weight factor.

[0077] Comparative experiments show that the proposed equivalent two-level fast dual-vector model predictive control method for three-level inverter has better output current quality and does not require the weight factor design of midpoint potential balance control.

[0078] The above description is only a preferred embodiment of the present invention and does not limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

[0079] Any matters not described in the present invention are applicable to the prior art.

Claims

1. An equivalent two-level fast dual-vector model predictive control method applied to a three-level inverter, characterized in that: The following steps are involved: Step 1: Sample and calculate the output current i at time k αβ (k) and the upper and lower capacitor voltages u1 and u2 on the DC side; Step 2: Predict the expected voltage u based on the three-level inverter mathematical model and the expected current αβ * (k): Where L is the filter inductance, T s is the sampling period, R is the load resistance, and the expected current i at time k+1 is ɑβ * (k+1) is obtained by Lagrange interpolation method: Step 3: Construct an equivalent two-level vector set based on the positive and negative small vectors around the zero vector, and substitute the six voltage vector coordinates representing the positive and negative small vectors into the cost function g1: Where u αβ (k) is the voltage vector coordinate of the positive and negative small vectors under the αβ coordinate axis. Compare the value function values ​​under the 6 different voltage vector coordinates, and select the voltage vector coordinate that minimizes g1 as the optimal small vector v1. Step 4: Set the expected voltage u αβ * (k) Subtract the optimal small vector v1 to obtain the modified expected voltage vector u′ in the equivalent two-level region where the optimal small vector is located αβ (k): Step 5. Substitute the six voltage vector coordinates representing the positive and negative small vectors into the value function g2: g2=|u′ αβ (k)-u αβ (k)| Compare the value function values ​​under 6 different voltage vector coordinates, and select the voltage vector coordinate that minimizes g2 as the suboptimal vector v2. Step 6: According to the characteristic that the action time of the vector is inversely proportional to the value function, calculate the action time of the optimal small vector v1 and the suboptimal vector v2: Where t1 and t2 are the action time of the optimal small vector v1 and the suboptimal vector v2, respectively, and t1+t2=T s . Step 7: Select the type of small vector according to the relationship between the upper and lower capacitor voltages u1 and u2 on the DC side, so as to obtain the actual switching states of the twelve switch tubes represented by the optimal small vector v1 and the suboptimal vector v2. Step 8. According to the switching states and action times t1 and t2 of the optimal small vector v1 and the sub-optimal vector v2, within one control period, when T s < t1 / 2, output the switching state represented by v1; when t1 / 2 ≤ T5 < t1 / 2 + t2, output the switching state represented by v2; when t1 / 2 + t2 ≤ T s , output the switching state represented by v1. The above switching states are applied to the three-level inverter topology to achieve current prediction control and midpoint potential balance control.

2. The method of equivalent two-level fast dual-vector model predictive control applied to a three-level inverter according to claim 1, characterized in that: The expected current is calculated by Lagrange interpolation method.

3. The equivalent two-level fast dual-vector model predictive control method applied to a three-level inverter according to claim 1, characterized in that: The expected voltage is calculated based on the deadbeat principle.

4. The equivalent two-level fast dual-vector model predictive control method applied to a three-level inverter according to claim 1, characterized in that: The equivalent two-level vector set is composed of small positive and negative vectors around the zero vector, and there are 6 different space vector positions in total.

5. The equivalent two-level fast dual-vector model predictive control method applied to a three-level inverter according to claim 1, characterized in that: The error between the expected voltage and the six spatial vector positions in the equivalent two-level vector set is calculated according to the value function, and the spatial vector position with the smallest error is selected as the spatial vector position of the optimal small vector. At the same time, according to the relationship between the upper and lower capacitor voltages u1 and u2 on the DC side according to claim 1, the type of positive and negative small vectors is selected to determine the optimal small vector.

6. The equivalent two-level fast dual-vector model predictive control method applied to a three-level inverter according to claim 1, characterized in that: According to the spatial vector position of the optimal small vector, six vectors around the optimal small vector are selected to establish an equivalent two-level vector set as an alternative control set for selecting the suboptimal vector.

7. The method of equivalent two-level fast dual-vector model predictive control applied to a three-level inverter according to claim 1, characterized in that: The optimal small vector is subtracted from the expected voltage to obtain a modified expected voltage vector in the equivalent two-level region where the optimal small vector is located.

8. The equivalent two-level fast dual-vector model predictive control method applied to a three-level inverter according to claim 1, characterized in that: The error between the corrected expected voltage and the six spatial vector positions in the suboptimal vector alternative control set is calculated according to the value function, and the spatial vector position with the smallest error is selected as the spatial vector position of the suboptimal vector. At the same time, according to the relationship between the upper and lower capacitor voltages u1 and u2 on the DC side as described in claim 1, the type of the suboptimal vector is selected to determine the suboptimal vector.

9. The equivalent two-level fast dual-vector model predictive control method applied to a three-level inverter according to claim 1, characterized in that: According to the characteristic that the action time of the vector is inversely proportional to the value function, when calculating the action of the optimal small vector and the suboptimal vector, the sum of their action times is equal to the sampling period.

10. The equivalent two-level fast dual-vector model predictive control method applied to a three-level inverter according to claim 1, characterized in that: A three-stage wave generation method is used to realize dual vector output, and the switching signal is applied to the three-level inverter topology.

Images