An inverter optimization synchronous SPWM modulation method based on non-equidistant carriers

Abstract

The present application relates to a kind of non-equal carrier-based inverter optimization synchronous SPWM modulation method, for two-level three-phase inverter, comprising the following steps: (1) by injecting zero sequence voltage in fundamental voltage, improve the utilization rate of DC voltage, obtain optimized reference voltage;(2) determine design principle and constraint condition: the fundamental period is divided into six regions according to ωt, each region is 60 °;Carrier waveform in region I, III, V remains consistent, the carrier waveform corresponding to region II, IV, VI also remains consistent;Region I and region II carrier waveform odd symmetry;Region I carrier waveform with center line even symmetry;Carrier design is carried out in 60 °-90 ° in region I;(3) in the range of single fundamental period, according to the distribution of region and the principle of satisfying waveform symmetry, carrier changes carrier width according to certain width ratio to form optimization synchronous SPWM modulation strategy, and the width ratio refers to the ratio of the angle between different carrier half waves in a fundamental period.

Description

Technical Field

[0001] This invention belongs to the field of power converters for drive motors. It relates to a pulse width modulation method for inverters. Background Technology

[0002] Inverters are widely used in industrial production, electric vehicles, and rail transportation. In some operating conditions, the inverters used have relatively high power; however, due to limitations in heat dissipation and switching losses, the inverter switching frequency is typically only a few hundred hertz. Throughout the entire speed regulation range, the carrier ratio (the ratio of the switching frequency to the output fundamental frequency) of the traction motor varies greatly. When the carrier ratio is low (≤15), the effect of waveform asymmetry cannot be ignored, necessitating the use of synchronous modulation.

[0003] High harmonic content and poor waveform quality in inverter output waveforms, coupled with inadequate harmonic suppression, lead to degraded control performance of the drive system. Therefore, designing and selecting high-performance synchronous modulation strategies to better suppress harmonics is crucial for improving system performance. Currently, widely used synchronous modulation strategies include Space Vector Modulation (SVPWM), Carrier Modulation (SPWM), and modulation based on optimization objectives. Among these, optimization-based modulation strategies include specific harmonic elimination modulation strategies and current harmonic minimization modulation strategies. These methods solve transcendental equations based on the optimization objective to obtain the switching angle, allowing for optimization of specific targets. However, they suffer from high computational complexity and implementation complexity. SVPWM and SPWM are often equivalent. SPWM obtains the control pulses for the switching devices in the inverter by comparing a reference waveform with the carrier wave. This strategy is more flexible and easier to implement, and is particularly widely used in multi-level topology inverters. Summary of the Invention

[0004] This invention provides an optimized synchronous SPWM modulation method for inverters based on non-equidistant carriers. Within the fundamental cycle of the inverter output, the output waveform satisfies three-phase, half-wave, and quarter-cycle symmetry. By changing the carrier width within the fundamental cycle to form non-equidistant carriers, an optimized method for generating these non-equidistant carriers is proposed. The optimized synchronous SPWM modulation strategy is obtained by comparing a reference voltage with the optimized non-equidistant carrier, enabling the inverter to better suppress voltage harmonics and improve overall inverter performance. The technical solution is as follows:

[0005] An optimized synchronous SPWM modulation method for inverters based on non-equidistant carrier waves, used in two-level three-phase inverters, is characterized by:

[0006] (1) By injecting zero-sequence voltage into the fundamental voltage, the DC voltage utilization rate is improved, and an optimized reference voltage is obtained. Let the three-phase fundamental voltage of the inverter be:

[0007]

[0008] In the formula: U m The reference voltage magnitude is ω; the phase voltage angular frequency is ω; the three phase voltages are U... a U b U c ;

[0009] The injected zero-sequence voltage is:

[0010]

[0011] In the formula: U0 is the zero-sequence voltage; U max =max{U a U b U c};U min =min{U a U b U c};

[0012] After injecting zero-sequence voltage, the three-phase reference voltages become:

[0013]

[0014] (2) Determine the design principles and constraints:

[0015] c) Divide the fundamental period into six regions based on ωt, each region being 60°; define the interval of region I as 60°~120°, and arrange the other regions sequentially; maintain consistency in the carrier waveforms of regions I, III, and V, and also maintain consistency in the carrier waveforms of regions II, IV, and VI; the carrier waveforms of regions I and II are odd-symmetric; the carrier waveform of region I is even-symmetric about the center line ωt=90°; perform carrier design within the 60°~90° range of region I, which is called the carrier design zone, and thus obtain the carrier waveform for the entire fundamental period;

[0016] d) The center line ωt = 90° of region I is the peak or valley of the carrier waveform; the boundary line between adjacent regions intersects the carrier waveform at the median point of the carrier waveform, which is half the difference between the maximum and minimum values ​​of the carrier waveform;

[0017] (3) Within a single fundamental period, based on the regional distribution and the principle of waveform symmetry, the carrier width is changed according to a certain width ratio to form an optimized synchronous SPWM modulation strategy. The width ratio refers to the ratio of the angles between the half-waves of different carriers in a fundamental period.

[0018] Furthermore, the optimized synchronous SPWM modulation strategy includes the following steps:

[0019] The center line of region I, ωt = 90°, is set as the peak point of the carrier waveform. The optimization process is as follows:

[0020] 1) Set the reference voltage magnitude U m The parameters related to the number of carrier waves in a single fundamental period are: m (where m is an odd number greater than or equal to 3), λ (optimization step size), and V (initial value of the weighted total harmonic distortion rate, a voltage harmonic evaluation index). WTHD0 =100%; number of carriers f in a single fundamental period c =3m, then the number of triangular carrier half-waves in a single fundamental period is 6m; the number of triangular carrier half-waves in region I, i.e., 60°~120°, is m, and the number of triangular carrier half-waves in the carrier design area is m / 2; let N=(m+1) / 2, let N=N1+N2, N1, N2 and N2 represent the number of two different width carrier half-waves respectively, and the initial value of N1 is 1; the angle occupied by the carrier half-wave corresponding to N1 is α, and the angle occupied by the carrier half-wave corresponding to N2 is β. Define the width ratio k as the ratio of α and β, that is, the width ratio of the two non-equidistant carriers; by determining the appropriate values ​​of N1, N2 and k, the optimized carrier is obtained. The optimization process of N1, N2 and k is as follows:

[0021] 2) Calculate N2;

[0022] 3) Set the width ratio k = k1 = λ;

[0023] 4) Based on the determined design principles and constraints, design the carrier waveform according to the values ​​of N1, N2, and k;

[0024] 5) Generate a PWM wave based on the reference voltage and carrier wave, and calculate the line voltage;

[0025] 6) Perform Fourier analysis on the line voltage to obtain the effective values ​​of each harmonic voltage, and obtain the formula for calculating the harmonic evaluation index, namely the weighted total harmonic distortion rate V. WTHD :

[0026]

[0027] In the formula, V1 and V n These are the effective values ​​of the fundamental and nth harmonic voltages of the line voltage waveform, respectively.

[0028] 7) Obtain the weighted total harmonic distortion (WHD) value V corresponding to k1, which is the voltage harmonic evaluation index. WTHD1 ;

[0029] 8) Next, take k = k2 = 1 / k1, and design the carrier waveform based on the values ​​of N1, N2, and k, repeating steps 4) to 6); calculate the weighted total harmonic distortion (WHD) value corresponding to k2 as the voltage harmonic evaluation index. WTHD2 Compare V WTHD1 and V WTHD2 The value of V is recorded, and the smaller value of k is recorded. WTHD =min(V WTHD1 V WTHD2 );

[0030] 9) The V calculated in step 8) WTHD V in external storage area WTHD0 In comparison, if V WTHD <V WTHD0 Update the value V in the external storage area. WTHD0 =V WTHD At the same time, use V WTHD Update the storage area with the corresponding N1, N2, and k values; otherwise, keep the values ​​in the storage area unchanged.

[0031] 10) Given k1 = k1 + λ, two cases occur:

[0032] If k1≤1, then repeat steps 4) to 9) to determine the minimum value V. WTHD The corresponding k, N1, and N2 values;

[0033] If k1 > 1, then N1 = N1 + 1; if N > N1, then return to step 2; if N ≤ N1, then the optimization process ends.

[0034] Set the center line ωt = 90° of region I as the valley point of the carrier waveform, and repeat the above process 1) to 10);

[0035] The minimum V obtained by calculating twice, once at the peak point and once at the trough point. WTHD The corresponding N1, N2, and k values ​​are used to obtain the optimal matching values ​​of N1, N2, and k, thus obtaining the optimal PWM modulation strategy;

[0036] Compared with the prior art, the beneficial effects of this invention are:

[0037] 1. A 30° carrier waveform design principle was proposed to simplify the design process.

[0038] 2. This paper changes the previous method of modulating with a fixed carrier width throughout the fundamental frequency period and adopts a non-equidistant triangular wave, proposing an optimization method for the non-equidistant triangular wave.

[0039] 3. Under the premise of satisfying the principle of symmetrical synchronization, when the carrier ratio remains unchanged (i.e., the switching frequency of the power device is fixed when the fundamental period is fixed), the inverter output harmonics are effectively suppressed by regularly changing the carrier width, the inverter output waveform quality is improved, the inverter output voltage has low harmonic content and good waveform quality, the torque fluctuation is reduced, and the overall performance of the inverter is improved.

[0040] 4. It can effectively reduce the additional losses of the load motor, prevent the motor from overheating, and thus improve the performance, efficiency and service life of the motor system. Attached Figure Description

[0041] Figure 1 This is a topology diagram of a two-level inverter;

[0042] Figure 2 This is a diagram showing the division of the three-phase sinusoidal reference voltage region.

[0043] Figure 3 (a) and (b) are carrier waveform diagrams when m = 3, N1 = 1, N2 = 1, and k = 1;

[0044] Figure 3 (c)(d) are carrier waveform diagrams when m=3, N1=1, N2=1, and k=0.5;

[0045] Figure 3 (e)(f) are carrier waveform diagrams when m=3, N1=1, N2=1, and k=2;

[0046] Figure 4 (a), (b), and (c) are the modulation wave, carrier wave, and line voltage waveforms for k=1, k=0.5, and k=2, respectively, when m=3, N1=1, and N2=1.

[0047] Figure 5 V for k=1, k=0.5, and k=2 when m=3, N1=1, and N2=1, respectively. WTHD Line graph;

[0048] Figure 6 Flowchart for optimization. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the present invention easier to understand, the specific circumstances will be further described below in conjunction with the accompanying drawings.

[0050] This invention proposes a non-equidistant carrier design method for synchronous symmetrical SPWM modulation and provides a detailed optimization algorithm for the non-equidistant carrier. Based on this method, the carrier width is regularly changed within the fundamental period range, and the optimized synchronous SPWM modulation strategy is obtained by comparing the reference waveform with the non-equidistant carrier. When operating at a low carrier ratio, inverter output harmonics are effectively suppressed.

[0051] The embodiments of the present invention are as follows:

[0052] like Figure 1 As shown, the inverter in this embodiment is a two-level three-phase inverter, including a DC side, an AC side, and three-phase bridge arms. The DC side includes a supporting capacitor and an input voltage, with the capacitor connected to both ends of the input voltage on the DC side. The AC side includes two power devices in each phase bridge arm, and the two power devices are connected in series. The motor load is connected between the two power devices in each phase bridge arm.

[0053] 1. Reference voltage calculation

[0054] An optimized reference voltage is obtained by injecting a zero-sequence voltage into the fundamental voltage. Inverter three-phase fundamental voltage:

[0055]

[0056] In the formula U m ω is the phase voltage amplitude; ω is the phase voltage angular frequency; the three phase voltages are U... a U b U c .

[0057] The injected zero-sequence voltage is:

[0058]

[0059] In the formula: U0 is the zero-sequence voltage; U max =max{U a U b U c 、};U min =min{U a U b U c ,};

[0060] After injecting zero-sequence voltage, the three-phase reference voltages become:

[0061]

[0062] 2. This invention designs a carrier design method and constraints based on the principle of synchronous symmetry. It proposes a 30° carrier design region and design constraints.

[0063] 1) Divide the fundamental period into six regions based on ωt, each region being 60°; define the interval as follows: Region I is 60°–120°, Region II is 120°–180°, Region III is 180°–240°, Region IV is 240°–300°, Region V is 300°–360°, and Region VI is 0°–60°. Figure 2 As shown.

[0064] 2) Design principles and constraints:

[0065] e) The carrier waveforms in regions I, III, and V should remain consistent, and similarly, the carrier waveforms in regions II, IV, and VI should also remain consistent; the carrier waveforms in region I and region II are odd-symmetric; the carrier waveform in region I is even-symmetric about the center line (ωt = 90°). ωt = 90°. By designing the carrier waveform within 60° to 90° in region I, the carrier waveform for the entire fundamental period can be derived, which is the 30° carrier design region proposed in this invention.

[0066] f) The center line of region I (ωt = 90°) is the peak (maximum value) or valley (minimum value) of the carrier waveform; the boundary line between adjacent regions is the midpoint of the carrier waveform (half the difference between the maximum and minimum values ​​of the carrier waveform).

[0067] 3. Optimization methods and processes for non-equidistant carrier waves

[0068] The center line of region I (ωt = 90°) is set as the peak point of the carrier waveform. The specific optimization process is as follows:

[0069] 1) Set the reference voltage modulus (modulation) U m The parameters related to the number of carrier waves in a single fundamental period are m (where m is an odd number greater than or equal to 3), the optimization step size is λ, and the initial value of the weighted total harmonic distortion (WHD) index for voltage harmonic evaluation is set as V. WTHD0 =100% and the initial value of N is (m+1) / 2, and the initial value of N1 is 1; the relevant parameters are explained as follows:

[0070] Number of carriers f in a single fundamental period c =3m (m is an odd number greater than or equal to 3), then the number of triangular carrier half-waves in a single fundamental period is 6m; in region I (60°~120°), the number of triangular carrier half-waves is m, and the number of triangular carrier half-waves in the carrier design area is m / 2. N=(m+1) / 2 (N is a positive integer), let N=N1+N2 (N1 and N2 are both positive integers), N1 and N2 represent the number of carrier half-waves with two different widths: the angle occupied by the carrier half-wave corresponding to N1 is α, and the angle occupied by the carrier half-wave corresponding to N2 is β. Define the width ratio k as the ratio of α and β, that is, the width ratio of the two non-equidistant carriers.

[0071] 2) Calculate N2 using N and N1:

[0072] N2 = N - N1

[0073] 3) Set the width ratio k = k1 = λ;

[0074] 4) Based on the design principles and constraints in section 2, design the carrier waveform according to the values ​​of N1, N2 and k.

[0075] 5) Generate a PWM wave based on the reference voltage and carrier wave, and calculate the line voltage;

[0076] 6) Perform Fourier analysis on the line voltage to obtain the effective values ​​of each harmonic voltage of the line voltage, and calculate the weighted total harmonic distortion (WHD) index for voltage harmonic evaluation. WTHD :

[0077]

[0078] In the formula, V1 and V n These are the effective values ​​of the fundamental and nth harmonic voltages of the line voltage waveform, respectively.

[0079] 7) Obtain the weighted total harmonic distortion (WHD) value V corresponding to k1, which is the voltage harmonic evaluation index. WTHD1 .

[0080] 8) Next, take k = k2 = 1 / k1, and design the carrier waveform based on the values ​​of N1, N2, and k, repeating steps 4) to 6); calculate the weighted total harmonic distortion (WHD) value corresponding to k2 as the voltage harmonic evaluation index. WTHD2 Compare V WTHD1 and V WTHD2 The value of V is recorded, and the smaller value of k is recorded. WTHD =min(V WTHD1 V WTHD2 ).

[0081] 9) The V calculated in step 8) WTHD V in external storage area WTHD0 In comparison, if V WTHD <V WTHD0 Update the value V in the external storage area. WTHD0 =V WTHD At the same time, use V WTHD The corresponding N1, N2, and k values ​​are updated in the storage area; otherwise, the values ​​in the storage area remain unchanged.

[0082] 10) After selecting the smaller k value through comparison, given k1 = k1 + λ, two situations arise:

[0083] If k1≤1, then repeat steps 4) to 10) to get the new V. WTHD Compared to the last V WTHD Compare the two results, take the minimum value, and record the minimum value V. WTHD The corresponding k, N1, and N2.

[0084] If k1 > 1, then N1 = N1 + 1. If N > N1, then repeat the above process. If N ≤ N1, then the optimization process ends.

[0085] 11) Set the center line of region I (ωt = 90°) as the valley point of the carrier waveform, and repeat steps 1) to 10). Then, take the minimum V obtained from the calculations at both the peak and valley points. WTHD The corresponding N1, N2, and k values ​​are used to obtain the optimal matching values ​​of N1, N2, and k, thus obtaining the optimal PWM modulation strategy.

[0086] In actual optimization, since the carrier ratio is relatively low, m is usually selected from three values: 3, 5, and 7. The optimization step size can be increased, and the optimization algorithm is simple and easy to implement. Figure 3 In the example, if m = 3, then N1 = 1 and N2 = 1. (a) and (b) are schematic diagrams of carrier waveforms with k = 1; (c) and (d) are schematic diagrams of carrier waveforms with k = 0.5; and (e) and (f) are schematic diagrams of carrier waveforms with k = 2.

[0087] Implementation effect

[0088] Taking the center line of region I (ωt=90°) as the valley point of the carrier waveform and m=3, with an optimization step size λ=0.5 as an example, the proposed method for optimizing synchronous SPWM modulation of inverters with non-equidistant carriers is verified, and the V values ​​during the optimization process are recorded. WTHD The data. Figure 4 (a) Represents the PWM output pulse sequence where k=1. Figure 4 (b) Represents the PWM output pulse sequence with k = 0.5. Figure 4 (c) represents the PWM output pulse sequence for k=2, where the PWM output pulse sequence for k=1 is equivalent to the traditional method. Figure 5 The graphs show the harmonic content curves of the modulation strategy under different modulation degrees for different k values, where WTHD represents the line voltage weighted total harmonic distortion (V). WTHD ), Figure 5 The circular curve, square curve, and triangular curve represent the voltage-weighted total harmonic distortion (THD) waveforms for different modulation indices (corresponding voltage amplitudes) under the conditions of k=0.5, k=1, and k=2, respectively.

[0089] Depend on Figure 5 It can be seen that the triangular curve represents the optimal effect for k=2 across the entire modulation range (modulation range 0.4-1), verifying the feasibility of the optimization method, and its effect is superior to traditional strategies. The method proposed in this invention effectively improves the output waveform quality of the inverter.

Claims

1. An inverter-optimized synchronous SPWM modulation method based on non-equidistant carrier waves, used in a two-level three-phase inverter, characterized in that, Includes the following steps: (1) By injecting zero-sequence voltage into the fundamental voltage, the DC voltage utilization rate is improved, and an optimized reference voltage is obtained. Let the three-phase fundamental voltage of the inverter be: In the formula: U m The reference voltage magnitude is ω; the phase voltage angular frequency is ω; the three phase voltages are U... a U b U c ; The injected zero-sequence voltage is: Where: U0 is the zero-sequence voltage; U max = max{U a , U b , U c}; U min = min{U a , U b , U c}; After injecting zero-sequence voltage, the three-phase reference voltages become: (2) Determine the design principles and constraints: a) Divide the fundamental period into six regions based on ωt, each region being 60°; define the interval of region I as 60°~120°, and arrange the other regions in sequence; the carrier waveforms in regions I, III, and V are consistent, and the carrier waveforms corresponding to regions II, IV, and VI are also consistent; the carrier waveforms of region I and region II are oddly symmetrical; The carrier waveform in region I is evenly symmetrical about the center line ωt = 90°; the carrier design is carried out in the range of 60° to 90° within region I, which is called the carrier design area, and thus the carrier waveform for the entire fundamental period is obtained. b) The center line ωt = 90° of region I is the peak or valley of the carrier waveform; the boundary line between adjacent regions intersects the carrier waveform at the median point of the carrier waveform, which is half the difference between the maximum and minimum values ​​of the carrier waveform; (3) Within a single fundamental period, based on the regional distribution and the principle of waveform symmetry, the carrier width is changed according to a certain width ratio to form an optimized synchronous SPWM modulation strategy. The width ratio refers to the ratio of the angles between the half-waves of different carriers in a fundamental period.

2. The inverter-optimized synchronous SPWM modulation method based on non-equidistant carriers according to claim 1, characterized in that: The optimized synchronous SPWM modulation strategy includes the following steps: The center line of region I, ωt = 90°, is set as the peak point of the carrier waveform. The optimization process is as follows: 1) Set the reference voltage magnitude U m The parameters related to the number of carrier waves in a single fundamental period are: m (where m is an odd number greater than or equal to 3), λ (optimization step size), and V (initial value of the weighted total harmonic distortion rate, a voltage harmonic evaluation index). WTHD0 =100%; number of carriers f in a single fundamental period c =3m, then the number of triangular carrier half-waves in a single fundamental period is 6m; the number of triangular carrier half-waves in region I, i.e., 60°~120°, is m, and the number of triangular carrier half-waves in the carrier design area is m / 2; let N=(m+1) / 2, let N=N1+N2, N1, N2 and N2 represent the number of two different width carrier half-waves respectively, and the initial value of N1 is 1; the angle occupied by the carrier half-wave corresponding to N1 is α, and the angle occupied by the carrier half-wave corresponding to N2 is β. Define the width ratio k as the ratio of α and β, that is, the width ratio of the two non-equidistant carriers; by determining the appropriate values ​​of N1, N2 and k, the optimized carrier is obtained. The optimization process of N1, N2 and k is as follows: 2) Calculate N2; 3) Set the width ratio k = k1 = λ; 4) Based on the determined design principles and constraints, design the carrier waveform according to the values ​​of N1, N2, and k; 5) Generate a PWM wave based on the reference voltage and carrier wave, and calculate the line voltage; 6) Perform Fourier analysis on the line voltage to obtain the effective values ​​of each harmonic voltage, and obtain the formula for calculating the harmonic evaluation index, namely the weighted total harmonic distortion rate V. WTHD : In the formula, V1 and V n These are the effective values ​​of the fundamental and nth harmonic voltages of the line voltage waveform, respectively. 7) Obtain the weighted total harmonic distortion (WHD) value V corresponding to k1, which is the voltage harmonic evaluation index. WTHD1 ; 8) Next, take k = k2 = 1 / k1, and design the carrier waveform based on the values ​​of N1, N2, and k, repeating steps 4) to 6); calculate the weighted total harmonic distortion (WHD) value corresponding to k2 as the voltage harmonic evaluation index. WTHD2 Compare V WTHD1 and V WTHD2 The value of V is recorded, and the smaller value of k is recorded. WTHD =min(V WTHD1 V WTHD2 ); 9) The V calculated in step 8) WTHD V in external storage area WTHD0 In comparison, if V WTHD <V WTHD0 Update the value V in the external storage area. WTHD0 =V WTHD At the same time, use V WTHD Update the storage area with the corresponding N1, N2, and k values; otherwise, keep the values ​​in the storage area unchanged. 10) Given k1 = k1 + λ, two cases occur: If k1≤1, then repeat steps 4) to 9) to determine the minimum value V. WTHD The corresponding k, N1, and N2 values; If k1 > 1, then N1 = N1 + 1; if N > N1, then return to step 2; if N ≤ N1, then the optimization process ends. Set the center line ωt = 90° of region I as the valley point of the carrier waveform, and repeat the above process 1) to 10); The minimum V obtained by calculating twice, once at the peak point and once at the trough point. WTHD The corresponding N1, N2, and k values ​​are used to obtain the optimal matching values ​​of N1, N2, and k, thus obtaining the optimal PWM modulation strategy.

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