A particular harmonic cancellation pulse width modulation method suitable for digital power amplifiers

Abstract

This invention discloses a specific harmonic cancellation pulse width modulation method suitable for digital power amplifiers. It involves fitting a periodic signal f(t) to obtain an approximate function g(t) and performing Fourier analysis to derive the Fourier coefficients b of the current. n Wherein, the Fourier coefficient b n With the switching angle sequence α q 'As a parameter; for the switching angle sequence α q 'Optimization is performed to obtain the optimized switching angle sequence α' q According to α q The corresponding circuit is controlled by pulse width modulation to output a voltage waveform with specific harmonics filtered out. This invention obtains a specific switching angle sequence by establishing and solving a system of nonlinear equations. The output voltage waveform with specific harmonics filtered out is then modulated based on this switching angle sequence. This method can generate the desired frequency domain component and eliminate unwanted harmonics. It is also applicable to the design of multiple H-bridge units. At the same switching frequency, this method can output higher-order harmonics than other modulation methods, thus reducing switching losses. Furthermore, its excellent harmonic suppression performance saves hardware costs.

Description

Technical Field

[0001] This invention relates to the field of modulation methods for power electronic systems, and more specifically to a specific harmonic elimination pulse width modulation method suitable for digital power amplifiers. Background Technology

[0002] Traditional power amplifiers are primarily analog power amplifiers, operating in the linear amplification region of switching devices, offering high linearity and low distortion. While they meet signal distortion requirements, they require a bias power supply, and the transistor losses in the amplification region are significant, resulting in low efficiency, large size, and low power ratings, making them unsuitable for high-voltage, high-power applications.

[0003] Digital power amplifiers, whose switching devices operate in the cutoff and saturation regions, can effectively improve conversion efficiency and power levels. However, their waveform distortion rate is relatively high. Therefore, designing a low-distortion digital power amplifier is of great significance for the engineering applications of power amplifiers. Thus, there is an urgent need to select appropriate modulation methods and control strategies to reduce the distortion of digital power amplifiers. Summary of the Invention

[0004] To address the problem that existing digital power amplifiers have high conversion efficiency and power rating but relatively high waveform distortion, this invention provides a specific harmonic cancellation pulse width modulation method and system suitable for digital power amplifiers.

[0005] The technical solution provided by this invention is:

[0006] By combining the H-bridge topology and using straight line segments to fit the periodic signal f(t) to be output, the approximate function of the output current g(t) is obtained;

[0007] Performing Fourier analysis on the approximate function of the output current g(t), the Fourier coefficients b of the corresponding coil current are obtained. n Wherein, the Fourier coefficient b n With the switching angle sequence α q 'As a parameter;

[0008] The switching angle sequence α is aimed at eliminating specific harmonics. q 'Optimization is performed to obtain the optimized switching angle sequence α' q ;

[0009] According to the optimized switching angle sequence α q The corresponding H-bridge circuit is controlled by pulse width modulation to output a voltage waveform that has been filtered out of specific harmonics.

[0010] Preferably, the optimization of the switching angle sequence with the goal of eliminating specific harmonics yields an optimized switching angle sequence α. q ,include:

[0011] The objective function is to minimize the weighted sum of squares of the differences between the Fourier coefficients of the desired frequency harmonics and the initial modulation ratio. A nonlinear constraint condition is set that the Fourier coefficients of a specific harmonic are less than a preset threshold. A solver is used to optimize the switching angle sequence, resulting in the optimized switching angle sequence α. q .

[0012] Preferably, the expression of the objective function is as follows:

[0013]

[0014] In the formula, α N Here, N is the initial value of the switching angle, n is the number of switching angles, and m is the harmonic order. n Φ is the voltage modulation ratio, λ is the set of order elements of the frequency harmonics to be retained, and Φ is the voltage modulation ratio. n Here, ω1 is the weighting coefficient for the nth harmonic, ω1 is the fundamental angular frequency, L is the coil inductance, and V is the weighting coefficient for the nth harmonic. dc DC-side power supply voltage for each submodule, b n These are the Fourier coefficients.

[0015] Preferably, the expression for the nonlinear constraint condition is as follows:

[0016]

[0017] In the formula, n is the harmonic order, ω1 is the fundamental angular frequency, L is the coil inductance, and V is the voltage. dc DC-side power supply voltage for each submodule, b n Here are the Fourier coefficients, ε n Ψ is the set of order elements of a specific harmonic, representing the threshold for eliminating undesirable harmonics.

[0018] Preferably, the output periodic signal f(t) is determined by the following formula:

[0019]

[0020] In the formula, n = 1, 2, ..., p represents the harmonic order, t represents time, p represents the highest harmonic order, ω1 represents the fundamental angular frequency, and θ represents the harmonic order. n Let ω be the phase angle of the nth harmonic. n F is the angular frequency of the nth harmonic. n Let be the amplitude of the nth harmonic current of the current signal to be amplified.

[0021] Preferably, the Fourier coefficients b n Determine by the following formula:

[0022]

[0023] In the formula, n is the harmonic order, ω1 is the fundamental angular frequency, and V dc For each submodule, the DC power supply voltage is given, L is the coil inductance, N is the number of switching angles, k is the sign power, and α is the inductance. q ' is the switching angle sequence.

[0024] Based on the same inventive concept, the present invention also provides a specific harmonic elimination pulse width modulation system suitable for digital power amplifiers, characterized in that it includes: a fitting signal function module, a Fourier analysis module, an optimized switching angle sequence module, and an output module;

[0025] The signal fitting function module is used to combine the H-bridge topology and use straight line segments to fit the periodic signal f(t) to be output, and obtain the approximate function g(t) of the output current.

[0026] Fourier Analysis Module: Used to perform Fourier analysis on the output current approximation function g(t) to obtain the Fourier coefficients b of the corresponding coil current. n Wherein, the Fourier coefficient b n With the switching angle sequence α q 'As a parameter;

[0027] Optimize switching angle sequence module: used to optimize the switching angle sequence α with the goal of eliminating specific harmonics. q 'Optimization is performed to obtain the optimized switching angle sequence α' q ;

[0028] Output module: used to calculate the optimized switching angle sequence α q The corresponding H-bridge circuit is controlled by pulse width modulation to output a voltage waveform that has been filtered out of specific harmonics.

[0029] Preferably, the optimized switching angle sequence module is specifically used for:

[0030] The objective function is to minimize the weighted sum of squares of the differences between the Fourier coefficients of the desired frequency harmonics and the initial modulation ratio. A nonlinear constraint condition is set that the Fourier coefficients of a specific harmonic are less than a preset threshold. A solver is used to optimize the switching angle sequence, resulting in the optimized switching angle sequence α. q .

[0031] Preferably, the objective function in the optimized switching angle sequence module is expressed as follows:

[0032]

[0033] In the formula, α N Here, N is the initial value of the switching angle, n is the number of switching angles, and m is the harmonic order. n Φ is the voltage modulation ratio, λ is the set of order elements of the frequency harmonics to be retained, and Φ is the voltage modulation ratio. nHere, ω1 is the weighting coefficient for the nth harmonic, ω1 is the fundamental angular frequency, L is the coil inductance, and V is the weighting coefficient for the nth harmonic. dc DC-side power supply voltage for each submodule, b n These are the Fourier coefficients.

[0034] Preferably, the expression for the nonlinear constraint condition in the optimized switching angle sequence module is as follows:

[0035]

[0036] In the formula, n is the harmonic order, ω1 is the fundamental angular frequency, L is the coil inductance, and V is the voltage. dc DC-side power supply voltage for each submodule, b n Here are the Fourier coefficients, ε n Ψ is the set of order elements of a specific harmonic, representing the threshold for eliminating undesirable harmonics.

[0037] Preferably, the periodic signal f(t) output by the output module is determined by the following formula:

[0038]

[0039] In the formula, n = 1, 2, ..., p represents the harmonic order, t represents time, p represents the highest harmonic order, ω1 represents the fundamental angular frequency, and θ represents the harmonic order. n Let ω be the phase angle of the nth harmonic. n F is the angular frequency of the nth harmonic. n Let be the amplitude of the nth harmonic current of the current signal to be amplified.

[0040] Preferably, the Fourier coefficients b in the Fourier analysis module n Determine by the following formula:

[0041]

[0042] In the formula, n is the harmonic order, ω1 is the fundamental angular frequency, and V dc For each submodule, the DC power supply voltage is given, L is the coil inductance, N is the number of switching angles, k is the sign power, and α is the inductance. q ' is the switching angle sequence.

[0043] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0044] This invention provides a specific harmonic cancellation pulse width modulation method and system suitable for digital power amplifiers. It combines an H-bridge topology and uses a straight line segment to fit the periodic signal f(t) to be output, obtaining an approximate output current function g(t). Fourier analysis is then performed on the approximate output current function g(t) to obtain the Fourier coefficients b of the corresponding coil current. n Wherein, the Fourier coefficient b nWith the switching angle sequence α q As a parameter; the switching angle sequence α is adjusted with the goal of eliminating specific harmonics. q 'Optimization is performed to obtain the optimized switching angle sequence α' q According to the optimized switching angle sequence α q The corresponding H-bridge circuit is controlled by pulse width modulation to output a voltage waveform with specific harmonics filtered out. This invention obtains a specific switching angle sequence by establishing and solving a set of nonlinear equations, and modulates the output voltage waveform with specific harmonics filtered out based on the switching angle sequence. This allows for the generation of frequency domain components at the desired frequency while eliminating unwanted harmonics in the output waveform. Attached Figure Description

[0045] Figure 1 This is a flowchart of a specific harmonic elimination pulse width modulation method applicable to digital power amplifiers according to the present invention;

[0046] Figure 2 This is a three-level topology diagram of a cascaded H-bridge digital power amplifier for the specific harmonic elimination pulse width modulation method applicable to digital power amplifiers according to the present invention;

[0047] Figure 3 This is a five-level topology diagram of a cascaded H-bridge digital power amplifier for the specific harmonic elimination pulse width modulation method applicable to digital power amplifiers according to the present invention;

[0048] Figure 4 This is a multilevel topology diagram of a cascaded H-bridge digital power amplifier, which is applicable to the specific harmonic elimination pulse width modulation method of digital power amplifiers according to the present invention.

[0049] Figure 5 The waveform and components of the specific harmonic elimination pulse width modulation method f1(t) applicable to digital power amplifiers according to the present invention are shown below.

[0050] Figure 6 The waveform of g1(t) is an approximate function of the pulse width modulation method for specific harmonic elimination of digital power amplifiers according to the present invention.

[0051] Figure 7 This is the output voltage waveform of the specific harmonic elimination pulse width modulation method g1(t) applicable to digital power amplifiers of the present invention after being controlled by six switching angles;

[0052] Figure 8 This invention relates to a specific harmonic elimination pulse width modulation method for digital power amplifiers, specifically the voltage waveform of a switching scheme using SHEPWM modulation on a multi-level H-bridge circuit.

[0053] Figure 9This is a flowchart of a specific embodiment of the pulse width modulation method for specific harmonic elimination applicable to digital power amplifiers according to the present invention;

[0054] Figure 10 This invention provides a specific harmonic elimination pulse width modulation method for digital power amplifiers, with pulse width modulation input to a single H-bridge and output pulse width modulation waveform.

[0055] Figure 11 This invention relates to a specific harmonic elimination pulse width modulation method for digital power amplifiers, and the voltage waveform of a single H-bridge VT1 is obtained by pulse width modulation input.

[0056] Figure 12 This is a schematic diagram of a specific harmonic elimination pulse width modulation system applicable to digital power amplifiers according to the present invention. Detailed Implementation

[0057] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0058] Example 1

[0059] This invention proposes a specific harmonic cancellation pulse width modulation method and system suitable for digital power amplifiers, the flowchart of which is shown below. Figure 1 As shown, it includes:

[0060] S1. Combining the H-bridge topology and using straight line segments to fit the periodic signal f(t) to be output, we obtain the approximate function g(t) of the output current.

[0061] S2. Perform Fourier analysis on the approximate function of the output current g(t) to obtain the Fourier coefficients b of the corresponding coil current. n Wherein, the Fourier coefficient b n With the switching angle sequence α q 'As a parameter;

[0062] S3. The switching angle sequence α is adjusted with the goal of eliminating specific harmonics. q 'Optimization is performed to obtain the optimized switching angle sequence α' q ;

[0063] S4. Based on the optimized switching angle sequence α q The corresponding H-bridge circuit is controlled by pulse width modulation to output a voltage waveform that has been filtered out of specific harmonics.

[0064] Step S1 specifically includes: Figure 2 , Figure 3 , Figure 4This is a digital power amplifier topology based on an H-bridge structure, where VT1 represents the upper transistor of the left bridge arm half-bridge, VT2 represents the lower transistor of the left bridge arm half-bridge, VT3 represents the upper transistor of the right bridge arm half-bridge, and VT4 represents the lower transistor of the right bridge arm half-bridge. Figure 2 The medium-voltage full-bridge inverter can output three voltage levels: -1, 0, and 1, i.e., -V dc ,0,+V dc . Figure 3 For two Figure 2 The cascaded structure can output five levels, and similarly... Figure 4 The structure shown consists of n identical sub-modules connected in series, and can output 2n+1 voltage levels, namely -nV. dc , …0, …+(n-1)V dc ,+nV dc The load L is the equivalent inductance of this type of digital power amplifier when applied to eddy current multi-frequency detection. Each submodule consists of an H-bridge. Under normal operating conditions, the trigger signals of VT1 and VT2 are complementary. When VT1 = 1 and VT2 = 0, the output voltage is the power supply voltage V. dc When VT1 = 0 and VT2 = 1, the output voltage is -V. dc The increase in voltage level makes the analog output waveform of the power amplifier more accurate, but it also increases the hardware burden. Therefore, it is necessary to reasonably consider the number of cascaded circuits to ensure a balance between accuracy and efficiency.

[0065] SHEPWM modulation is a computational PWM modulation method introduced in the 1970s. SHEPWM expands the output waveform of the inverter using a Fourier series, and after parity and symmetry processing, simplifies the Fourier coefficients of the waveform. Then, the amplitude of the harmonics to be eliminated is set to zero, resulting in a set of nonlinear transcendental equations with the switching angle as the variable. The unwanted specific frequency harmonics are filtered out by transforming the switching angle.

[0066] The objective function to be output in the time domain is f(t), which is a periodic signal containing n fundamental sinusoidal components. Where ω n and θ n These are the angular frequency and phase angle of the nth harmonic, respectively, F n To amplify the amplitude of the nth harmonic current of the current signal to be amplified, the function f(t) represents the target coil current to be generated. Furthermore, f(t) has three conditions. First, the lowest frequency is set to the fundamental frequency (the same fundamental angular frequency) ω1, and the higher frequencies are harmonics based on the fundamental frequency ω1, i.e., ω... n =nω1. Secondly, the phase angle θ n The value is zero, which means that all fundamental components are in phase. Third, the coefficient ω... nThe selected frequency is chosen to be inversely proportional to the harmonic order, and zero is chosen for non-existent harmonics. Generally, the amplitude of the response signal tends to increase with increasing frequency. To achieve a similar signal-to-noise ratio across the entire spectrum, the coefficient ω... n Selected as the frequency ω n It is inversely proportional to the harmonic order n.

[0067] Figure 5 An example signal f1(t) following these principles is shown. Here, f1(t) is a superposition of five basic sinusoidal signals with frequencies chosen geometrically as ω1, 3ω1, 9ω1, 27ω1, and 81ω1. The weights are set to 1, 1 / 3, 1 / 9, 1 / 27, and 1 / 81.

[0068] Right now

[0069] Once the waveform and harmonic components of the objective function are determined, straight line segments can be used to simulate this waveform. The approximation function g(t) is a piecewise linear function with different gradients, approximating the objective function f(t). For a three-level H-bridge, if only +V is output... dc and -V dc Two voltages, for example Figure 6 The graph shows the approximate function g1(t) of f1(t). The slopes of the straight line segments of the approximate function are fixed values ​​K and -K. This is because the current in the inductor is represented as an integral of the voltage, and the voltage value is fixed in the waveform shown. Figure 7 As shown, the inductance can be considered a fixed value. The initial switching angle is the extreme point of this function. Cascading multiple H-bridges can output a signal closer to the actual waveform. The voltage rises or falls by one voltage level at each switching angle, so the slope of the fitting function of the cascaded H-bridges should be a multiple of K and -K, with K increasing or decreasing by a fixed amount at each switching angle. However, this increases the computational and operational burden on the system. Therefore, the choice of voltage level is a trade-off between signal fidelity and practical feasibility. The number of time steps used for g(t) is usually determined by the clock frequency used to drive the bridge circuit and is limited by the dynamic characteristics of the transistors. In addition, the lowest harmonic frequency in the inverter output harmonics is (3N+2)F1, where F1 represents the amplitude of the fundamental wave of the current signal to be amplified. That is, the determination of the number of switching angles is also related to the highest harmonic frequency to be output. In fact, as long as the number of switching angles is large enough, the accuracy of the output current waveform of a single H-bridge is already high enough.

[0070] The objective function f(t) and its approximate function g(t) are generated by a multi-stage H-bridge digital power amplifier, and their output level is the power supply voltage V. dc Integer multiples of. For SHEPWM modulation, the most commonly used modulation method produces output voltage waveforms that are half-wave odd-symmetric and quarter-cycle even-symmetric, with switching schemes such as... Figure 8 As shown, there are N switching angles that satisfy 0≤α1≤α2≤···≤α N ≤π / 2, at each angle, the voltage can rise or fall by V. dc Until the limit is reached, it can output 2n+1 levels, each representing -nV. dc , …0, …(n-1)V dc ,nV dc , where n is the number of submodules with the same structure (refer to...). Figure 4 Due to the characteristics of typical SHEPWM, the modulation voltage is odd-symmetric about half a period (symmetry axis is π+kπ) and even-symmetric about a quarter period (symmetry axis is π / 2+kπ). The Fourier spectrum of the output voltage contains only the odd harmonics of the sin term, while the even harmonics of the cos and sin terms are eliminated due to half-wave symmetry, and the odd harmonics of the cos term are eliminated due to the even symmetry of the quarter period.

[0071] The coil current is the integral of the voltage. According to the Fourier transform, the coil current can be expressed as (1)

[0072]

[0073] Step S2 specifically includes:

[0074] The Fourier coefficients of (1) are calculated as (2). This is the switching angle sequence α before optimization. q (N switching angles), coil inductance L, harmonic order n, and voltage step size V dc The function.

[0075]

[0076] For a single H-bridge using only two voltage levels, since only positive and negative voltage levels are used, the gradient change at each switching angle is 2V. dc Furthermore, the sign of the gradient at π / 2 must be considered; therefore, the Fourier coefficients of a single H-bridge can be expressed as:

[0077]

[0078] After obtaining the Fourier coefficients of similar coil currents, these coefficients need to be processed and optimized to eliminate unwanted harmonics.

[0079] b n Using the switching angle sequence α q ' indicates that b is optimized n Optimize the switching angle sequence α q ', thus obtaining the optimized switching angle sequence α q .

[0080] Once the waveform of the approximate function is obtained based on the gradient, the spectrum of g(t) can be controlled by adjusting N switching angles to eliminate specific frequency harmonics that we do not want. This is essentially a problem of solving simultaneous transcendental equations. Each equation corresponds to the amplitude of the harmonic to be controlled. Various methods have been developed to obtain one or more solutions to the harmonic amplitude equation. A common approach is based on polynomial elimination theory and using the results. Unfortunately, the order of the polynomial increases with the number of harmonics to be controlled, which leads to a huge computational burden if the application requires a wide spectrum. In addition, solving the equation completely can be computationally complex and requires high accuracy. In fact, in practical applications, the difference can be tolerated within a threshold. Another approach tends to transform the harmonic amplitude equation into an optimization problem. Due to the trigonometric and non-convex nature of the harmonic amplitude equation, it is difficult to guarantee a globally optimal solution. Metaheuristic algorithms, such as differential evolution, genetic algorithms, and particle swarm optimization, have been applied to obtain global solutions through modern stochastic search techniques. However, since these algorithms rely on stochastic search, they may return different results for the same problem. On the other hand, many gradient-based algorithms theoretically guarantee that local optima can be obtained. If a good estimate of the solution exists, gradient-based algorithms can converge quickly to the optimal solution.

[0081] According to (2), in order to make the output coil current close to the Fourier coefficients of the approximate function, the following nonlinear optimization problem needs to be solved:

[0082] Step S3 specifically includes:

[0083] According to (2), in order to make the output coil current close to the Fourier coefficients of the approximate function, the following nonlinear optimization problem needs to be solved:

[0084]

[0085] Where Φ is the set of order elements of the selected harmonics, Ψ is the set of order elements of the harmonics to be eliminated, and λ n ε represents the weighting coefficients of the function. n m represents the threshold for eliminating unwanted harmonics. n ω1 is the voltage modulation ratio. This formula means that if the content of a specific harmonic to be eliminated by modulation is less than the elimination threshold, the Fourier coefficient of the required harmonic frequency is close to the modulation ratio of that harmonic frequency under this condition, and ω1 is the fundamental angular frequency.

[0086] Where, m n =V n / V dc V nThis represents the amplitude of the nth harmonic in the output voltage. The modulation index characterizes the relative amplitude of the output voltage in a multilevel inverter. It is the sum of the weighted squared residuals of the modulation indices of the harmonics, which are affected by the modulation coefficients of the unwanted harmonics with a threshold ε. n Constraints defined by boundaries. The ε value can be set independently. n and λ n In practice, this allows for a lot of flexibility. For example, adjacent harmonics to the target frequency will produce stronger interference at that frequency; therefore, the corresponding threshold for adjacent harmonics should be lower than the thresholds for other less critical harmonics.

[0087] In summary, the specific process of this invention is as follows: Figure 9 As shown. After completing the Fourier analysis of g(t), the constraint problem (4) is solved using the nonlinear optimization problem solver fmincon in the MATLAB optimization toolbox. In the solution process, the optimization parameters are N switching angles. If the number of required harmonic frequencies is r, the optimization function is the weighted sum of the squares of the differences between the Fourier coefficients of the r required harmonic frequencies and the initial modulation ratio. The nonlinear constraint conditions are pr nonlinear inequalities, that is, the Fourier coefficients of the harmonics to be eliminated are less than a certain threshold. In general, λ n Set to 1. Furthermore, if the objective function cannot be cancelled, the weights of more important harmonics can be increased while the weights of other harmonics are decreased. Simultaneously, the higher the harmonic order, the larger the number of switching angles required; therefore, the number of switching angles needs to be adjusted according to the highest harmonic order. More switching angles result in more accurate simulation of similar waveforms.

[0088] The constraint threshold is set so that the modulation ratio exponents of unwanted harmonics have the same boundary. Eliminating the boundary ε n Adjust by pressing n.

[0089] like If ε5 is set to 0.1, then ε9 will be 0.18, ε 15 The value is 0.3. After solving for the optimized parameters, the FPGA periodically reads the switching sequence and outputs a pulse signal through the PWM logic block. The pulse signal is then input to the H-bridge driver.

[0090] Figure 10 , Figure 11 This illustrates the method of using a single H-bridge with pulse width modulation input. Within a 1 / 4 cycle, the number of switching angles is N (6 in the diagram). First, the initial output voltage polarity is determined based on the slope at the initial point 0 of g(t). If the initial slope is positive, then the output voltage is positive starting from 0, and the output PWM waveform is as follows: Figure 10 As shown, the output voltage polarity is reversed at each subsequent switching angle. The control signals for VT1 and VT4 are the same, as follows: Figure 11As shown, the control signals for VT2 and VT3 are the same and complementary to those for VT1.

[0091] Example 2

[0092] Based on the same inventive concept, this invention also provides a specific harmonic cancellation pulse width modulation system suitable for digital power amplifiers, as shown in the schematic diagram below. Figure 12 It includes: a signal function fitting module, a Fourier analysis module, an optimized switching angle sequence module, and an output module;

[0093] The signal fitting function module is used to combine the H-bridge topology and use straight line segments to fit the periodic signal f(t) to be output, and obtain the approximate function g(t) of the output current.

[0094] Fourier Analysis Module: Used to perform Fourier analysis on the output current approximation function g(t) to obtain the Fourier coefficients b of the corresponding coil current. n Wherein, the Fourier coefficient b n With the switching angle sequence α q 'As a parameter;

[0095] Optimize switching angle sequence module: used to optimize the switching angle sequence α with the goal of eliminating specific harmonics. q 'Optimization is performed to obtain the optimized switching angle sequence α' q ;

[0096] Output module: used to calculate the optimized switching angle sequence α q The corresponding H-bridge circuit is controlled by pulse width modulation to output a voltage waveform that has been filtered out of specific harmonics.

[0097] Preferably, the optimized switching angle sequence module is specifically used for:

[0098] The objective function is to minimize the weighted sum of squares of the differences between the Fourier coefficients of the desired frequency harmonics and the initial modulation ratio. A nonlinear constraint condition is set that the Fourier coefficients of a specific harmonic are less than a preset threshold. A solver is used to optimize the switching angle sequence, resulting in the optimized switching angle sequence α. q .

[0099] Preferably, the objective function in the optimized switching angle sequence module is expressed as follows:

[0100]

[0101] In the formula, α N Here, N is the initial value of the switching angle, n is the number of switching angles, and m is the harmonic order. n Φ is the voltage modulation ratio, λ is the set of order elements of the frequency harmonics to be retained, and Φ is the voltage modulation ratio. nHere, ω1 is the weighting coefficient for the nth harmonic, ω1 is the fundamental angular frequency, L is the coil inductance, and V is the weighting coefficient for the nth harmonic. dc DC-side power supply voltage for each submodule, b n These are the Fourier coefficients.

[0102] Preferably, the expression for the nonlinear constraint condition in the optimized switching angle sequence module is as follows:

[0103]

[0104] In the formula, n is the harmonic order, ω1 is the fundamental angular frequency, L is the coil inductance, and V is the voltage. dc DC-side power supply voltage for each submodule, b n Here are the Fourier coefficients, ε n Ψ is the set of order elements of a specific harmonic, representing the threshold for eliminating undesirable harmonics.

[0105] Preferably, the periodic signal f(t) output by the output module is determined by the following formula:

[0106]

[0107] In the formula, n = 1, 2, ..., p represents the harmonic order, t represents time, p represents the highest harmonic order, ω1 represents the fundamental angular frequency, and θ represents the harmonic order. n Let ω be the phase angle of the nth harmonic. n F is the angular frequency of the nth harmonic. n Let be the amplitude of the nth harmonic current of the current signal to be amplified.

[0108] Preferably, the Fourier coefficients b in the Fourier analysis module n Determine by the following formula:

[0109]

[0110] In the formula, n is the harmonic order, ω1 is the fundamental angular frequency, and V dc For each submodule, the DC power supply voltage is given, L is the coil inductance, N is the number of switching angles, k is the sign power, and α is the inductance. q ' is the switching angle sequence.

[0111] In summary, this invention provides a specific harmonic cancellation pulse width modulation method and system suitable for digital power amplifiers, comprising: combining an H-bridge topology and using a straight line segment to fit the periodic signal f(t) to be output, obtaining an approximate function g(t) for the output current; performing Fourier analysis on the approximate function g(t) to obtain the Fourier coefficients b of the current in the corresponding coil. n Wherein, the Fourier coefficient b n With the switching angle sequence α qAs a parameter; the switching angle sequence α is adjusted with the goal of eliminating specific harmonics. q 'Optimization is performed to obtain the optimized switching angle sequence α' q According to the optimized switching angle sequence α q The corresponding H-bridge circuit is controlled by pulse width modulation to output a voltage waveform with specific harmonics filtered out. This invention obtains a specific switching angle sequence by establishing and solving a set of nonlinear equations, and modulates the output voltage waveform with specific harmonics filtered out based on the switching angle sequence. This allows for the generation of frequency domain components at the desired frequency while eliminating unwanted harmonics in the output waveform.

[0112] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0113] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0114] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0115] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0116] The above are merely embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of the claims of the present invention pending approval.

Claims

1. A specific harmonic cancellation pulse width modulation method suitable for digital power amplifiers, characterized in that, include: By combining the H-bridge topology and using straight line segments to fit the periodic signal f(t) to be output, the approximate function of the output current g(t) is obtained; Performing Fourier analysis on the approximate function of the output current g(t), the Fourier coefficients b of the corresponding coil current are obtained. n Wherein, the Fourier coefficient b n With the switching angle sequence α q 'As a parameter; The switching angle sequence α is aimed at eliminating specific harmonics. q 'Optimization is performed to obtain the optimized switching angle sequence α' q ; According to the optimized switching angle sequence α q The corresponding H-bridge circuit is controlled by pulse width modulation to output a voltage waveform that has been filtered out of specific harmonics.

2. The method as described in claim 1, characterized in that, The switching angle sequence is optimized with the goal of eliminating specific harmonics, resulting in an optimized switching angle sequence α. q ,include: The objective function is to minimize the weighted sum of squares of the differences between the Fourier coefficients of the desired frequency harmonics and the initial modulation ratio. A nonlinear constraint condition is set that the Fourier coefficients of a specific harmonic are less than a preset threshold. A solver is used to optimize the switching angle sequence, resulting in the optimized switching angle sequence α. q .

3. The method as described in claim 2, characterized in that, The expression for the objective function is as follows: In the formula, α N Here, N is the initial value of the switching angle, n is the number of switching angles, and m is the harmonic order. n Φ is the voltage modulation ratio, λ is the set of order elements of the frequency harmonics to be retained, and Φ is the voltage modulation ratio. n Here, ω1 is the weighting coefficient for the nth harmonic, ω1 is the fundamental angular frequency, L is the coil inductance, and V is the weighting coefficient for the nth harmonic. dc DC-side power supply voltage for each submodule, b n These are the Fourier coefficients.

4. The method as described in claim 2, characterized in that, The expression for the nonlinear constraint condition is as follows: In the formula, n is the harmonic order, ω1 is the fundamental angular frequency, L is the coil inductance, and V is the voltage. dc DC-side power supply voltage for each submodule, b n Here are the Fourier coefficients, ε n Ψ is the set of order elements of a specific harmonic, representing the threshold for eliminating undesirable harmonics.

5. The method as described in claim 1, characterized in that, The periodic signal f(t) output is determined by the following formula: In the formula, n = 1, 2, ..., p represents the harmonic order, t represents time, p represents the highest harmonic order, ω1 represents the fundamental angular frequency, and θ represents the harmonic order. n Let ω be the phase angle of the nth harmonic. n F is the angular frequency of the nth harmonic. n Let be the amplitude of the nth harmonic current of the current signal to be amplified.

6. The method as described in claim 1, characterized in that, The Fourier coefficients b n Determine by the following formula: In the formula, n is the harmonic order, ω1 is the fundamental angular frequency, and V dc For each submodule, the DC power supply voltage is given, L is the coil inductance, N is the number of switching angles, k is the sign power, and α is the inductance. q ' is the switching angle sequence.

7. A specific harmonic cancellation pulse width modulation system suitable for digital power amplifiers, characterized in that, include: The module includes a signal function fitting module, a Fourier analysis module, a switch angle sequence optimization module, and an output module. The signal fitting function module is used to combine the H-bridge topology and use straight line segments to fit the periodic signal f(t) to be output, and obtain the approximate function g(t) of the output current. Fourier Analysis Module: Used to perform Fourier analysis on the output current approximation function g(t) to obtain the Fourier coefficients b of the corresponding coil current. n Wherein, the Fourier coefficient b n With the switching angle sequence α q 'As a parameter; Optimize switching angle sequence module: used to optimize the switching angle sequence α with the goal of eliminating specific harmonics. q 'Optimization is performed to obtain the optimized switching angle sequence α' q ; Output Module: Used to determine the optimal switching angle sequence α q The corresponding H-bridge circuit is controlled by pulse width modulation to output a voltage waveform that has been filtered out of specific harmonics.

8. The system as described in claim 7, characterized in that, The optimized switching angle sequence module is specifically used for: The objective function is to minimize the weighted sum of squares of the differences between the Fourier coefficients of the desired frequency harmonics and the initial modulation ratio. A nonlinear constraint condition is set that the Fourier coefficients of a specific harmonic are less than a preset threshold. A solver is used to optimize the switching angle sequence, resulting in the optimized switching angle sequence α. q .

9. The system as described in claim 8, characterized in that, The objective function in the optimized switching angle sequence module is expressed as follows: In the formula, α N Here, N is the initial value of the switching angle, n is the number of switching angles, and m is the harmonic order. n Φ is the voltage modulation ratio, λ is the set of order elements of the frequency harmonics to be retained, and Φ is the voltage modulation ratio. n Here, ω1 is the weighting coefficient for the nth harmonic, ω1 is the fundamental angular frequency, L is the coil inductance, and V is the weighting coefficient for the nth harmonic. dc DC-side power supply voltage for each submodule, b n These are the Fourier coefficients.

10. The system as described in claim 8, characterized in that, The expression for the nonlinear constraint condition in the optimized switching angle sequence module is as follows: In the formula, n is the harmonic order, ω1 is the fundamental angular frequency, L is the coil inductance, and V is the voltage. dc DC-side power supply voltage for each submodule, b n Here are the Fourier coefficients, ε n Ψ is the set of order elements of a specific harmonic, representing the threshold for eliminating undesirable harmonics.

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