A cascaded H-bridge inverter SHEPWM method based on NR-ACA algorithm

Abstract

The application discloses a cascaded H-bridge inverter SHEPWM method based on an NR-ACA algorithm, which comprises the following steps: expanding a cascaded output voltage expression by using a Fourier series to obtain an expression of harmonic amplitude; according to a harmonic to be eliminated, making the corresponding harmonic amplitude expression 0, thereby establishing a nonlinear equation group; converting the nonlinear equation group into a single-target optimization problem by using an ant colony algorithm; taking the switch angle obtained by the ant colony algorithm as a switch angle initial value of a Newton iteration method to calculate a high-precision switch angle; and generating a driving pulse of the cascaded H-bridge by using the switch angle calculated by the algorithm. The application greatly reduces the calculation amount, improves the convergence speed, makes the calculated switch angle more accurate than a single intelligent algorithm, basically eliminates the selected harmonic, greatly reduces the switch loss, and makes the application more applicable to engineering.

Description

Technical Field

[0001] This invention belongs to the field of power electronics technology, specifically a SHEPWM method for cascaded H-bridge inverters based on the NR-ACA algorithm. Background Technology

[0002] Cascaded H-bridge multilevel inverters are widely used due to their identical unit structure, ease of modularization and expansion, and voltage redundancy. To achieve better output waveform quality and reduce harmonic content, SHEPWM technology was developed. Specific Harmonic Elimination Pulse Width Modulation (SHEPWM) technology calculates the optimal switching angle to effectively eliminate selected low-order harmonics while ensuring the desired fundamental voltage output.

[0003] Traditional SHEPWM technology in cascaded multilevel inverters is only suitable when the DC-side power supplies of each unit are completely equal. However, in practical applications, the power supply voltage may deviate to some extent, which worsens the harmonic suppression effect of SHEPWM. Although the traditional Newton-Raphson iteration method has high accuracy, inappropriate initial values ​​can lead to a decrease in solution speed or even non-convergence. In recent years, although scholars at home and abroad have proposed intelligent algorithms to solve the established nonlinear equations, intelligent algorithms generally suffer from low accuracy due to the randomness of the search. Summary of the Invention

[0004] The purpose of this invention is to provide a SHEPWM method for cascaded H-bridge inverters based on the NR-ACA algorithm.

[0005] The technical solution to achieve the purpose of this invention is: a SHEPWM method for cascaded H-bridge inverters based on the NR-ACA algorithm, the specific steps of which are as follows:

[0006] 1) Expand the expression of the cascaded output voltage using Fourier series to obtain the expression of the harmonic amplitude; based on the harmonics to be eliminated, make the corresponding harmonic amplitude expression 0, and establish a system of nonlinear equations;

[0007] 2) The nonlinear equation system is transformed into a single-objective optimization problem using the ant colony algorithm to obtain the switching angle;

[0008] 3) Use the switching angle obtained by the ant colony algorithm as the initial value of the switching angle for the Newton iteration method to calculate the high-precision switching angle;

[0009] 4) Use the calculated switching angle to generate the drive pulse for the cascaded H-bridge.

[0010] Preferably, the steps for establishing a system of nonlinear equations include:

[0011] (1) Make the positive and negative half-cycles of the output voltage waveform of the cascaded H-bridge inverter mirror symmetrical about the point (π,0);

[0012] (2) Make the waveform symmetrical about π / 2 as the axis in the first and second quarter periods of the positive half period;

[0013] (3) Represent the transformed waveform using Fourier series;

[0014] (4) Expand the cascaded output voltage expression obtained in step (3) to obtain the cascaded output voltage V. (wt) ;

[0015] (5) Based on the cascaded output voltage V (wt) The magnitude V of the nth harmonic is obtained. n ;

[0016] (6) Based on the fundamental amplitude to be controlled and the harmonic order to be eliminated, establish a set of nonlinear equations to be solved.

[0017] Preferably, the amplitude V of the nth harmonic is... n for:

[0018]

[0019] In the formula, θ1, θ2, ..., θ N It is the switching angle, E is the DC bus voltage, and N is the number of cascaded H-bridges.

[0020] Preferably, the system of nonlinear equations to be solved is:

[0021]

[0022] Where the harmonic order n = 1, 3, 5..., m represents the modulation ratio, E is the DC bus voltage, and V h1 θ1, θ2, ..., θ3 represent the fundamental frequency amplitude, N is the number of cascaded H-bridges, and θ1, θ2, ..., θ3 represent the fundamental frequency amplitude. N It is the switching angle.

[0023] Preferably, transforming the nonlinear equation system into a single-objective optimization problem involves converting the solution of the nonlinear equation system into finding the minimum fitness value, specifically:

[0024] By rearranging the system of nonlinear equations to be solved, we can construct the following functions y1, y2...y n :

[0025]

[0026] The above equation can be equivalent to a single-objective optimization problem:

[0027]

[0028] in,

[0029] Where y is the fitness, θ1, θ2, ..., θ N It refers to the switching angle. If the switching angle calculated using this algorithm is accurate, then the function y1, y2, ..., y... n All values ​​approach 0, the minimum value of fitness y is -1, and the closer the result is to -1, the more accurate the result is and the better the harmonic elimination effect.

[0030] Preferably, the steps for obtaining the initial value of the switching angle using the ant colony algorithm include:

[0031] (1) Initialization parameters: number of ants m, maximum number of iterations N cmax Ant search step size, pheromone intensity Q, pheromone evaporation coefficient γ;

[0032] (2) Select a node and update the local pheromone;

[0033] (3) Decode the constructed objective function value y;

[0034] (4) Determine whether the maximum number of iterations has been reached. If the maximum number of iterations has not been reached, return to step (2).

[0035] If the maximum number of iterations is reached, the calculated switching angle is used as the initial value of the switching angle for Newton's iteration method.

[0036] Preferably, the specific formula for selecting nodes is as follows:

[0037]

[0038]

[0039] In the formula, the probability that the k-th ant visits node j from node i is P. ij K The information heuristic factor α represents the rate of pheromone secretion, and the heuristic function factor β is a parameter characterizing the importance of the heuristic factor; at the t-th iteration, the pheromone concentration on the path from node i to node j is τ. ij (t),allow k To determine the next selectable node based on the tabu list, we need the set of nodes that have not yet been visited. The heuristic function η... ij (t) represents the visibility of the ant from node i to node j. d ij This is the path distance between two nodes i and j. The taboo list for ant movement is continuously updated until each node is visited, completing one iteration to calculate the optimal value. One iteration means that each ant has visited all the nodes.

[0040] Preferably, the local pheromone update formula is:

[0041]

[0042] τ ij (t+1) represents the pheromone content from node i to node j after the (t+1)th cycle. γ represents the pheromone evaporation coefficient. Δτ ij Δτ represents the newly added pheromone concentration between node i and node j. ij k The pheromone left by the k-th ant on the path from node i to node j is represented by the following formula:

[0043]

[0044] Q is the pheromone intensity and is a constant, L k This represents the total length of all nodes visited by the ant.

[0045] Preferably, the switching angle obtained using the ant colony algorithm is used as the initial value of the switching angle for the Newton iteration method. The specific method for calculating the high-precision switching angle is as follows:

[0046] By rearranging the terms of the nonlinear equation system and subtracting the left and right sides, we obtain:

[0047]

[0048] Notation:

[0049] F(θ) = 0

[0050] In the formula

[0051]

[0052] (1) The switching angle obtained using the ant colony algorithm is used as the initial value θ0 of the switching angle:

[0053]

[0054] (2) Substitute the initial value of the switching angle θ0 into F(θ), denoted as F0

[0055] F(θ0)=F0

[0056] (3) Linearize F(θ) to obtain

[0057] F(θ)≈F0+F′(θ0)dθ=0

[0058] In the formula

[0059]

[0060] (4) Solve the system of linear equations to obtain the error dθ of the switching angle:

[0061] dθ=-(F′(θ0)) -1 *F0

[0062] (6) Replace θ with θ1=θ0+dθ as the initial value, and repeat (2)~(4) above until the value obtained meets the required precision.

[0063] Preferably, when the accuracy requirement is met, the error dθ of the switching angle satisfies:

[0064] -10 -15 ≤dθ≤10 -15 .

[0065] Compared with existing technologies, the significant advantages of this invention are: 1) The NR-ACA algorithm is applicable to situations where the DC-side power supplies of each unit are not equal; 2) The NR-ACA algorithm overcomes the problem of difficulty in selecting the initial value of the switching angle in traditional methods; 3) The NR-ACA algorithm overcomes the problem of low accuracy caused by the randomness of the search, which is common in intelligent algorithms. It greatly reduces the amount of computation, improves the convergence speed, and makes the calculated switching angle more accurate than that of a single intelligent algorithm. The selected harmonic content can be reduced to 0.01% or even to 0%, which means it is completely eliminated. This greatly reduces switching losses and makes it easier to apply in engineering; 4) This invention is not only applicable to selective harmonic elimination of cascaded H-bridges, but also to selective harmonic elimination of output voltages that are unipolar or bipolar, and significant application effects can be achieved in both cases. Attached Figure Description

[0066] Figure 1 This is the topology of a cascaded H-bridge multilevel inverter.

[0067] Figure 2 The stepped wave voltage of the (2N+1) level cascaded H-bridge inverter.

[0068] Figure 3 The optimal route for solving the TSP optimization problem using the ant colony algorithm.

[0069] Figure 4 Comparison of shortest distance and average distance across generations for solving the TSP optimization problem using the ant colony algorithm.

[0070] Figure 5 A flowchart for solving the switching angle using the ant colony optimization algorithm.

[0071] Figure 6 The fitness evolution curve for solving the switching angle is provided using the ant colony algorithm.

[0072] Figure 7 The flowchart shows the procedure for solving the switching angle using the Newton-Raphson algorithm.

[0073] Figure 8 This is a flowchart of the NR-ACA algorithm.

[0074] Figure 9 The relationship between the switching angle and modulation ratio obtained by the NR-ACA algorithm when the DC bus voltage E is equal and the 5th and 7th harmonics are eliminated.

[0075] Figure 10 The output voltage of a cascaded 7-level inverter is analyzed using FFT with a modulation ratio m = 0.9 and the elimination of the 5th and 7th harmonics.

[0076] Figure 11 FFT analysis of the output voltage of a cascaded 7-level inverter with modulation ratio m = 0.8 and elimination of 3rd and 5th harmonics.

[0077] Figure 12 The graph shows the relationship between the switching angle and the modulation ratio when the DC bus voltages are unequal and the 5th and 7th harmonics are eliminated.

[0078] Figure 13 For the DC bus voltage unequal, with m=0.9 and the 5th and 7th harmonics eliminated, the output voltage of the cascaded 7-level inverter is analyzed using FFT.

[0079] Figure 14 The graph shows the relationship between the switching angle and the modulation ratio when the number of switching angles N=3, the output voltage is unipolar, and the 3rd and 5th harmonics are eliminated.

[0080] Figure 15 The output voltage and its FFT analysis are performed when the output voltage is unipolar, the modulation ratio m = 0.9 and the 3rd and 5th harmonics are eliminated. Detailed Implementation

[0081] To more clearly describe the ideas, technical solutions, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0082] A SHEPWM method for cascaded H-bridge inverters based on the NR-ACA algorithm is presented. This method is applicable to situations where the DC-side power supplies of each unit are unequal. It overcomes the reliance on initial values ​​in traditional methods and leverages the high accuracy of the Newton-Raphson iteration method. It also overcomes the accuracy issues commonly found in intelligent algorithms due to search randomness, significantly reducing computational load and improving convergence speed. The calculated switching angles are more accurate than those of single intelligent algorithms, and the selected harmonics are almost completely eliminated, greatly reducing switching losses and making it easier to apply in engineering. Furthermore, this invention is also applicable to selective harmonic elimination in unipolar and bipolar output voltages, achieving significant application results. This demonstrates the algorithm's clear advantages, meets the operating requirements of high-voltage, high-power applications, and has important practical significance for improving power quality and reducing the harm of harmonics to electrical equipment.

[0083] like Figure 1 As shown, the topology of a cascaded H-bridge multilevel inverter consists of N cascaded H-bridges. Each H-bridge module has an independent DC input power supply E with the same voltage. This independent DC power supply can be obtained from solar cells, fuel cells, or supercapacitors. Connecting the AC output sides of each H-bridge module in series yields a stepped output waveform. By independently controlling different combinations of the four switches in each H-bridge module, each inverter module can generate three different output levels: +E, 0, and -E. The cascaded output voltage Uo is (2N+1) level. Connecting the AC sides of multiple full-bridge inverters with different conduction angles in series results in a composite stepped waveform, as shown below. Figure 2 As shown.

[0084] Step 1: Establish a system of nonlinear equations based on the specific harmonics to be eliminated;

[0085] To eliminate selected harmonics and simplify control, the waveform should be symmetrical. First, to eliminate even harmonics, the positive and negative half-cycles of the waveform should be mirror-symmetrical about the point (π, 0), i.e.:

[0086] u(ωt)=-u(ωt+π)

[0087] Secondly, to eliminate the cosine terms in the harmonics, the waveform should be symmetrical about π / 2 about the axis of 1 / 4 of the positive half-cycle, that is, symmetrical about the axis x = π / 2.

[0088] u(ωt)=u(ωt-π)

[0089] A waveform that satisfies both of the above equations is called a 1 / 4 periodic symmetrical waveform. This waveform can be represented by a Fourier series as follows:

[0090]

[0091]

[0092] Where n = 1, 3, 5, 7... therefore

[0093] For a 2N+1 level cascaded H-bridge inverter, the harmonic content is the sum of the corresponding harmonics of N H-bridge inverter modules. Taking N=3 as an example, the cascaded output voltage V(wt) is:

[0094]

[0095] The amplitude V of the nth harmonic n for

[0096]

[0097] The switching angle satisfies:

[0098]

[0099] The H-bridge unit of a cascaded 2N+1 level H-bridge inverter changes state N times within half a cycle, where N is the number of cascaded H-bridge inverter modules. Considering the 1 / 4 cycle symmetry of the PWM wave, there are N controllable switching moments. Excluding using one degree of freedom to control the fundamental amplitude, N-1 harmonics of specific frequencies can be eliminated. The transcendental equations to be solved are as follows:

[0100]

[0101] Where m is the modulation ratio, m = V h1 / (NE)=Vh1 / (3E), where Vh1 is the fundamental amplitude of the output voltage, N is the number of cascaded H-bridges, and E is the DC bus voltage.

[0102] Step 2: Use the ant colony algorithm to transform the nonlinear equation system into a single-objective optimization problem;

[0103] This section illustrates the principles and solution steps of the ant colony algorithm by solving a typical TSP (Tracking Shortest Path) optimization problem. It sets up city locations and solves for the shortest path starting from a certain point, passing through all cities, and returning to the starting point only once. This is similar to solving for the minimum objective function in the next section. Taking an n-city optimization problem as an example, let the number of ants be m, and initially, the pheromone concentration τ is equal on all paths. ij (0) = τ0. Ants k (k = 1, 2, ..., m), each city's location is a node, and the probability formula for an ant choosing the next node in the flowchart is as follows.

[0104]

[0105]

[0106] In the formula, the probability that the k-th ant visits node j from node i is P. ij K The information heuristic factor α represents the rate of pheromone secretion, and the heuristic function factor β is a parameter characterizing the importance of the heuristic factor; at the t-th iteration, the pheromone concentration on the path from node i to node j is τ. ij (t),allow k To determine the next selectable node based on the tabu list, we need the set of nodes that have not yet been visited. The heuristic function η... ij (t) represents the visibility of the ant from node i to node j. d ijis the path distance between two nodes i and j. As the ants move, the taboo list is continuously updated until each node has been visited to complete one iteration for calculating the optimal value. One iteration means that each ant has traversed all the nodes

[0107] The pheromone is a dynamic process. After each cycle, it is updated according to the pheromone persistence coefficient according to the following formula:

[0108]

[0109] τ ij (t + 1) represents the pheromone content from node i to node j after the (t + 1)-th cycle. γ represents the pheromone evaporation coefficient. Δτ ij is the newly added pheromone concentration between nodes i and j. Δτ ij k represents the pheromone left by the k-th ant on the path from node i to node j, and the calculation formula is as follows:

[0110]

[0111] Q is the pheromone intensity and is a constant. L k represents the total length of the path that the ant has passed through all nodes. The steps of the ant colony algorithm are as follows:

[0112] Step1: Initialize the parameters, set the number of nodes as n, the number of ants as m, and the maximum number of iterations as N cmax , the pheromone evaporation coefficient γ, the pheromone intensity Q, the initial state Δτ ij (0) = 0, the information heuristic factor α, and the importance degree β of the heuristic factor

[0113] Step2: The number of iterations N c = N c + 1; the taboo list index number k = k + 1; the number of ants k = k + 1

[0114] Step3: Calculate the traveling direction of the next node of each ant according to the pheromone concentration probability selection formula;

[0115] Step4: Modify the taboo list;

[0116] Step5: If k < m, return to step4, otherwise go to step6;

[0117] Step6: Update the pheromone concentration according to formula (10);

[0118] Step7: If N c < N cmax , return to step2, otherwise output the result.

[0119] A coordinate sample of 14 cities was selected and simulated in MATLAB to verify the effectiveness of the algorithm. The ant colony algorithm for finding the optimal route in the TSP optimization problem is as follows: Figure 3 As shown:

[0120] As shown in the graph, the shortest distance is 35.6082, and the shortest path is 2, 1, 3, 6, 7, 12, 5, 9, 13, 8, 11, 10, 4, 14, 2.

[0121] Comparison of shortest distance and average distance across generations in solving the TSP optimization problem using ant colony algorithm. Figure 4 As shown.

[0122] As shown in the figure, after each iteration, the ant colony algorithm significantly shortens the path and average path length, and finds the optimal path after the 5th iteration, demonstrating the algorithm's effectiveness in finding the best path.

[0123] The establishment of the harmonic elimination equations has been described in detail previously. The nonlinear equations that need to be solved are as follows:

[0124]

[0125] By rearranging terms in the harmonic-eliminating equation system, subtracting the left and right sides, and constructing functions y1, y2, ... y... n The original expression is transformed into:

[0126]

[0127] Solving using the ant colony optimization algorithm, the above equation is equivalent to a single-objective optimization problem, that is, the nonlinear equation system is transformed into finding the minimum value of the following fitness y:

[0128]

[0129] in,

[0130] Where y is the fitness, θ1, θ2, ..., θ N It refers to the switching angle. If the switching angle calculated using this algorithm is accurate, then the function y1, y2, ... y n All values ​​approach 0, the minimum value of fitness y is -1, and the closer the result is to -1, the more accurate the result is and the better the harmonic elimination effect.

[0131] In summary, eliminating the specified harmonics is transformed into finding the minimum value of the constructed fitness y. Ant colony optimization algorithm is used to find the maximum and minimum values ​​of the function, so it can be used to solve for the switching angle.

[0132] The flowchart of the ant colony optimization algorithm for solving the switching angle is as follows: Figure 5 As shown.

[0133] Using the ant colony algorithm, the switching angles when the number of cascaded H-bridges N=3, the 5th and 7th harmonics are eliminated, and the modulation ratio m=0.8 are as follows: θ1=29.237100°, θ2=54.437312°, θ3=64.484507°.

[0134] The fitness evolution curve of the switching angle is solved using the ant colony algorithm, as shown below. Figure 6 As shown:

[0135] As can be seen, when iterating to the 15th generation, the fitness, i.e. the minimum value of the function, is very close to -1, which makes the obtained initial value continuously approach the solution of the nonlinear equation system to meet the requirements of Newton's iteration method. This proves that the results are accurate and that the ACA algorithm has fewer iterations, faster convergence speed, and better optimization effectiveness.

[0136] Table 1 lists the initial switching angles obtained for some different modulation ratios when the DC bus voltage E is equal and the 5th and 7th harmonics are eliminated;

[0137] Table 1

[0138]

[0139] Step 3: Use the switching angle obtained by the ant colony algorithm as the initial value of the switching angle for the Newton iteration method, and calculate the high-precision switching angle.

[0140] The principle of the Newton-Raphson method (NR) is as follows:

[0141] As described above, for N cascaded H-bridges, the following set of nonlinear equations needs to be solved to eliminate the 3rd, 5th, 7th, ..., Nth harmonics:

[0142]

[0143] By rearranging the terms of the harmonic elimination equations and subtracting the left and right sides, we get:

[0144]

[0145] Notation:

[0146] F(θ) = 0

[0147] In the formula

[0148]

[0149] (1) Determine the initial value of the switching angle θ0

[0150]

[0151] (2) Substitute the initial value of the switching angle θ0 into F(θ), denoted as F0

[0152] F(θ0)=F0

[0153] (3) Linearize F(θ) to obtain

[0154] F(θ)≈F0+F′(θ0)dθ=0

[0155] In the formula

[0156]

[0157] (4) Solve the linear equation system to obtain the error dθ of the switching angle.

[0158] dθ=-(F′(θ0)) -1 *F0

[0159] (5) Replace θ with θ1 = θ0 + dθ as the initial value, and repeat steps 2 to 4 above until the obtained value meets the required accuracy. The higher the accuracy, the smaller the error dθ of the switching angle. Therefore, the error can be set as follows.

[0160] -10 -15 ≤dθ≤10 -15

[0161] To clearly understand this process, the flowchart of the Newton-Raphson algorithm for solving the switching angle is as follows: Figure 7 As shown:

[0162] The switching angle obtained using the ant colony algorithm is used as the initial value for the switching angle in the Newton-Raphson iteration method. The switching angle is then calculated using the Newton-Raphson iteration method. The flowchart of the NR-ACA algorithm is as follows: Figure 8 As shown; using the NR-ACA algorithm, the relationship between the switching angle and the modulation ratio when the voltages of the three DC buses are equal and the 5th and 7th harmonics are eliminated is shown in the figure below. Figure 9 As shown:

[0163] Step 4: Use the calculated switching angle to generate the driving pulse of the cascaded H-bridge, and perform FFT analysis on its output voltage. It can be observed that specific harmonics have been completely eliminated, and the accuracy is higher than that of the current single intelligent algorithm, which shows the obvious advantages of the algorithm.

[0164] The simulation parameters for the cascaded H-bridge are set as follows: DC bus voltage E = 10V for each power unit, load inductance L = 2mH, and load resistance R = 100Ω.

[0165] The following simulation was performed with a modulation ratio m = 0.9 and elimination of the 5th and 7th harmonics. The resulting switching angles are: θ1 = 17.5104°, θ2 = 43.0523°, and θ3 = 64.1395°.

[0166] With a modulation ratio m = 0.9 and elimination of the 5th and 7th harmonics, the output voltage of the cascaded 7-level inverter and FFT analysis are as follows: Figure 10 As shown.

[0167] As shown in the diagram, the cascaded output voltage Uo has a voltage level of 2N+1 = 2*3+1 = 7V. The amplitudes at the three transition points are respectively equal to E = 10V, 2E = 20V, 3E = 30V, and V. H1 =27V equals the theoretical value V H1 =m*(NE)=0.9*(3*10)=27V, eliminating the 5th and 7th harmonics, achieving almost zero error, proving the accuracy of the switching angle and the accuracy of the proposed algorithm.

[0168] Similarly, when the modulation ratio m = 0.8 and the 3rd and 5th harmonics are eliminated, the output voltage of the cascaded 7-level inverter and FFT analysis are as follows: Figure 11 As shown:

[0169] As shown in the figure, by controlling the fundamental amplitude and eliminating specific 3rd and 5th harmonics, almost zero error is achieved, proving the accuracy of the switching angle and the accuracy of the proposed algorithm.

[0170] To verify the accuracy of the proposed NR-ACA algorithm, it can be applied to the case where the DC-side power supplies of each unit are not equal.

[0171] When the voltages of the three DC buses are unequal, the system of equations becomes as follows:

[0172]

[0173] The relationship between the switching angle and the modulation ratio when the three DC bus voltages are not equal, obtained using the NR-ACA algorithm, is shown in the following graph. Figure 12 As shown.

[0174] like Figure 12 As shown, the switching angle trajectory under the condition of unequal DC-side voltage is continuous, just like the switching angle trajectory under the condition of equal DC-side voltage in the traditional case. This satisfies the commonality of the traditional case, indicating that the study of the case of unequal DC-side voltage is meaningful and can serve as a reference for the selection of switching angle.

[0175] The simulation uses E1 = 9V, E2 = 10V, and E3 = 11V. The simulation is performed with a modulation ratio of 0.9, yielding the following switching angles: θ1 = 16.2970°, θ2 = 40.4296°, and θ3 = 63.2252°. When the DC bus voltages are unequal and the modulation ratio m = 0.9, the output voltage of the cascaded 7-level inverter and FFT analysis are as follows: Figure 13 As shown:

[0176] As shown in the diagram, the amplitudes at the three inflection points of the cascaded output voltage are respectively equal to E1 = 9V, E1 + E2 = 19V, and E1 + E2 + E3 = 30V. H1 =27V equals the theoretical value V H1 =m*(E1+E2+E3)=0.9*(9+10+11)=27V, eliminating the 5th and 7th harmonics, achieving almost zero error, proving the accuracy of the switching angle.

[0177] To verify the accuracy of this invention, the NR-ACA algorithm can be applied to a single H-bridge with a unipolar output voltage. Taking a unipolar output voltage and eliminating the 3rd and 5th harmonics as an example, the following system of nonlinear equations needs to be solved:

[0178]

[0179] Where m is the modulation ratio, the relationship between the switching angle and the modulation ratio when E = 100V, the number of switching angles N = 3, the output voltage is unipolar and the 3rd and 5th harmonics are eliminated is shown in the figure below. Figure 14 As shown:

[0180] With N = 3 and m = 0.9, the switching angles are: θ1 = 29.4054°, θ2 = 53.4507°, and θ3 = 64.4559°. When the output voltage is unipolar and the modulation ratio m = 0.9, the output voltage and its FFT analysis are as follows: Figure 15 As shown:

[0181] As can be seen from the figure, V h1 =90.01V is almost equal to the theoretical value V h1 =m*E=0.9*100=90V, which eliminates the 3rd and 5th harmonics, proving the accuracy of the switching angle and the accuracy of the proposed algorithm.

[0182] This invention proposes an NR-ACA algorithm that combines the Ant Colony Algorithm (ACA) with the Newton-Raphson method (NR). It fully leverages the advantages of both algorithms, using the switching angle obtained from the ant colony algorithm as the initial value for the Newton-Raphson method. The algorithm then performs iterative calculations using the Newton-Raphson method. This approach is applicable to situations where the DC-side power supplies of each unit are unequal, overcomes the difficulty of initial value selection, and utilizes the high accuracy of the Newton-Raphson method to reduce computational load and improve convergence speed. The calculated switching angle is more accurate than that of a single intelligent algorithm, and the selected harmonics are essentially completely eliminated. The reliability and speed of the NR-ACA solution are verified by solving the SHEPWM nonlinear equations using Matlab programming. A simulation system of a cascaded 7-level H-bridge inverter is built to verify that the switching angle obtained by the NR-ACA can achieve the fundamental frequency control target and effectively eliminate selected low-order harmonics. Furthermore, the NR-ACA algorithm is applied to a case where the output voltage is unipolar, also achieving selective harmonic elimination, thus verifying the accuracy of the proposed NR-ACA algorithm. This invention is applicable to situations where the DC power supplies of each unit are unequal, overcomes the difficulty in selecting the initial value of the switching angle, and leverages the high accuracy of the Newton-Raphson iteration method to overcome the low accuracy problem caused by the randomness of the search in intelligent algorithms. It significantly reduces the computational load, improves the convergence speed, and makes the calculated switching angle more accurate than that of a single intelligent algorithm. The selected harmonics are essentially completely eliminated, greatly reducing switching losses and making it easier to apply in engineering. Furthermore, this invention is also applicable to selective harmonic elimination in unipolar and bipolar output voltages, achieving significant application results. It demonstrates the clear advantages of the algorithm, meets the working requirements of high-voltage, high-power applications, and has important practical significance for improving power quality and reducing the harm of harmonics to electrical equipment.

Claims

1. A cascaded H-bridge inverter SHEPWM method based on NR-ACA algorithm, characterized in that, The specific steps are: 1) Express the output voltage of the cascade with Fourier series, and obtain the expression of the harmonic amplitude; According to the harmonic to be eliminated, make the corresponding harmonic amplitude expression equal to 0, and establish a nonlinear equation group, including: (1) Make the positive and negative half cycles of the output voltage waveform of the cascade H-bridge inverter mirror symmetric, and symmetric about the point (pi, 0); (2) Make the waveform symmetric about the axis of pi / 2 in the front and back 1 / 4 cycles in the positive half cycle; (3) Express the transformed waveform with Fourier series; (4) The expression of the cascade output voltage obtained in step (3) is expanded to obtain the cascade output voltage V (wt) ; (5) According to the cascade output voltage V (wt) , the amplitude of the nth harmonic V n is obtained. (6) According to the fundamental amplitude to be controlled and the harmonic order to be eliminated, establish the nonlinear equation group to be solved; 2) Use the ant colony algorithm to convert the nonlinear equation group into a single-objective optimization problem to obtain the switching angle, specifically: The nonlinear equations to be solved are moved to construct the following function y1, y 2... y n : The above formula is equivalent to a single-objective optimization problem: wherein where y is fitness, θ1, θ2,.. θ N are switching angles, if the switching angles calculated by the algorithm are accurate, the functions y1, y 2.. , y n all approach 0, the minimum value of the fitness y is -1, and if the result approaches -1 more, the result is more accurate, and the harmonic elimination effect is better; 3) Use the switching angle obtained by the ant colony algorithm as the initial value of the switching angle of the Newton iteration method to calculate the high-precision switching angle, including: (1) initialization parameters: the number of ants m, the maximum number of iterations N cmax , the ant search step size, Q represents the pheromone intensity, i.e. the total amount of pheromone that each ant can secrete, the pheromone evaporation coefficient γ; (2) Select nodes and update local pheromone; (3) Decode to obtain the value of the constructed objective function y; (4) Determine whether the maximum number of iterations is reached, if not, return to step (2); If the maximum number of iterations is reached, the obtained switching angle is used as the initial value of the switching angle of the Newton iteration method 4) Generate the drive pulse of the cascade H-bridge with the calculated switching angle.

2. The cascaded H-bridge inverter SHEPWM method based on NR-ACA algorithm according to claim 1, characterized in that, The amplitude size V of the nth harmonic n is: In the formula, θ1, θ2, ..., θ N It is the switching angle, E is the DC bus voltage, and N is the number of cascaded H-bridges.

3. The cascaded H-bridge inverter SHEPWM method based on NR-ACA algorithm according to claim 1, characterized in that, The nonlinear equation group to be solved is: where the harmonic number n = 1, 3, 5..., m represents the modulation ratio, E is the DC bus voltage, V h1 is the fundamental amplitude, N is the number of cascaded H-bridges, θ1, θ2,.. θ N are switching angles.

4. The cascaded H-bridge inverter SHEPWM method based on NR-ACA algorithm according to claim 1, characterized in that, The specific formula for selecting nodes is: where P ij k is the probability of the kth ant visiting node j from node i, the information heuristic factor a represents the speed of secreting pheromone, and the heuristic function factor β represents the parameter of the importance degree of the heuristic factor; the pheromone concentration on the path from node i to node j at the tth cycle is τ ij (t),allow k to be the next node selected according to the tabu list, i.e., the set of nodes that have not been visited; the heuristic function η ij (t) represents the visibility of the ant from node i to node j; d ij is the path distance between the two nodes i and j.

5. The cascaded H-bridge inverter SHEPWM method based on NR-ACA algorithm according to claim 1, wherein, The update formula for local pheromone is: τ ij (t+1) represents the pheromone content from node i to node j after the t+1th cycle, γ represents the pheromone evaporation coefficient, Δτ ij is the newly added pheromone concentration between node i and node j; Δτ ij k represents the pheromone left by the kth ant on the path from node i to node j, and the calculation formula is as follows: Q is pheromone intensity and is constant, L k represents the sum of paths passed by the kth ant.

6. The cascaded H-bridge inverter SHEPWM method based on NR-ACA algorithm according to claim 1, wherein, The specific method for calculating the high-precision switching angle using the switching angle obtained by the ant colony algorithm as the initial value of the switching angle of the Newton iteration method is: Move the term to the right side, and subtract the left side from the right side to obtain: Let it be: F(theta) = 0 In the formula (1) Use the switching angle obtained by the ant colony algorithm as the initial value of the switching angle theta0: (2) Substitute the initial value of the switching angle theta0 into F(theta) to obtain F0 F(theta0) = F0 (3) Linearize F(theta) to obtain F(theta) approximately equals F0 + F'(theta0)dtheta = 0 In the formula (4) Solve the linear equation group to obtain the error dtheta of the switching angle: dθ = - (F'(θ0)) -1 *F0 (5) Replace theta with theta0 + dtheta to obtain the initial value, and repeat steps (2) to (4) until the value obtained meets the required accuracy.

7. The cascaded H-bridge inverter SHEPWM method based on NR-ACA algorithm according to claim 6, characterized in that, When the accuracy requirement is met, the error dtheta of the switching angle meets: -10 -15 ≤ dθ ≤ 10 -15 .

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