A numerical calculation method for large ripple capacitor voltage

Abstract

The present invention discloses a numerical calculation method for large ripple capacitor voltage, including a capacitor voltage function relationship whose original function containing integral term is implicit, that is, the relationship is a complex implicit transcendental function equation (1), the integral term in the function relationship is discretized and expressed in the form of cumulative sum, and two adjacent points are made into difference and discretized expressions to establish a recursive relationship, and programming iterative calculation is performed according to the corresponding assumption of integration. The present invention respectively provides two algorithms for large ripple voltage of different converters, and provides an effective numerical solution method for transcendental functions containing integral terms and whose original integral function is implicit.

Description

Technical Field

[0001] The present invention belongs to a numerical calculation method for a transcendental function whose integral term original function in a function expression is implicit, and particularly relates to a large ripple capacitor voltage numerical calculation method. Background Art

[0002] In power electronics technology, electrolytic capacitors are often used as energy storage capacitors for power converters due to their large capacitance and volume. At the same time, the service life and volume of electrolytic capacitors seriously restrict the working life and power density of the converter. In order to solve this problem, electrolytic capacitors are replaced with capacitors with longer life, smaller volume but smaller capacitance, which leads to an increase in the voltage ripple of the converter capacitor. This voltage with relatively large ripple is called large ripple voltage. A calculation method for capacitor voltage waveform under different parameters is designed, which can provide a reference for the design of the converter and provide an effective reference tool for the control, design and optimization of the converter system.

[0003] The waveform function relationship of large ripple voltage is a complex transcendental function whose integral term is implicit. Conventional numerical solution methods are difficult to solve. The present invention discretizes the integral term relationship contained in the function relationship based on the idea of ​​limit, establishes an iterative relationship by subtracting the discretized relationship between two adjacent points, and solves its value using a numerical iteration method. The present invention provides two algorithms for large ripple voltage of different converters, and experiments prove the effectiveness of the algorithm proposed by the present invention, which provides an effective numerical solution method for transcendental functions containing integral terms and whose integral original functions are implicit. Summary of the invention

[0004] The purpose of the present invention is to address the deficiencies of the above-mentioned background technology and to provide a numerical calculation method for large ripple capacitor voltage, which is used to solve the numerical optimization method of the integral primitive function containing implicit transcendental functions.

[0005] The present invention adopts the following technical solutions to achieve the above-mentioned invention object:

[0006] A method for numerically calculating large ripple capacitor voltage, wherein the original function of the capacitor voltage function relationship containing the integral term is implicit, that is, the relationship is a complex implicit transcendental function equation (1), the integral term in the function relationship is discretized and expressed in the form of cumulative sum, and the difference between two adjacent points and the discretized expression are used to establish a recursive relationship, and the programming iterative calculation is performed according to the corresponding assumption of the integral;

[0007]

[0008] In equation (1), v b The function relationship to be sought is t as the independent variable, V m , C b, P o , θ1, θ2, and ω are all constants.

[0009] Preferably, the integral term contained in the objective function can be regarded as the projection area formed by the original function and the X-axis, the definite integrals of the implicit equation (2) and the explicit (analytical) equation (3) contained in the original function are recorded as different constants, and the variable limit integral can be uniformly discretized into the form of cumulative sum (such as equation (4));

[0010]

[0011] In equations (2), (3), and (4), A, B, and N are constants, and ΔT is the distance between two adjacent discrete points.

[0012] The principle of integral discretization is to approximate the integral term with a basic matrix. The projection area formed by the original function of the integral and the X-axis is expressed as the accumulation of the areas of rectangles with the same width and different lengths on the coordinate axis.

[0013] Preferably, after discretizing the functional relationship, a recursive relationship is established based on the relationship between the two points, and the objective function is discretized, as shown in equation (5). After subtracting the expressions of equations (5) and (6) between two adjacent points, recursive relationships (7) and (8) can be established;

[0014]

[0015] The left side of equation (8) is different from the left side of equation (7). The analytical expression on the left side of equation (7) shows that when N is large enough, the output voltage v b The difference between the values ​​of two adjacent points is small, so equation (8) can be simplified to an analytical expression such as equation (9):

[0016]

[0017] Preferably, the programming calculation is performed according to the recursive formula, and the basic flow of the algorithm is as follows:

[0018] 1) Input basic parameters and set corresponding error tolerance;

[0019] 2) Predict the initial value A and set the error tolerance A_eps corresponding to its parameters according to the actual objective function relationship;

[0020] 3) According to the recursive formula, the numerical solution matrix v in the definition domain is solved cyclically;

[0021] 4) Recalculate the value of parameter A with the solved v and record it as A_new;

[0022] 5) When the error between A_new and A is less than A_eps, go to step 6); otherwise, assign A_new to A and go to step 3);

[0023] 6) Output numerical calculation results.

[0024] Compared with the prior art, the present invention adopts the above technical solution and has the following beneficial effects:

[0025] 1. The present invention provides a numerical calculation method for large ripple capacitor voltage. Based on the idea of ​​limit, the integral term relation contained in the function relation is discretized, and the discretized relation between two adjacent points is subtracted to establish an iterative relation, and its value is solved using a numerical iteration method.

[0026] 2. The present invention provides a numerical calculation method for large ripple capacitor voltage, and provides algorithms for large ripple voltage of two different converters, respectively, providing an effective numerical solution method for transcendental functions containing integral terms and whose integral primitive functions are implicit. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0028] Figure 1 It is a flow chart of the implicit transcendental function solving algorithm of the present invention;

[0029] Figure 2 1 is a main circuit diagram of a DCM Buck PFC converter according to an embodiment of the present invention;

[0030] Figure 3 is a capacitor voltage waveform diagram in an embodiment of the present invention;

[0031] Figure 4 is a flow chart of a DCM BUCK large ripple output voltage algorithm in an embodiment of the present invention;

[0032] Figure 3 In the figure, the dead zone angles are θ1 and θ2, which means that in a cycle [0,π], the converter only works in [θ1,θ2]. g Less than the capacitor voltage v b , the converter does not work. The average output voltage V b_avg Indicates the average value of the output voltage in one cycle;

[0033] Figure 4The hump dashed line is the input voltage waveform v in one cycle. g , the flat dotted line represents the average output voltage v b_avg , the solid line is the large ripple voltage v b The waveform of

[0034] Figure 5 The result of running the algorithm. DETAILED DESCRIPTION

[0035] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0036] In order to better describe the numerical solution method proposed in the present invention, a solution example of a BUCK converter under current discontinuity (DCM BUCK converter) is given below.

[0037] 1DCM Buck converter large ripple voltage numerical solution example

[0038] The main circuit of the DCM Buck converter is as follows Figure 1 , grid voltage v in After passing through the rectifier bridge, the voltage can be expressed as v g (like Figure 3 The red dotted line), the input current of the rectifier bridge is represented by i in , the capacitor voltage under constant power load is expressed as v b (like Figure 3 Blue solid line), its voltage is consistent with the rectifier bridge output voltage v g The waveform of Figure 3 .

[0039] Figure 3 In the figure, the dead zone angles are θ1 and θ2, which means that in a cycle [0,π], the converter only works in [θ1,θ2]. g Less than the capacitor voltage v b , the converter does not work. The average output voltage V b_avg (like Figure 3 The red solid line) represents the average value of the output voltage in one cycle.

[0040] After theoretical analysis, the DCM Buck output voltage relationship is as shown in equation (1-1):

[0041]

[0042] Where ω is the angular frequency and t is the time variable. θ1, θ2 and v b The relationship between V b_avg With v b The functional relationship is equations (1-2) and (1-3):

[0043]

[0044] Among them, the initial values ​​of θ1 and θ2 are 1_initial ,θ 2_initial It can be approximately solved by equations (1-4) and (1-5).

[0045]

[0046] It can be seen that v b The difficulty in solving the function numerically is that the relationship in the interval [θ1, θ2] contains square roots, integrals, and the original integral function is implicit, which makes it difficult to use conventional differential derivation methods. Equations (1-4) and (1-5) are the initial values ​​of θ1 and θ2, because the output waveform calculation process of the DCM BUCK circuit requires the assumption of integral terms, and the calculated value V under the current assumption is b_avg Compared with the theoretical setting value V b_avg_set There is a certain error, and θ1 needs to be adjusted so that V b_avg With V b_avg_set The error value between them is less than the error tolerance V b_avg_eps .

[0047] For the convenience of description, since the relationship (1-1) is explicit in the interval [0, θ1], [θ2, π], the function relationship of equation (1-1) in the interval [θ1, θ2] is discretized into N points in the interval [θ1, θ2] with the limit idea. When N is larger, its numerical accuracy is higher, but the amount of calculation required is larger. In practical applications, the calculation accuracy and calculation resources should be weighed. At this time, the interval between adjacent points can be expressed as ΔT (Equation (1-6)):

[0048]

[0049] According to the implicit transformation equation (1-7) of the original function of the definite integral, the explicit transformation equation (1-8) of the original function of the definite integral, and the discretization expression of the variable limit integral as equation (1-9), equation (1-1) in the interval [θ1,θ2] can be expressed as (1-10):

[0050]

[0051] The recursive relationship can be expressed as equation (1-11)

[0052]

[0053] Since the functional relationship is continuous in the interval 0<ωt<π, a one-dimensional matrix v will be created for ease of programming. b N×1 , and v b (θ1) is assigned to the matrix v b (0), matrix v b (k) refers to the function v b (θ1+kΔT)(k=1,2,3,…,N). According to equation (1-11) and the initial value v b (0) can be obtained b The numerical solution v of (θ1+ΔT) b (1) With v b (1) According to (1-11) again, we can obtain v b (2), ..., and similarly, we can iterate and solve the problem in the interval v b All values ​​of (k).

[0054] DCM BUCK large ripple voltage numerical solution algorithm process:

[0055] 1) Input the necessary parameters of the algorithm program, P o , C b 、V m ,ω,N,V b_avg_set 、V b_avg_eps ;

[0056] 2) Establish the solution function of parameter B equation (1-8), assign A initial value and set error tolerance A_eps;

[0057] 3) Calculate the initial value of θ1 according to equation (1-4);

[0058] 4) Use the optimization toolbox to find the optimal θ2 based on the initial value of θ1 using equation (1-5) and equation (1-2);

[0059] 5) Calculate the function expression of the interval [0,θ1] from equation (1-1) to find v b (θ1), initialize the matrix v b (0) = v b (θ1);

[0060] 6) According to the recursive equation (1-10), iterate and solve the matrix v b (k);

[0061] 7) Solve the parameter A_new according to equation (1-7). When the difference between A_new and A is less than the error tolerance A_eps, exit the loop and enter step 8); otherwise, assign A_new to A and enter 5);

[0062] 8) Calculate v segment by segment according to equation (1-3) b The integral in the interval gives V b_avg , when it is equal to V b_avg_set The error is less than V b_avg_eps When θ1* is θ1, go to step 9), otherwise adjust the value of θ1* according to certain rules and go to step 4);

[0063] 9) Output v at this time b The value is the optimal solution under the current error.

[0064] The algorithm flow chart is as follows Figure 4

[0065] In actual calculation and solution, the recursive equation (9) has higher accuracy and stronger applicability than the recursive equation (7).

[0066] The method of adjusting θ1 in the present invention is:

[0067] a)V b_avg - b_avg_set >V b_avg_eps

[0068] θ1=θ1*0.995

[0069] b)V b_avg -V b_avg_set <- b_avg_eps

[0070] θ1=θ1*1.003

[0071] Figure 5 The result of running the algorithm.

[0072] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for numerically calculating large ripple capacitor voltage, characterized in that: The original function of the capacitor-voltage function relationship containing the integral term is implicit, that is, the relationship is a complex implicit transcendental function equation (1). The integral term in the function relationship is discretized and expressed in the form of cumulative sum, and the difference between two adjacent points and the discretized expression are used to establish a recursive relationship, and the programming iterative calculation is performed according to the corresponding assumptions of the integral. In equation (1), v b is the output voltage, t is the time variable, θ1 and θ2 are the dead zone angles, and ω is the angular frequency; V m , C b , P o , θ1, θ2, ω are all constants; The integral term contained in the objective function can be regarded as the projection area formed by the original function and the X-axis. The definite integrals of the implicit equation (2) and the explicit equation (3) contained in the original function are recorded as different constants respectively, and the variable limit integral can be uniformly discretized into the form of cumulative sum, as shown in equation (4); In equations (2), (3), and (4), A, B, and N are constants, and ΔT is the distance between two adjacent discrete points; The principle of integral discretization is to approximate the integral term with a basic matrix, and the projection area formed by the original function of the integral and the X-axis is expressed as the accumulation of the areas of rectangles with the same width and different lengths on the coordinate axis; After discretizing the functional relationship, a recursive relationship is established based on the relationship between the two points, and the objective function is discretized as shown in equation (5). The recursive relationship equations (7) and (8) can be established by subtracting the expressions (5) and (6) between two adjacent points. The left side of equation (8) is different from the left side of equation (7). The analytical expression on the left side of equation (7) shows that when N is large enough, the output voltage v b The difference between the values ​​of two adjacent points is small, so equation (8) is approximated as shown in equation (9):

2. A method for calculating the large ripple capacitor voltage numerical value according to claim 1, characterized in that: According to the recursive formula, programming calculation is performed, and the basic process of the algorithm is as follows: 1) Input basic parameters and set corresponding error tolerance; 2) According to the actual objective function relationship, the initial value of the prediction parameter A is set and the error tolerance A_eps corresponding to the parameter is set; 3) According to the recursive formula, the numerical solution matrix v in the definition domain is solved cyclically; 4) Recalculate the value of parameter A with the solved v and record it as A_new; 5) When the error between A_new and A is less than A_eps, go to step 6); otherwise, assign A_new to A and go to step 3); 6) Output numerical calculation results.

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