Method for self-adaptively optimizing parameters of a main circuit in a BBMC based on a current rating

Abstract

Taking parameters of a main circuit in a BBMC as optimization objects, and a total harmonic distortion of an output voltage of the BBMC, a deviation between an actual output current and a corresponding rated output current as optimization objectives, a mathematical model between optimization objects and optimization objectives is established. A multi-objective optimization satisfaction function and a multi-objective optimization fitness function are established by selecting a current rating as a rated output current of the BBMC. An adaptive wolf pack optimization algorithm is adopted to obtain a set of optimal parameters of the main circuit. The rated output current is changed to obtain n sets of optimal parameters, and functional relationships between the optimal parameters of the main circuit in the BBMC are obtained using a numerical fitting method. Optimal parameters of the main circuit corresponding to different current ratings are determined according to the functional relationships.

Description

TECHNICAL FIELD

The present application relates to power electronics, and more particularly to a method for self-adaptively optimizing parameters of a main circuit in a BBMC based on a current rating.

BACKGROUND

As a novel power converter, Buck-Boost matrix converter (BBMC) has a high voltage transfer ratio and is capable of directly outputting high-quality sine waves. However, the research shows that inductance and capacitance parameters of the main circuit in the BBMC have a great impact on the magnitude of output current of the BBMC. When the output current changes, the inductance and capacitance parameters need to be optimized accordingly to obtain a minimum harmonic distortion of the output voltage of the BBMC, thereby improving the quality of output voltage waveforms of the BBMC.

Therefore, it is of great significance to determine the optimal parameters of the BBMC according to different rated output currents, and find out the change rules between the optimal parameters of the main circuit of the BBMC and the rated output currents thereof, so as to optimize the main circuit of the BBMC.

SUMMARY

In order to solve the above-mentioned technical problems, the present disclosure provides a method for self-adaptively optimizing parameters of a main circuit in a BBMC based on a current rating.

The technical solutions of the disclosure are described as follows.

The present disclosure provides a method for self-adaptively optimizing parameters of a main circuit in a BBMC based on a current rating, comprising:

(1) taking an inductance parameter L and a capacitance parameter C in bridge arms of the main circuit in the BBMC as optimization objects, a total harmonic distortion THD of an output voltage of the BBMC and a deviation Δi between an actual output current of the BBMC and a rated output current of the BBMC as optimization objectives, establishing a mathematical model between the optimization objects and the optimization objective;

(2) selecting a current rating as the rated output current of the BBMC; and establishing a multi-objective optimization satisfaction function and a multi-objective optimization fitness function;

(3) iteratively optimizing parameters of the main circuit in the BBMC using an adaptive wolf pack optimization algorithm to maximize a function value of the multi-objective optimization fitness function, so that an optimal collaboration between the total harmonic distortion THD and the deviation Δi is obtained, so as to obtain a set of optimal parameters of the main circuit in the BBMC; changing the magnitude of the rated output current of the BBMC at a certain interval to obtain n sets of optimal parameters of the main circuit in the BBMC; and

(4) obtaining functional relationships using a numerical fitting method according to the obtained n sets of optimal parameters and the current ratings corresponding to the n sets of optimal parameters of the main circuit in the BBMC; and determining optimal parameters of the main circuit in the BBMC corresponding to respective current ratings according to the functional relationships.

Compared to the prior art, the disclosure has the following beneficial effects.

The disclosure provides a method for self-adaptively optimizing parameters of a main circuit in a BBMC based on a current rating, in which a mathematical model between optimization objects and optimization objectives is established by taking parameters of the main circuit in the BBMC as the optimization objects, a total harmonic distortion THD of an output voltage of the BBMC, a deviation Δi between an actual output current of the BBMC and a rated output current as optimization objectives; a multi-objective optimization satisfaction function and a multi-objective optimization fitness function are established by selecting a current rating as the rated output current of the BBMC. parameters of the main circuit in the BBMC are iteratively optimized using an adaptive wolf pack optimization algorithm to maximize a function value of the multi-objective optimization fitness function, so that an optimal collaboration between the total harmonic distortion THD and the deviation Δi is obtained, so as to obtain a set of optimal parameters of the main circuit in the BBMC; and n sets of optimal parameters of the main circuit in the BBMC are obtained by changing the magnitude of the rated output current of the BBMC at a certain interval; functional relationships are obtained using a numerical fitting method according to the obtained n sets of optimal parameters of the main circuit in the BBMC and the corresponding rated currents; and the optimal parameters of the main circuit in the BBMC corresponding to respective current ratings are determined according to the functional relationships. The present disclosure provides a theoretical basis for the optimal design of main circuits of the BBMC with different output current ratings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a topology diagram showing a main circuit in a BBMC according to the present disclosure.

FIG. 2 is a flowchart of a method for self-adaptively optimizing parameters of the main circuit in the BBMC based on a current rating according to the present disclosure.

FIG. 3 is a flowchart of an adaptive wolf pack algorithm according to the present disclosure.

FIG. 4A shows a curve of a fitting function between an optimal inductance parameter of the main circuit in the BBMC and the current rating according to an embodiment of the present disclosure; and FIG. 4B shows a curve of a fitting function between an optimal capacitance parameter of the main circuit in the BBMC and the current rating according to an embodiment of the present disclosure.

DETAILED DESCRIPTION OF EMBODIMENTS

The present disclosure will be further described in detail below with reference to the accompanying drawings and embodiments.

As shown in FIG. 1, provided is a main circuit in a BBMC according to the present disclosure. The BBMC includes a rectifier side and an inverter side, where the rectifier side is a three-phase PWM rectifier circuit for rectifying a three-phase AC voltage into a PWM-modulated DC voltage; and the inverter side is a three-phase Buck-Boost inverter, which consists of three Buck-Boost DC/DC converters with the same structure.

As shown in FIG. 2, provides is a flowchart of a method for self-adaptively optimizing parameters of a main circuit in a BBMC based on a current rating according to the present disclosure, including the following steps:

(1) taking an inductance parameter L and a capacitance parameter C in bridge arms of a main circuit as optimization objects, and a total harmonic distortion THD of an output voltage of the BBMC and a deviation Δi between an actual output current of the BBMC and a rated output current of the BBMC as optimization objectives, a mathematical model between the optimization objects and the optimization objectives is established; where specific steps are as follows:

(1.1) taking a capacitor voltage u_C and an inductor current i_L of the BBMC as control variables, a state differential equation of the BBMC is established, which is shown as:

$\begin{array}{cc}\{\begin{array}{c}{\stackrel{.}{i}}_L=\frac{u_C}{L}+\frac{u_C+u_D}{L}d\\ {\stackrel{.}{u}}_C=\frac{i_L}{C}-\frac{u_C}{\mathrm{RC}}-\frac{i_L}{C}d\end{array};& \left(1\right)\end{array}$

where u_D is the voltage in a DC side of the BBMC; L and C are respectively the inductance parameter and the capacitance parameter of the BBMC; R is the load resistance of the BBMC; and d is the duty cycle of a power switch tube in the BBMC, where d∈[0,1];

(1.2) since the output voltage u in the BBMC is an AC component of the capacitor voltage u_C, an analytical equation of the output voltage u is obtained according to the state differential equation (1):

$\begin{array}{cc}u=e^{\frac{t}{2}\sqrt{\frac{1}{{\left(\mathrm{RC}\right)}^2}-\frac{4{\left(1-d\right)}^2}{\mathrm{LC}}}+\frac{t}{2\mathrm{RC}}}+\frac{U_{D}d}{1-d};& \left(2\right)\end{array}$

(1.3) an analytical equation of an output current i is obtained according to the output voltage u and the load resistance R:

$\begin{array}{cc}u=e^{\frac{t}{2}\sqrt{\frac{1}{{\left(\mathrm{RC}\right)}^2}-\frac{4{\left(1-d\right)}^2}{\mathrm{LC}}}+\frac{t}{2\mathrm{RC}}}+\frac{U_{D}d}{1-d};& \left(3\right)\end{array}$

(1.4) the total harmonic distortion of the output voltage u is obtained according to a definition of the total harmonic distortion:

$\begin{array}{cc}\mathrm{THD}=\frac{\sqrt{\begin{array}{c}(2\exp (\left({T\left(E_1+4\left(2d-1-d^2\right)/E_2\right)}^{\left(1/2\right)}\right)/4+\\ T/\left(4F_2\right))\left(H\right))/(T\left(F_1^2+4{\omega }^2\right)-\left(2G+1/F_2\right)/\\ {\left(T\left(H^2+4{\omega }^2\right)\right)}^2+(2\exp ((T(E_1+4\left(2d-1-d^2\right)/\\ {E_2)}^{\left(1/2\right)})/4+T/\left(4F_2\right))\left(-H\right))/\left(T\left(F_1^2+9{\omega }^2\right)\right)-\\ \left(2G+1/F_2\right)/{\left(T\left(H^2+9{\omega }^2\right)\right)}^2\end{array}}}{\begin{array}{c}2\exp \left(\left({T\left(E_1+4\left(2d-1-d^2\right)/E_2\right)}^{\left(1/2\right)}\right)/4+T/\left(4F_2\right)\right)\\ \left(-H\right)/\left(T\left(F_1^2+{\omega }^2\right)\right)-\left(2G+1/F_2\right)/(T\left(H^2+{\omega }^2\right)\end{array}};& \left(4\right)\end{array}$

where

$E_1=1/{\left(RC\right)}^2,F_1={\left(1-d\right)}^2,E_2=\mathrm{LC},F_2=\mathrm{RC},H=\frac{1}{{\left(RC\right)}^2}-\sqrt{\frac{{\left(1-d\right)}^2}{LC}}+\frac{1}{2RC},$ T is the period of the output voltage, and ω is the angular frequency of the output voltage; and

(1.5) the deviation Δi between the actual output current of the BBMC and the rated output current of the BBMC is obtained according to the analytical equation of the output current i obtained from the step (1.3):

$\begin{array}{cc}\Delta i=i-I_e=\frac{e^{\frac{t}{2}\sqrt{\frac{1}{{\left(\mathrm{RC}\right)}^2}-\frac{4{\left(1-d\right)}^2}{\mathrm{LC}}}+\frac{t}{2\mathrm{RC}}}}{R}-\frac{U_{D}d}{\left(1-d\right)R}-I_e;& \left(5\right)\end{array}$

(2) a multi-objective optimization satisfaction function and a multi-objective optimization fitness function are established by selecting a current rating as the rated output current of the BBMC, where specific steps are shown as follows:

(2.1) satisfaction functions of optimization objectives THD and Ai are respectively established, where

a satisfaction function of THD is shown as:

$\begin{array}{cc}{f}_1=\{\begin{array}{cc}1& \mathrm{THD}\le {\mathrm{THD}}^{\prime }\\ {\left[\ln c_1\left(\mathrm{THD}-{\mathrm{THD}}^{\prime }+1\right)+1\right]}^{-1}& \mathrm{THD}>{\mathrm{THD}}^{\prime }\end{array};& \left(6\right)\end{array}$

a satisfaction function of Δi is shown as:

$\begin{array}{cc}{f}_2=\{\begin{array}{cc}1& \Delta i\le \Delta i^{\prime }\\ {\left[\ln c_2\left(\Delta i-\Delta i^{\prime }+1\right)+1\right]}^{-1}& \Delta i>\Delta i^{\prime }\end{array};& \left(7\right)\end{array}$

where THD′ and A′ are respectively the thresholds of the THD and the Δi; c₁ and c₂ are respectively coefficients of satisfaction curves of THD and Δi, where c₁>0 and c₂>0; and

(2.2) the multi-objective optimization satisfaction function is established as shown in equation (8):ƒ=k₁ƒ₁+k₂ƒ₂  (8);

where k₁ and k₂ are respectively weight coefficients of the optimization objectives THD and Δi, and k₁+k₂=1; and

(2.3) if a satisfaction value ƒ_j of each of the optimization objectives is smaller than a corresponding satisfaction threshold M (j=1, 2), the multi-objective optimization satisfaction function is multiplied by a corresponding penalty factor b_j, where a range of the satisfaction threshold M is 0.5˜0.8, and a range of the penalty factor b_j is 0.4˜0.6; and

otherwise, i.e., if the satisfaction value ƒ_j of each of the optimization objectives is greater than or equal to the corresponding satisfaction threshold M (j=1, 2), the penalty factor b_j is set as 1; the multi-objective optimization fitness function ƒ, is established as shown in equation (9):ƒ_s=k₁b₁ƒ₁+k₂b₂ƒ₂  (9);

(3) parameters of the main circuit in the BBMC are iteratively optimized using an adaptive wolf pack optimization algorithm to maximize a function value of the multi-objective optimization fitness function, so that an optimal collaboration between the total harmonic distortion THD and the deviation Δi is obtained, so as to obtain a set of optimal parameters of the main circuit in the BBMC; FIG. 3 is a flowchart of the adaptive wolf pack optimization algorithm, where specific steps of the adaptive wolf pack optimization algorithm are as follows:

(3.1) the selected rated output current of the BBMC is taken as a judgment reference value of a concentration of prey's smell of the adaptive wolf pack optimization algorithm;

(3.2) the parameters are initialized, where the parameters include: the number N of wolves representing N sets of parameters of the main circuit, position information X_i(L,C), (i=(1,N)) of each wolf, the maximum number k_max of iterations, the maximum number T_max of repetitions in a scouting behavior, a scale coefficient α of scout wolves, a step length coefficient β, and the multi-objective optimization fitness function ƒ, representing the concentration S(i) of prey's smell;

(3.3) a wolf with the highest concentration S(i)=S_m of prey's smell in the wolf pack is selected as a lead wolf, and a position of the lead wolf is recorded as X_m(L,C); in a process of randomly scouting and searching for preys, if the scout wolves find the concentration of prey's smell in a position is greater than that of the lead wolf, the position X_m(L,C) of the lead wolf is updated and the lead wolf summons ferocious wolves at the same time; otherwise, the scout wolves continue to scout until the maximum number T_max of repetitions in a scouting behavior is reached, and the lead wolf summons the ferocious wolves in the original position X_m(L,C);

(3.4) when the ferocious wolves (the wolf pack includes the lead wolf, the scouting wolves and the ferocious wolves) rush towards the lead wolf with twice step length of scouting after hearing a summons from the lead wolf; during the rushing, if concentrations of the prey's smell of the ferocious wolves are greater than that of the lead wolf, the position X_m(L,C) of the lead wolf is updated; otherwise, the ferocious wolves continue to rush into a besieging range;

(3.5) the ferocious wolves closer to the lead wolf and the scout wolves capture the prey (prey's smell perceived by the lead wolf is regarded as the prey); if a concentration of the prey's smell of a wolf is greater than that of the lead wolf in the capturing process, the position X_m(L,C) of the lead wolf is updated; otherwise, the original position X_m(L,C) of the lead wolf is retained;

(3.6) N/10 wolves in the wolf pack with smaller concentrations of the prey's smell are eliminated, and the same number of new wolves are randomly generated in a solution space to update the wolf pack;

(3.7) whether the maximum number of iterations is reached is determined; if yes, the position X_m(L,C) of the lead wolf is outputted, i.e., an optimal solution of the parameters L and C of the main circuit is outputted; otherwise, 1 is added to the number of iterations, and the process is returned to the step (3.3);

(3.8) whether n sets of optimal parameters of the main circuit are obtained is determined; if no, the rated output current of the BBMC is changed at a certain interval, and the process is returned to the step (3.1); and

(3.9) the n sets of optimal parameters of the main circuit and the corresponding current ratings are outputted;

(4) functional relationships are obtained using a numerical fitting method according to the n sets of optimal parameters of the main circuit in the BBMC and the current ratings corresponding to the n sets of optimal parameters of the main circuit in the BBMC; and optimal parameters of the main circuit in the BBMC corresponding to respective current ratings are determined according to the functional relationships.

FIG. 4A shows a curve of a fitting function between an optimal inductance parameter of the main circuit in the BBMC and the current rating according to an embodiment of the present disclosure; and FIG. 4B shows a curve of a fitting function between an optimal capacitance parameter of the main circuit in the BBMC and the current rating according to an embodiment of the present disclosure. For example, a range of the rated output current is 0.5˜45 A, and 90 current ratings are selected at intervals of 0.5 A in the range of the rated output current; optimal parameters of the main circuit corresponding to each of the current rating data is calculated by adopting the adaptive wolf pack optimization algorithm; a functional relationship is obtained using the numerical fitting method according to the obtained 90 sets of optimal parameters of the main circuit in the BBMC and the corresponding current ratings; in some embodiments, the numerical fitting method is a least square method; the functional relationships include a functional relationship between an optimal inductance parameter L and the current rating I_e, and a functional relationship between an optimal capacitance parameter C and the current rating I_e; where

(4.1) the functional relationship between the optimal inductance parameter L and the current rating I_e is shown in equation (10):ƒ_L(I_e)=a₁I_e⁵+a₂I_e⁴+a₃I_e³+a₄I_e²+a₅I_e+a₆  (10);

where a₁=7.344×10⁻¹¹, a₂=−7.677×10⁻⁹, a₃=2.746×10⁻⁷, a₄=−3.369×10⁻⁶, a₅=3.284×10⁻⁵ and a₆=9.174×10⁻⁵;

(4.2) the functional relationship between the optimal capacitance parameter C and the current rating I_e is shown in equation (11):ƒ_C(I_e)=b₁I_e⁵+b₂I_e⁴+b₃I_e³+b₄I_e²+b₅I_e+b₆  (11);

where b₁=8.289×10⁻¹², b₂=−1.04×10⁻⁹, b₃=5.377×10⁻⁸, b₄=−1.02×10⁻⁶, b₅=1.148×10⁻⁵ and b₆=1.789×10⁻⁵;

the optimal parameters of the main circuit corresponding to respective current ratings are determined according to the functional relationships between the optimal parameters of the main circuit and the corresponding current ratings.

Described above is only a preferred embodiment of the present disclosure. It should be noted that any improvement and variation made by those skilled in the art without departing from the spirit of the present disclosure shall fall within the scope of the appended claims.

Claims

1. A method for self-adaptively optimizing parameters of a main circuit in a BBMC based on a current rating, comprising: (1) taking an inductance parameter L and a capacitance parameter C in bridge arms of the main circuit in the BBMC as optimization objects, a total harmonic distortion THD of an output voltage of the BBMC and a deviation Δi between an actual output current of the BBMC and a rated output current of the BBMC as optimization objectives, establishing a mathematical model between the optimization objects and the optimization objectives, comprising:(1.1) taking a capacitor voltage uC and an inductor current iL of the BBMC as control variables, establishing a state differential equation of the BBMC:

2. The method of claim 1, wherein establishing a multi-objective optimization satisfaction function in the step 2 comprises: (a) respectively establishing satisfaction functions of optimization objectives THD and Δi, whereina satisfaction function of the THD is shown in equation (6):

3. The method of claim 1, wherein establishing the multi-objective optimization fitness function in the step (2) comprises: (a) if a satisfaction value ƒj of each of the optimization objectives is smaller than the corresponding satisfaction threshold M (j=1, 2), multiplying the satisfaction value by a penalty factor bj; wherein a range of the satisfaction threshold M is 0.5˜0.8, and a range of the penalty factor bj is 0.4˜0.6;otherwise, setting the penalty factor bj as 1; and(b) establishing the multi-objective optimization fitness function ƒs as shown in equation (9): ƒs=k1b1ƒ1+k2b2ƒ2  (9).

4. The method of claim 1, wherein iteratively optimizing parameters of the main circuit in the BBMC using an adaptive wolf pack optimization algorithm in the step (3) comprises: (3.1) taking the selected rated output current of the BBMC as a judgment reference value of a concentration of prey's smell of the adaptive wolf pack optimization algorithm;(3.2) initializing parameters, wherein the parameters comprise: the number N representing N sets of parameters (L,C) of the main circuit, the maximum number kmax of iterations, the maximum number Tmax of repetitions of a scouting behavior, a scale coefficient α of scout wolves, a step length coefficient β and the multi-objective optimization fitness function ƒs representing the concentration of prey's smell S(i);(3.3) selecting a wolf with the highest concentration S(i)=Sm of prey's smell in the wolf pack as a lead wolf, and recording a position Xm(L,C) of the lead wolf; in a process of randomly scouting and searching for preys, if the scout wolves find the concentration of prey's smell in a position is greater than that of the lead wolf, updating the position Xm(L,C) of the lead wolf while the lead wolf summoning ferocious wolves at the same time; otherwise, making the scouting wolves continue to scout until the maximum number Tmax of repetitions of a scouting behavior is reached, letting the lead wolf summon the ferocious wolves in the original position Xm(L,C);(3.4) letting the ferocious wolves rush towards the lead wolf with a twice step length of scouting after hearing a summons from the lead wolf, if concentrations of the prey's smell of the ferocious wolves in a rush process are greater than that of the lead wolf, updating the position Xm(L,C) of the lead wolf; otherwise, letting the ferocious wolves continue to rush into a besieging range;(3.5) letting the ferocious wolves close to the lead wolf and the scout wolves capture a prey; if a concentration of the prey's smell of a wolf in the capturing process is greater than that of the lead wolf, updating the position Xm(L,C) of the lead wolf; otherwise, retaining the original position Xm(L,C) of the lead wolf;(3.6) eliminating N/10 wolves in the wolf pack with a small concentration of the prey's smell, and randomly generating a same number of new wolves in a solution space to update the wolf pack;(3.7) determining whether the maximum number of iterations is reached; if yes, outputting the position Xm(L,C) of the lead wolf, that is, outputting an optimal solution of the parameters L and C of the main circuit; otherwise, adding 1 to the number of iterations, and returning to the step (3.3);(3.8) determining whether n sets of optimal parameters of the main circuit are obtained; if no, changing the rated output current of the BBMC at a certain interval, and returning to the step (3.1); and(3.9) outputting the n sets of optimal parameters of the main circuit and the corresponding current ratings.

5. The method of claim 4, wherein n≥6.

6. The method of claim 1, wherein in the step (4) the numerical fitting method is a least square method; the functional relationships comprise a functional relationship between an optimal inductance parameter L and the current rating Ie, and a functional relationship between an optimal capacitance parameter C and the current rating Ie; wherein the functional relationship between the optimal inductance parameter L of the main circuit and the current rating Ie is shown in equation (10): ƒL(Ie)=a1Ie5+a2Ie4+a3Ie3+a4Ie2+a5Ie+a6  (10);the functional relationship between the optimal capacitance parameter C of the main circuit and the current rating e is shown in equation (11): ƒC(Ie)=b1Ie5+b2Ie4+b3Ie3+b4Ie2+b5Ie+b6  (11);wherein ƒL(Ie) and ƒC(Ie) are respectively a function of the optimal inductance parameter of the main circuit and a function of the optimal capacitance parameter of the main circuit; a1, a2, a3, a4, a5 and a6 are respectively coefficients of the function of the optimal inductance parameter; b1, b2, b3, b4, b5 and b6 are respectively coefficients of the function of the optimal capacitance parameter.