An Integration Optimization Strategy of Line Voltage Cascaded Quasi-Z-Source Inverter Parameters Based on GRA-FA
Abstract
:1. Introduction
- (1)
- In the LVC-qZSI system, there are complex coupling relations between DC voltage and current vectors, AC voltage and current vectors, total output voltage and current vectors after cascading, etc. Therefore, it is not feasible to establish a mathematical model to determine the reasonable range of LVC-qZSI parameters;
- (2)
- LVC-qZSI is a complex dynamic system composed of a quasi-Z network, three three-phase inverter bridges, and a LVC network. There are many circuit parameters in the system, and most of the parameter design methods rely on repeated tests. Under different experimental conditions, it is time-consuming and laborious to determine multiple LVC-qZSI parameters and circuit performance evaluation indexes;
- (3)
- The influence of circuit parameters on LVC-qZSI performance indexes is nonlinear and antagonistic. For example, increasing the quasi-Z network inductance and capacitance can effectively reduce the double frequency ripple, but it will increase the power loss. Therefore, there are contradictions in the selection of parameters. The trial and error method based on previous experience is not easy to find the optimal parameters.
- (1)
- In this paper, a single module model of qZSI and a cascaded network coupling model of LVC-qZSI are established. According to the analysis of LVC-qZSI, three optimization objective functions including double frequency voltage ripples ratios and power loss ratio are listed;
- (2)
- In GRA, six parameters in LVC-qZSI that affect the optimization objective functions are summarized and sorted in descending order of correlation degrees, then three main parameters are selected to construct the FA solution vector based on the introduction of preference coefficient;
- (3)
- The paper adopts the information entropy weighting method to establish a multi-objective optimization model of LVC-qZSI parameters, and uses penalty factors to modify the model;
- (4)
- The paper establishes GRA-FA to simplify the multi-objective optimization model, and proposes an integration optimization strategy of LVC-qZSI parameters based on GRA-FA;
- (5)
- The effectiveness of the proposed integration optimization strategy is verified by simulation experiments. The experimental results show that the double frequency voltage ripples ratios are reduced by 87.48% and 87.57%, and the power loss ratio is reduced by 82.78%.
2. Establishment and Analysis of LVC-qZSI Model
2.1. LVC-qZSI
2.2. Performance Index
2.2.1. Double Frequency Voltage Ripple Ratio
2.2.2. Power Loss Ratio
3. GRA of LVC-qZSI Parameters
3.1. Description
3.2. Sorting of LVC-qZSI Parameters Based on GRA
- (1)
- For the value range of preference coefficient , with the increase of , the main influence factors are constantly changing. When , Z-source network inductance, Z-source network capacitance, and filter inductance have the greatest influence on objective functions; when , Z-source network inductance, Z-source network capacitance, and cascaded inductance are selected as main influence factors; when , the results of influence factors are complex and confusing, which need to be analyzed according to the specific situation; when , shoot-through duty cycle, modulation index, and cascaded inductance have the greatest influence;
- (2)
- For the trend, the correlation degrees of Z-source network inductance, Z-source network capacitance, filter inductance, and cascaded inductance are negatively correlated with preference coefficient ; the correlation degrees of modulation index and shoot-through duty cycle are positively correlated with preference coefficient ;
- (3)
- When the power loss is not considered, the influence of circuit device parameters (including Z-source network inductance, Z-source network capacitance, filter inductance, and cascaded inductance) on the comprehensive correlation degrees is obvious; when the power loss is considered, the influence of circuit control parameters (including shoot-through duty cycle and modulation index) is obvious.
4. Integration Optimization Strategy of LVC-qZSI Parameters Based on GRA-FA
4.1. GRA-FA
- Set the sample size to 30 and randomly adjust the values of six circuit parameters in LVC-qZSI to obtain training samples (including three reference indexes and six influence factors);
- Nondimensionalize the training samples;
- Calculate the correlation degrees between three reference indexes and six influence factors;
- By introducing the preference coefficient, three main influence factors are selected as optimization variables, and the three-dimensional solution vector is constructed;
- Set the population size, the total number of iterations, and the spatial dimension, then randomly initialize the individual position and the fluorescence brightness of the fireflies;
- Train the network and transform the objective functions into the fluorescence brightness of fireflies;
- Exploitation phase (update fireflies locations);
- Judge whether the number of iterations reaches the upper limit. If the upper limit is reached, the optimal solution will be output; otherwise, return to step f for the next iteration.
4.2. Multi-Objective Optimization
4.2.1. Optimization Variables
4.2.2. Objective Functions
4.2.3. Constraints
5. Experiment and Analysis
5.1. Experimental Setup
5.2. Numerical Results
5.3. Results Assessment and Comparison
6. Conclusions
- (1)
- Establish a small signal model of LVC-qZSI, and calculate the double frequency voltage ripples ratios and power loss ratio;
- (2)
- Summarize the six LVC-qZSI parameters and use GRA to sort them in descending order, then select three main influence factors as optimization variables based on the introduction of preference coefficient;
- (3)
- Use the information entropy method to assign weights to three objective functions, and construct a multi-objective optimization model of LVC-qZSI parameters;
- (4)
- Use GRA to improve FA and propose an integration optimization strategy of LVC-qZSI parameters based on GRA-FA;
- (5)
- After the iterative calculation of GRA-FA, the values of , , and are 0.95%, 1.59%, and 1.25%, which are reduced by 87.48%, 87.57%, and 82.78%, respectively. The results indicate that the proposed strategy has excellent optimization ability.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Symbol | Definition | Value Range | Unit |
---|---|---|---|
Z-source network inductance | 450–2000 | ||
Z-source network capacitance | 300–1500 | ||
Filter inductance | 0.50–20 | ||
Cascaded inductance | 0.50–20 | ||
Modulation index | 0.50–1.00 | ||
Shoot-through duty cycle | 0.05–0.40 |
LVC-qZSI Parameters | ||||||
---|---|---|---|---|---|---|
7.17 | 200 | 200 | 12 | 10 | 0.69 | 0.16 |
13.33 | 300 | 250 | 6 | 16 | 0.52 | 0.37 |
0.88 | 400 | 300 | 5 | 7 | 0.75 | 0.09 |
0.59 | 420 | 300 | 2 | 3 | 0.90 | 0.14 |
9.77 | 500 | 400 | 10 | 9 | 0.70 | 0.33 |
12.73 | 550 | 500 | 5 | 11 | 0.72 | 0.30 |
3.39 | 600 | 1300 | 4 | 14 | 0.82 | 0.19 |
0.12 | 640 | 850 | 3 | 5 | 0.55 | 0.15 |
2.23 | 680 | 700 | 12 | 9 | 0.67 | 0.22 |
4.34 | 700 | 600 | 15 | 12 | 0.77 | 0.25 |
2.06 | 750 | 1300 | 7 | 6 | 0.61 | 0.27 |
5.06 | 800 | 700 | 13 | 10 | 0.75 | 0.30 |
11.89 | 830 | 300 | 10 | 8 | 0.82 | 0.35 |
10.40 | 880 | 500 | 8 | 10 | 0.71 | 0.32 |
1.79 | 920 | 1070 | 16 | 7 | 0.74 | 0.22 |
1.70 | 960 | 950 | 12 | 11 | 0.66 | 0.24 |
5.05 | 1000 | 800 | 8 | 15 | 0.65 | 0.35 |
8.99 | 1080 | 400 | 6 | 9 | 0.59 | 0.31 |
4.86 | 1150 | 760 | 10 | 6 | 0.56 | 0.38 |
3.90 | 1200 | 900 | 12 | 13 | 0.60 | 0.40 |
1.97 | 1260 | 1000 | 6 | 10 | 0.64 | 0.23 |
1.82 | 1300 | 1100 | 17 | 8 | 0.80 | 0.20 |
3.85 | 1350 | 1000 | 10 | 4 | 0.78 | 0.22 |
11.59 | 1470 | 400 | 5 | 9 | 0.55 | 0.36 |
2.23 | 1500 | 1200 | 11 | 5 | 0.85 | 0.15 |
2.02 | 1550 | 800 | 13 | 8 | 0.63 | 0.26 |
0.92 | 1600 | 1400 | 9 | 11 | 0.55 | 0.28 |
5.26 | 1640 | 900 | 10 | 16 | 0.83 | 0.35 |
5.03 | 1750 | 1050 | 8 | 4 | 0.88 | 0.18 |
0.03 | 1800 | 1500 | 6 | 7 | 0.57 | 0.10 |
LVC-qZSI Parameters | ||||||
---|---|---|---|---|---|---|
1.4838 | 0.2015 | 0.2561 | 1.3284 | 1.0989 | 0.9923 | 0.6258 |
2.7585 | 0.3022 | 0.3201 | 0.6642 | 1.7582 | 0.7478 | 1.4472 |
0.1821 | 0.4030 | 0.3841 | 0.5535 | 0.7692 | 1.0786 | 0.3520 |
0.1221 | 0.4231 | 0.3841 | 0.2214 | 0.3297 | 1.2943 | 0.5476 |
2.0218 | 0.5037 | 0.5122 | 1.1070 | 0.9890 | 1.0067 | 1.2907 |
2.6343 | 0.5541 | 0.6402 | 0.5535 | 1.2088 | 1.0355 | 1.1734 |
0.7015 | 0.6044 | 1.6645 | 0.4428 | 1.5385 | 1.1793 | 0.7432 |
0.0248 | 0.6447 | 1.0883 | 0.3321 | 0.5495 | 0.7910 | 0.5867 |
0.4615 | 0.6850 | 0.8963 | 1.3284 | 0.9890 | 0.9636 | 0.8605 |
0.8981 | 0.7052 | 0.7682 | 1.6605 | 1.3187 | 1.1074 | 0.9778 |
0.4263 | 0.7555 | 1.6645 | 0.7749 | 0.6593 | 0.8773 | 1.0561 |
1.0471 | 0.8059 | 0.8963 | 1.4391 | 1.0989 | 1.0786 | 1.1734 |
2.4605 | 0.8361 | 0.3841 | 1.1070 | 0.8791 | 1.1793 | 1.3690 |
2.1522 | 0.8865 | 0.6402 | 0.8856 | 1.0989 | 1.0211 | 1.2516 |
0.3704 | 0.9268 | 1.3700 | 1.7712 | 0.7692 | 1.0642 | 0.8605 |
0.3518 | 0.9671 | 1.2164 | 1.3284 | 1.2088 | 0.9492 | 0.9387 |
1.0450 | 1.0074 | 1.0243 | 0.8856 | 1.6484 | 0.9348 | 1.3690 |
1.8604 | 1.0880 | 0.5122 | 0.6642 | 0.9890 | 0.8485 | 1.2125 |
1.0057 | 1.1585 | 0.9731 | 1.1070 | 0.6593 | 0.8054 | 1.4863 |
0.8071 | 1.2089 | 1.1524 | 1.3284 | 1.4286 | 0.8629 | 1.5645 |
0.4077 | 1.2693 | 1.2804 | 0.6642 | 1.0989 | 0.9204 | 0.8996 |
0.3766 | 1.3096 | 1.4085 | 1.8819 | 0.8791 | 1.1505 | 0.7823 |
0.7967 | 1.3600 | 1.2804 | 1.1070 | 0.4396 | 1.1218 | 0.8605 |
2.3984 | 1.4809 | 0.5122 | 0.5535 | 0.9890 | 0.7910 | 1.4081 |
0.4615 | 1.5111 | 1.5365 | 1.2177 | 0.5495 | 1.2224 | 0.5867 |
0.4180 | 1.5615 | 1.0243 | 1.4391 | 0.8791 | 0.9060 | 1.0169 |
0.1904 | 1.6118 | 1.7926 | 0.9963 | 1.2088 | 0.7910 | 1.0952 |
1.0885 | 1.6521 | 1.1524 | 1.1070 | 1.7582 | 1.1937 | 1.3690 |
1.0409 | 1.7629 | 1.3444 | 0.8856 | 0.4396 | 1.2656 | 0.7040 |
0.0062 | 1.8133 | 1.9206 | 0.6642 | 0.7692 | 0.8198 | 0.3911 |
0.4966 | 0.5076 | 0.9011 | 0.7729 | 0.7250 | 0.5976 |
0.3384 | 0.3400 | 0.3752 | 0.5594 | 0.3849 | 0.4909 |
0.8604 | 0.8717 | 0.7794 | 0.6868 | 0.5868 | 0.8917 |
0.8153 | 0.8366 | 0.9391 | 0.8683 | 0.5194 | 0.7539 |
0.4539 | 0.4554 | 0.5818 | 0.5514 | 0.5557 | 0.6363 |
0.3768 | 0.3869 | 0.3767 | 0.4698 | 0.4410 | 0.4636 |
0.9407 | 0.5689 | 0.8384 | 0.6037 | 0.7308 | 0.9818 |
0.6746 | 0.5440 | 0.8119 | 0.7113 | 0.6251 | 0.6964 |
0.8588 | 0.7497 | 0.5950 | 0.7101 | 0.7205 | 0.7662 |
0.8773 | 0.9180 | 0.6263 | 0.7561 | 0.8673 | 0.9532 |
0.8005 | 0.5055 | 0.7906 | 0.8532 | 0.7424 | 0.6710 |
0.8484 | 0.9040 | 0.7695 | 0.9740 | 0.9897 | 0.9204 |
0.4370 | 0.3773 | 0.4829 | 0.4437 | 0.4968 | 0.5374 |
0.4999 | 0.4550 | 0.4997 | 0.5464 | 0.5284 | 0.5856 |
0.6986 | 0.5596 | 0.4742 | 0.7663 | 0.6486 | 0.7256 |
0.6763 | 0.5957 | 0.5654 | 0.5979 | 0.6829 | 0.6868 |
0.9849 | 0.9982 | 0.8984 | 0.6807 | 0.9315 | 0.8032 |
0.6232 | 0.4839 | 0.5142 | 0.5938 | 0.5565 | 0.6645 |
0.9028 | 0.9888 | 0.9377 | 0.7918 | 0.8727 | 0.7296 |
0.7648 | 0.7923 | 0.7126 | 0.6740 | 0.9709 | 0.6278 |
0.5965 | 0.5934 | 0.8397 | 0.6495 | 0.7161 | 0.7248 |
0.5769 | 0.5516 | 0.4561 | 0.7203 | 0.6227 | 0.7630 |
0.6959 | 0.7283 | 0.8103 | 0.7864 | 0.8026 | 0.9650 |
0.5810 | 0.4003 | 0.4057 | 0.4727 | 0.4396 | 0.5619 |
0.5473 | 0.5413 | 0.6282 | 0.9472 | 0.6267 | 0.9211 |
0.5257 | 0.6796 | 0.5543 | 0.7380 | 0.7264 | 0.6823 |
0.4705 | 0.4405 | 0.6129 | 0.5549 | 0.6817 | 0.5845 |
0.6958 | 0.9649 | 1.0000 | 0.6569 | 0.9350 | 0.8264 |
0.6393 | 0.8139 | 0.9011 | 0.6814 | 0.8581 | 0.7966 |
0.4107 | 0.3967 | 0.6610 | 0.6261 | 0.6106 | 0.7728 |
Reference Index | Influence Factors | |||||
---|---|---|---|---|---|---|
0.6556 | 0.6316 | 0.6780 | 0.6815 | 0.6866 | 0.7261 | |
0.7789 | 0.8254 | 0.6811 | 0.7461 | 0.6609 | 0.7926 | |
0.9573 | 0.9498 | 0.8692 | 0.8045 | 0.5098 | 0.5237 |
Definition | Value |
---|---|
Z-source network inductance | 500 |
Z-source network capacitance | 400 |
Filter inductance | 4.00 |
Cascaded inductance | 4.00 |
Voltage of DC source | 320 |
Modulation index | 0.60 |
Shoot-through duty cycle | 0.25 |
Output frequency | 50 |
Carrier frequency | 10 |
Iterations | Optimization Variables | Value |
---|---|---|
(%) | (%) | (%) | |
---|---|---|---|
Before optimization | 7.59 | 12.79 | 7.26 |
After optimization | 0.95 | 1.59 | 1.25 |
Optimization Strategy | (%) | (%) | (%) |
---|---|---|---|
RVCMS | 2.53 | 7.75 | 8.17 |
APF | 0.89 | 1.34 | 9.32 |
MOGA | 1.27 | 1.78 | 2.41 |
Proposed | 0.95 | 1.59 | 1.25 |
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Share and Cite
Li, Z.; Pu, S.; Chen, Y.; Wei, R. An Integration Optimization Strategy of Line Voltage Cascaded Quasi-Z-Source Inverter Parameters Based on GRA-FA. Energies 2020, 13, 4391. https://doi.org/10.3390/en13174391
Li Z, Pu S, Chen Y, Wei R. An Integration Optimization Strategy of Line Voltage Cascaded Quasi-Z-Source Inverter Parameters Based on GRA-FA. Energies. 2020; 13(17):4391. https://doi.org/10.3390/en13174391
Chicago/Turabian StyleLi, Zhiyong, Shiping Pu, Yougen Chen, and Renyong Wei. 2020. "An Integration Optimization Strategy of Line Voltage Cascaded Quasi-Z-Source Inverter Parameters Based on GRA-FA" Energies 13, no. 17: 4391. https://doi.org/10.3390/en13174391