Research Article | Open Access

Volume 2015 |Article ID 623161 | https://doi.org/10.1155/2015/623161

Chih-Lung Shen, Tsair-Chun Liang, Siou-Hong Zhou, Su-Wen Wang, "Voltage Gain Derivation Based on Energy-Balanced Criterion for a Novel Hybrid-Input PV-Wind Power Conversion System", Mathematical Problems in Engineering, vol. 2015, Article ID 623161, 8 pages, 2015. https://doi.org/10.1155/2015/623161

# Voltage Gain Derivation Based on Energy-Balanced Criterion for a Novel Hybrid-Input PV-Wind Power Conversion System

Accepted07 Dec 2014
Published17 Mar 2015

#### Abstract

This paper applies energy-balanced criterion to a novel hybrid-input PV-wind power conversion system (HPWPCS) for voltage gain derivation. With the energy-balanced concept, complicated mathematical problems related to voltage gain derivation can be readily resolved. Based on the derived results, it is proven that the proposed HPWPCS is able to process two different kinds of renewable energy resources simultaneously. Even though the HPWPCS includes seven capacitors and three magnetic components, its voltage gain still can be found by the mathematical analysis. In the theoretical derivation, only the energy status of output inductor is dealt with such that complicated derivation procedure is avoided. This analysis method can also be applied to other hybrid green-energy conversion systems. In this paper, a 200 W 50 kHz prototype of HPWPCS is built and examined to verify the mathematical results.

#### 1. Introduction

With rapid development of industry and commerce, requirement for electricity has been growing dramatically. Conventionally, electric power is mainly generated from fossil fuels. However, this kind of energy resources is highly limited and will exhaust in the near future. Furthermore, the environmental pollution caused from overuse of fossil energy has destroyed ecological balance, and a large amount of carbon dioxide yielded from combustion of fossil fuels has also resulted in greenhouse effects seriously. Therefore, adopting renewable and clean energy resources to replace fossil fuels for electric power generation is a research of great urgency .

At present, various renewable energy resources, such as hydraulic energy, wind energy, tidal energy, and solar energy, are feasible for power generation. Among them, solar energy and wind energy attract more interests owing to the noiseless, pollution-free, nonradioactive, and inexhaustible characteristics. Solar energy is converted into electric power by photovoltaic (PV) arrays, while wind energy is converted into electric power by wind turbine. In PV or wind generation system, converters have to be adopted to accomplish power processing . Traditionally, the structure containing two separate converters is commonly used to accomplish power conversion. Since PV arrays and wind turbine are complementary power sources, development of single converter, instead of two individual converters, simultaneously to cope with the hybrid inputs of PV and wind power is current trend . However, finding voltage gain for a single-structure converter is a complex mathematical problem.

In this paper, a novel hybrid-input PV-wind power converter is proposed first, and then energy-balanced criterion is applied to derive the voltage gain of the converter. The proposed HPWPCS has the intrinsic characteristics of galvanic isolation, extra high voltage gain, and individual power control. The HPWPCS comprises two active switches, ten diodes, seven capacitors, two coupled inductors, and one output inductor. While applying energy-balanced criterion to the output inductor, the voltage gain can readily be found without complex calculation. This paper will detail the corresponding derivation procedure. To prove that the theoretically derived voltage gain can be consistent with practical system, a prototype of HPWPCS is designed, built, and measured. Hardware measurements have verified the correctness of the derivation and the validity of the proposed HPWPCS.

#### 2. Power Stage Configuration

The proposed HPWPCS not only can process PV power but also deals with wind energy. Figure 1 shows its power stage configuration, which immerges two double-ended forward converters into a single stage to possess two input ports and one output port. In Figure 1, active switches can operate individually so as to convert two different kinds of renewable energy sources. The coupled inductors, and , galvanically isolate the primary side from the secondary one and can step up/down input voltage. In addition, both coupled inductors can fulfill forward and flyback behaviors to process input energy to achieve voltage stacking for high voltage output. The energy stored in the two leakage inductances of the coupled inductors, and , can be recycled totally, which, as a result, can improve conversion efficiency significantly. The HPWPCS can draw the upmost power from PV arrays and wind turbine by means of controlling active switches and fulfilling maximum power point tracking (MPPT). The control of HPWPCS is implemented on the chip of dsPIC30F4011 to lower discrete components and cost.

#### 3. Operation Analysis

Before the operation analysis, some assumptions are made as follows. (1) All diodes are ideal. (2) The output inductor and magnetizing inductances, and , are in continuous conduction mode (CCM). (3) The internal resistance and parasitic capacitance in active switch are neglected. (4) Both leakage inductances and are much less than and . Based on the above assumptions, the operation of HPWPCS contains six stages over one switching cycle. The six corresponding equivalents and related conceptual key waveforms are presented in Figures 2 and 3, respectively. The followings will detail its operation principle stage by stage.(1)Stage 1 (Figure 2(a), ): during this time interval, the power switches and are turned on simultaneously but and are in off state. The leakage inductance and magnetizing inductance are charging and so does the output inductor . The current flowing through will be transferred to the secondary winding , to charge the capacitors and . Meanwhile, the inductor dumps energy to secondary winding via transformer . The energy in and charges . This stage is ended as soon as the switches and are turned off.(2)Stage 2 (Figure 2(b), ): at the moment that the switches and are turned off, the operation of HPWPCS enters into Stage 2. The energy stored in leakage inductance is recycled to the input and transferred to the secondary winding via the path of , , and . This mode ends when the current of leakage inductance dumps to zero.(3)Stage 3 (Figure 2(c), ): during this stage, all the active switches , , , and are kept in off state. The magnetizing inductance dumps energy to secondary winding to charge the capacitor via , , and . Meanwhile, the inductance also dumps energy to via , , and . The output inductor releases energy to the dc link for load powering. As and are turned on, the next stage begins.(4)Stage 4 (Figure 2(d), ): the power switches and are on but and are off. The HPWPCS will forward PV power to the output. The magnetizing inductance starts charging during this interval, and the current through is transferred to the secondary winding of to charge the capacitor . With respect to the processing of wind energy, the HPWPCS sustains the same circuit behavior as in Stage 3.(5)Stage 5 (Figure 2(e), ): as the switches and are turned off, Stage 5 begins and the energy stored in leakage inductance will be recycled to the input by the path of . The current of decreases linearly. While this current drops to zero, circuit operation enters into next stage.(6)Stage 6 (Figure 2(f), ): in this mode, all active switches are open and the operation is the same as that in Stage 3. The magnetizing inductance releases energy to the secondary of and so does the to the secondary of . When and are closed again, the operation of HPWPCS returns to Stage 1.

#### 4. Voltage Gain Derivation

Suppose that all capacitances are large enough to sustain capacitor voltages at constants and the leakage inductances of and are much smaller than magnetizing inductances. As shown in Figure 4, the switching period of the HPWPCS is . During the time interval , switches and are closed for and open for while switches and are closed for and open for . The stands for the interval that the HPWPCS deals with wind turbine energy, while stands for PV panel. That is,According to the operation principle described in Stages 1, 3, 4, and 6, the output inductor current will increase linearly while absorbing energy and decrease linearly while releasing energy. The waveform of output inductor current is illustrated in Figure 4.

Since HPWPCS adopts two coupled inductors, the coupling coefficient will be a key parameter in the derivation. The can be found by the following relationship:where is the measured inductance from the primary while the secondary is short circuit and represents the measured primary-side inductance while the secondary is open circuit. With respect to , when the switches and are closed, the voltage across is in which expresses the coupled coefficient of . Thus, at this switch-on status the voltage is calculated by Substituting (3) into (4) yieldsFrom the equivalent of Stage 2 (switches and are off), it can be found that the voltage of the capacitor , , is equal to the voltage of the secondary of . That is,Therefore, the following equation holds:From Figure 2(c), the voltage across the capacitor can be determined byFrom (7), the above equation can be rewritten asRearranging (9) gives

While and are closed, referring to Figure 2(a) and applying Kirchhoff’s voltage law (KVL) to the loop of , the output inductor voltage can be obtained:Substituting (5) and (10) into (11) results in

Regarding the expression for during the period of both switches and being open, we can apply KVL to the loop of as shown in Figure 2(c) and then obtain

While considering the expression of during the period of , Figures 2(d) and 2(f) will be contacted and the similar derivation procedure as above is adopted. During the period of , referring to Figure 2(d), the and can be found as follows: where the is the coupling coefficient of . The voltage across , , is equal to . That is,From Figure 2(f), the is the sum of and . As a result, the can be described as While and are closed, as shown in Figure 2(d), from the loop enclosed by , , , , and , one can find by the use of KVL:The and are substituted for (15) and (17), respectively, which yields In regard to the expression for output inductor voltage while and are off, from the loop of shown in Figure 2(f), one can find

The output inductor charges energy during the two time intervals, and . On the contrary, during and , the output inductor discharges. In steady state operation and over one switching cycle, the stored energy and released energy in output inductor are identical. Thus, from (12), (13), (19), and (20), one can derive the following relationship:Simplifying (21) results inwhich reveals that the voltage gain is found and the dc-link voltage can be controlled by the duty ratios of the active switches.

#### 5. Experimental Verification

To demonstrate the derived voltage gain of the proposed HPWPCS, a prototype is designed, built, and measured, of which specifications are presented in Table 1. According to the given specifications, key parameters of the prototype are analyzed and then power components are chosen. Table 2 summaries the determined parameters. In the case that all active switches are interleavedly turned on with a duty ratio of 0.38, the corresponding control signals and input currents are presented in Figure 5. Figure 6 shows the voltages across the capacitors and , which depicts that the voltages and can be sustained at constant level. Output inductor current is illustrated in Figure 7, in which the interval of current increasing expresses energy charging and during the current decreasing interval the inductor energy releases. Figure 8 shows the input voltages of wind turbine, PV panel, and output voltage. By substituting related parameter values into (22), it can be found that the magnitude of output voltage in Figure 8 can meet the theoretical computing result. This has verified the correctness of the mathematical derivation in this paper. Another conclusion observed from Figure 8 is that the proposed HPWPCS still can function when PV panel is shut down from the generation system. Equation (22) can also estimate the output voltage under this situation. The measured efficiency from light load to heavy load is presented in Figure 9, in which the maximum efficiency is around 92.5%.

 Switching frequency of each channel () 50 kHz Output voltage () 400 V Output power () 1 kW Voltage ripple () <0.5 V Rated input voltage of wind turbine () 120 V Rated input voltage of PV panel () 80 V Efficiency () >85%
 Parameter Value Output capacitance () 10 F Output inductance () 5 mH Input capacitance () 100 μF Capacitances (, , , and ) 5 μF Turn ratio of coupled inductor 1 : 2 Turn ratio of coupled inductor 1 : 3 Magnetizing inductance of () 800 F Magnetizing inductance of () 800 F Leakage inductance of () 5 H Leakage inductance of () 8 H Active switches (, , , and ) IRFI4227 Diodes (, , , and ) BYV42 Diodes (, , , , , and ) BYV34-500

#### 6. Conclusion

In this paper, a novel PV-wind hybrid power conversion system is proposed first. Then, energy-balanced criterion is applied to the derivation of the voltage gain of the power conversion system. This criterion simplifies the mathematical derivation of the PV-wind hybrid system. For verification, a prototype of the proposed PV-wind hybrid-power conversion system is set up and measured. The practical measurements have proven the correctness of the mathematical derivation. This analysis procedure can be applied to other hybrid green-energy conversion systems to resolve complicated mathematical problems related to the solution of voltage gain.

#### Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

#### Acknowledgment

The authors gratefully acknowledge financial support from the Ministry of Science and Technology, Taiwan, under Contract no. MOST 103-3113-E-006-011.

1. C.-L. Shen and J.-C. Su, “Grid-connection half-bridge PV inverter system for power flow controlling and active power filtering,” International Journal of Photoenergy, vol. 2012, Article ID 760791, 8 pages, 2012. View at: Publisher Site | Google Scholar
2. N. Onat, “Recent developments in maximum power point tracking technologies for photovoltaic systems,” International Journal of Photoenergy, vol. 2010, Article ID 245316, 11 pages, 2010. View at: Publisher Site | Google Scholar
3. N. Vázquez, C. M. Sanchez, C. Hernández, E. Vázquez, L. D. C. García, and J. Arau, “A different three-port DC/DC converter for standalone PV system,” International Journal of Photoenergy, vol. 2014, Article ID 692934, 13 pages, 2014. View at: Publisher Site | Google Scholar
4. S.-Y. Tseng, C.-C. Chen, and H.-Y. Wang, “Buck-boost/forward hybrid converter for PV energy conversion applications,” International Journal of Photoenergy, vol. 2014, Article ID 392394, 14 pages, 2014. View at: Publisher Site | Google Scholar
5. K. I. Hwu, W. C. Tu, and C. R. Wang, “Photovoltaic energy conversion system constructed by high step-up converter with hybrid maximum power point tracking,” International Journal of Photoenergy, vol. 2013, Article ID 275210, 9 pages, 2013. View at: Publisher Site | Google Scholar
6. S.-Y. Tseng and C.-T. Tsai, “Photovoltaic power system with an interleaving boost converter for battery charger applications,” International Journal of Photoenergy, vol. 2012, Article ID 936843, 15 pages, 2012. View at: Publisher Site | Google Scholar
7. S.-K. Changchien, T.-J. Liang, J.-F. Chen, and L.-S. Yang, “Step-up DC-DC converter by coupled inductor and voltage-lift technique,” IET Power Electronics, vol. 3, no. 3, pp. 369–378, 2010. View at: Publisher Site | Google Scholar
8. Z. Zhang, O. C. Thomsen, M. A. E. Andersen, and H. R. Nielsen, “A novel dual-input isolated current-fed DC-DC converter for renewable energy system,” in Proceedings of the 26th Annual IEEE Applied Power Electronics Conference and Exposition (APEC '11), pp. 1494–1501, March 2011. View at: Publisher Site | Google Scholar
9. X. Y. Xu, A. M. Khambadkone, and R. Oruganti, “An asymmetrical half bridge flyback converter with zero-voltage and zero-current switching,” in Proceedings of the 30th Annual Conference of IEEE Industrial Electronics Society (IECON '04), vol. 1, pp. 767–772, November 2004. View at: Publisher Site | Google Scholar
10. S.-K. Changchien, T.-J. Liang, J.-F. Chen, and L.-S. Yang, “Novel high step-up DCDC converter for fuel cell energy conversion system,” IEEE Transactions on Industrial Electronics, vol. 57, no. 6, pp. 2007–2017, 2010. View at: Publisher Site | Google Scholar
11. Z. Wang, F. Liu, Y. Mao, and X. Ruan, “Asymmetrical half-bridge double-input DC/DC converters adopting pulsating voltage source cells for low power applications,” IEEE Transactions on Power Electronics, vol. 29, no. 9, pp. 4741–4751, 2014. View at: Publisher Site | Google Scholar
12. K.-C. Tseng and C.-C. Huang, “High step-up high-efficiency interleaved converter with voltage multiplier module for renewable energy system,” IEEE Transactions on Industrial Electronics, vol. 61, no. 3, pp. 1311–1319, 2014. View at: Publisher Site | Google Scholar
13. F. Nejabatkhah, S. Danyali, S. H. Hosseini, M. Sabahi, and S. M. Niapour, “Modeling and control of a new three-input dc-dc boost converter for hybrid PV/FC/battery power system,” IEEE Transactions on Power Electronics, vol. 27, no. 5, pp. 2309–2324, 2012. View at: Publisher Site | Google Scholar
14. C.-L. Shen and T.-C. Liang, “Design and implementation of a high-voltage generator with output voltage control for vehicle ER shock-absorber applications,” Mathematical Problems in Engineering, vol. 2013, Article ID 324590, 6 pages, 2013. View at: Publisher Site | Google Scholar
15. C.-L. Shen and S.-H. Yang, “Multi-input converter with MPPT feature for wind-PV power generation system,” International Journal of Photoenergy, vol. 2013, Article ID 129254, 13 pages, 2013. View at: Publisher Site | Google Scholar
16. R.-J. Wai, W.-H. Wang, and C.-Y. Lin, “High-performance stand-alone photovoltaic generation system,” IEEE Transactions on Industrial Electronics, vol. 55, no. 1, pp. 240–250, 2008. View at: Publisher Site | Google Scholar

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