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

Authors: Chih-Lung Shen; Tsair-Chun Liang; Siou-Hong Zhou; Su-Wen Wang
Journal: Mathematical Problems in Engineering
 (2015)

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## 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.


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## Body

## 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 [1–5].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 [6–12]. 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 [13–16]. 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. Figure1 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, T1 and T2, 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, Lleak,wind and Lleak,pv, 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.Figure 1
The power circuit of the proposed HPWPCS.


## 3. Operation Analysis

Before the operation analysis, some assumptions are made as follows. (1) All diodes are ideal. (2) The output inductorLo and magnetizing inductances, Lm,wind and Lm,pv, are in continuous conduction mode (CCM). (3) The internal resistance and parasitic capacitance in active switch are neglected. (4) Both leakage inductances Lleak,wind and Lleak,pv are much less than Lm,wind and Lm,pv. 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 (Figure2(a), t0-t1): during this time interval, the power switches SW1,wind and SW2,wind are turned on simultaneously but SW1,pv and SW2,pv are in off state. The leakage inductance Lleak,wind and magnetizing inductance Lm,wind are charging and so does the output inductor Lo. The current flowing through N1,wind will be transferred to the secondary winding N2,wind, to charge the capacitors C2,wind and Co. Meanwhile, the inductor Lm,pv dumps energy to secondary winding via transformer T2. The energy in Lm,pv and C2,pv charges C1,pv. This stage is ended as soon as the switches SW1,wind and SW2,wind are turned off.(2)
Stage 2 (Figure2(b), t1-t2): at the moment that the switches SW1,wind and SW2,wind are turned off, the operation of HPWPCS enters into Stage 2. The energy stored in leakage inductance Lleak,wind is recycled to the input and transferred to the secondary winding via the path of N1,wind, D1,wind, and D2,wind. This mode ends when the current of leakage inductance Lleak,wind dumps to zero.(3)
Stage 3 (Figure2(c), t2-t3): during this stage, all the active switches SW1,wind, SW2,wind, SW1,pv, and SW2,pv are kept in off state. The magnetizing inductance Lm,wind dumps energy to secondary winding to charge the capacitor C1,wind via N2,wind, C2,wind, and D3,wind. Meanwhile, the inductance Lm,pv also dumps energy to C1,pv via N2,pv, C2,pv, and D3,pv. The output inductor Lo releases energy to the dc link for load powering. As SW1,pv and SW2,pv are turned on, the next stage begins.(4)
Stage 4 (Figure2(d), t3-t4): the power switches SW1,pv and SW2,pv are on but SW1,wind and SW2,wind are off. The HPWPCS will forward PV power to the output. The magnetizing inductance Lm,pv starts charging during this interval, and the current through N1,pv is transferred to the secondary winding of T2 to charge the capacitor C2,pv. With respect to the processing of wind energy, the HPWPCS sustains the same circuit behavior as in Stage 3.(5)
Stage 5 (Figure2(e), t4-t5): as the switches SW1,pv and SW2,pv are turned off, Stage 5 begins and the energy stored in leakage inductance Lleak,pv will be recycled to the input by the path of Lleak,pv-N1,pv-D1,pv-D2,pv. The current of Lleak,pv decreases linearly. While this current drops to zero, circuit operation enters into next stage.(6)
Stage 6 (Figure2(f), t5-t6): in this mode, all active switches are open and the operation is the same as that in Stage 3. The magnetizing inductance Lm,wind releases energy to the secondary of T1 and so does the Lm,pv to the secondary of T2. When SW1,wind and SW2,wind are closed again, the operation of HPWPCS returns to Stage 1.Figure 2
Equivalent circuits of the proposed HPWPCS: (a) Stage 1, (b) Stage 2, (c) Stage 3, (d) Stage 4, (e) Stage 5, and (f) Stage 6.
(a)
(b)
(c)
(d)
(e)
(f)Figure 3
Conceptual waveforms to depict the operation of the proposed HPWPCS.


## 4. Voltage Gain Derivation

Suppose that all capacitances are large enough to sustain capacitor voltages at constants and the leakage inductances ofT1 and T2 are much smaller than magnetizing inductances. As shown in Figure 4, the switching period of the HPWPCS is Ts. During the time interval Ts, switches SW1,wind and SW2,wind are closed for DwindTs,wind and open for 1-DwindTs,wind while switches SW1,pv and SW2,pv are closed for DpvTs,pv and open for 1-DpvTs,pv. The Ts,wind stands for the interval that the HPWPCS deals with wind turbine energy, while Ts,pv stands for PV panel. That is,(1)Ts,wind+Ts,pv=Ts.According to the operation principle described in Stages 1, 3, 4, and 6, the output inductor current iLo will increase linearly while absorbing energy and decrease linearly while releasing energy. The waveform of output inductor current is illustrated in Figure 4.Figure 4
Illustration of the current waveform of output inductor and related time intervals.Since HPWPCS adopts two coupled inductors, the coupling coefficientk will be a key parameter in the derivation. The k can be found by the following relationship:(2)k=1-LscLopen,where Lsc is the measured inductance from the primary while the secondary is short circuit and Lopen represents the measured primary-side inductance while the secondary is open circuit. With respect to T1, when the switches SW1,wind and SW2,wind are closed, the voltage across N1 is (3)vn1,wind=vwind·kwind2,in which kwind expresses the coupled coefficient of T1. Thus, at this switch-on status the voltage vn2,wind is calculated by (4)vn2,wind=vn1,wind·N2,windN1,wind.Substituting (3) into (4) yields(5)vn2,wind=vwind·kwind2·N2,windN1,wind.From the equivalent of Stage 2 (switches SW1,wind and SW2,wind are off), it can be found that the voltage of the capacitor C2,wind, vC2,wind, is equal to the voltage of the secondary of T1. That is,(6)vC2,wind=vn2,wind.Therefore, the following equation holds:(7)vC2,wind=vwind·kwind2·N2,windN1,wind.From Figure 2(c), the voltage across the capacitor C1,wind can be determined by(8)vC1,wind=vC2,wind+vn2,wind.From (7), the above equation can be rewritten as(9)vC1,wind=vwind·kwind2·N2,windN1,wind+vwind·kwind2·N2,windN1,wind·Dwind1-Dwind.Rearranging (9) gives(10)vC1,wind=kwind21-Dwind·N2,windN1,wind·vwind.WhileSW1,wind and SW2,wind are closed, referring to Figure 2(a) and applying Kirchhoff’s voltage law (KVL) to the loop of N2,wind-C1,wind-D4,wind-Lo-Co, the output inductor voltage vLo can be obtained:(11)vLo=LodiLodt=vn2,wind+vC1,wind-Vdc,link.Substituting (5) and (10) into (11) results in(12)vLo=vwind·kwind2·N2,windN1,wind+kwind2·vwind·N2,wind1-Dwind·N1,wind-Vdc,link.Regarding the expression forvLo during the period of both switches SW1,wind and SW2,wind being open, we can apply KVL to the loop of C2,wind-D3,wind-D4,wind-Lo-Co as shown in Figure 2(c) and then obtain(13)vLo=vwind·kwind2·N2,windN1,wind-Vdc,link.While considering the expression ofvLo during the period of Ts,pv, Figures 2(d) and 2(f) will be contacted and the similar derivation procedure as above is adopted. During the period of DpvTs,pv, referring to Figure 2(d), the vn1,pv and vn2,pv can be found as follows: (14)vn1,pv=vpv·kpv2,(15)vn2,pv=vn1,pv·N2,pvN1,pv=vpv·kpv2·N2,pvN1,pv,where the kpv is the coupling coefficient of T2. The voltage across C2, vC2,pv, is equal to vn2,pv. That is,(16)vC2,pv=vpv·kpv2·N2,pvN1,pv.From Figure 2(f), the vC1,pv is the sum of vC2,pv and vn2,pv. As a result, the vC1,pv can be described as (17)vC1,pv=kpv21-Dpv·N2,pvN1,pv·vpv.While SW1,pv and SW2,pv are closed, as shown in Figure 2(d), from the loop enclosed by N2,pv, C1,pv, D4,pv, Lo, and Co, one can find vLo by the use of KVL:(18)vLo=vn2,pv+vC1,pv-Vdc,link.The vn2,pv and vC1,pv are substituted for (15) and (17), respectively, which yields (19)vLo=vpv·kpv2·N2,pvN1,pv+kpv2·vpv·N2,pv1-Dpv·N1,pv-Vdc,link.In regard to the expression for output inductor voltage while SW1,pv and SW2,pv are off, from the loop of C2,pv-D3,pv-D4,pv-Lo-Co shown in Figure 2(f), one can find(20)vLo=vpv·kpv2·N2,pvN1,pv-Vdc,link.The output inductor charges energy during the two time intervals,DwindTs,wind and DpvTs,pv. On the contrary, during 1-DwindTs,wind and 1-DpvTs,pv, 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:(21)vwind·N2,windN1,wind·kwind2+vwind·N2,wind/N1,wind·kwind21-Dwind-Vdc,linkN2,windN1,wind·Dwind·Ts,wind+vpv·N2,pvN1,pv·kpv2+vpv·N2,pv/N1,pv·kpv21-Dpv-Vdc,linkN2,windN1,wind·Dpv·Ts,pv=Vdc,link-vwind·N2,windN1,wind·kwind2N2,windN1,wind·(1-Dwind)·Ts,wind+Vdc,link-vpv·N2,pvN1,pv·kpv2N2,windN1,wind·(1-Dpv)·Ts,pv.Simplifying (21) results in(22)Vdc,link=12N2,wind/N1,wind·kwind2·vwind1-DwindN2,pv/N1,pv·kpv2·vpv1-Dpv+N2,pv/N1,pv·kpv2·vpv1-Dpv,which 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 Table1. 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 C1,wind and C1,pv, which depicts that the voltages vC1,wind and C1,pv can be sustained at constant level. Output inductor current iLo 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 vo 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%.Table 1
The specifications of the prototype.
Switching frequency of each channel (fs)
50 kHz
Output voltage (Vo)
400 V
Output power (Po)
1 kW
Voltage ripple (Vo,ripple)
<0.5 V
Rated input voltage of wind turbine (vwind)
120 V
Rated input voltage of PV panel (vpv)
80 V
Efficiency (η)
>85%Table 2
The parameters of the prototype.
Parameter
Value
Output capacitance (Co)
10μF
Output inductance (Lo)
5 mH
Input capacitance (Cin)
100μF
Capacitances (C1,wind, C2,wind, C1,pv, and C2,pv)
5μF
Turn ratio of coupled inductorT1
1 : 2
Turn ratio of coupled inductorT2
1 : 3
Magnetizing inductance ofT1 (Lm,wind)
800μF
Magnetizing inductance ofT2 (Lm,pv)
800μF
Leakage inductance ofT1 (Lleak,wind)
5μH
Leakage inductance ofT2 (Lleak,pv)
8μH
Active switches (SW1,wind, SW2,wind, SW1,pv, and SW2,pv)
IRFI4227
Diodes (D1,wind, D2,wind, D1,pv, and D2,pv)
BYV42
Diodes (D3,wind, D4,wind, D5,wind, D3,pv, D4,pv, and D5,pv)
BYV34-500Figure 5
Waveforms of control signals (vgs,pv and vgs,wind) and input current (iin,pv and iin,wind).Figure 6
Waveforms of control signals (vgs,pv and vgs,wind) and capacitor voltage (vC1,wind and vC1,pv).Figure 7
Waveforms of control signals (vgs,pv and vgs,wind) and output inductor current (iLo).Figure 8
The measured output voltage waveform (vo) to demonstrate the correctness of the mathematically derived result.Figure 9
The measured efficiency over the range from light load to full load.


## 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.



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*Source: 623161-2015-03-17.xml*