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

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, complicatedmathematical 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 200W 50 kHz prototype of HPWPCS is built and examined to verify the mathematical results.


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][2][3][4][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][7][8][9][10][11][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][14][15][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.

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,  1 and  2 , 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,  leak,wind and  leak,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.

Operation Analysis
Before the operation analysis, some assumptions are made as follows.(1) All diodes are ideal.(2) The output inductor   and magnetizing inductances,  ,wind and  ,pv , are in continuous conduction mode (CCM).(3) The internal resistance and parasitic capacitance in active switch are neglected.(4) Both leakage inductances  leak,wind and  leak,pv are much less than  ,wind and  ,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.

Voltage Gain Derivation
Suppose that all capacitances are large enough to sustain capacitor voltages at constants and the leakage inductances of  1 and  2 are much smaller than magnetizing inductances.As shown in Figure 4, the switching period of the HPWPCS is   .
During the time interval   , switches SW 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  sc is the measured inductance from the primary while the secondary is short circuit and  open represents the measured primary-side inductance while the secondary is open circuit.With respect to  1 , when the switches SW 1,wind and SW 2,wind are closed, the voltage across  1 is in which  wind expresses the coupled coefficient of  1 .Thus, at this switch-on status the voltage V  2 ,wind is calculated by Substituting ( 3) into (4) yields From the equivalent of Stage 2 (switches SW 1,wind and SW 2,wind are off), it can be found that the voltage of the capacitor  2,wind , V  2 ,wind , is equal to the voltage of the secondary of  1 .That is, Therefore, the following equation holds: From Figure 2(c), the voltage across the capacitor  1,wind can be determined by From ( 7), the above equation can be rewritten as Rearranging ( 9) gives While SW 1,wind and SW 2,wind are closed, referring to Figure 2(a) and applying Kirchhoff 's voltage law (KVL) to the loop of  2,wind - 1,wind - 4,wind -  -  , the output inductor voltage V   can be obtained: Substituting ( 5) and ( 10) into ( 11) results in Regarding the expression for V   during the period of both switches SW 1,wind and SW 2,wind being open, we can apply KVL to the loop of  2,wind - 3,wind - 4,wind -  -  as shown in Figure 2(c) and then obtain While considering the expression of V   during the period of  ,pv , Figures 2(d) and 2(f) will be contacted and the similar derivation procedure as above is adopted.During the period of  pv  ,pv , referring to Figure 2(d), the V  1 ,pv and V  2 ,pv can be found as follows: where the  pv is the coupling coefficient of  2 .The voltage across  2 , V  2 ,pv , is equal to V  2 ,pv .That is, From Figure 2(f), the V  1 ,pv is the sum of V  2 ,pv and V  2 ,pv .As a result, the V  1 ,pv can be described as While SW 1,pv and SW 2,pv are closed, as shown in Figure 2(d), from the loop enclosed by  2,pv ,  1,pv ,  4,pv ,   , and   , one can find V   by the use of KVL: The V  2 ,pv and V  1 ,pv are substituted for ( 15) and ( 17), respectively, which yields In regard to the expression for output inductor voltage while SW 1,pv and SW 2,pv are off, from the loop of  2,pv - 3,pv - 4,pv -  -  shown in Figure 2(f), one can find The output inductor charges energy during the two time intervals,  wind  ,wind and  pv  ,pv .On the contrary, during (1 −  wind ) ,wind and (1 −  pv ) ,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) which reveals that the voltage gain is found and the dc-link voltage can be controlled by the duty ratios of the active switches.

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  1,wind and  1,pv , which depicts that the voltages V  1 ,wind and  1,pv 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 V  in Figure 8 can meet the theoretical ( gs,pv and gs,wind : 10 V/div, i in,pv and i in,wind : 10 A/div, time: 10 s/div) 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%.

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 greenenergy conversion systems to resolve complicated mathematical problems related to the solution of voltage gain.

Figure 1 :
Figure 1: The power circuit of the proposed HPWPCS.

Figure 3 :
Figure 3: Conceptual waveforms to depict the operation of the proposed HPWPCS.

Figure 5 :
Figure 5: Waveforms of control signals (V gs,pv and V gs,wind ) and input current ( in,pv and  in,wind ).

Figure 6 :
Figure 6: Waveforms of control signals (V gs,pv and V gs,wind ) and capacitor voltage (V  1 ,wind and V  1 ,pv ).

Figure 7 :
Figure 7: Waveforms of control signals (V gs,pv and V gs,wind ) and output inductor current (   ).

Figure 8 :
Figure 8: The measured output voltage waveform (V  ) to demonstrate the correctness of the mathematically derived result.

Figure 9 :
Figure 9: The measured efficiency over the range from light load to full load.
1,wind and SW 2,wind are turned on simultaneously but SW 1,pv and SW 2,pv are in off state.The leakage inductance  leak,wind and magnetizing inductance  ,wind are charging and so does the output inductor   .The current flowing through  1,wind will be transferred to the secondary winding  2,wind , to charge the capacitors  2,wind and   .Meanwhile, the inductor  ,pv dumps energy to secondary winding via transformer  2 .The energy in  ,pv and  2,pv charges  1,pv .This stage is ended as soon as the switches SW 1,wind and SW 2,wind are turned off.(2)Stage 2 (Figure2(b),  1 - 2 ): at the moment that the switches SW 1,wind and SW 2,wind are turned off, the operation of HPWPCS enters into Stage 2. The energy stored in leakage inductance  leak,wind is recycled to the input and transferred to the secondary winding via the path of  1,wind ,  1,wind , and  2,wind .This mode ends when the current of leakage inductance  leak,wind dumps to zero.
(3) Stage 3 (Figure2(c),  2 - 3 ): during this stage, all the active switches SW 1,wind , SW 2,wind , SW 1,pv , and SW 2,pv are kept in off state.The magnetizing inductance  ,wind dumps energy to secondary winding to charge the capacitor  1,wind via  2,wind ,  2,wind , and  3,wind .Meanwhile, the inductance  ,pv also dumps energy 1,pv via  2,pv ,  2,pv , and  3,pv .The output inductor   releases energy to the dc link for load powering.As SW 1,pv and SW 2,pv are turned on, the next stage begins.(4) Stage 4 (Figure 2(d),  3 - 4 ): the power switches SW 1,pv and SW 2,pv are on but SW 1,wind and SW 2,wind are off.The HPWPCS will forward PV power to the output.The magnetizing inductance  ,pv starts charging during this interval, and the current through  1,pv is transferred to the secondary winding of  2 to charge the capacitor  2,pv .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),  4 - 5 ): as the switches SW 1,pv and SW 2,pv are turned off, Stage 5 begins and the energy stored in leakage inductance  leak,pv will be recycled to the input by the path of  leak,pv - 1,pv - 1,pv - 2,pv .The current of  leak,pv decreases linearly.While this current drops to zero, circuit operation enters into next stage.(6) Stage 6 (Figure 2(f),  5 - 6 ): in this mode, all active switches are open and the operation is the same as that in Stage 3. The magnetizing inductance  ,wind releases energy to the secondary of  1 and so does the  ,pv to the secondary of  2 .When SW 1,wind and SW 2,wind are closed again, the operation of HPWPCS returns to Stage 1.
closed for  wind  ,wind and open for (1− wind ) ,wind while switches SW 1,pv and SW 2,pv are closed for  pv  ,pv and open for (1 −  pv ) ,pv .The  ,wind stands for the interval that the HPWPCS deals with wind turbine energy, while  ,pv stands for PV panel.That is,  ,wind +  ,pv =   .
1,wind and SW 2,wind are

Table 1 :
The specifications of the prototype.