Abstract

The modeling, simulation and analysis of the energy conversion equations describing the behavior of a hybrid system PV and wind turbine, and hybrid system for electrical power generation are presented. A numerical model based on the aforementioned equations was developed, coded and results were presented, discussed compared to experimental data reported in the literature. The model is intended for optimization and as design tool for such hybrid systems. The model predicted results compared fairly to experimental data under various conditions. A stability analysis was also performed by the mathematical modeling for the hybrid system. It is important to point out that this analysis has been carried out so that in the near future one of these power generation systems to be exploited to a great extent in the locality of Quingeo-Puntahacienda.

Keywords: Hybrid system, Solar PV, Wind turbine, Modeling, Simulation, Stability analysis, MATLAB, Experimental validation.

Received: 19 January 2018 / Revised: 15 February 2018 / Accepted: 19 February 2018 / Published: 21 February 2018

Contribution/ Originality

This study contributes to the optimization of hybrid systems PV-Wind and that can be used as design tool for hybrid systems intended for implementation in remote zones without access to the grid. It is important to point out that this study has been carried out so that in the near future remote areas localities such as Quingeo-Puntahacienda can benefit from renewable energy technologies.

1. INTRODUCTION

Renewable and non-conventional energy generation methods such as wind, solar, hydropower, biomass, geothermal, thermal storage and waste heat recovery solutions for remote areas of Quingeo such as the localities surrounding Puntahacienda in Ecuador are not directly accessible by the electrical grid. A hybrid system is an integrated system of two or more renewable energy systems, and can complement each other, provides a higher quality and reliable power source independent of the utility's grid network (Garcia, 2006 ; Department of Energy, 2007 ; Kavitha and Kamdi, 2013 ; Zhang et al., 2013 ; Binayak et al., 2014 ; Neira and Velecela, 2014 ; Peterseim et al., 2014 ; Srinivas and Reddy, 2014 ; Iftekhar et al., 2015 ; Sami and Icaza, 2015 ; Sami and Icaza, 2015 ; Sami and Marin, 2017 ). Wind turbine and PV, has became increasingly an attractive option, compared to cost of fossil fuels, land developments and thermal technology (Garcia, 2006 ; Department of Energy, 2007 ; Kavitha and Kamdi, 2013 ; Binayak et al., 2014 ; Srinivas and Reddy, 2014 ; Iftekhar et al., 2015 ; Sami and Icaza, 2015 ; Sami and Icaza, 2015 ; Sami and Marin, 2017 ).

Neira and Velecela (2014 ) presented and discussed the electrification of the rural area and a review of the autonomous system of power such as; Solar and wind. In addition, references (Kavitha and Kamdi, 2013 ) and (Deissler, 1964 ; Howell et al., 1982 ; Covarrubias et al., 2005 ; Wenham, 2007 ; Atideh and Zhenhua, 2008 ; Fargali et al., 2010 ; Craig and Zhiwen, 2011 ; Marreno, 2011 ; Penyarat and Pascal, 2012 ; Akikur et al., 2013 ; Mustafa, 2013; Saha et al., 2013 ; Castillo et al., 2014 ; Dustin and Jack, 2014 ; Yoshimasa et al., 2015 ) presented and analyzed the feasibility and importance of the use of wind energy in global electrification. Reference (Sami and Icaza, 2015) analyzed and compared a simulation model of the proposed system for remote areas hereby and compared to with the literatures reported in the literature (Sami and Icaza, 2015 ).

Another study was proposed by for implementation in rural areas disconnected from the network. In addition, a photovoltaic and wind system designed for remote areas has been also suggested to supply uninterrupted power to a remote village in Chile by Covarrubias et al. (2005 ).

Figure-1. Wind turbine under investigation [http://www.elmercurio.com.ec/342627-electricidad-domestica-con-la-fuerza-del-viento/].

In addition, other studies were reported on PV-wind-battery hybrids and PV-wind-diesel-battery hybrids for rural electrification in Colombia (Howell et al., 1982 ; Atideh and Zhenhua, 2008 ; Fargali et al., 2010 ; Craig and Zhiwen, 2011 ; Mustafa, 2013 ; Saha et al., 2013 ; Yoshimasa et al., 2015 ). Furthermore, a numerical model based upon the energy conversion equations integrated and simultaneously solved to describe the total power generated by a hybrid solar photovoltaic, wind turbine and hydraulic turbine system was presented by Sami and Icaza (2015 ) where a simulation model was validated against experimental data. It is worthwhile noting that the energy conversion equations were coded with MATLAB-V13.2. In addition, reference (Sami and Icaza, 2015 ) presented an analysis of stability through the traces of the locus of the roots.

Puntahacienda is located in the Parish of Quingeo, Canton Cuenca, Province of Azuay, Ecuador, approximately 30 Km from the city of Cuenca going along Via El Valle passing through the localities of Santa Ana and La Libertad. Unfortunately this remote area is not connected to the grid. Therefore, the present model and analysis will be beneficial to this remote area.

This paper describes the simulation and validation of a combined wind and solar system for electric power generation with energy storage facilities. In addition, multivariable weather data including the wind speed and direction, the solar radiation, the rain fall and humidity as well as temperature were obtained using a weather station installed at Puntahacienda- Quingeo. Moreover, the simulation model presented hereby includes modeling of battery, modern load controller and inverter.

1.1. Mathematical Modeling

The mathematical model is based upon the energy conversion equations and this simplified model that is a representative of the parameters of the mechanical and electrical systems under investigation that directly influence the power. The model uses the LaPlace formulation to carry out the simulations of the energy transformation equations of the electric energy and solar radiation (Spiegel, 1991 ; Whiteman, 2000 ; Katsuhiko, 2003 ; Garcia, 2006 ; Wenham, 2007; Marreno, 2011 ; Penyarat and Pascal, 2012 ; Akikur et al., 2013 ; Dustin and Jack, 2014 ). This process allows us to find the best design option of the hybrid system. Figure. 2 presents the scheme used to study and simulation the energy formulation of the PV and wind turbine and can be used in the future for other types of renewable energy. However it should be pointed out that adjustments and calibrations must be made for integration of new types of renewable energy. In our case study, this model is intended for remote areas that are not connected to the grid.

1.2. Laplace Formulation

1.2.1. General Block Diagram

The following describes the simulation model, energy conversion equations, and linear programming principles as well as the description of MATLAB block diagrams;

Figure-2. Electric Power Conversion Energy.

Figures 2 through (4) describe the block diagrams of the electric power conversion energy, the wind power generation as well as the direct current wind turbine formulations.

Figure-3. Block diagram of wind power generation.

Figure-4. Simplified diagram of the direct current wind turbine.

Where the following define the nomenclatures used in these figures;
K = Coefficient of proportionality of Ec.

J= Moment of inertia at generator shaft. [[Kg-m2]

B= Viscous coefficient of friction of the generator. [N-m/rad/seg]

La= Armature Inductance [H]
Ra= Armor Resistance [Ω]

ωi= Angular input speed (blades)

θi= Angular displacement of input (blades)

Tg= Torque generator input (blades)

Furthermore, the following equations present the specific electrical parameters;

It is worthwhile pointing that the simplified block diagram shown in Figure.5 represents of the wind turbine according to equations (1), (2) and 3 in the Laplace domain;

1.4. Load Controller

The proportional industrial controller formula can be used to represent the load controller as shown in Figure.6;

Figure-6. General diagram of the load controller.

Where parameters shown in Figure.6 are;

Kp= Proportional coefficient.

Td= Derivative time of the controller.

1.5. Inverter

Figure-7. General diagram of the inverter.

The formulations describing the inverter in the time domain are presented as follows;

Direct loop general diagram displays the wind generation system with operating parameters for the wind turbine as shown in Figure.8.

With the aforementioned transfer function, the system parameters can be evaluated.

1.6. Block Diagram Solar Panel

Figures (9) through (11) describe the block diagrams of the electric power conversion energy, the solar panel Photovoltaic PV power generation as well as the direct current solar PV formulations.

Figure-10. Diagram for the mathematical model for solar panel.

Solar panel PV collector current can be calculated as follows (Sami and Icaza, 2015 ; Sami and Icaza, 2015 ; Sami and Marin, 2017 ).

The general diagram of the solar generation system with operating parameters is presented in Figure .11

1.7. Energy Conversion Equations

1.7.1. Wind turbine Simulation

The power of a particular wind turbine is given by (Peterseim et al., 2014 ; Sami and Icaza, 2015 ; Sami and Icaza, 2015 ).

1.8. Efficiency of Photovoltaic PV System

The thermal energy absorbed by the PV solar collector is (Neira and Velecela, 2014 ; Peterseim et al., 2014 ; Sami and Icaza, 2015 ; Sami and Icaza, 2015 ; Sami and Marin, 2017 ).

The characteristics performance” I-V” of the PV solar panel can be described by the following (Peterseim et al., 2014 ; Srinivas and Reddy, 2014 ; Sami and Marin, 2017 ).

Where:
Ns is the number of solar cells in series.
Np is the number of cells in parallel.
K is the Boltzman constant.
qe is the charge of the electron.
m is the diode ideality factor; 1 <m <2.
T1 is the working temperature of the solar panel in ° C.
Rs is the series resistor.
Rp is the resistance in parallel.
IL (G1, T1) is the photogenerated current and approximately equal to the short-circuit current Isc (G1, T1).
Io is the inverse saturation current of the diode.
Voc is the open circuit voltage (Fargali et al., 2010 ; Sami and Marin, 2017 ).

The electric PV power output in DC taking into account the efficiency of conversion to electric energy is;

1.10. Battery Charging and Discharging Model

The battery stores excess power going through the load charge controller (figure 12-a, and figure 12b). The battery also keeps voltage within the specified voltage and thus, protects over discharge rates, and prevent overload.

During the charging period, the voltage-current relationship can be described as follows (Marreno, 2011 ; Sami and Icaza, 2015 ; Sami and Icaza, 2015 ; Yoshimasa et al., 2015 ; Sami and Marin, 2017 ).

2. NUMERICAL PROCEDURE

The energy conversion and heat transfer mechanisms taking place during various processes shown in figure 12a and figure 12b, are described in Equations (15) through (33). These equations have been solved as per the logical flow diagram presented in Figure 13, to obtain the input parameters of wind and solar PV under different input conditions. Dependent parameters were calculated and integrated into the system of equations and solved numerically by convergence iterative method. Iterations were performed until a solution is reached with acceptable iteration error.

Figure-12-b. Solar subsystem.

Figure-13. Flow diagram of Hybrid system calculation

3. RESULTS AND DISCUSSION

Equations (15) to (33) described earlier in this article were solved taking into account that the total power is not always be simultaneous, and for validation purposes, this simulation model and the equations were coded using MATLAB. In addition, in order to validate the model presented hereby and the simulated results were compared against literature data under various conditions. In the following sections, we present, analyze and discuss the predicted numerical results, as well as the validations of the simulation model in question.

In the Figure 14 through 16 the typical profiles of environmental parameters at the site during such as ambient temperature, solar radiation and wind speed are presented several the year 2016 at different times of the day. The environmental data presented in the aforementioned figures were used in the modeling and simulation of the system.

Figure-14. Ambient temperatures (°C) profile August 2016- December 2016

3.1. Wind Turbine Simulation

Figures 17 through 19 present the wind turbine simulation results where Betz Coefficient, wind turbine power and efficiency were displayed. In particular, the impact wind speed on the electrical power output generated by the wind turbine has been illustrated in Figures 17, 18 and 19. The predicted results displayed in these figures show that at the lower cut off speed of 2.5 m/s and higher cut off speed 9 m/s, the wind electrical power generated is 60 and 1900 Watts which coincide with the wind turbine specifications provided by the manufacturer (Sami and Icaza, 2015 ; Sami and Icaza, 2015 ). Furthermore, Figure 19 has been constructed to show the impact of the wind speed on the energy conversion efficiency from wind energy to electrical energy. It is quite clear that the higher wind speed results in higher energy conversion efficiency and produces more power output. However, for the wind turbine under investigation, the minimum starting wind speed is 2.5 m/s, at this particular condition, the power output and conversion efficiency are significantly low and economically viable.

Figure-15. Profile of Speed in m/s Aug2016- Dec 2016

Figure-16. Solar irradiances (W/m2) Profile Aug 2016-Dec 2016

Figure-17. Power-speed curve for different values of Betz Coefficient.

Figure-18. DC Power- DC Current for wind Speed (m/s).

Figure-19. Energy conversion efficiency at various wind speeds

Figure-20. Voltage-Current curve for different values of irradiance- W/m2.

Figure-21. DC Voltage PV- DC Power PV for different values of irradiance (W/m2).

Figure-22. DC Power PV- Efficiency Conversion PV for different values of irradiance (W/m2).

3.2. PV Simulation

The PV characteristics such as voltage, amperage, output power and solar panel efficiency are displayed in Figures 20 through 22. In addition, these figures demonstrate the basic concept of energy conversion from the solar insolation into electrical energy as shown in particular in Figure 22. This figure shows the effect of solar radiation on the PV electrical power produced and energy conversion efficiency. It is worth noting that the numerical simulation presented hereby include the variation of PV cell temperatures from 10°C through 22°C (C.F. Figure.14). It is quite clear from figures 21 and 22 that higher solar radiation results in higher energy conversion efficiency and output PV electrical power. Therefore, it is quite evident that the solar panels will more efficient to operate at sites with higher solar irradiance (Sami and Icaza, 2015 ; Sami and Icaza, 2015 ; Sami and Marin, 2017 ).

On the other hand, using equation (31), the different possibilities of generation of electric energy in alternating current can be simulated and displayed in Figure.23. In this particular case, the values of Cos j = 0.9, system performance efficiency, h= 0.5 and at different single phase AC current and considering the selected inverter, we can obtain in the single phase power in alternating current, as demonstrated in Figure 23.

Figure-23. AC Current (A)– Electrical Power (W) for 110V, Cosj 0.9.

3.3. Stability Analysis of the Hybrid System

The geometric root locus method (GRL) is very useful in designing a linear control system, since it describes how an open loop poles must be modified in order for meet the response and performance specifications of the system. This method is particularly convenient in obtaining approximate results very quickly.

Figures 24 and 25 were constructed after the transfer function described in equations (12) and (14), respectively for the wind and the PV systems, corresponding to the model is shown in Figure 8 and Figure 11. The input parameters are those generated in Figures 24 and 25 where the poles and zeros are located to determine if the status of the system is stable. In the case under investigation, it is stable because the poles are to the left with respect to the imaginary axis.

Figure-24. Graph of the geometric location of the roots referring to the wind turbine.

Figure-25. Graph of the geometric location of the roots referring to the PV.

3.4. Validation of the Simulation Model

In order to validate our numerical model prediction described in equations (15 through 33), the numerical results simulating the hybrid system in question were compared to data presented in reference (Fargali et al., 2010 ; Sami and Icaza, 2015 ). To that end Figures 26, 27 and 28 have been constructed to present the model validation.

In Figure 26, we have presented the results from the mathematical model used simulated in Matlab and compared to the power data measured at different wind velocities (Sami and Icaza, 2015 ). The discrepancy between the model and the simulated data can be attributed to the fact that the Betz coefficient considered in the modeling was the optimum value; Cp = 0.59, and the data available were at approximately using Co=0.46.
The numerical results predicted by the model in Matlab and compared well to the measurements (Fargali et al., 2010 ) for voltages higher than 7 V in Figure .27. However, lower current were predicted at voltages under 7 V.

A comparison between the results of the Matlab model and solar panel data is presented in (Kavitha and Kamdi, 2013 ; Sami and Icaza, 2015 ) in Figure. 28. It can be observed from this figure that solar panel power increases as a function of the generated voltage up to a certain limit of 14 V and then significantly power is reduced

Figure-26. Comparison of Wind speed – Wind Power (Sami and Icaza, 2015 ).

Figure-27. PV output data (Fargali et al., 2010 ) compared to model prediction at 500 W/m2.

Figure-28. PV output data compared to model prediction at 500 W/m2 (Kavitha and Kamdi, 2013 ; Sami and Icaza, 2015 ).

4. CONCLUSIONS

A stability analysis was also performed by the mathematical modeling for the hybrid system. It is important to point out that this analysis has been carried out so that in the near future one of these power generation systems to be exploited to a great extent in the locality of Quingeo-Puntahacienda, It is concluded that the present system can be considered for Quingeo-Puntahacienda as a renewable energy system and it is favorable.

4.1. Nomenclature

Funding: The research work presented in this paper was made possible through the support of the Catholic University of Cuenca.

Competing Interests: The authors declare that they have no competing interests.

Contributors/Acknowledgement: The research work presented in this paper was also made possible in part by the support of Daniel Icaza’s family who helped to move the equipment to where the tests were carried out. The co-author Daniel Icaza acknowledges the support of Professor Dr. Samuel Sami Howard who forged him as a researcher at the Research Center for Renewable Energy, CER, when he started to work at the Catholic University of Cuenca.

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Index