Reliability analysis of hybrid renewable energy system by fault tree analysis

Abstract

This study is based on the simulation and optimization of renewable energy system of a Police Control Room Sagar Central India. The meteorological data of solar insolation, hourly wind speed, are taken from Sagar Central India (Longitude 78° 45′ and Latitude 23°50) and the pattern of load consumption of Police control room is studied and suitably modeled for the optimization of the hybrid energy system using HOMER software. The report offers a reliability assessment of hybrid renewable energy system of the field region. Weather data and the load profile of the study area are recorded and fault tree analysis is used for the reliability assessment of hybrid renewable energy system which further provides a static depiction of the combinations of failures and actions that can cause the specified critical fault to occur.

Keywords

Solar energy wind energy reliability fault tree analysis

Introduction

Due to high fossil fuel price and compatible political, socio-economic and environmental condition have tremendously increased with the adoption of non-conventional energy source. In remote region, cost and unfavorable condition are the main problem to get electricity from conventional power system.¹ Renewable energy system is a safer option to generate electricity rather than conventional energy sources. A more intensive usage of alternative energy sources is considered an important solution to the large atmospheric pollution caused due to fossil fuel combustion, upon which current energy production and use pattern throughout the world still rely heavily.^2,3 The wind and solar energy are ubiquitous, freely available and environmental friendly. The wind energy systems may not be technically viable at all sites because of low wind speeds and being more unpredictable than solar energy. The combined utilization of these renewable energy sources is therefore becoming increasingly attractive and is being widely used as alternative of oil-produced energy.⁴ Renewable energy sources such as wind energy and solar energy have made public and private sector to invest in energy generation from these sources extensively. The common drawbacks of these sources are their unforeseeable nature and their dependency on the climate change. Stable power output could be required through the hybrid power system.^5,6

Reliability is defined as the probability of device and system performing its purpose adequately for the intended operating period of time. An electrical energy power system is defined as the ability of electrical power system to supply the power system load with reasonable continuity and quality of provision.^8,9,10 This paper presents reliability analysis of wind energy system, photo-voltaic system, battery and converter with the help of reliability index and fault tree.

Dialynas et al. presented reliability and reserve capacity assessment of isolated power systems with increased penetration of RES. This report identifies the principal characteristics of a developed computational methodology that can be employed for the reliability and reserve capacity assessment of isolated renewable energy system.⁷ Billinton et al., maintained supply reliability of the small isolated power system using renewable energy. Brown et al.⁴ improved the reliability of islanded distribution systems with distributed renewable energy resources. Ardakani et al. developed design of an optimum HRES considering the reliability indices. Hybrid wind/PV/battery generation system is designed and technical constraint related to system reliability is expressed by the equivalent loss factor. Khare et al. developed the solar wind hybrid renewable energy system by HOMER software and cost validation is done by particle swarm optimization and chaotic particle swarm optimization technique and the result shows that 99% of renewable fraction is achieved. Khan et al.¹² gave a meticulous description about pre-feasibility study of stand-alone solar-wind hybrid energy system with the help of HOMER software for the application in Newfoundland with a drop of fuel cell cost to 65%, and a wind-diesel fuel cell battery system would be feasible. The paper demonstrates hybrid energy system with hydrogen as an energy transporter for the application in Newfoundland, Canada. Sizing, recital and various cost indexes were also analyzed in this article.⁹

Some of the system is also introduced with the concept of solar and wind energy system, and fuel cell is the principal ingredient in the system. The battery is used for storage purpose and hydrogen is used as an energy carrier. The hydrogen tank stores the hydrogen for use at the time of generation. The cost of a tank with 1 kg capacity is assumed to be $800. The replacement cost and O&M cost are taken as $700 and $15/year.

There are different types of fuel cells, which differ by the electrolyte, operation temperature, electrodes, and using precious catalysts. When we model the fuel cell, the performance of fuel cell depends on some losses such as: activation losses, ohmic losses, concentration losses, crossover losses. In the modeling of fuel cell, it is necessary to calculate the real output voltage of the fuel cell which can be calculated by subtracting all the overvoltage losses from the thermodynamically predicted voltage and it is given by

V_{fuel cell} = E_{thermo} - η_{act} - η_{ohmic} - η_{conc}

(1)

where E_thermo is the thermodynamically predicted voltage of fuel cell, η_act is the activation loss, η_ohmic is the ohmic losses from the ionic and electronic resistance, η_conc is the concentration loss due to mass transport.^10,11

Study area and renewable energy resources for hybrid system

Many parts of India, including central region have wind and solar energy available in abundance. Sagar district lies at the northeastern edge of the Malwa plateau, which widens in the south and southwest. The weather data are significant inputs for the pre-feasibility study of renewable hybrid energy system for any particular site. The wind and solar energy resources data are taken from a database for the city of Sagar-Central India.^12,13

The state of M.P. is not blessed with an excellent potential of wind, but bears an excellent potential of solar energy with approximately 275 sunny days in a year. This yielded estimation for a hybrid regime of PV and wind energy to keep the police station well lit round the year. The availability of renewable energy resources of police control room sites is an important factor to develop the hybrid system.¹⁴ Figure 1 presented solar radiation and wind velocity data of Sagar city. These energy sources are intermittent and naturally available and hence become the first choice to power the remotely located police control room sites.

Figure 1.

Solar radiation and wind velocity data of the study area.

Standalone energy system

A hybrid energy system generally consists of primary renewable sources working in analog with a standby secondary renewable module and storage unit. Figure 2 shows the proposed scheme as implemented in the HOMER simulation tool. HOMER, the micro power optimization model, simplifies the task of evaluating design of both off-grid and grid tied power systems for a variety of applications and general scheme is reflected in the HOMER model. Solar and wind system works as renewable energy sources, the battery is used for storage purpose and backup is provided by the diesel generator.

Figure 2.

Hybrid system components.

A model with inputs which describe technology options, component costs, and resource availability is created. Homer uses these inputs to simulate different system configuration or combinations of components and generate results that can be viewed as a list of feasible configurations sorted by net present cost. Simulation results in a full diversity of tables and graphs are also displayed that can help compare configurations and evaluate them on their economic and technological virtues.

Electrical load

A survey was conducted to identify energy consumption in a typical grid-connected police control room in central India.It consumes around 17 KWh/d with a peak demand of 1.5 KW. Figure 3 presents seasonal load profiles of police control room in Sagar. Meeting such a load by only renewable or hybrid energy sources is not practical, especially in a city area. A set of energy consumption data for a typical grid-connected police control room in Sagar collected samples at every 1 h for 365 days of a year. In a typical day, energy consumption is higher in the morning 6 a.m. to 10 a.m. and in evening 6 p.m. to 11 p.m.

Figure 3.

Seasonal load profile of study area.

Hybrid system component

Photovoltaic systems

In the solar resource input window, global horizontal radiation specifies for each time step. So at each time step, HOMER must calculate the global solar radiation incident on the surface of the PV array. If the effect of temperature on the PV array is not considered then HOMER assumes the temperature coefficient of zero. The initial cost of PV array may vary from $1 to $2/W. A more optimistic case, a 3 KW solar energy system installation cost is $3163 and the cost of replacing a component at the end of its lifetime is $2846. Three different sizes are considered, which are 3 KW, 6 KW, 8 KW and the life time of the PV array is taken as 20 years.⁹

Wind turbine

Choosing a suitable model is very important for wind turbine power output simulations. The wind resource input window is used to describe the available wind resources and HOMER uses this data to calculate the output of the wind turbine each hour of the year. Figure 1 represents wind resource data of case study. The baseline data are the set of 8760 values representing the average wind speed expressed in m/s and for each hour of the year, HOMER displays the monthly average data from the baseline in the wind resource table and graph. In this analysis, SW Whisper 500 model is considered with a rated capacity of 3 KW having rotor diameter of 4.5 m. The cost of one unit is considered to be $13,000 and the cost of replacing a component at the end of its lifetime is $11,000. To allow the simulation program of overall system to find an optimum solution, provision for using 0 (no turbine) or 1 unit is used.

Battery

When the power generated by WGs and PVs are greater than the load demand, the surplus power will be stored in the storage batteries for future use. On the contrary, when there is any deficiency in the power generation of renewable sources, the stored power will be used to supply the load. This will enhance the system reliability.

In the HOMER, battery window displays the properties of the selected battery type. HOMER models the battery as a two-tank energy storage device and calculates the parameter of a system that best fits the data given in the capacity curve. Commercially available models such as Surrette battery S460 (6 V, 460 Ah, 2.76 KWh) are considered here for analysis. Capital cost of 1 battery is $350, and for 12 no. of batteries, the capital cost is $4200. The round trip efficiency is 80% and minimum state of charge is 40%. The maximum charge rate is 1 A/Ah and the maximum charge current is 18 A.⁹

Converter

Any system that contains both AC and DC elements requires a converter. Curve input window defines the curve of that converter. Homer will use the information that entered in the cost table to estimate the costs of each converter size. Here converter is applied which can work both as an inverter and rectifier depending on the direction of the flow of power. In the present instance, the size of the converter ranges from 0 to 4 KW for simulation purposes. Cost of 1 KW unit is considered to be $200 and the cost of replacing a component at the end of its lifetime is $160.^15,16

Diesel generator

The cost of a commercially available diesel generator may vary from $600 to $950/KW. Cost of 3.5 KW unit is considered to be $2100 and the cost of replacing a component at the end of its lifetime is $1300.

Economics and constraints

Regarding the project lifetime to be 25 years, the annual real interest rate is taken as 6%. The maximum annual capacity shortage is 1% and operating reserve as a percentage of hourly load is 6.5%, where maximum annual capacity shortage is the maximum allowable value of the capacity shortage fraction which is the total capacity shortage divided by the total electric load. The Ministry of New & Renewable Energy has been providing incentives/subsidy for the number of renewable energy products/systems available in the market to make these products affordable to consumers. Figure 4 shows that best configuration according to HOMER optimization is the result of PV-Wind hybrid renewable energy system.^17,18

Figure 4.

Optimization result of PV-wind hybrid system.

Reliability analysis of study area

It is defined as the probability that an item performs the required function for an intended period of time under given environmental and operational condition. To get the real profit of renewable energy system and confidence by continual working of the hybrid system to supply the load, we require to calculate the system reliability.

Reliability is explained as the probability of equipment and given that the system performs its purpose adequately for the intended operating period of time. Renewable energy system reliability is defined as the ability of renewable energy system to supply the system load with reasonable consistency and quality of supply.^19,20

Major subdivisions of renewable energy system reliability are ‘system sufficiency’ and ‘system safety’. The term system sufficiently related to the existence of sufficient of facilities within the system to satisfy the consumer load demand and system operational constraints.

Reliability analysis of weather data in study location

Based on weather data, we measure the reliability analysis of a specified location. Based on solar radiation and wind velocity data, it is realized in specified location in March, April and May that PV system is working in a more convenient way to compare the wind energy system. We experience that wind energy system worked in a more convenient way, if the wind velocity lies between 5 m/s and 25 m/s. Merely in the specified location with reference to Table 1, in October, November and December, wind velocity is less than 5 m/s and in September, it is nearly about 5 m/s. Average solar radiation and average wind velocity of the study area are 5.404 and 5.46, respectively. Table 1 shows the reliability index and the failure rate of individual solar and wind energy system and total failure rate and reliability of hybrid renewable energy system. Based on solar radiation and wind velocity, data show that reliability of solar system and wind system is 96.5% and 97.97%, respectively, and reliability of total system based on weather data is 94.67%. Table 2 shows that reliability analysis is based on monthly load profile. Data show that according to the load consumption, optimized system is 98.35% reliable.

Table 1.

Reliability analysis based on weather data.

Month	Solar Radiation	Reliability Index	Failure Rate	Reliability %	Wind Velocity	Reliability Index	Failure Rate	Reliability %	Total Failure Rate	Reliability %
January	4.55	0.83	.17	91.85	5.35	.99	.01	99	.18	91.4
February	5.42	1.003	0	100	5.53	1.02	0	100	0	100
March	6.14	1.13	0	100	5.65	1.03	0	100	0	100
April	6.83	1.26	0	100	5.92	1.08	0	100	0	100
May	6.96	1.28	0	100	6.27	1.148	0	100	0	100
June	5.95	1.10	0	100	6.26	1.146	0	100	0	100
July	4.85	.898	.102	95	5.85	1.07	0	100	.102	95
August	4.25	.787	.213	90	5.34	.978	.022	98.9	.235	89
September	5.14	.95	.05	97	5.07	.928	.072	96.46	.122	94
October	5.67	1.05	0	100	4.59	.840	.16	92.3	.16	92.3
November	4.79	.88	.12	94.25	4.70	.860	.14	93.2	.26	87.8
December	4.30	.796	.204	90	4.99	.914	.086	95.8	0.29	86.5
				96.5				97.97		94.67

Table 2.

Reliability analysis based on monthly load profile of study area.

Month	Load (KW)	Reliability index	Failure rate	Reliability %
January	1.3	1.04	.04	98
February	1.5	1.2	.2	90
March	1.2	.96	0	100
April	1.15	.92	0	100
May	1.25	1	0	100
June	1.38	1.104	.104	95
July	1.32	1.056	.056	97.2
August	1.02	.816	0	100
September	1.25	1	0	100
October	1.2	.96	0	100
November	1.18	.944	0	100
December	1.27	1.016	0	100

Reliability analysis by fault tree analysis

Reliability is defined as the probability of a device or system performing its purpose adequately for the intended operating period of time. There are different reliability and prediction analysis which is used in a study such that reliability block diagram, fault tree analysis and Markov analysis.^21,22

In this paper, we used fault tree analysis for the reliability assessment of the study area. Fault tree analysis is a systematic and stylized process in which undesired event is defined. In this analysis, event is resolved into its immediate causes and the resolution of events continues until basic causes are identified.

The fault tree explicitly shows all the different relationships that are necessary to result in the top event. It is also a tangible record of the systematic analysis of the logic and basic causes leading to the top result. Fault tree provides a framework for a qualitative and quantitative evaluation of the top event.²³

The four necessary steps to begin a fault tree

Define the undesired event to be analyzed.

Define the boundary of the system.

Define the basic causal events to be considered.

Define the initial state of the system.

Causes of failure in hybrid renewable energy system

Reliability analysis is a well-developed statistical tool for predicting the system performance in many industries. There are several tools used for reliability prediction, but fault tree analysis provides a diagrammatic representation of a system’s reliability. The aim is to calculate the probability of a critical fault occurring because fault tree analysis provides a static depiction of the combinations of failures and consequences that can cause the specified critical fault to occur.^24,25

Figure 5 represents a fault tree analysis of solar-wind hybrid renewable energy system. Fault tree basically divides into three types: (i) top undesired event (ii) intermediate event (iii) basic event. In this analysis, top undesired event is hybrid renewable energy system which does not develop sufficient amount of energy. In another way, solar-wind renewable energy system does not fulfill the load demand. In this paper, we develop fault analysis in two ways, first related to wind energy and the second one is a solar energy system.

Wind energy system

Reliability and performance of wind energy system are mainly affected by bad environment condition and unimproved power quality. A wind velocity fluctuates with time and for proper electric power generation, the minimum average wind speed required is 5 m/s. A site is not favourable for wind power generation, if the wind velocity is less than 5 m/s and more than 25 m/s. Reliability of the system is also affected due to the distribution of wind energy on the surface of the earth and variation of wind speed with height. The standard wind speed measurements are often held at a height of 10 m from the earth.

Failure of wind energy system is due to unimproved power quality and it extensively affects the reliability of whole hybrid renewable energy system. Disturbance in power quality occurs due to the tower shadow effect, wind turbulence and switching of wind mills. A tower shadow effect is aggravated in wind power farms consisting of several windmills due to a tendency of the wind mills to operate in synchronism with each other, particularly in cases where the fault level of the system is weak.

Solar energy system

Performance and reliability of solar energy system are affected due to bad environment condition and unimproved power quality. The solar energy system output is directly proportional to the solar intensity; if solar insolation is not at the desired level then the system does not fulfill the desired load demand.

Some variables such as daily hour by hour solar insolation variation, seasonal variation, degree of latitude of the location and clarity index also affect the reliability of system. If the spectral content of the radiation remains unaltered and all other factors remain same, both short circuit current and open circuit voltage increase with increasing the intensity of radiation. Therefore, the short circuit current depends linearly, while the open circuit voltage depends logarithmically on the insolation.²³ Sometime component fault is responsible for the detritions of reliability of the system due to following reason,

Bad characteristics of active material of PV cell.

Improper junction structure of PV cell.

Some problem in texturization of the surface of material.

For better reliability of the solar system and hybrid system, some desirable condition is following:

The temperature of the PV array is uniform over the entire array.

The wind and ambient temperature effects on PV array were neglected.

The effect of albedo was neglected.

PV inverter efficiency was assumed to be 95%.

The insolation is uniform across the entire PV array.

Effects of shading are neglected.

The PV array is south facing only.

Reliability measurement

According to fault tree analysis (Figure 5) is total failure rate is given by in equation below:

Figure 5.

Fault tree analysis of hybrid renewable energy system.

From the below equation (Figure 5), we conclude

\begin{matrix} O . P . I + S + T + U + V + M . N + K + L + (LL) (MM) (NN) + Z (AA) + (HH) (II) (JJ) \\ + (FF) . (GG) + (BB) . (CC) \end{matrix}

(2)

According to the data of Table 3, put the different value of failure rate in equation (9)

\begin{array}{l} Total failure rate = A = (0.00 11 * .0 3 * .0 25) + (.00 1) + (.00 1) + (0.0 35) + (0.0 22) + (0.0 19 * 0.0 22) \\ + (0.0 22) + (0.0 25) + (0.0 55 * 0.0 55 * 0.0 55) + (0.00 15 * 0.00 15) \\ + (0.00 18 * 0.00 18 * 0.00 18) + (0.0 45 * 0.0 45) + (0.0 25 * 0.0 25) \end{array}

Total failure rate = 0. 109 * 100 = 1 0. 9

Table 3.

Fault condition and failure rate of hybrid renewable energy system.

SYMBOL	CONDITION OF FAULT	EVENTS/ FAILURE RATE
A	Hybrid RES does not develop sufficient amount of energy	Top events
B	WES does not work properly	Intermediate events
C	Hybrid system is primary failed	Intermediate events
D	SES does not worked properly	Intermediate events
E	Bad environment condition	Basic events
F	Component fault in wind energy system	Basic event
G	Unimproved power quality	Basic event
H	Effect of velocity	.0408
I	Effect of temperature	0.025
J	Tower shadow effect	.022
K	Wind turbulence	.022
L	Switching of wind mills	.025
M	Wind turbine blade	.019
N	Due to synchronism of wind mill	.022
O	Variation due to surface of earth	.0011
P	Variation with Height	.03
Q	Wind Turbine performance	Basic event
R	Controller in solar system	Basic event
S	Deteriorate the performance of wind turbine	0.001
T	Uncontrolled operation of controller	0.001
U	Improper arrangement of converter with wind energy system	0.035
V	Improper switching regulator with wind energy system	0.022
W	Bad environment condition	Basic event
X	Component fault	0.045
Y	Unimproved power quality	Basic event
Z	Effect of variation of insolation	0.0015
AA	Effect of variation of temperature	0.00155
BB	Voltage fluctuation	0.025
CC	Current fluctuation	0.025
DD	Fault in PV arrangement	0.055
EE	Controller in solar system	Basic event
FF	Improper arrangement of converter with solar energy system	0.045
GG	Improper switching regulator with solar energy system	0.045
HH	On the basis of thickness of active material of PV system	0.0018
II	On the basis of junction structure of PV system	0.0018
JJ	On the basis of type of active material of PV system	0.0018
KK	Unbalance of system component	Basic event
LL	Improper distribution panel of hybrid system	0.055
MM	Improper wiring and connector of hybrid system	0.055
NN	Improper arrangement of junction box of hybrid system	0.055

According to the fault tree analysis, the fault rate is .109 which shows that based on all the faults, the system is 90% reliable. Based on solar radiation and wind velocity, the data show that reliability of solar system and wind system is 96.5% and 97.97%, respectively, and reliability of total system based on weather data is 94.67%.

Conclusion

In this paper, optimization and reliability assessment of the study area is considered. HOMER is used for the optimization purpose and reliability assessment is done by the fault tree analysis.

The following results are finding out by both the analysis:

Solar resources in Sagar (India) bear excellent potential compared to wind energy and utilization of wind resources might not be cost effective in most cases.

PV-wind-diesel-battery system is the most feasible solution for standalone application in Sagar from an environmental point of view.

From the net present cost point of view, PV-diesel-battery system is the feasible solution for the case under consideration.

Based on solar radiation and wind velocity, data show that reliability of solar system and wind system is 96.5% and 97.97% respectively, and reliability of total system based on weather data is 94.67%.

Data show that according to the load consumption, optimized system is 98.35% reliable.

According to the fault tree analysis, fault rate is .109 which shows that based on all the fault, the system is 90% reliable.

Footnotes

Authors' note

Vikas Khare is an associate professor in School of Technology, Management and Engineering, NMIMS, Indore MP, India. He is also a certified energy manager under the Bureau of Energy Efficiency, New Delhi, India.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Vikas Khare is an associate professor in School of Technology, Management and Engineering, NMIMS, Indore MP, India. He obtained his M.Tech (Honours) in Energy Management from DAVV Indore, India, and Ph.D. from National Institute of Technology Bhopal, India. His main research interests are renewable energy systems, optimization techniques and game theory. He is also a certified energy manager under the bureau of energy efficiency in India. Dr. Khare has published various research paper in respected journals and published books on renewable energy and fundamentals of electrical and electronics and one of the book on “Tidal Energy System” under the publication of Elsevier Publication USA.

Savita Nema has over 20 years of experience in research in renewable energy and control systems, including ME in Control Systems and PhD in Solar Photovoltaics. Dr. Nema has led several research projects, as well as published over 40 journal and conference papers. She is currently a Professor & Head at the Department of Electrical Engineering in MANIT, Bhopal, India.

Prashant Baredar is an associate professor in Energy Department, MANIT, in India. He achieved his PhD degree in Hybrid Energy System from Rajiv Gandhi Technological University Bhopal. Dr. Baredar has 20 years’ experience in Mechanical Engineering. He is in the editorial board of many international Journals: BLBIJEST and National Journal of Engineering Science and a reviewer for four international journals. He has successfully organized five national seminars and conferences on Energy topic and delivered 25 expert lectures & invited talks. He has guided 6 PhD thesis and 42 M.Tech thesis. He has published one patent on reconfigurable mechanism for wind turbine blade.

References

Jain

Balasubramanian

Tripathy

SC.

Reliability analysis of wind embedded power generation system for Indian scenario. Int J Eng Sci Tech 2011; 3: 93–99.

Dialynas

Daoutis

Toufexis

et al. Reliability and reserve capacity assessment of isolated power system with increased penetration of renewable energy system. 7th Mediterranean Conference and exhibition on power generation, transmission, distribution and energy conversion IEEE-IET; 7–10 November 2010, Agia Napa Cyprus.

Billinton

Karki

Maintaining supply reliability of small isolated power system using renewable energy. IEE Proc Gener Transm Distrib 2001; 148: 530–534.

Brown

Suryanarayan

Natarajan

SA.

Improving reliability of islanded distribution system with distributed renewable energy resources. IEEE Trans Smart Grid 2012; 3: 2028–2038.

Ardakani

Riahy

Abedi

Design of an optimum hybrid renewable energy system considering reliability indices. In: 18th Iranian conference on electrical engineering 11–13 May 2010, pp.842–847. Isfahan University of Technology, Iran.

Cristobal

JMS.

A multi criteria data envelopment analysis model to evaluate the efficiency of the renewable energy technologies. Renew Energ 2011; 36: 2742–2746.

Madlener

Antunes

Dias

LC.

Assessing the performance of biogas plants with multi-criteria and data envelopment analysis. Eur J Operat Res 2006; 197: 1084–1094.

Jose

Agustin

DufoLopez

Simulation and optimization of standalone hybrid renewable energy system. Renew Sustain Energ Rev 2009; 13: 2011–2018.

Khare Nema

Baredar

Optimization of hybrid renewable energy system by HOMER, PSO and CPSO for the study area. Int J Sustain Energ 2017; 36: 326–343.

10.

Khare Nema

Baredar

Optimization of hydrogen based hybrid renewable energy system using HOMER, BB, BC AND GAMBIT. Int J Hydrog Energ 2016; 41: 16743–16751.

11.

Gupta

AAI.

Feasibility of solar wind hybrid renewable energy in India. Int J Eng Res Gen Sci 2017; 5: 1–10.

12.

Saeed

Warkozek

Modeling and analysis of renewable PEM fuel cell system. Energy Proc 2015; 74: 87–101.

13.

Sagar district from Wikipedia, the free encyclopedia. Available at: http://hi.wikipedia.org/wiki/sagar

14.

Sagar Madhya Pradesh from Wikipedia, the free encyclopedia. Available at: http://en.wikipedia.org/wiki/sagar_madhya_pradesh

15.

National oceanic and atmospheric administration. Available at: http://en.wikipedia.org/wiki/National_oceanic_and_atmospheric_administration (accessed 22 December 2012).

16.

Bartolucci

Cordiner

Hybrid renewable energy system for renewable integration of microgrids: influence of seizing on performance. Energy 2018; 152: 744–758.

17.

Adefarati

Bansal

Reliability and Economic assessment of the microgrid power system with the integration of renewable energy resources. Appl Energ 2017; 206: 911–933.

18.

Mohammadi

Ghasempour

Optimal planning of renewable energy resources for a residential house considering economic and reliability criteria. Int J Elect Power Energ Syst 2018; 96: 261–273.

19.

Khan

Pal

Saeed

SH.

Review of solar photovoltaic and wind hybrid energy system for sizing strategies, optimization techniques and cost analysis methodologies. Renew Sustain Energ Rev 2018; 92: 937–947.

20.

Menniti

Burgio

Pinnarelli

et al . The reliability evaluation of a power system in presence of photovoltaic and wind power generation plants and UPS. In: Proceedings of EPQU, 9–11 October 2007, Barcelona.

21.

Billinton

Allan

RN.

Reliability assessment of large electric power systems. Switzerland: Kluwer Academic Publishers, 1988.

22.

Borges

CLT

Pinto

RJ.

Small hydro power plants energy availability modeling for generation reliability evaluation. IEEE Trans Power Syst 2008; 23: 1125–1135.

23.

Park

Liang

Choi

et al . A probabilistic reliability evaluation of a power system including solar/photovoltaic cell generator. IEEE Transac Power Syst 2009; 24: 1–6.

24.

Stamatelatos M and Velsely W. Fault tree handbook with aerospace application. Washington DC: NASA Publication, 2002.

25.

Billinton

Allan

Reliability evaluation of power systems. 2nd ed. New York: Plenum Press, 1996.

26.

Borges

CLT

Falcão

DM.

Optimal distributed generation allocation for reliability, losses, and voltage improvement. Int J Elect Power Energy Syst 2006; 28: 413–420.