9. Modeling and Simulation of a Sustainable Hybrid Energy System under Changing Power Reliability Index at User End

If the present policy on the use of coal, oil, and gas persist, then by the year 2020, the global temperature is expected to be increased by 2°C. The rise in temperature will result in flooding in lowland areas, increase in the process of desertification, and change in climate all over the world. Therefore, it is required to find the suitable sustainable alternative of fossil fuels. Renewable energy sources require no fossil fuels for power generation and, hence, produce the least negative impact on environment. These sources can be utilized in both utility grid mode and off-grid mode [1, 2, 3, 4, 5, 6, 7, 8, 9 and 10].

Aktas et al. [11] proposed a novel energy management algorithm for the hybrid energy storage system (HESS) supplied from a three-phase four-wire grid-connected photovoltaic (PV) power system. The considered system comprised battery and ultra-capacitor energy storage units for energy sustainability from the solar-based power generation system. They performed and analyzed eight different operation cases experimentally. They found that the developed algorithm supplied the required load power with the lower operational costs and higher efficiency of the system.

Goel and Sharma [12] presented a comprehensive overview on performance evaluation of a stand-alone, grid-connected, and hybrid renewable energy system for rural areas. They studied several issues of the stand-alone PV system, grid-connected PV system, hybrid energy system, optimization of hybrid system, and plug-in hybrid electric vehicle.

Rajbongshi et al. [13] performed the optimization of a PV/biomass/diesel based and grid-connected hybrid system for rural areas. They considered different load profiles for the size optimization of the system configuration. They found that the cost of energy generation for a grid-connected hybrid system was lower compared to that of an off-grid hybrid system for same pattern of load profiles. Also, they estimated the economic distance limit between grid extension and off-grid system.

Nojavan et al. [14] studied a PV/fuel cell/battery-based hybrid system along with upstream grid to meet out the electrical and thermal load. They have proposed an information gap decision theory (IGDT) technique to model the uncertainty of electrical load. Further, they formulated uncertainty model, robustness function, and opportunity function. Finally, they minimized IGDT-based risk-constrained operation cost of the hybrid system by considering electrical load uncertainty.

Mohamed et al. [15] suggested a particle swarm optimization (PSO) algorithm for the optimal design of hybrid PV-wind energy systems in grid-connected mode. They minimized the total investment cost of the system under the constraints of load-generation balance and loss of load probability as power reliability index. They also considered maximum power point tracking (MPPT) of PV array and wind turbine system. Based on hourly simulation, they found that the cost of supplying the load demand from the hybrid system connected to grid was lower than the cost of energy supplied from the grid only after 25 years.

Sanajaoba and Fernandez [16] investigated the size optimization of three schemes namely PV-battery, wind-battery, and PV-wind-battery system. They minimized the total system cost considering the seasonal changes of load and wind turbine force outage rate. Further, a comparison of results obtained from Cuckoo search algorithm with PSO and genetic algorithm (GA) was performed. Tito et al. [17] accounted socio-demographic load profiles while designing a wind-PV-battery based hybrid system. Based on the analysis, they found that the system cost was affected significantly by the magnitude and temporal positions of the peak demand.

Ahadi et al. [18] minimized the annual capital cost of a hybrid system consisting of wind and PV array resources. They optimized the cost under the constraints of operative reserve of 10% of the load, 50% of wind turbine output, and 25% of PV output. They found that battery bank storage compensated the fluctuations of renewable energy sources. Maleki et al. [19] conducted the size optimization of different combinations of renewable energy sources such as hybrid PV/wind turbine/fuel cell, PV/fuel cell systems and wind turbine/fuel cell. They included the swept area of wind turbine and PV panels and number of storage tanks as decision variables. They minimized the life cycle cost (LCC) by filling the maximum allowable loss of power supply probability.

This chapter presents the modeling and simulation of a sustainable hybrid energy system for different values of power reliability index at user end. Mathematical modeling of the considered system components is discussed in Section 9.2. Further, objective function and constraints are modeled in Section 9.3. Technical and economical data required for this study are given and explained in Section 9.4. The algorithm employed for the optimization of the system is discussed in Section 9.5. Finally, results and discussions for different values of power reliability are summarized in Section 9.6. The main findings of the study are given in Section 9.7.

9.2 Study Area

In this chapter, a small unelectrified village located in the Bijnor district of Indian state of Uttar Pradesh is considered as the study area. The study area is located at the latitude of 29.47°N and longitude of 78.11°E. The population of the village is 421 with a total of 84 households [20].

This village has abundant potential of solar and biomass energy. It receives solar radiation of around 5.14 kWh/m²/day with more than 300 sunny days. Also, the study area is surrounded by forest. Therefore, a huge amount of biomass in terms of forest foliage and crop residue is available which can be used for the operation of biomass-operated generator. Utilization of these resources in grid-connected environment is recognized as an attractive option to fulfill the domestic energy demand of the village.

9.3 Mathematical Modeling

A configuration of the hybrid system is considered in order to supply energy to the rural households as shown in Figure 9.1. Besides PV array and biomass-operated generator, grid is also incorporated in the system which can supply the deficit load that cannot be met out by the available resources. Also, the surplus electricity can be sold to grid in case available generation exceeds the load demand. Converter is included in order to alter the DC power into AC power.

9.3.1 Biomass-Operated Generator

Power output of a biomass generator depends upon the availability of biomass, calorific value, and operating hours in day. The mathematical model for the power output of the biomass generator is given by following equation:

$\begin{matrix} P_{B} = \frac{Q_{B} \times {CV}_{B} \times η_{B} \times 1000}{365 \times 860 \times H} \end{matrix} (9.1)$

where Q_B is the availability of forest foliage (tons/year), η_B is the conversion efficiency (20%), CV_B is the calorific value of biomass (kcal/kg), and H is the daily operating hours. The factor of 1/860 is used to convert kcal into kWh.

Images

FIGURE 9.1
Schematic of grid connected PV-biomass based hybrid energy system.

9.3.2 PV Array

The power generated from a PV system depends upon different parameters such as incident solar radiation and atmospheric temperature. A mathematical model of PV array is described by following equation:

$\begin{matrix} P_{PV} (t) = [N_{PV} \times V_{OC} (t) \times I_{SC} (t) \times FF] / 1000 \end{matrix} (9.2)$

where P_PV(t) is the power output of PV array at tth hour, N_PV is the number of PV modules, V_OC is the open-circuit voltage, I_SC is the short-circuit current, and FF is the fill factor.

Short-circuit current and open-circuit voltage at any time ‘t’ can be calculated as

$\begin{matrix} I_{SC} (t) = [I_{SC, STC} + K_{I} {T_{C} (t) - 25}] \frac{β (t)}{1000} \end{matrix} (9.3)$

$\begin{matrix} V_{OC} (t) = V_{OC, STC} - K_{V} T_{C} (t) \end{matrix} (9.4)$

where I_{SC, STC} is the short-circuit current under STC, K_I is the short-circuit current temperature coefficient, T_C is the cell temperature, $β$ is the hourly average solar radiation (W/m²), V_{OC, STC} is the open-circuit voltage under STC, and K_V is the open-circuit voltage temperature coefficient.

The cell temperature of the PV module can be calculated as

$\begin{matrix} T_{C} (t) = T_{A} (t) + (\frac{NCOT - 20}{800}) β (t) \end{matrix} (9.5)$

where NCOT is the nominal cell operating temperature (43°C) and T_A is the ambient temperature.

9.3.3 Utility Grid

In the considered hybrid system, utility grid is incorporated in order to maintain the power reliability at the user end. At hour ‘t’, when available generation is more than the load demand, the surplus amount of energy can be sold to grid which can be mathematically modeled as

$\begin{matrix} E_{EE} (t) = [(E_{PV} (t) \times η_{I}) + E_{BM} (t) - E_{Load} (t)] \end{matrix} (9.6)$

$\begin{matrix} E_{GS} (t) = E_{EE} (t) \end{matrix} (9.7)$

where E_GS is the amount of electricity sold to grid, E_EE is the excess electricity, $η_{I}$ is the inverter efficiency, E_PV, E_BM, E_Load, respectively, represent hourly PV array generation, biomass gasifier generation and load demand.

When available generation from PV array and biomass generator is not able to fulfill the demand, the remaining deficit demand is supplied by the utility grid as

$\begin{matrix} E_{DE} (t) = E_{Load} (t) - [(E_{PV} (t) \times η_{I}) + E_{BM} (t)] \end{matrix} (9.8)$

$\begin{matrix} E_{GP} (t) = E_{DE} (t) \end{matrix} (9.9)$

where E_DE is the hourly deficit electricity and E_GP is the grid purchase electricity.

9.4 Problem Statement

The techno-economic viability of any project depends on the total cost. Therefore, minimization of total cost (TC) of grid-connected hybrid energy system is considered as the objective function. The total cost has been optimized under technical, social, and environmental constraints.

9.4.1 Objective Function

The total cost of hybrid system is the sum of costs of individual system components during the lifetime of the project and it can be calculated as

$\begin{matrix} TC = C_{PV} + C_{BM} + C_{Conv} + C_{grid, sale} - C_{grid, pur} \end{matrix} (9.10)$

where C_PV, C_BM, C_Conv, respectively, represent the cost of the PV array system, biomass gasifier system, and converter, C_{grid, sale} is the total revenue from grid sale, and C_{grid, pur} is the total cost of grid purchase.

The total cost of PV array, biomass system, and converter can be calculated by following equations:

$\begin{matrix} C_{PV} = \sum_{i = 1}^{N_{PV}} (A_{i} P_{i} \times CRF) + OM (P_{i}) + REP (P_{i}) \end{matrix} (9.11)$

$\begin{matrix} C_{BM} = \sum_{j = 1}^{N_{BG}} (A_{j} P_{j} \times CRF) + OM (P_{j}) + REP (P_{j}) \end{matrix} (9.12)$

$\begin{matrix} C_{Conv} = \sum_{k = 1}^{N_{Conv}} (A_{k} P_{k} \times CRF) + OM (P_{k}) + REP (P_{k}) \end{matrix} (9.13)$

where CRF is the capital recovery factor, N_PV, N_BG, and N_Conv, respectively, are the numbers PV panels, biogas generators, and converter; A_i, A_j, A_k are the unit cost (INR/kW); P_i, P_j, P_k are the required power capacity (kW); REP(P_i), REP(P_j), REP(P_k) are the replacement cost and OM(P_i), OM(P_j), OM(P_k) are the operation and maintenance (O&M) cost.

The capital recovery factor (CRF) can be determined as

$\begin{matrix} CRF = \frac{R_{0} {(1 + R_{0})}^{n}}{{(1 + R_{0})}^{n} - 1} \end{matrix} (9.14)$

where n is the system lifetime and R₀ is the interest rate.

The excess electricity can be sold to grid to earn revenue which is estimated:

$\begin{matrix} C_{grid, sale} = \sum_{d = 1}^{365} \sum_{t = 1}^{24} [E_{gs} (d, t) \times c_{gs}] \end{matrix} (9.15)$

where E_gs(d, t) is the grid sale at hour ‘t’ of day ‘d’ and c_gs is the price of grid sale (INR/kWh).

The deficit amount of electricity can be purchased from the grid and the total cost of grid electricity purchase is calculated as

$\begin{matrix} C_{grid, pur} = \sum_{d = 1}^{365} \sum_{t = 1}^{24} [E_{gp} (d, t) \times c_{gp}] \end{matrix} (9.16)$

where E_gp(d, t) is the grid purchase at hour ‘t’ of day ‘d’, and c_gp represent the price of grid purchase (INR/kWh).

The per unit cost of electricity generation (COEG) for the considered system can be estimated as

$\begin{matrix} COEG = \frac{TC}{E_{D} + E_{GS}} \end{matrix} (9.17)$

where E_D is the annual demand (kWh) and E_GS is the annual electricity sold to grid (kWh).

9.4.2 Operating Constraints

The total cost of the hybrid system is optimized under the following constraints:

9.4.2.1 Upper and Lower Limit of Power Output

The power output of individual component of the system depends on the number of the units. Therefore, the limits of power output of PV array, biomass generator, and converter are described by the following constraint as:

$\begin{matrix} 0 \leq N_{PV} \leq N_{PV, max} \end{matrix} (9.18)$

$\begin{matrix} 0 \leq N_{BG} \leq N_{BG, max} \end{matrix} (9.19)$

$\begin{matrix} 0 \leq N_{Conv} \leq N_{Conv, max} \end{matrix} (9.20)$

where N_{PV, wmax}, N_{BG, max}, and N_{Conv, max}, respectively, represent the maximum numbers of PV modules, biomass generator unit, and converter unit.

9.4.2.2 Grid Sale and Grid Purchase Constraint

The upper limit of grid sale and grid purchase of electricity in hybrid system are considered that can be expressed as

$\begin{matrix} E_{gs} (t) \leq E_{gs, max} \end{matrix} (9.21)$

$\begin{matrix} E_{gp} (t) \leq E_{gp, max} \end{matrix} (9.22)$

where E_{gs, max} and E_{gp, max} are the upper limit of grid sale and grid purchase of electricity at any hour.

9.4.2.3 Power Reliability Constraint

In this study, the system is designed such that it must fulfill the hourly load demand of the area through the local generation and utility grid. Therefore, unmet load (UL) has been incorporated as the power reliability constraint. It can be determined as

$\begin{matrix} UL = (\frac{Non-served load for a year}{Total load for a year}) . \end{matrix} (9.23)$

9.4.2.4 Greenhouse Gas Emission

The greenhouse gas emission generated by a hybrid energy system in grid environment has been incorporated as environmental constraint. In this study, emission from the utilization of solar PV, biomass gasifier and grid electricity is considered.

9.5 Optimization Algorithm

In the literature, many metaheuristic algorithms are reported for the size optimization of hybrid energy systems as these algorithms can handle the linear and nonlinear variations of the system components. Metaheuristic algorithms such as GA, PSO, ant colony optimization (ACO), simulated annealing (SA), harmony search (HS), etc. are extensively used. Among all the algorithms, PSO offers high convergence rate with less time.

Therefore, the PSO algorithm has been used for the optimal design of the considered grid-connected hybrid system. This algorithm is originally discovered by Kennedy and Eberhart in the year 1995. The PSO algorithm searches the global optimum solution vector of a problem based on the concept of social behavior of bird flocking fish schooling, etc.

Stepwise implementation of the PSO algorithm is described as follows [21,22]:

Step 1: The position and velocity of different particles are decided with the help of random variables. The values are generated between the upper and lower limits of the decision vectors.

Step 2: Further, the initial position of individual particle is selected as its pbest. Out of which, gbest has been chosen as the best particle among the total population considered in the algorithm.

Step 3: At each iteration, the velocity of individual particle is modified as

$v_{k}^{(t + 1)} = γ \times (w \times v_{k}^{(t)}) + c_{1} \times rand () \times (pbest - x_{k}^{(t)}) + c_{2} \times rand () \times (gbest - x_{k}^{(t)}) .$

Also, the position of individual particle is modified as

$x_{k}^{(t + 1)} = x_{k}^{(t)} + v_{k}^{(t + 1)}, k = 1, 2, 3, \dots, N$

where rand () is the uniform random values between 0 and 1, t is the iteration index, $γ ε [0, 1]$ , $v_{k}^{(t)}$ is the velocity of kth particle at generation t, $x_{k}^{(t)}$ is the current position of kth particle in generation t, w is the inertia weight factor, N is the number of particles in a swarm, c₁ and c₂ are acceleration constants.

Step 4: If the particle crosses the lower and upper limit of allowed range, it is replaced by previous values.

Step 5: Further, the value of objective function is estimated for each particle. At each iteration, pbest and gbest are updated.

Step 6: Finally, simulation is terminated as the stopping criteria is reached.

Based on the steps discussed above, a flowchart of PSO algorithm is prepared, shown in Figure 9.2.

9.6 Database

9.6.1 Hourly Load Demand of the Study Area

Hourly load demand of the study area is depicted in Figure 9.3. Peak demand for season 1, season 2, and season 3 are estimated as 44.57, 36.07, and 22.63 kW, respectively. The total demand of the area is calculated as 209,295 kWh/year. Among all the seasons, the study area has the highest energy demand during season 1, while the lowest energy demand has been recorded for season 3. Season-wise daily energy demand of the area has been estimated as 755, 640, and 320 kWh for season 1, season 2, and season 3, respectively.

Images

FIGURE 9.2
Flowchart of PSO algorithm.

Images

FIGURE 9.3
Hourly load profile of the study area.

9.6.2 Hourly Solar Potential

Hourly solar radiation availability in the study area for different seasons is shown in Figure 9.4. It has been observed that the highest radiation of 800, 700, and 600 W/m² are recorded during season 1, season 2, and season 3, respectively. The Hourly average temperature for the area is shown in Figure 9.5. It has been found that the highest temperature for season 1, season 2, and season 3 are 36.3°C, 33.8°C, and 24°C, respectively. The season-wise average temperature are recorded as 36.3°C, 33.8°C, and 24°C, respectively 27.9°C, 28.4°C and 15.9°C, respectively [23].

Images

FIGURE 9.4
Hourly average solar radiation availability in the study area [23].

Images

FIGURE 9.5
Hourly average temperature of the study area [23].

9.6.3 Biomass Potential

Biomass potential depends upon the biomass availability in the study area and operating hours. In this study, total biomass availability and operating hours per day are considered as 100 tons/day and 10 h/day. Accordingly, the size of biomass gasifier-based generator has been estimated.

9.6.4 Technical and Economical Data of System Components

Technical and economical data of different system components are given in Tables 9.1–9.3. Economical data include capital cost, replacement cost, and O&M cost of system components. Technical data consist of rating, lifetime, and other specifications of system components. During simulation, 300 W_p PV module, 1 kW size of biomass gasifier system, and 1 kW converter have been considered. Prices of grid sale and grid purchase are taken as INR 6.50 per kWh and INR 3.25 per kWh, respectively, as given in Table 9.4.

Annual real interest rate of 6% and project lifetime of 25 years have been considered in this study.

9.6.5 CO₂ Emission Rate

Emission from the utilization of solar PV, biomass gasifier, and grid purchase for electricity generation are considered and its rates are given in Table 9.5. As grid electricity is highly dependent on coal-based power plant in the area, the emission rate of grid purchase electricity is the highest among all the considered technologies.

TABLE 9.1 Techno-Economical Data of PV Array [24]

Images

TABLE 9.2
Techno-Economical Data of Biomass Gasifier System [25]

S. No.	Indicators	Unit	Value
1	Capital cost	INR/kW	45,000
2	O&M cost	INR/kW	2,250
3	Replacement cost	INR/kW	45,000
4	Lifetime	year	5

TABLE 9.3
Techno-Economical Data of Converter [26]

S. No.	Indicators	Unit	Value
1	Capital cost	INR/kW	3000
2	O&M cost	INR/kW	0
3	Replacement cost	INR/kW	3000
4	Lifetime	year	10

TABLE 9.4
Price of Grid Sale and Grid Purchase

S. No.	Indicators	Unit	Value
1	Price of grid sale	INR/kWh	6.50
2	Price of grid purchase	INR/kWh	3.25

TABLE 9.5
CO₂ Emission Rate for Different Technologies

S. No.	Energy Technologies	CO₂ Emission (g/kWh)
1	PV array system	130
2	Biomass gasifier system	20
3	Grid electricity	955

9.7 Results and Discussions

The considered configuration of the hybrid system is optimized using the PSO algorithm for different values of power reliability. Codes are developed in MATLAB environment to obtain the optimum size of system components. Based on hourly simulation, the optimum sizes for different values of power reliability have been reported in Table 9.6.

9.7.1 Optimum Size of Energy System Model

In the hybrid system, both PV array and biomass resources along with utility grid are considered to supply the energy demand of the end user. In simulation, hourly data of load demand, hourly solar radiation, temperature, and biomass generator output are used as input. For 0% UL, the optimum total cost is calculated as INR 1.1933 million at the COEG of INR 5.28 per kWh. The optimum size of system components are obtained as 48.90 kW PV array, 24 kW biomass gasifier system, and 40 kW converter. The annual electricity from grid purchase and sale are estimated as 55,168 and 16,644 kWh.

TABLE 9.6
Optimum Size of System Components

Images

Further, the value of power reliability has been changed from 0% to 20% UL. It has been found that the cost of energy of the system varies from INR 5.28 per kWh to INR 4.30 per kWh for the UL changing from 0% to 20%. The optimum sizes of hybrid systems for different power reliability values are reported in Table 9.6.

9.7.2 Breakdown of the Total Cost

Breakdown of the total cost for 0% UL is given in Table 9.7. It has been found that the revenue from grid sale is maximum which accounts for INR 54,092 per year. It has been observed that the considered system needs grid purchase of INR 358,593. The contribution of biomass gasifier in total cost is found to be the highest as INR 476,420 followed by PV array with INR 384,260, grid purchase with INR 358,593, grid sale with INR 54,092, and converter with INR 28,162.

9.7.3 Percentage-Wise Contribution of System Components in Total Cost

Percentage-wise contribution of different components in total cost for 0% UL is depicted in Figure 9.6. It has been found that the contribution of a biomass gasifier system is maximum which accounts for 37% of the total cost followed by PV array system with 29%, grid purchase with 28%, grid sale with 4%, and converter with 2%. As the replacement cost of biomass gasifier system is the highest, it has the major share in total cost.

TABLE 9.7 Breakdown of Total Cost for 0% Unmet Load

Images

FIGURE 9.6
Percentage-wise contribution of different components in total cost for 0% unmet load.

Images

FIGURE 9.7
Season-wise electricity generation of resources/grid sale/grid purchase for 0% unmet load.

9.7.4 Electricity Generation of Resources/Grid Sale/Grid Purchase on Seasonal Basis

Season-wise generation of different resources/grid sale/grid purchase for the hybrid system is shown in Figure 9.7. It has been observed that a PV array system produces the highest amount of electricity as 37,996 kWh during season 1. While it generates minimum electricity of 22,965 kWh during season 3 due to low availability of solar radiation. The generation from biomass gasifier remains consistent throughout the year. It has been calculated as 29,280, 29,520, and 28,800 kWh for season 1, season 2, and season 3, respectively. The grid sale and grid purchase for each season are also depicted in Figure 9.6.

9.8 Conclusions

This chapter is focused on the modeling and simulation of a grid-connected PV/biomass based hybrid system for an unelectrified village of India. A mathematical model of each system component is presented in detail. Furthermore, the total cost of the system has been formulated by combining capital cost, maintenance cost, replacement cost, grid sale price, and grid purchase price. The total cost has been optimized under the technical, environmental, and power reliability constraints.

Seasonal changes in solar radiation, temperature, and load demand are incorporated in the study. Furthermore, the considered system is optimized for different values of power reliability. It has been found that the cost of generation was reduced with increase in the value of UL. Further, grid sale and grid purchase for different seasons are calculated.

The optimal model consists of 48.90 kW_p PV array system, 24 kW biomass generator, and 40 kW converter. The total cost of this combination has been calculated as INR 1.1933 million at the COEG of INR 5.28 per kWh. The total grid purchase and grid sale for this model are obtained as 55,168 and 16,644 kWh/year, respectively. Therefore, this configuration is recommended for energy access in the area. The results obtained in this study may be helpful for the design and development of hybrid system for other similar unelectrified rural households.

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Table of Contents for
9. Modeling and Simulation of a Sustainable Hybrid Energy System under Changing Power Reliability Index at User End

9

Modeling and Simulation of a Sustainable Hybrid Energy System under Changing Power Reliability Index at User End

CONTENTS

9.1 Introduction

9.2 Study Area

9.3 Mathematical Modeling

9.3.1 Biomass-Operated Generator

9.3.2 PV Array

9.3.3 Utility Grid

9.4 Problem Statement

9.4.1 Objective Function

9.4.2 Operating Constraints

9.4.2.1 Upper and Lower Limit of Power Output

9.4.2.2 Grid Sale and Grid Purchase Constraint

9.4.2.3 Power Reliability Constraint

9.4.2.4 Greenhouse Gas Emission

9.5 Optimization Algorithm

9.6 Database

9.6.1 Hourly Load Demand of the Study Area

9.6.2 Hourly Solar Potential

9.6.3 Biomass Potential

9.6.4 Technical and Economical Data of System Components

9.6.5 CO₂ Emission Rate

9.7 Results and Discussions

9.7.1 Optimum Size of Energy System Model

9.7.2 Breakdown of the Total Cost

9.7.3 Percentage-Wise Contribution of System Components in Total Cost

9.7.4 Electricity Generation of Resources/Grid Sale/Grid Purchase on Seasonal Basis

9.8 Conclusions

References

Table of Contents for 9. Modeling and Simulation of a Sustainable Hybrid Energy System under Changing Power Reliability Index at User End

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CONTENTS

Table of Contents for
9. Modeling and Simulation of a Sustainable Hybrid Energy System under Changing Power Reliability Index at User End