# Optimal design of solar–wind hybrid system-connected to the network with cost-saving approach and improved network reliability index

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## Abstract

In this paper, the optimal design of a grid-connected the hybrid energy system for a sample area in the north Iran is studied. A new innovative cost-based objective function is proposed which is combination of life cycle cost and reliability cost. Also, loss of power supply probability (LPSP) criteria, is considered as constraint for ensuring at the same time certain level of system reliability. Designing process is implemented in such a way that the total cost of the system reaches its minimum. For this purpose, a modified version of Bee algorithm has been proposed to achieve this goal. In order to carry out studies, the actual sample system, whose data has been available, has been studied. The results indicate the good performance of proposed hybrid system to reduce system cost.

## Keywords

Modified bee algorithm Hybrid system Solar–wind system PSO DE## 1 Introduction

Renewable energy sources such as wind and solar have grown dramatically due to the need to preserve fossil fuel resources for future generations and to prevent the burning environmental damage caused by them, and they can be found near utilization centers in order to decrease losses [1, 2, 3]. For improve renewable resources performance, the sources work together and complement each other, known as hybrid systems. Because the power systems with two or more different sources of energy, they are more reliable than systems with one source. The hybrid of photovoltaic and wind turbine systems can provide a wide range of facilities. But these systems should be more robust and flexible in terms of power generation [4]. One solution to this is the optimal design of solar and wind combined systems. Various purposes for designing hybrid systems such as reducing costs, reducing emissions, improving power quality indicators, and improving reliability are considered [5].

Designing optimal and determining the optimum capacity of different sources of energy production and with different approaches in these references has been discussed. In recent years, the use of renewable energy in order to generate energy and supply to the grid has increased steadily. For example, in [6], heuristic based algorithm is proposed for optimal design of independent solar and wind power system incorporating load forecasting. In [7], the design of a hybrid solar–wind and battery system, and considering the probability of losing power source (LPSP). In this paper, a differential evolution algorithm has been used. In [8], a hybrid search optimization algorithm is used for optimal design of a solar wind power plant with hydrogen sources is presented. In designing procedure, weather forecasting is also used for accurate results of simulations. In [9], a new optimization method called Swine Flu modeling based on quarantine optimization is proposed to determine the optimal location and size of dispersed generation units in the distribution network, in order to minimize the active power losses. The above algorithm performs randomization through quarantine and healing. The proposed algorithm has been applied to a 33-bus distribution system and the results of the proposed method have been compared with the results of the PSO optimization method. In [10], simulated annealing-chaotic search algorithm-based optimization is proposed optimal design of reverse osmosis hybrid desalination system driven by wind and solar energies. The model used in this work includes a solar-powered hybrid system with energy storage, or the same battery. In [11], applications of distributed generation sources are integrated and transmitted separately from the network. Homer, HOGA and Ret Screen were introduced in this reference. DE algorithm, particle communities, and harmonic search of intelligent methods have led to the design of optimal hybrid power generation systems. In this paper, the main objective of the design of the hybrid power generation system in the studied grid, the reduction of energy production costs and the improvement of system reliability indices such as unprotected energy (ENS) and LPSP in design considerations are taken. Considering the cost per kilowatt of energy not provided and adding this cost to energy costs, a single target goal of energy will be created. As a result, the algorithm must minimize this function. On the other hand, according to the defined standards, the LPSP limit value should be less than the permissible limit (2% per year), which is applied as an optimization limitation in the problem [12].

In this paper a new comprehensive objective function is proposed for designing solar–wind hybrid system in an area in the north of Iran. The proposed objective function is a combination of life cycle cost and reliability cost. Also, reliability constraints are considered in the design process. A modified version of the bee algorithm is also proposed to solve the optimization problem.

The remainder of this article is presented in the second part of the study network. In the third section, the relationships required for modeling the proposed system are described, and in Sect. 4, the Bee algorithm is briefly described. In the fourth section, simulation results were presented in three scenarios. Finally, this article ends with the results and conclusions in Sect. 5.

## 2 Power generation hybrid system

## 3 Objective function and constraints

_{pv}and A

_{W}variables per square meter. Therefore, the total setup cost is:

_{PV}), so the cost of replacing this component from the system is zero. (R

_{NPV_PV}= 0). The useful life of wind turbines (L

_{W}) is usually less than that of solar panels (here it is equal to N). Therefore, additional investment for wind turbines will be required before the horizon of the project is completed. The number of times the N-year horizon of the wind turbine project should be replaced is equal to X

_{W}= N/L

_{W}[16]. If α

_{W}is the initial investment in the current time in dollars pe r square meter, then the investment in year y is equal to:

_{d}wind turbine in dollars per square meter during its useful life is linearly reduced from α

_{W}to S

_{W}.

_{s}and the annual energy sales to the P

_{s}network are in $/kWh, then the annual energy sales to the network are equal to I

_{a}= P

_{s}.E

_{s}, so the total net sales value of energy sales to the network is equal to With:

## 4 Under study network

^{2}/d and the average wind speed is 1.73 m/s. Due to network constraints for power supply, its availability per hour with a normal function with an average of 40 kV and a standard deviation of 20 is considered to provide the required data for 8760 h. In Fig. 7, the network capacity is shown.

## 5 Bee optimization algorithm

The bee colony algorithm was first introduced in 2005, an algorithm inspired by colonial bee behavior. Bee colony algorithm is used to solve continuous optimization problems and to find optimal values of a function or a combination of multivariate numeric functions. This method has better performance with less control parameters than other algorithms. The population in this algorithm consists of three groups of worker bees, treadmills and spectators. The first half of the population includes artificial laborer bees and the second half of the spectators’ bees. For each food source, there is only one worker bee. In other words, the number of worker bees is equal to the number of sources of food around the hive. The beekeeper whose food supply is out of date becomes a predator bee [18].

_{i}is the cost of solving the possible x

_{i}. Any worker or spectator bee may make changes to the available food source (possible resolution) in its memory and calculate its fitness. If the new solution’s resolution is greater than the previous one, the new solution will be chosen and the old one will be forgotten; otherwise, it will keep the same solution in memory. In this algorithm, the new solution is the solution of the previous solution based on Eq. (15):

_{ij}is a random number in the range [1, − 1]. This number controls the production of food sources around x

_{ij}, indicating a comparison of the two food sources by a bee. With this equation, the difference between x

_{ij}and x

_{kj}decreases, the deviation from the x

_{ij}location will also decrease. Therefore, as the search process approaches the optimal solution in search space, the deviation from the optimal solution decreases. In this equation, one dimension of one of the food sources is tried to be selected and, depending on the value of Φ, in its direction or opposite direction. If the variable generated by Eq. (15) violates its limit, its value is replaced by an acceptable value. If it violates its upper limit, the upper limit value replaces it and if it violates the lower limit, the lower limit value is replaced. After exchanging information between the worker and spectator bees, spectators choose a food source with a probability that fits the quality of the nectar in the food source. This probability can be calculated in various ways, which are expressed in the equations [19].

## 6 Simulation results

The parameters of the algorithm BA, PSO and DE

BA | nScoutBee | MaxIt | nSelectedSite | nEliteSite | nSelectedSiteBee | nEliteSiteBee |

100 | 40 | 10 | 4 | 10 | 20 | |

PSO | pop | max_ite | c1= c2 | w | V | V |

100 | 40 | 2 | 0.7 | 0.6 | 0.9 | |

DE | pop | max_ite | β | β | PCR | |

100 | 40 | 0.4 | 0.8 | 0.6 |

Requested energy of the network and cost for the base mode

Eb(KWh/year) | C | C | LPSP | C |
---|---|---|---|---|

45,624 | 174,560 | 839.17 | 0.0368 | 228,120 |

The amount of energy demanded from the upstream network in one year of study is 45,625 kilowatt-hours per year. The annual cost of purchased energy is 174,560$ and the non-energy fines are estimated at 840$. The LPSP constraint is obtained in the absence of dispersed generation sources of 3.68%. For a standard stand-alone system, the LPSP should be less than 2% in a year.

### 6.1 The first scenario

Optimal design results in the first scenario

A | Eb (KWh/year) | C | SCOC ($) | I | ENS (Kwh) | LPSP | C | |
---|---|---|---|---|---|---|---|---|

BA | 138 | 26,145 | 8691 | 657 | 689 | 1722 | 0.0198 | 77,556 |

PSO | 140 | 26,663 | 9109 | 685 | 612 | 1712 | 0.02 | 77,574 |

DE | 161 | 25,125 | 8432 | 376 | 861 | 940 | 0.019 | 77,560 |

The comparison and comparison of optimization results with three algorithms in Table 3 shows that the BA algorithm has reached 147 wind turbines, while the algorithm of PSO aggregation has 140 numbers and the DE algorithm has 161 numbers. The value of LPSP for the BA algorithm is 0.0198 and for the PSO and DE algorithms, respectively, is 0.02 and 0.019, respectively. The annual cost of purchased energy for BA, PSO and DE algorithm are 8691$, 9109$ and 8432$ respectively. Also, SCOC is 657 $ for BA, 658$ for PSO and 376$ for DE algorithm. Although the energy demanded from the grid is less than two other algorithms using the DE algorithm, the cost of energy purchased from the network is reduced, but due to the higher number of wind turbines, the overall system costs have increased. According, the final cost of the system based on the bee colony algorithm is less than the proposed two alternative algorithms. Similarly, the annual amount of energy demanded by each home of the network was less than that calculated by calculating the bee colony algorithm.

### 6.2 Second scenario

Optimal design results in the second scenario

Npv | Eb (KWh/year) | C | SCOC ($) | I | LPSP | C | |
---|---|---|---|---|---|---|---|

BA | 121 | 27,700 | 9664 | 685 | 1593 | 0.02 | 166,291 |

PSO | 113 | 28,007 | 9700 | 685 | 1392 | 0.02 | 166,426 |

DE | 115 | 27,922 | 9663 | 685 | 1444 | 0.02 | 166,362 |

The number of solar panels offered by the BA algorithm is 121, while the number for both DE and PSO algorithms is 115 and 113, respectively. The final cost of the system based on calculations of the bee colony algorithm is 135$ less than the PSO algorithm calculations and 71$ less than the DE algorithm. Also, the amount of energy that each house requests per year, and the annual cost of purchasing electrical energy from the network under the proposed conditions of the colony bee colony algorithm is less.

### 6.3 Third scenario

Optimal design results in the third scenario

A | A | Eb (KWh/year) | C | SCOC($) | I | ENS (Kwh) | LPSP | C | |
---|---|---|---|---|---|---|---|---|---|

BA | 80 | 63 | 23,853 | 7872 | 226 | 1192 | 565 | 0.0182 | 75,105 |

PSO | 67 | 74 | 23,716 | 7812 | 210 | 976 | 525 | 0.018 | 75,643 |

DE | 93 | 52 | 24,255 | 8036 | 376 | 1390 | 940 | 0.0191 | 77,553 |

The comparison of the proposed optimal state with each algorithm shows that in the output of the PSO algorithm, due to the increase in the amount of wind turbine (compared with the output of the BA algorithm), due to the more uniform nature of the energy produced by wind turbines, the amount of energy Each house per year requests the network has declined proportionally. However, due to the intensity of radiation and wind speed in the study area, reducing the number of solar panels has reduced annual revenue from the sale of excess energy to the network in the output of the PSO. In the case that the annual cost of purchasing electrical energy from the network and the LPSP constraint is almost identical in both outputs, the total cost of the system as a function of the system objective in the proposed model of the BA algorithm has decreased by 358$ compared to the output of the PSO algorithm.

### 6.4 Numerical studies of the results

Compare the results of different scenarios

A | A | Eb (KWh/year) | C | SCOC($) | I | LPSP | C | |
---|---|---|---|---|---|---|---|---|

Base | 0 | 0 | 45,624 | 17,456 | 839 | 0 | 0.0368 | 220,747 |

Scenario 1 | 0 | 138 | 26,145 | 8691 | 657 | 689 | 0.0198 | 87,956 |

Scenario 2 | 121 | 0 | 27,700 | 9664 | 685 | 1593 | 0.02 | 176,291 |

Scenario 3 | 80 | 63 | 23,853 | 7872 | 226 | 1192 | 0.0182 | 75,105 |

The sale of surplus equipment and surplus energy to the network are system revenues that are shown in a negative graph (income), and other items that are costing are plotted with positive outcomes. As shown, the purchase of energy shortage from the network has the largest share of the final cost of the system, and the initial installation of equipment is in the second order of cost.

## 7 Conclusion

In this paper, the optimal design of the hybrid power generation system in Sari has been studied. The main objective of this study is to provide a model for designing a hybrid power generation system that uses solar cell panels and wind turbines. Designs are implemented in such a way that the total cost of the system reaches its minimum. These costs can be the cost of initial investment, the cost of maintenance, the cost of purchasing energy from the grid, and so on. To this end, the BA algorithm was used to achieve this goal and the results were compared with the results of DE algorithms and PSO. In order to carry out studies, the actual sample system, whose data has been available, has been studied. Using the geographic location of the area, the amount of sun radiation and wind speed is obtained from NASA’s site. Then, studies have been conducted in three scenarios. In the first scenario, the system only includes wind turbines. The final system cost was 192,908$. In the second scenario, the only energy sources of solar panels are the system, with a final system cost of 17,691$. In the third scenario, the combination of a solar–wind system has been used to provide power. The total cost of the system in this scenario is estimated at 171,489$. The results of this section indicate that the hybrid system has a better performance than the other two scenarios in terms of the objective function (total cost of the system), and the scenario of the solar panel is better after the hybrid mode.

Comparison of the energy that each house requests per year in different scenarios shows that according to the prediction of the hybrid scenario with 23,853 kilowatt hours per year, it is less than the other scenarios, and unlike the overall cost of energy demand from the network in the wind scenario the solar scenario is less.

## Notes

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no competing interests.

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