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Different load levels are considered by employing non-dispatchable distributed generations. The objective function includes minimising the energy losses cost, the cost of peak power losses, and the cost of the capacitor. The optimization problem is solved using the spotted hyena optimizer (SHO) algorithm to determine the optimal size and location of capacitors, considering different loading levels and the two operation modes. In this study, a three-level load and various types of loads, including constant power, constant current, and constant impedance are considered. The proposed method is implemented on a 24-bus radial distribution network. To evaluate the performance of the SHO, the results are compared with GWO and the genetic algorithm (GA). The simulation results demonstrate the superior performance of the SHO in reducing the cost of losses and improving the voltage profile during injection and non-injection of reactive power by distributed generations in two operation modes. The total cost and net saving values for DGs only with the capability of active power injection is achieved 105,780 $ and 100,560.54 $, respectively and for DGs with the capability of active and reactive power injection is obtained 89,568 $ and 76,850.46 $, respectively using the SHO. The proposed method has achieved more annual net savings due to the lower cost of losses than other optimization methods.<\/jats:p>","DOI":"10.1038\/s41598-021-82440-9","type":"journal-article","created":{"date-parts":[[2021,2,1]],"date-time":"2021-02-01T11:06:44Z","timestamp":1612177604000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":78,"title":["Spotted hyena optimizer algorithm for capacitor allocation in radial distribution system with distributed generation and microgrid operation considering different load types"],"prefix":"10.1038","volume":"11","author":[{"given":"Amirreza","family":"Naderipour","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zulkurnain","family":"Abdul-Malek","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohammad","family":"Hajivand","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zahra Mirzaei","family":"Seifabad","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohammad Ali","family":"Farsi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Saber Arabi","family":"Nowdeh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Iraj Faraji","family":"Davoudkhani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,2,1]]},"reference":[{"key":"82440_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/nenergy.2017.129","volume":"2","author":"A Facchini","year":"2017","unstructured":"Facchini, A. 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