Research article Special Issues

Fuzzy logic controller and game theory based distributed energy resources allocation

  • Received: 30 November 2020 Accepted: 13 May 2020 Published: 15 June 2020
  • Energy management and demand control through conventional energy generation sources are challenging for energy providers. Distributed energy resources (DERs) allocation near load centers may provide a suitable solution. The main contribution of the paper improves the voltage profile and reduce the active and reactive power losses in the distribution network. DERs are integrated with IEEE 33 bus system using fuzzy logic controller (FLC) and game theory for two different cases with unity and 0.9 power factor (PF) and compares with conventional methods of integration (i.e., modified novel method, power loss sensitivity method, voltage sensitivity analysis method). The capacity of DERs is optimized by FLC with the help of three triangular input functions voltage profile, active power loss, and reactive power loss. The location of integration of DERs in the radial distribution network is identified by game theory. Game theory is a mathematical algorithm, the results of multiple runs of DERs integration with the desired capacity calculated by FLC, identify the location for integration. The results comparison of DERs integration with the proposed methodology and conventional method shows the effectiveness of the proposed methodology. The voltage profile of the IEEE 33 bus system is increased by 6.70% with unity PF and 7.10% with 0.9 PF most among the applied methodologies and reduce the active and reactive power losses for both unity and 0.9 PF cases.

    Citation: Akash Talwariya, Pushpendra Singh, Mohan Lal Kolhe, Jalpa H. Jobanputra. Fuzzy logic controller and game theory based distributed energy resources allocation[J]. AIMS Energy, 2020, 8(3): 474-492. doi: 10.3934/energy.2020.3.474

    Related Papers:

    [1] Dorra Djebbi-Simmons, Mohammed Alhejaili, Marlene Janes, Joan King, Wenqing Xu . Survival and inactivation of human norovirus GII.4 Sydney on commonly touched airplane cabin surfaces. AIMS Public Health, 2020, 7(3): 574-586. doi: 10.3934/publichealth.2020046
    [2] Terri Rebmann, Kristin D. Wilson, Travis Loux, Ayesha Z. Iqbal, Eleanor B. Peters, Olivia Peavler . Outcomes, Approaches, and Challenges to Developing and Passing a Countywide Mandatory Vaccination Policy: St. Louis County’s Experience with Hepatitis A Vaccine for Food Service Personnel. AIMS Public Health, 2016, 3(1): 116-130. doi: 10.3934/publichealth.2016.1.116
    [3] Christy Pu . The Influence of the Common Cold on Self-Rated Health: A Population-Based Study. AIMS Public Health, 2015, 2(3): 247-255. doi: 10.3934/publichealth.2015.3.247
    [4] Yenisetti SC, Muralidhara . Beneficial Role of Coffee and Caffeine in Neurodegenerative Diseases: A Minireview. AIMS Public Health, 2016, 3(2): 407-422. doi: 10.3934/publichealth.2016.2.407
    [5] S. J. Olshansky, L. Hayflick . The Role of the WI-38 Cell Strain in Saving Lives and Reducing Morbidity. AIMS Public Health, 2017, 4(2): 127-138. doi: 10.3934/publichealth.2017.2.127
    [6] Junji Takaya . Small for Gestational Age and Magnesium: Intrauterine magnesium deficiency may induce metabolic syndrome in later life. AIMS Public Health, 2015, 2(4): 793-803. doi: 10.3934/publichealth.2015.4.793
    [7] Viorica Munteanu, Antonella Petaccia, Nicolae Contecaru, Emanuele Amodio, Carlo Virginio Agostoni . Paediatric acute rheumatic fever in developed countries: Neglected or negligible disease? Results from an observational study in Lombardy (Italy). AIMS Public Health, 2018, 5(2): 135-143. doi: 10.3934/publichealth.2018.2.135
    [8] Sudip Bhattacharya, Amarjeet Singh . Phasing out of the Universal Mega Dose of Vitamin-A Prophylaxis to Avoid Toxicity. AIMS Public Health, 2017, 4(1): 38-46. doi: 10.3934/publichealth.2017.1.38
    [9] Ali Hussain Ansari, Saqib Hussain Ansari, Mubarak Jabeen Salman, Muhammad Usman Hussain Ansari, Rawshan Jabeen . A scoping review on the obstacles faced by beta thalassemia major patients in Pakistan- Matter of policy investment. AIMS Public Health, 2024, 11(4): 1105-1124. doi: 10.3934/publichealth.2024057
    [10] Tran Thi Hai, Saptawati Bardosono, Luh Ade Ari Wiradnyani, Le Thi Hop, Hoang T. Duc Ngan, Huynh Nam Phuong . The optimal mid-upper-arm circumference cutoffs to screen severe acute malnutrition in Vietnamese children. AIMS Public Health, 2020, 7(1): 188-196. doi: 10.3934/publichealth.2020016
  • Energy management and demand control through conventional energy generation sources are challenging for energy providers. Distributed energy resources (DERs) allocation near load centers may provide a suitable solution. The main contribution of the paper improves the voltage profile and reduce the active and reactive power losses in the distribution network. DERs are integrated with IEEE 33 bus system using fuzzy logic controller (FLC) and game theory for two different cases with unity and 0.9 power factor (PF) and compares with conventional methods of integration (i.e., modified novel method, power loss sensitivity method, voltage sensitivity analysis method). The capacity of DERs is optimized by FLC with the help of three triangular input functions voltage profile, active power loss, and reactive power loss. The location of integration of DERs in the radial distribution network is identified by game theory. Game theory is a mathematical algorithm, the results of multiple runs of DERs integration with the desired capacity calculated by FLC, identify the location for integration. The results comparison of DERs integration with the proposed methodology and conventional method shows the effectiveness of the proposed methodology. The voltage profile of the IEEE 33 bus system is increased by 6.70% with unity PF and 7.10% with 0.9 PF most among the applied methodologies and reduce the active and reactive power losses for both unity and 0.9 PF cases.


    Human norovirus is an RNA virus of the family Caliciviridae, and a leading cause of acute viral gastroenteritis, resulting in significant morbidity worldwide [1],[2]. In the United States, it has been estimated that there are 5.5 million cases of norovirus gastroenteritis per year, which represents 58% of cases of acute gastroenteritis [3]. Infection with norovirus typically causes nausea, vomiting, diarrhoea and abdominal pain. The symptoms usually develop 12 to 48 hours after infection, and on the average could last between 1 to 3 days. However, for some individuals, especially children, the elderly and individuals with underlying diseases, these symptoms can be severe and lead to dehydration, and in very rare cases even cause death [3],[4].

    For decades, norovirus infection has not been associated with extra intestinal manifestation, particularly causing liver injury. Although, hepatotropic viruses, such as hepatitis A through to E, are the most common viral cause of acute hepatitis, other viruses such as rotavirus, Epstein-Barr virus (EBV), herpes simplex virus (HSV), cytomegalovirus (CMV), and varicella zoster virus (VZV) can also cause acute liver injury [5]. However, there has been recent reports of extra intestinal disease following norovirus infection [6][8], but little is known of norovirus association with acute hepatitis. We, therefore, review all published studies to evaluate the clinical presentation, management and outcomes of acute hepatitis following norovirus acute gastroenteritis. It is hoped that the findings of this review will provide clinicians with a robust evidence base to investigate and manage patients suspected with norovirus induced hepatitis.

    A search strategy was designed to identify studies reporting elevated transaminitis (acute hepatitis) following norovirus acute gastroenteritis. We searched MEDLINE, EMBASE, and the Cochrane library from 01 January 1967 to 15 April 2019. The medical subject headings (MeSH) terms used included “hepatitis”, “transaminitis”, “liver function test”, “transaminases”, “liver”, “norovirus”, “norovirus-induced” and “Norwalk”. These MeSH terms were used in different combinations. The primary search strategy was “norovirus” AND (“hepatitis” OR “transaminitis” OR “transaminase” OR “liver”). We only included studies published in the English language in our review. In addition, we screened reference lists of selected papers to retrieve relevant studies. Appendix 1 shows the full search strategies used.

    Inclusion criteria required the study to report norovirus induced hepatitis or transaminitis, which was defined as evidence by elevated transaminitis (Aspartate transaminase +/− Alanine aminotransferase). Studies were excluded if they were studies not written in the English language, laboratory, experimental, animal or not original studies. Two independent reviewers (C.H. and G.O.) screened the title and abstract of papers identified by the electronic searches, evaluating inclusion and exclusion criteria for all papers. We retrieved full articles of included publications and each publication was then independently reviewed for eligibility.

    Two reviewers (C.H. and G.O.) independently reviewed the methodological quality of included studies, comparability of case and controls, and outcomes. Discrepancies were resolved by discussion with a third author (F.A.). The specific variables extracted from the publications included: study design, country, age of participants, year of study, method of data collection, method of diagnosis of norovirus, definition of hepatitis, whether other causes of hepatitis, such as EBV and CMV, were excluded, clinical presentation, liver function test (LFT) results, other abnormal test results, duration of illness, management, any previous medical issues and outcomes. The study quality assessment for reporting systematic reviews was done according to the Preferred Reporting Items for Systematic Reviews and Meta-analyses (PRISMA) statement [9].

    All studies included in the review were summarised using descriptive analyses to provide an overview of the information on norovirus induced hepatitis, clinical presentations, management, complications and outcome.

    Figure 1.  PRISMA flow diagram demonstrating identification and selection of eligible studies in the systematic review.

    We identified 126 potential studies during the initial search, of which 20 were duplicates. Of the remaining 106 studies, 98 studies were excluded on the basis of title and abstracts, and a further 3 articles did not meet the inclusion criteria (Figure 1). Kucuk et al. [10] investigated all cases of transaminitis following viral gastroenteritis but we were able to extract data on norovirus associated transaminitis. Of the included studies, all cases were identified using routine investigations. Five studies [6],[10][13] were eligible for inclusion in the final analysis. Most articles were published from Japan (60%, n = 3/5), and one study each from Turkey and USA respectively. Out of the five studies, 2 were case reports, 2 were case series and the remaining one was a retrospective hospital-based study. Three articles involved patients who were younger than 18 years old [10],[12],[13] and the remaining two articles described patients older than 18 years [6],[11]. Three articles had a detailed description of the patient's past medical history [6],[11],[13]. Two of the five articles [11],[13] mentioned using stool specimens for norovirus antigens and three articles used polymerase chain reaction (PCR) [6],[10],[12]. A third diagnostic method, used by two of the articles, were rapid antigen tests [6],[10]. All articles stated that they excluded other possible causes of hepatitis and all included the levels of aspartate transaminase (AST) and alanine aminotransferase (ALT) measured. A summary of the study design, data collection method, study subjects, definition of hepatitis, management and outcome is presented in Tables 1 and 2.

    There was a total of 17 cases of norovirus induced hepatitis, and all had elevated ALT (146–458IU/l) and AST levels (700–1150IU/l). The exact peak AST and ALT values were not provided by Kucuk et al. Majority of the cases were below the age of 18 (88%, n = 15) and almost two-third (64.7%, n = 11) had supportive treatment with intravenous fluid administration. In cases reporting sex, there were more females than males (62.5%, 5/8 vs. 37.5%, 3/8). The timing between norovirus infection, as shown by the presence of symptoms, and the detection of elevated LFTs was not specified by Kucuk et al., however amongst the 4 patients in the study from Tsuge et al., on average, this was 6 days. For the 3 remaining studies, norovirus infection and detection of transaminitis was on the same day. The duration from onset of illness to recovery of symptoms was on average 10 days, but this value excludes the patients from Kucuk et al. [10] and Khayat et al. [13] because Kucuk et al. did not provide this information and Khayat et al. had a patient requiring 5 months to recover. This patient reported by Khayat et al., however, had an underlying disease. The duration from onset to recovery of the elevated LFT was available for 6 cases (excluding children with underlying conditions) at 22.5 days.

    All cases recovered fully with no reported chronic liver disease or ongoing morbidity. There was no fatality reported.

    Of all the cases with transaminitis, 17.6% (n = 3) had underlying medical conditions (comorbidities); one case previously had cholelithiasis and had undergone cholecystectomy, however the duration for recovery from norovirus induced acute hepatitis was not much longer than other cases. Two other cases previously had liver transplants; therefore, they were immunocompromised. Their duration for recovery of symptoms (14 days and 150 days respectively) and LFT results were significantly longer than other cases with an average of 375 days (Table 2).

    Table 1.  Description of study designs and reported norovirus induced transaminitis.
    Study reference Year of Publication Country Study design Age group studied (years) Data collection methods Diagnostic method for norovirus Timing between norovirus infection and hepatitis/transaminitis Definition of hepatitis Excluded other hepatotrophic causes (Y/N)
    Nakajima H et al. [6] 2012 Japan (Tokyo) Case Report 48 Retrospective routine laboratory investigations. Detected by viral antigen check and confirmed by reverse transcription PCR. Same day Elevated LFTs Y
    Zenda T et al. [11] 2011 Japan (Ishikawa) Case Report 56 Retrospective routine laboratory investigations. Positive test for norovirus antigens in stool using immunochromatographic assay kits. Same day Elevated LFTs Y
    Kucuk O et al. [10] 2016 Turkey (Istanbul) Retrospective hospital-based 0 to 17 Retrospective study from 2010 and 2013 of acute viral gastroenteritis. Rapid antigen tests and PCR. N/A Elevated LFTs Y
    Tsuge et al. [12] 2010 Japan (Okayama) Case series 1 to 7 Prospective study measuring LFTs and bloods in children presenting with gastroenteritis. RT-PCR assay Case 1: 5 days
    Case 2: 1 day
    Case 3: 6 days
    Case 4: 11 days
    Elevated LFTs Y
    Khayat AA et al. [13] 2019 USA (Wisconsin) Case series 3 and 8 Retrospective routine laboratory investigations. Stool specimens for norovirus antigens. Case 1 and 2: Same day Elevated LFTs Y

    Notes: Abbreviations: FBC, full blood count; LFT, liver function test; USA, United States of America; PCR, polymerase chain reaction; RT-PCR, reverse transcription-polymerase chain reaction.

     | Show Table
    DownLoad: CSV
    Table 2.  Characteristics of studies included in the review.
    Characteristics Studies
    Study reference Nakajima H et al. [6] Zenda T et al. [11] Kucuk O et al. [10] Tsuge et al. [12] Khayat AA et al. [13]
    No. of patients 1 1 74 4 2
    No. of cases 1 1 9 4 2
    Sex (M/F) F F N/A Case 1: F; Case 2: F
    Case 3: M; Case 4: M
    Case 1: F
    Case 2: M
    Patient Age (yrs) 48 56 0–17 1–7 Case 1: 3
    Case 2: 8
    Symptoms Abdominal pain and diarrhoea. Tenderness in epigastrium and right hypochondrium. Abdominal cramps, vomiting, diarrhoea.
    Tenderness in left lower abdomen.
    Vomiting, diarrhoea, and dehydration. Vomiting, diarrhoea, dehydration, and fever with reduced bowel sounds.
    Case 2 had convulsions.
    Anaemia, haematemesis, diarrhoea.
    Peak AST (IU/l) 892 1150 45.6 794 700
    Peak ALT (IU/l) 146 458 31.7 423 400
    Peak GGT (IU/l) N/A 73 N/A N/A N/A
    Peak ALP (IU/l) No rise 318 N/A N/A N/A
    Other abnormal results None None Hct 36.9, WCC 13510, CRP 9.7 Case 2: leucocytosis (WBC 13670IU/l)
    Case 3: hyponatraemia
    Case 1 had normal liver biopsy.
    Onset to recovery of symptoms (days) 7 4 N/A Day 8, day 13, day 8 and day 18 in cases 1, 2, 3 and 4 respectively. Case 1: 150; Case 2: 14.
    Onset of illness to LFT recovery (days) 14 14 N/A Case 1: 26; Case 2: 26;Case 3: 27; Case4: 28 . Case 1: 480; Case 2: 270
    Requiring hospitalisation/IV support Hospitalisation Hospitalisation 40 (54%) were hospitalized and 34 (46%) had an observed follow-up. Cases 1–3 were hospitalized. Hospitalised
    Management Supportive therapy Bowel rest and intravenous rehydration. IV rehydration Intravenous fluids for cases 1-3 and oral/IV glycyrrhizin for all. Case 1 had IV IVIG during their recovery from norovirus infection.
    PMH Cholelithiasis and cholecystectomy 4 years ago. Drinks alcohol. Surgery for appendicitis, myoma uteri, gallstones (cholecystectomy) N/A N/A Case 1 had a liver transplant due to hepatoblastoma.
    Case 2 had liver transplant due to congenital hepatic fibrosis and Caroli's disease.
    Outcome of cases Alive without chronic liver disease. Alive without chronic liver disease. N/A Alive without chronic liver disease. Alive without chronic liver disease.

    Notes: Abbreviations: PMH, past medical history; IV, intravenous; Hct, haematocrit; WCC, white cell count; CRP, c-reactive protein; IVIG, immunoglobulins; M, male; F, female; N/A, not available.

     | Show Table
    DownLoad: CSV

    Acute hepatitis due to non-hepatotropic viruses such as EBV and HSV have been well described in the literature, but extra intestinal presentations of norovirus, such as disseminated coagulopathy and febrile convulsions, have been considered until recently, a rare phenomenon [7],[8]. A thorough review of the literature identified a very low reported rate of norovirus induced hepatitis, most likely because norovirus gastroenteritis is usually self-limiting and there has been no indication for invasive investigations, such as LFTs, in patients presenting with norovirus. There was a good clinical history of transaminitis, and acutely elevated liver enzymes as described by Zenda T and colleagues [11].

    Interestingly, all published articles of norovirus induced acute hepatitis are less than a decade, which also support our findings. This review, in addition to other previously reported cases, would suggest that norovirus induced transaminitis is more common than previously reported in the literature. However, the mechanism of liver injury caused by norovirus remains unclear. One of the factors postulated is the release of pro-inflammatory cytokines induced by the viruses, which affects the inherent hepatic function, while other authors propose a host immune response with activated cytotoxic T cells affecting the hepatocytes [14],[15]. These presumptions are yet to be established by further studies.

    Clinical presentations were similar in all cases, mainly vomiting and diarrhoea except one case that was complicated with convulsions [12], and another case with anaemia and haematemesis [13]. However, there seems to be an increase in abdominal tenderness in those with elevated transaminitis. Majority of the cases reported occurred in children and over two-thirds were treated in hospital with intravenous fluid administration. This was not surprising as children are likely to deteriorate faster with norovirus gastroenteritis compared to adults, but whether the liver of a child is more prone to extra intestinal manifestations of norovirus with acute hepatitis will require further investigations. Similar to the management of non-hepatotropic viruses, the treatment of acute hepatitis following norovirus gastroenteritis is mainly supportive, involving primarily rehydration and correction of electrolyte abnormalities. These patients are expected to recover, on average, between 1 to 3 days. However, for some individuals, particularly children, the elderly and individuals with underlying diseases, these symptoms can be severe and lead to dehydration, and in very rare cases even cause death [3],[4]. It is also important to note that many of these patients would have severe dehydration from vomiting and diarrhoea, which are both common symptoms of norovirus infection. As a result, elevated LFTs may result, however, this would not explain the lymphocytic infiltration seen using pathological investigations in the study from Khayat et al.

    A longer recovery period in cases with norovirus induced hepatitis was observed. In another retrospective study in Japan, including 71 children with norovirus acute gastroenteritis, the mean duration of illness was twice as long in infants and these infants have a greater severity of illness [16]. However, concomitant extra intestinal manifestations were not explored, possibly because this is such a rare event and there was no robust evidence base to investigate children with suspected norovirus induced acute hepatitis, it is therefore prudent that children with protracted course of illness following norovirus gastroenteritis should be evaluated for possible extra intestinal manifestation, including acute hepatitis.

    This study is not without limitations. Most of the included studies were either case reports or case series, which are generally of low evidence. In addition, 17.6% cases had an underlying liver disease, which will predispose them to liver diseases, and these were adjusted for in this review. In particular, Khayat et al. [13] describes two patients with liver transplants and who experienced norovirus induced hepatitis. Nevertheless, all cases were thoroughly investigated for other possible causes of liver dysfunction, and one of the articles completely excluded patients who were positive for other viruses [10]. All papers defined hepatitis as having elevated LFT results. Reassuringly, the elevated LFTs settled within three weeks and all cases recovered with no evidence of chronicity including fatality, but we observed a much longer recovery period in cases with underlying medical conditions.

    Norovirus gastroenteritis is usually a self-limiting illness, requiring mainly supportive therapy. This review therefore highlights the need for clinicians to consider norovirus induced acute hepatitis, especially in children with protracted illness, and as a potential cause of elevated transaminases.



    [1] Justo JJ, Mwasilu F, Lee J, et al. (2013) AC-microgrids versus DC-microgrids with distributed energy resources: A review. Renewable Sustainable Energy Rev 24: 387-405. doi: 10.1016/j.rser.2013.03.067
    [2] Ehsan A, Yang Q (2018) Optimal integration and planning of renewable distributed generation in the power distribution networks: A review of analytical techniques. Appl Energy 210: 44-59. doi: 10.1016/j.apenergy.2017.10.106
    [3] Singh P, Kothari DP, Singh M (2014) Interconnected distribution network for the integration of distributed energy resources. Res J Appl Sci, Eng Technol 7: 240-250. doi: 10.19026/rjaset.7.247
    [4] World Energy Council, World Energy Scenario-2019. Exploring Innovation Pathways to 2040. 2019. Available from: https://www.worldenergy.org/assets/downloads/2019_Scenarios_Full_Report.pdf
    [5] Keane A, Ochoa LF, Borages CL, et al. (2012) State-of-the-art techniques and challenges ahead for distributed generation planning and optimization. IEEE Trans Power Syst 28: 1493-1502.
    [6] Alarcon-Rodriguez A, Ault G, Galloway S (2010) Multi-objective planning of distributed energy resources: A review of the state-of-the-art. Renewable Sustainable Energy Rev 14: 1353-1366. doi: 10.1016/j.rser.2010.01.006
    [7] Ameli A, Bahrami S, Khazaeli F, et al. (2014) A multiobjective particle swarm optimization for sizing and placement of DGs from DG owner's and distribution company's viewpoints. IEEE Trans Power Delivery 29: 1831-1840.
    [8] Syahputra R, Robandi I, Ashari M (2015) Reconfiguration of distribution network with distributed energy resources integration using PSO algorithm. Telkomnika 13: 759-766. doi: 10.12928/telkomnika.v13i3.1790
    [9] Kothari DP, Singh P, Singh M (2010) Concept of energy highways for industrial growth and national prosperity. Int J Electron Electr Eng 9: 9-15.
    [10] Singh P, Kothari DP, Singh P (2010) Voltage control in distribution networks having DGs by using UPFC. Int J Electro Electr Eng Syst 2: 31-38.
    [11] Talwariya A, Singh P (2019) Optimization of distribution networks with integration of distributed generators using cooperative Game Theory. Int J Power Energy Syst 39: 1-7.
    [12] Mumtaz F, Syed MH, Al Hosani M, et al. (2015) A novel approach to solve power flow for islanded microgrids using modified Newton Raphson with droop control of DG. IEEE Trans Sustainable Energy 7: 493-503.
    [13] Imran AM, Kowsalya M, Kothari DP (2014) A novel integration technique for optimal network reconfiguration and distributed generation placement in power distribution networks. Int J Electr Power Energy Syst 63: 461-472. doi: 10.1016/j.ijepes.2014.06.011
    [14] Abdmouleh Z, Gastli A, Ben-Brahim L, et al. (2017) Review of optimization techniques applied for the integration of distributed generation from renewable energy sources. Renewable Energy 113: 266-280. doi: 10.1016/j.renene.2017.05.087
    [15] Rao RS, Ravindra K, Satish K, et al. (2012) Power loss minimization in distribution system using network reconfiguration in the presence of distributed generation. IEEE Trans Power Syst 28: 317-325.
    [16] Prakash P, Khatod DK (2016) Optimal sizing and siting techniques for distributed generation in distribution systems: A review. Renewable Sustainable Energy Rev 57: 111-130. doi: 10.1016/j.rser.2015.12.099
    [17] Talwariya A, Sharma D, Pandey AK, et al. An execution of smart grid with game theory. In: 2016 International Conference on Recent Advances and Innovations in Engineering Dec 23-25, 2016. IEEE; 1-4.
    [18] Talwariya A, Sharma SK, Singh P, et al. (2018) A game theory approach and tariff strategy for demand side management, In: 2018 3rd International Conference and Workshops on Recent Advances and Innovations in Engineering Nov 22-25, 2018. IEEE; 1-5.
    [19] Talwariya A, Singh P, Kolhe M (2019) A stepwise power tariff model with game theory based on Monte-Carlo simulation and its applications for household, agricultural, commercial and industrial consumers. Int J Electr Power Energy Syst 111: 14-24. doi: 10.1016/j.ijepes.2019.03.058
    [20] Mei S, Wei W, Liu F (2017) On engineering game theory with its application in power systems. Control Theory Technol 15: 1-12. doi: 10.1007/s11768-017-6186-y
    [21] Lalitha MP, Reddy VV, Reddy NS, et al. (2011) DG source allocation by fuzzy and clonal selection algorithm for minimum loss in distribution system. Distrib Gener Altern Energy J 26: 17-35.
    [22] Murthy VVSN, Kumar A (2013) Comparison of optimal DG allocation methods in radial distribution systems based on sensitivity approaches. Int J Electr Power Energy Syst 53: 450-467. doi: 10.1016/j.ijepes.2013.05.018
    [23] Qian K, Zhou C, Allan M, et al. (2011) Effect of load models on assessment of energy losses in distribution generation planning. Int J Electr Power Energy Syst 33: 1243-1250. doi: 10.1016/j.ijepes.2011.04.003
    [24] Rueda-Medina AC, Franco JF, Rider MJ, et al. (2013) A mixed-integer linear programming approach for optimal type, size and allocation of distributed generation in radial distribution systems. Electr Power Syst Res 97:133-43. doi: 10.1016/j.epsr.2012.12.009
    [25] Hasanien HM, Matar M (2014) A fuzzy logic controller for autonomous operation of a voltage source converter-based distributed generation system. IEEE Trans Smart Grid 6: 158-165.
  • This article has been cited by:

    1. He-Teng Zhang, Hao Wang, Hai-Sheng Wu, Jian Zeng, Yan Yang, Comparison of viromes in vaginal secretion from pregnant women with and without vaginitis, 2021, 18, 1743-422X, 10.1186/s12985-020-01482-z
    2. Yalda Lucero, David O. Matson, Shai Ashkenazi, Sergio George, Miguel O’Ryan, Norovirus: Facts and Reflections from Past, Present, and Future, 2021, 13, 1999-4915, 2399, 10.3390/v13122399
    3. Syafruddin Ilyas, Salomo Hutahaean, Putri Cahaya Sit, Analysis of Cytochrome c Expression on Liver Histology of Hepatitis Rats after Administration of Tin and Olive Leaf Ethanol Extract, 2022, 25, 10288880, 835, 10.3923/pjbs.2022.835.842
    4. Louisa F. Ludwig-Begall, Axel Mauroy, Etienne Thiry, Noroviruses—The State of the Art, Nearly Fifty Years after Their Initial Discovery, 2021, 13, 1999-4915, 1541, 10.3390/v13081541
    5. Prashasti Sinha, Anil Kumar Yadav, Theoretical Study of Azetidine Derivative by Quantum Chemical Methods, Molecular Docking and Molecular Dynamic Simulations, 2023, 8, 2365-6549, 10.1002/slct.202300190
    6. Rabab Taha, Noura Elazhary, Sarah Alqhtani, Walaa Almansouri, Fatal Acute Liver Failure Following Norovirus Gastroenteritis in a Child: A Case Report, 2025, 18760341, 102675, 10.1016/j.jiph.2025.102675
    7. Yalda C. Lucero, Miguel L. O’Ryan, 2025, 9780323827638, 1643, 10.1016/B978-0-323-82763-8.00169-2
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(4770) PDF downloads(304) Cited by(8)

Figures and Tables

Figures(14)  /  Tables(7)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog