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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">umovest</journal-id><journal-title-group><journal-title xml:lang="ru">Статистика и Экономика</journal-title><trans-title-group xml:lang="en"><trans-title>Statistics and Economics</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2500-3925</issn><publisher><publisher-name>Plekhanov Russian University of Economics</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21686/2500-3925-2018-2-59-68</article-id><article-id custom-type="elpub" pub-id-type="custom">umovest-1255</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>СТАТИСТИКА И МАТЕМАТИЧЕСКИЕ МЕТОДЫ В ЭКОНОМИКЕ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>STATISTICAL AND MATHEMATICAL METHODS  IN ECONOMICS</subject></subj-group></article-categories><title-group><article-title>Проблемы оптимизации энергопотребления домохозяйств в задачах повышения энергоэффективности жилищного сектора</article-title><trans-title-group xml:lang="en"><trans-title>Problems of optimizing the energy consumption of households in the tasks of improving the energy efficiency of the housing sector</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Гребенюк</surname><given-names>Г. Г.</given-names></name><name name-style="western" xml:lang="en"><surname>Grebenuk</surname><given-names>G. G.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ИПУ им. В.А. Трапезникова РАН, Москва, Россия</p></bio><bio xml:lang="en"><p>V. A. Trapeznikov Institute of Control Sciences of RAS, Moscow, Russia</p></bio><email xlink:type="simple">grebenuk@lab49.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Никишов</surname><given-names>С. М.</given-names></name><name name-style="western" xml:lang="en"><surname>Nikishov</surname><given-names>S. M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ИПУ им. В.А. Трапезникова РАН, Москва, Россия</p></bio><bio xml:lang="en"><p>V. A. Trapeznikov Institute of Control Sciences of RAS, Moscow, Russia</p></bio><email xlink:type="simple">nikishov@lab49.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Крыгин</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Krygin</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ИПУ им. В.А. Трапезникова РАН, Москва, Россия</p></bio><bio xml:lang="en"><p>V. A. Trapeznikov Institute of Control Sciences of RAS, Moscow, Russia</p></bio><email xlink:type="simple">andreyakr@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Середа</surname><given-names>Л. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Sereda</surname><given-names>L. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ИПУ им. В.А. Трапезникова РАН, Москва, Россия</p></bio><bio xml:lang="en"><p>V. A. Trapeznikov Institute of Control Sciences of RAS, Moscow, Russia</p></bio><email xlink:type="simple">sereda@lab49.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Институт проблем управления им. В.А. Трапезникова РАН</institution><country>Россия</country></aff><aff xml:lang="en"><institution>V. A. Trapeznikov Institute of Control Sciences of RAS</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2018</year></pub-date><pub-date pub-type="epub"><day>10</day><month>06</month><year>2018</year></pub-date><volume>15</volume><issue>2</issue><fpage>59</fpage><lpage>68</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Гребенюк Г.Г., Никишов С.М., Крыгин А.А., Середа Л.А., 2018</copyright-statement><copyright-year>2018</copyright-year><copyright-holder xml:lang="ru">Гребенюк Г.Г., Никишов С.М., Крыгин А.А., Середа Л.А.</copyright-holder><copyright-holder xml:lang="en">Grebenuk G.G., Nikishov S.M., Krygin A.A., Sereda L.A.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://statecon.rea.ru/jour/article/view/1255">https://statecon.rea.ru/jour/article/view/1255</self-uri><abstract><p>Целью работы является исследование проблемы оптимизации энергопотребления и  практического применения методов повышения энергоэффективности в жилищном секторе.  Оптимизация управления энергоэффективностью позволяет уменьшать расходование  энергоресурсов при выполнении различных работ, отопление зданий и т.д. Создание  методов оптимизации позволит в короткие сроки снизить платежи за коммунальные услуги,  а в целом для отрасли, будет способствовать уменьшению потребления различных ресурсов  и улучшению экологического состояния региона. В отличии от других подходов, акцент в  данной работе ставится на удобство и простоту, необходимую для использования этой  методики населением в домашних хозяйствах. В предложенном комплексном подходе  используются методы теории вероятностей, линейного программирования, модели теплообмена. Проведенное исследование подтверждает эффективность полученного  решения и может служить основой для создания учебно-исследовательских стендов. Статья  состоит из двух частей: в первой части выполнен анализ ведущих работ в этой тематике и  определены причины, затрудняющие массовое применение предлагаемых в этих работах  решений. Далее предложена и обоснована постановка задачи и сформулирован ряд  основных требований к математической модели энергопотребления, необходимых для того, чтобы сконструированную методику можно было применять для оптимизации  энергопотребления в домашних хозяйствах. Во второй части на примерах конкретных  бытовых электроприборов предлагается математическая модель их функционирования. При  исследовании существующих методов оптимизации энергопотребления в домохозяйствах  были выявлены проблемы, заключающиеся в сложности применения этих методов на практике и получены рекомендации, позволяющие сформулировать основные принципы  построения методики оптимизации, удобной для практического применения. Было показано, что при построении такой методики первичным является вопрос о данных, которые может  предоставить пользователь. Был определен минимальный состав входных данных, по которым сконструированы необходимые алгоритмы оптимизации энергопотребления. Так же был предложен ряд алгоритмов определения некоторых входных показателей, которые  легко использовать в домашних хозяйствах. Таким образом, общий план исследований в  данной работе заключается в следующем:• провести группировку приборов по способу задания функциональных требований;• выяснить приемлемый для пользователя состав и вид входных данных;• определить минимальный набор входных данных для формализации ограничения суммарной потребляемой мощности;• сконструировать алгоритмы оптимизации, работающие с указанными выше входными данными.Важнейшими результатами выполненной работы являются следующие:• разработана методика прогнозирования графика максимальной суммарной мощности потребления.• разработаны методики оптимизации энергопотребления для каждого из выделенных подмножеств бытовых приборов.• выполнено моделирование полученных алгоритмов оптимизации, которое показало их  работоспособность, эффективность и возможность их практического применения без какой- либо адаптации.Таким образом, в статье предложено решение задачи оптимизации энергопотребления в  жилищном секторе, ориентированное на практическое применение.</p></abstract><trans-abstract xml:lang="en"><p>The aim of the work is to study the problem of optimizing energy consumption and practical application of methods for  improving energy efficiency in the housing sector. Optimization of  energy efficiency management allows to reduce the expenditure of  energy resources in the performance of various works, heating of buildings, etc. The creation of optimization methods will make it  possible to reduce payments for utilities in a short time, and in  general for the industry, will help reduce the consumption of various  resources and improve the ecological state of the region. Unlike  other approaches, the emphasis in this paper is on the convenience  and simplicity necessary for using this technique by the population in households. The proposed integrated approach uses methods of  probability theory, linear programming, heat exchange models. The  conducted research confirms the effectiveness of the solution  obtained and can serve as a basis for the creation of training and  research stands. The article consists of two parts: the first part  analyzes the leading works in this field and identifies the reasons  that make it difficult to apply the solutions proposed in these papers. Further, the statement of the problem was proposed and justified,  and a number of basic requirements to the mathematical model of  energy consumption, necessary for the constructed technique to be  used to optimize energy consumption in households, were  formulated. In the second part, a mathematical model of their  functioning is proposed using examples of specific household  electrical appliances. When researching existing methods for  optimizing energy consumption in households, problems were  identified that were difficult to apply these methods in practice and  recommendations were obtained that allowed to formulate the basic  principles of constructing an optimization technique that was  convenient for practical application. It was shown that when  constructing such a technique, the primary question is the data that  the user can provide. The minimum composition of input data was  determined, according to which the necessary algorithms for  optimizing energy consumption were designed. A number of  algorithms for determining some input indicators that are easy to use in households have also been proposed. Thus, the general plan of research in this paper is as follows:</p><p>• carry out grouping of devices by the way of setting functionalrequirements;• determine the acceptable composition and type of input data forthe user;• define the minimum set of input data for formalizing the limitationof the total power consumption;• design optimization algorithms that work with the input dataspecified above. The most important results of the work performed are the following:• the methodology for forecasting the graph of the maximum totalpower consumption has been developed.• methods for optimizing energy consumption for each of the selected subsets of household appliances have been developed.• the optimization algorithms obtained have been simulated, which showed their operability, efficiency and the possibility of their practical application without any adaptation.Thus, the article proposes the solution of the problem of optimization of energy consumption in the housing sector, oriented to practical application.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>энергоэффективность</kwd><kwd>домохозяйство</kwd><kwd>профиль нагрузки</kwd></kwd-group><kwd-group xml:lang="en"><kwd>energy efficiency</kwd><kwd>household</kwd><kwd>load profile</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Na Li, Lijun Chen, Steven H. Low Optimal Demand Response Based on Utility Maximization in Power Networks Power and Energy Society General Meeting// IEEE Power and Energy Society General Meeting. 2011. P. 1–8.</mixed-citation><mixed-citation xml:lang="en">Na Li, Lijun Chen, Steven H. Low Optimal Demand Response Based on Utility  Maximization in Power Networks Power and Energy Society General Meeting// IEEE Power  and Energy Society General Meeting. 2011. P. 1–8.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Volkova I.O., Gubko M.V., Salnikova E.A. Active consumer: optimization problems of power consumption and self-generation // Automation and remote control. 2014. 75. 3. P. 551– 562. doi: http://dx.doi.org/10.1134/S0005117914030114.</mixed-citation><mixed-citation xml:lang="en">Volkova I.O., Gubko M.V., Salnikova E.A. Active consumer: optimization problems  of power consumption and self-generation. Automation and remote control. 2014. 75.  3. P. 551–562. doi: http://dx.doi.org/10.1134/S0005117914030114.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Albani M.H., El-Saadany E.F. A summary of demand response in electricity markets// Electric power systems Research. 2008. 11. 78. P. 1989– 1996.</mixed-citation><mixed-citation xml:lang="en">Albani M.H., El-Saadany E.F. A summary of demand response in electricity  markets// Electric power systems Research. 2008. 11. 78. P. 1989– 1996.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Ann-Piette M., Ghatikar G., Kiliccote S., Watson D., Koch E., Hennage D. Design and operation of an open, interoperable automated demand response infrastructure for commercial buildings // J. Comput. Inf. Sci. Eng. Jun. 2009. Vol. 9. P. 1–9.</mixed-citation><mixed-citation xml:lang="en">Ann-Piette M., Ghatikar G., Kiliccote S., Watson D., Koch E., Hennage D. Design  and operation of an open, interoperable automated demand response infrastructure for  commercial buildings.J. Comput. Inf. Sci. Eng. Jun. 2009. Vol. 9. P. 1–9.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Saeid Bashash, Hosam K. Fathy Modeling and Control Insights into Demand-side Energy Management through Setpoint Control of Thermostatic Loads// American Control Conference on O'Farrell Street. San Francisco. CA. USA. 2011 June 29 – July 01. P. 4546– 4553. doi: http://dx.doi.org/10.1109/ACC.2011.5990939.</mixed-citation><mixed-citation xml:lang="en">Saeid Bashash, Hosam K. Fathy Modeling and Control Insights into Demand-side  Energy Management through Setpoint Control of Thermostatic Loads// American Control  Conference on O'Farrell Street. San Francisco. CA. USA. 2011 June 29 – July 01. P. 4546–4553. doi: http://dx.doi.org/10.1109/ACC.2011.5990939.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Bradac Z., Kaczmarczyk V., Fiedler P. Optimal scheduling of domestic appliances via MILP// Energies. 2015. 8. 1. P. 217–232. doi: http://dx.doi.org/10.3390/en8010217.</mixed-citation><mixed-citation xml:lang="en">Bradac Z., Kaczmarczyk V., Fiedler P. Optimal scheduling of domestic appliances  via MILP// Energies. 2015. 8. 1. P. 217–232. doi: http://dx.doi.org/10.3390/en8010217.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">S-C Chan Load/price forecasting and managing demand response for smart grids: Methodologies and challenges// Signal processing magazine. 2012. 29. 5. P. 68–85. doi: http://dx.doi.org/10.1109/MSP.2012.2186531.</mixed-citation><mixed-citation xml:lang="en">S-C Chan Load/price forecasting and managing demand response for smart grids: Methodologies and challenges// Signal processing magazine. 2012. 29. 5. P. 68–85.  doi: http://dx.doi.org/10.1109/MSP.2012.2186531.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">A.J. Conejo, J.M. Morales, L. Baringo Realtime demand response model// Smart grid, IEEE transactions. 2010. 1. 3. P. 236–242. doi: http://dx.doi.org/10.1109/TSG.2010.2078843.</mixed-citation><mixed-citation xml:lang="en">A.J. Conejo, J.M. Morales, L. Baringo Realtime demand response model// Smart  grid, IEEE transactions. 2010. 1. 3. P. 236–242. doi: http://dx.doi.org/10.1109/TSG.2010.2078843.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">R.S. Ferreira, L.A.N. Barroso, M.M. Carvalho Demand response models with correlated price data: a robust optimization approach// App. Energy. 2012. 96. P. 133–149. doi: http://dx.doi.org/10.1016/j.apenergy.2012.01.016.</mixed-citation><mixed-citation xml:lang="en">R.S. Ferreira, L.A.N. Barroso, M.M. Carvalho Demand response models with  correlated price data: a robust optimization approach. App. Energy. 2012. 96. P.  133–149. doi: http://dx.doi.org/10.1016/j.apenergy. 2012.01.16.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">S. Gottwalt Demand side management – a simulation of household behavior under variable prices// Energy policy. 2011. 39. 12. P. 3–8174. doi: http://dx.doi.org/10.1016/j.enpol.2011.10.016.</mixed-citation><mixed-citation xml:lang="en">S. Gottwalt Demand side management – a simulation of household behavior under  variable prices// Energy policy. 2011. 39. 12. P. 3–8174. doi: http://dx.doi.org/10.1016/j.enpol.2011.10.016.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">B. Li Predicting user comfort level using machine learning for smart grid environments// Innovative smart grid technologies (ISGT 2011). P. 1–6.</mixed-citation><mixed-citation xml:lang="en">B. Li Predicting user comfort level using machine learning for smart grid  environments//Innovative smart grid technologies (ISGT 2011). P. 1–6.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">J.M. Lujano-Rojas Optimum residential load management strategy for real time pricing demand response programs// Energy policy. 2012. 45. P. 671–679. doi: http://dx.doi.org/10.1016/j.enpol.2012.03.019.</mixed-citation><mixed-citation xml:lang="en">J.M. Lujano-Rojas Optimum residential load management strategy for real time  pricing demand response programs// Energy policy. 2012. 45. P. 671–679. doi:  http://dx.doi.org/10.1016/j.enpol.2012.03.019.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Amir-Hamed Mohsenian-Rad, Alberto Leon-Garcia Optimal Residential Load Control With Price Prediction in Real-Time Electricity Pricing Environments// IEEE Transactions on smart grid.Sept. 2010. Vol.1. No.2. P. 120–133. doi: http://dx.doi.org/10.1109/TSG.2010.2055903.</mixed-citation><mixed-citation xml:lang="en">Amir-Hamed Mohsenian-Rad, Alberto Leon-Garcia Optimal Residential Load Control  With Price Prediction in Real-Time Electricity Pricing Environments// IEEE  Transactions on smart grid. Sept. 2010. Vol. 1. No. 2. P. 120–133. doi: http://dx.doi.org/10.1109/TSG.2010.2055903.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">M.A.A. Pedrasa, T.D. Spooner, I.F. MaxGill Scheduling of demand side resources using binary particke swarm optimization// IEEE Transactions on Power Systems. Aug. 2009. Vol. 24. No. 3. P. 1173–1181.</mixed-citation><mixed-citation xml:lang="en">M.A.A. Pedrasa, T.D. Spooner, I.F. MaxGill Scheduling of demand side resources  using binary particke swarm optimization// IEEE Transactions on Power Systems. Aug.  2009. Vol. 24. No. 3.P. 1173–1181.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">B. Ramanathan, V. Vittal A framework for evaluation of advanced direct load control with minimum disruption// IEEE Transactions on Power Systems. Nov. 2008 Vol. 23. No.4. P. 1681–1688. doi: http://dx.doi.org/10.1109/TPWRS.2008.2004732.</mixed-citation><mixed-citation xml:lang="en">B. Ramanathan, V. Vittal A framework for evaluation of advanced direct load  control with minimum disruption// IEEE Transactions on Power Systems. Nov. 2008 Vol.  23. No.4. P. 1681–1688. doi: http://dx.doi.org/10.1109/TPWRS.2008.2004732.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">K.C. Sou Scheduling smart home appliances using mixed integer linear programming// 50th IEEE conference on decision and control and European control conference (CDC-ECC 2011). P. 5144–5149. doi: http://dx.doi.org/10.1109/CDC.2011.6161081.</mixed-citation><mixed-citation xml:lang="en">K.C. Sou Scheduling smart home appliances using mixed integer linear  programming// 50th IEEE conference on decision and control and European control  conference (CDC-ECC 2011). P. 5144–5149. doi: http://dx.doi.org/10.1109/CDC.2011.6161081.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Scott Ziegenfus Demand Response And Light Control // ASHRAE Journal. November. 2012. P B20–B24.</mixed-citation><mixed-citation xml:lang="en">Scott Ziegenfus Demand Response And Light Control. ASHRAE Journal. November.  2012. P. B20–B24.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Capasso A., Grattieri W., Lamedica R., Prudenzi A. A bottom-up approach to residential load modeling// IEEE Transactions on Power Systems. Sept. 1994. Vol. 2. P. 957–965. doi: http://dx.doi.org/10.1109/59.317650.</mixed-citation><mixed-citation xml:lang="en">Capasso A., Grattieri W., Lamedica R., Prudenzi A. A bottom-up approach to  residential load modeling// IEEE Transactions on Power Systems. Sept. 1994. Vol. 2.  P. 957–965. doi: http://dx.doi.org/10.1109/59.317650.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Гребенюк Г.Г., Ковалев С.П., Крыгин А.А., Середа Л.А. Организация энергоменеджмента и планирование электрической нагрузки домохозяйств// Энергобезопасность и энергосбережение. 2015. № 3. С. 22–27.</mixed-citation><mixed-citation xml:lang="en">Grebenyuk G.G., Kovalev S.P., Krygin A.A., Sereda L.A. Organizatsiya  energomenedzhmenta i planirovaniye elektricheskoy nagruzki domokhozyaystv// Energobezopasnost’ i energosberezheniye. 2015. No. 3. P. 22–27. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Зоркальцев В.И., Филатов А.Ю. Новые варианты двойственных алгоритмов внутренних точек для систем линейных неравенств // Журнал вычислительной математики и математической физики. 2004. Том 44. № 7. С. 1234–1243.</mixed-citation><mixed-citation xml:lang="en">Zorkal’tsev V.I., Filatov A.YU. Novyye varianty dvoystvennykh algoritmov  vnutrennikh tochek dlya sistem lineynykh neravenstv. ZHurnal vychislitel’noy  matematiki i matematicheskoy fiziki. 2004. Tom 44. No. 7. P. 1234–1243. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Усков Е.И. Численное сравнение оптимизационных алгоритмов // Теоретические и прикладные задачи нелинейного анализа. ВЦ РАН Москва. 2012. С. 118–131.</mixed-citation><mixed-citation xml:lang="en">Uskov E.I. CHislennoye sravneniye optimizatsionnykh algoritmov. Teoreticheskiye  i prikladnyye zadachi nelineynogo analiza. VTS RAN Moskva. 2012. P. 118–131. (In  Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Callaway D. S. Tapping the energy storage potential in electric loads to deliver load following and regulation, with application to wind energy // Energy Conversion and Management. 2009, Vol. 50, P. 1389–1400. doi: http://dx.doi.org/10.1016/j.enconman.2008.12.012</mixed-citation><mixed-citation xml:lang="en">Callaway D. S. Tapping the energy storage potential in electric loads to deliver  load following and regulation, with application to wind energy. Energy Conversion  and Management. 2009, Vol. 50, P. 1389–1400. doi: http://dx.doi.org/10.1016/j.enconman. 2008.12.012</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
