An algorithm for solving the dual problem of hydrothermal scheduling
Lagrangian relaxation has been widely used for the hydrothermal scheduling of power systems. The idea is to use Lagrangian multipliers to relax system-wide demand and reserve requirements, and decompose the problem into unit-wise subproblems that are much easier to solve. The multipliers are then up...
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| Veröffentlicht in: | IEEE transactions on power systems 1998-05, Vol.13 (2), p.593-600 |
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| container_title | IEEE transactions on power systems |
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| creator | Luh, P.B. Zhang, D. Tomastik, R.N. |
| description | Lagrangian relaxation has been widely used for the hydrothermal scheduling of power systems. The idea is to use Lagrangian multipliers to relax system-wide demand and reserve requirements, and decompose the problem into unit-wise subproblems that are much easier to solve. The multipliers are then updated at the high level, most commonly by using a subgradient method (SGM). Since the high level dual function is nondifferentiable with many "ridges", the SGM may zigzag across ridges resulting in slow convergence. This paper presents an algorithm that utilizes a recently developed "reduced complexity bundle method" (RCBM) to update the multipliers at the high level. The RCBM is a kind of "bundle method" that enjoy faster convergence compared to SGM, but has much reduced complexity as compared to a conventional bundle method. Testing results show that RCBM can find better directions, avoid zigzagging behavior and obtain better dual and feasible solutions as compared to the SGM. |
| doi_str_mv | 10.1109/59.667387 |
| format | Article |
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The idea is to use Lagrangian multipliers to relax system-wide demand and reserve requirements, and decompose the problem into unit-wise subproblems that are much easier to solve. The multipliers are then updated at the high level, most commonly by using a subgradient method (SGM). Since the high level dual function is nondifferentiable with many "ridges", the SGM may zigzag across ridges resulting in slow convergence. This paper presents an algorithm that utilizes a recently developed "reduced complexity bundle method" (RCBM) to update the multipliers at the high level. The RCBM is a kind of "bundle method" that enjoy faster convergence compared to SGM, but has much reduced complexity as compared to a conventional bundle method. Testing results show that RCBM can find better directions, avoid zigzagging behavior and obtain better dual and feasible solutions as compared to the SGM.</description><identifier>ISSN: 0885-8950</identifier><identifier>EISSN: 1558-0679</identifier><identifier>DOI: 10.1109/59.667387</identifier><identifier>CODEN: ITPSEG</identifier><language>eng</language><publisher>IEEE</publisher><subject>Algorithms ; Computational complexity ; Convergence ; Costs ; Hydroelectric generators ; Lagrange multipliers ; Lagrangian functions ; Linear programming ; Power engineering and energy ; Power systems ; Problem solving ; Processor scheduling ; Scheduling algorithm ; Systems engineering and theory ; Testing</subject><ispartof>IEEE transactions on power systems, 1998-05, Vol.13 (2), p.593-600</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c350t-5209bebbe216011c90a4f65ac9cf3fa68310af2b15d92ab30bf145a157dbb7b3</citedby><cites>FETCH-LOGICAL-c350t-5209bebbe216011c90a4f65ac9cf3fa68310af2b15d92ab30bf145a157dbb7b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/667387$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/667387$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Luh, P.B.</creatorcontrib><creatorcontrib>Zhang, D.</creatorcontrib><creatorcontrib>Tomastik, R.N.</creatorcontrib><title>An algorithm for solving the dual problem of hydrothermal scheduling</title><title>IEEE transactions on power systems</title><addtitle>TPWRS</addtitle><description>Lagrangian relaxation has been widely used for the hydrothermal scheduling of power systems. 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Testing results show that RCBM can find better directions, avoid zigzagging behavior and obtain better dual and feasible solutions as compared to the SGM.</description><subject>Algorithms</subject><subject>Computational complexity</subject><subject>Convergence</subject><subject>Costs</subject><subject>Hydroelectric generators</subject><subject>Lagrange multipliers</subject><subject>Lagrangian functions</subject><subject>Linear programming</subject><subject>Power engineering and energy</subject><subject>Power systems</subject><subject>Problem solving</subject><subject>Processor scheduling</subject><subject>Scheduling algorithm</subject><subject>Systems engineering and theory</subject><subject>Testing</subject><issn>0885-8950</issn><issn>1558-0679</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1998</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNqF0D1rwzAQBmBRWmiadujaSVOhg9OT7JOlMaSfEOiS3Ui2lLjIUSrZhfz7ujh07XRw78NxvITcMlgwBuoR1UKIMpflGZkxRJmBKNU5mYGUmEmFcEmuUvoEgJGpGXla7qn22xDbftdRFyJNwX-3-y3td5Y2g_b0EIPxtqPB0d2xiWEMYjfuU72zzeBHe00unPbJ3pzmnGxenjert2z98fq-Wq6zOkfoM-SgjDXGciaAsVqBLpxAXava5U4LmTPQjhuGjeLa5GAcK1AzLBtjSpPPyf10dvzoa7Cpr7o21dZ7vbdhSBWXBUco-P9QCI6S4wgfJljHkFK0rjrEttPxWDGofvusUFVTn6O9m2xrrf1zp_AHLI5wTg</recordid><startdate>19980501</startdate><enddate>19980501</enddate><creator>Luh, P.B.</creator><creator>Zhang, D.</creator><creator>Tomastik, R.N.</creator><general>IEEE</general><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>7SU</scope><scope>8FD</scope><scope>C1K</scope><scope>FR3</scope><scope>L7M</scope></search><sort><creationdate>19980501</creationdate><title>An algorithm for solving the dual problem of hydrothermal scheduling</title><author>Luh, P.B. ; Zhang, D. ; Tomastik, R.N.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c350t-5209bebbe216011c90a4f65ac9cf3fa68310af2b15d92ab30bf145a157dbb7b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1998</creationdate><topic>Algorithms</topic><topic>Computational complexity</topic><topic>Convergence</topic><topic>Costs</topic><topic>Hydroelectric generators</topic><topic>Lagrange multipliers</topic><topic>Lagrangian functions</topic><topic>Linear programming</topic><topic>Power engineering and energy</topic><topic>Power systems</topic><topic>Problem solving</topic><topic>Processor scheduling</topic><topic>Scheduling algorithm</topic><topic>Systems engineering and theory</topic><topic>Testing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Luh, P.B.</creatorcontrib><creatorcontrib>Zhang, D.</creatorcontrib><creatorcontrib>Tomastik, R.N.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Environmental Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Environmental Sciences and Pollution Management</collection><collection>Engineering Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>IEEE transactions on power systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Luh, P.B.</au><au>Zhang, D.</au><au>Tomastik, R.N.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An algorithm for solving the dual problem of hydrothermal scheduling</atitle><jtitle>IEEE transactions on power systems</jtitle><stitle>TPWRS</stitle><date>1998-05-01</date><risdate>1998</risdate><volume>13</volume><issue>2</issue><spage>593</spage><epage>600</epage><pages>593-600</pages><issn>0885-8950</issn><eissn>1558-0679</eissn><coden>ITPSEG</coden><abstract>Lagrangian relaxation has been widely used for the hydrothermal scheduling of power systems. The idea is to use Lagrangian multipliers to relax system-wide demand and reserve requirements, and decompose the problem into unit-wise subproblems that are much easier to solve. The multipliers are then updated at the high level, most commonly by using a subgradient method (SGM). Since the high level dual function is nondifferentiable with many "ridges", the SGM may zigzag across ridges resulting in slow convergence. This paper presents an algorithm that utilizes a recently developed "reduced complexity bundle method" (RCBM) to update the multipliers at the high level. The RCBM is a kind of "bundle method" that enjoy faster convergence compared to SGM, but has much reduced complexity as compared to a conventional bundle method. Testing results show that RCBM can find better directions, avoid zigzagging behavior and obtain better dual and feasible solutions as compared to the SGM.</abstract><pub>IEEE</pub><doi>10.1109/59.667387</doi><tpages>8</tpages></addata></record> |
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| ispartof | IEEE transactions on power systems, 1998-05, Vol.13 (2), p.593-600 |
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| source | IEEE Electronic Library (IEL) |
| subjects | Algorithms Computational complexity Convergence Costs Hydroelectric generators Lagrange multipliers Lagrangian functions Linear programming Power engineering and energy Power systems Problem solving Processor scheduling Scheduling algorithm Systems engineering and theory Testing |
| title | An algorithm for solving the dual problem of hydrothermal scheduling |
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