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A least squares solution for optimal power flow sensitivity calculation
A least-squares-based algorithm is proposed that is suitable for post optimal power flow (OPF) sensitivity calculations. It computes Lagrange multipliers. The algorithm involves the formulation of a Lagrangian which includes the appropriate objective function and all the enforced constraints. By app...
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| Published in: | IEEE transactions on power systems 1992-08, Vol.7 (3), p.1394-1401 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c304t-ba6f7c4665ed383f839e2c95733d7e3cc8549e180868df2cb2d5953749ad4ba83 |
| container_end_page | 1401 |
| container_issue | 3 |
| container_start_page | 1394 |
| container_title | IEEE transactions on power systems |
| container_volume | 7 |
| creator | Venkatesh, S.V. Liu, W.-H.E. Papalexopoulos, A.D. |
| description | A least-squares-based algorithm is proposed that is suitable for post optimal power flow (OPF) sensitivity calculations. It computes Lagrange multipliers. The algorithm involves the formulation of a Lagrangian which includes the appropriate objective function and all the enforced constraints. By applying the Kuhn-Tucker conditions, the derivatives of the Lagrangian at the solution with respect to free variables provide a set of over-determined equations for the Lagrange multipliers. A least-squares estimation of the Lagrange multipliers with the over-determined set of equations is used. The mathematical formulation of the least-squares problem for the sensitivity calculation is presented. A computationally efficient method of solving the normal equation is derived. Special care has been taken to accurately model all controls and all operating and security constraints. The algorithm has been tested on a reasonably large system. The results indicate the validity of the approach.< > |
| doi_str_mv | 10.1109/59.207359 |
| format | article |
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It computes Lagrange multipliers. The algorithm involves the formulation of a Lagrangian which includes the appropriate objective function and all the enforced constraints. By applying the Kuhn-Tucker conditions, the derivatives of the Lagrangian at the solution with respect to free variables provide a set of over-determined equations for the Lagrange multipliers. A least-squares estimation of the Lagrange multipliers with the over-determined set of equations is used. The mathematical formulation of the least-squares problem for the sensitivity calculation is presented. A computationally efficient method of solving the normal equation is derived. Special care has been taken to accurately model all controls and all operating and security constraints. The algorithm has been tested on a reasonably large system. The results indicate the validity of the approach.< ></description><identifier>ISSN: 0885-8950</identifier><identifier>EISSN: 1558-0679</identifier><identifier>DOI: 10.1109/59.207359</identifier><identifier>CODEN: ITPSEG</identifier><language>eng</language><publisher>United States: IEEE</publisher><subject>240200 - Power System Networks, Transmission & Distribution- (1990-) ; 990200 - Mathematics & Computers ; ALGORITHMS ; COMPUTER CODES ; Control systems ; Costs ; ELECTRIC UTILITIES ; GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE ; LEAST SQUARE FIT ; Least squares approximation ; Least squares methods ; Linear programming ; Load flow ; MATHEMATICAL LOGIC ; MAXIMUM-LIKELIHOOD FIT ; Medical services ; NUMERICAL SOLUTION ; OPTIMIZATION ; POWER ; Power generation ; POWER TRANSMISSION AND DISTRIBUTION ; Power transmission lines ; Production ; PUBLIC UTILITIES ; SENSITIVITY</subject><ispartof>IEEE transactions on power systems, 1992-08, Vol.7 (3), p.1394-1401</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c304t-ba6f7c4665ed383f839e2c95733d7e3cc8549e180868df2cb2d5953749ad4ba83</citedby><cites>FETCH-LOGICAL-c304t-ba6f7c4665ed383f839e2c95733d7e3cc8549e180868df2cb2d5953749ad4ba83</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/207359$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>230,314,780,784,885,27924,27925,54796</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/7281205$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Venkatesh, S.V.</creatorcontrib><creatorcontrib>Liu, W.-H.E.</creatorcontrib><creatorcontrib>Papalexopoulos, A.D.</creatorcontrib><title>A least squares solution for optimal power flow sensitivity calculation</title><title>IEEE transactions on power systems</title><addtitle>TPWRS</addtitle><description>A least-squares-based algorithm is proposed that is suitable for post optimal power flow (OPF) sensitivity calculations. It computes Lagrange multipliers. The algorithm involves the formulation of a Lagrangian which includes the appropriate objective function and all the enforced constraints. By applying the Kuhn-Tucker conditions, the derivatives of the Lagrangian at the solution with respect to free variables provide a set of over-determined equations for the Lagrange multipliers. A least-squares estimation of the Lagrange multipliers with the over-determined set of equations is used. The mathematical formulation of the least-squares problem for the sensitivity calculation is presented. A computationally efficient method of solving the normal equation is derived. Special care has been taken to accurately model all controls and all operating and security constraints. The algorithm has been tested on a reasonably large system. The results indicate the validity of the approach.< ></description><subject>240200 - Power System Networks, Transmission & Distribution- (1990-)</subject><subject>990200 - Mathematics & Computers</subject><subject>ALGORITHMS</subject><subject>COMPUTER CODES</subject><subject>Control systems</subject><subject>Costs</subject><subject>ELECTRIC UTILITIES</subject><subject>GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE</subject><subject>LEAST SQUARE FIT</subject><subject>Least squares approximation</subject><subject>Least squares methods</subject><subject>Linear programming</subject><subject>Load flow</subject><subject>MATHEMATICAL LOGIC</subject><subject>MAXIMUM-LIKELIHOOD FIT</subject><subject>Medical services</subject><subject>NUMERICAL SOLUTION</subject><subject>OPTIMIZATION</subject><subject>POWER</subject><subject>Power generation</subject><subject>POWER TRANSMISSION AND DISTRIBUTION</subject><subject>Power transmission lines</subject><subject>Production</subject><subject>PUBLIC UTILITIES</subject><subject>SENSITIVITY</subject><issn>0885-8950</issn><issn>1558-0679</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1992</creationdate><recordtype>article</recordtype><recordid>eNo90MFLwzAUBvAgCs7pwaun4EHw0JkmTZscx9ApDLzoOWTpK0ayputLHfvvrXR4eofvxwfvI-Q2Z4s8Z_pJ6gVnlZD6jMxyKVXGykqfkxlTSmZKS3ZJrhC_GWPlGMzIekkDWEwU94PtASnGMCQfW9rEnsYu-Z0NtIsH6GkT4oEitOiT__HpSJ0Nbgj2j1-Ti8YGhJvTnZPPl-eP1Wu2eV-_rZabzAlWpGxry6ZyRVlKqIUSjRIauNOyEqKuQDinZKEhV0yVqm642_JaaimqQtu62Fol5uR-6o2YvEHnE7gvF9sWXDIVVzlnckQPE-r6uB8Ak9l5dBCCbSEOaLgSJeNajPBxgq6PiD00puvHh_ujyZn529NIbaY9R3s3WQ8A_-4U_gJwMnAI</recordid><startdate>19920801</startdate><enddate>19920801</enddate><creator>Venkatesh, S.V.</creator><creator>Liu, W.-H.E.</creator><creator>Papalexopoulos, A.D.</creator><general>IEEE</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>8FD</scope><scope>L7M</scope><scope>OTOTI</scope></search><sort><creationdate>19920801</creationdate><title>A least squares solution for optimal power flow sensitivity calculation</title><author>Venkatesh, S.V. ; Liu, W.-H.E. ; Papalexopoulos, A.D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c304t-ba6f7c4665ed383f839e2c95733d7e3cc8549e180868df2cb2d5953749ad4ba83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1992</creationdate><topic>240200 - Power System Networks, Transmission & Distribution- (1990-)</topic><topic>990200 - Mathematics & Computers</topic><topic>ALGORITHMS</topic><topic>COMPUTER CODES</topic><topic>Control systems</topic><topic>Costs</topic><topic>ELECTRIC UTILITIES</topic><topic>GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE</topic><topic>LEAST SQUARE FIT</topic><topic>Least squares approximation</topic><topic>Least squares methods</topic><topic>Linear programming</topic><topic>Load flow</topic><topic>MATHEMATICAL LOGIC</topic><topic>MAXIMUM-LIKELIHOOD FIT</topic><topic>Medical services</topic><topic>NUMERICAL SOLUTION</topic><topic>OPTIMIZATION</topic><topic>POWER</topic><topic>Power generation</topic><topic>POWER TRANSMISSION AND DISTRIBUTION</topic><topic>Power transmission lines</topic><topic>Production</topic><topic>PUBLIC UTILITIES</topic><topic>SENSITIVITY</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Venkatesh, S.V.</creatorcontrib><creatorcontrib>Liu, W.-H.E.</creatorcontrib><creatorcontrib>Papalexopoulos, A.D.</creatorcontrib><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>OSTI.GOV</collection><jtitle>IEEE transactions on power systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Venkatesh, S.V.</au><au>Liu, W.-H.E.</au><au>Papalexopoulos, A.D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A least squares solution for optimal power flow sensitivity calculation</atitle><jtitle>IEEE transactions on power systems</jtitle><stitle>TPWRS</stitle><date>1992-08-01</date><risdate>1992</risdate><volume>7</volume><issue>3</issue><spage>1394</spage><epage>1401</epage><pages>1394-1401</pages><issn>0885-8950</issn><eissn>1558-0679</eissn><coden>ITPSEG</coden><abstract>A least-squares-based algorithm is proposed that is suitable for post optimal power flow (OPF) sensitivity calculations. It computes Lagrange multipliers. The algorithm involves the formulation of a Lagrangian which includes the appropriate objective function and all the enforced constraints. By applying the Kuhn-Tucker conditions, the derivatives of the Lagrangian at the solution with respect to free variables provide a set of over-determined equations for the Lagrange multipliers. A least-squares estimation of the Lagrange multipliers with the over-determined set of equations is used. The mathematical formulation of the least-squares problem for the sensitivity calculation is presented. A computationally efficient method of solving the normal equation is derived. Special care has been taken to accurately model all controls and all operating and security constraints. The algorithm has been tested on a reasonably large system. The results indicate the validity of the approach.< ></abstract><cop>United States</cop><pub>IEEE</pub><doi>10.1109/59.207359</doi><tpages>8</tpages></addata></record> |
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| ispartof | IEEE transactions on power systems, 1992-08, Vol.7 (3), p.1394-1401 |
| issn | 0885-8950 1558-0679 |
| language | eng |
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| source | IEEE Electronic Library (IEL) Journals |
| subjects | 240200 - Power System Networks, Transmission & Distribution- (1990-) 990200 - Mathematics & Computers ALGORITHMS COMPUTER CODES Control systems Costs ELECTRIC UTILITIES GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE LEAST SQUARE FIT Least squares approximation Least squares methods Linear programming Load flow MATHEMATICAL LOGIC MAXIMUM-LIKELIHOOD FIT Medical services NUMERICAL SOLUTION OPTIMIZATION POWER Power generation POWER TRANSMISSION AND DISTRIBUTION Power transmission lines Production PUBLIC UTILITIES SENSITIVITY |
| title | A least squares solution for optimal power flow sensitivity calculation |
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