DistFlow ODE: Modeling, analyzing and controlling long distribution feeder
We consider a linear feeder connecting multiple distributed loads and generators to the sub-station. Voltage is controlled directly at the sub-station, however, voltage down the line shifts up or down, in particular depending on if the feeder operates in the power export regime or power import regim...
| Main Authors: | , , |
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers
2013
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| Online Access: | http://hdl.handle.net/1721.1/82525 https://orcid.org/0000-0002-7997-8962 |
| _version_ | 1826216690437849088 |
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| author | Wang, Danhua Turitsyn, Konstantin Chertkov, Michael |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Wang, Danhua Turitsyn, Konstantin Chertkov, Michael |
| author_sort | Wang, Danhua |
| collection | MIT |
| description | We consider a linear feeder connecting multiple distributed loads and generators to the sub-station. Voltage is controlled directly at the sub-station, however, voltage down the line shifts up or down, in particular depending on if the feeder operates in the power export regime or power import regime. Starting from this finite element description of the feeder, assuming that the consumption/generation is distributed heterogeneously along the feeder, and following the asymptotic homogenization approach, we derive simple low-parametric ODE model of the feeder. We also explain how the homogeneous ODE modeling is generalized to account for other distributed effects, e.g. for inverter based and voltage dependent control of reactive power. The resulting system of the DistFlow-ODEs, relating homogenized voltage to flows of real and reactive power along the lines, admits computationally efficient analysis in terms of the minimal number of the feeder line “media” parameters, such as the ratio of the inductance-to-resistance densities. Exploring the space of the media and control parameters allows us to test and juxtapose different measures of the system performance, in particular expressed in terms of the voltage drop along the feeder, power import/export from the feeder line as the whole, power losses within the feeder, and critical (with respect to possible voltage collapse) length of the feeder. Our most surprising funding relates to performance of a feeder rich on PhotoVoltaic (PV) systems during a sunny day. We observe that if the feeder is sufficiently long the DistFlow-ODEs may have multiple stable solutions. The multiplicity may mean troubles for successful recovery of the feeder after a very short, few periods long, fault at the head of the line. |
| first_indexed | 2024-09-23T16:51:32Z |
| format | Article |
| id | mit-1721.1/82525 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:51:32Z |
| publishDate | 2013 |
| publisher | Institute of Electrical and Electronics Engineers |
| record_format | dspace |
| spelling | mit-1721.1/825252022-10-03T08:45:23Z DistFlow ODE: Modeling, analyzing and controlling long distribution feeder Wang, Danhua Turitsyn, Konstantin Chertkov, Michael Massachusetts Institute of Technology. Department of Mechanical Engineering Turitsyn, Konstantin We consider a linear feeder connecting multiple distributed loads and generators to the sub-station. Voltage is controlled directly at the sub-station, however, voltage down the line shifts up or down, in particular depending on if the feeder operates in the power export regime or power import regime. Starting from this finite element description of the feeder, assuming that the consumption/generation is distributed heterogeneously along the feeder, and following the asymptotic homogenization approach, we derive simple low-parametric ODE model of the feeder. We also explain how the homogeneous ODE modeling is generalized to account for other distributed effects, e.g. for inverter based and voltage dependent control of reactive power. The resulting system of the DistFlow-ODEs, relating homogenized voltage to flows of real and reactive power along the lines, admits computationally efficient analysis in terms of the minimal number of the feeder line “media” parameters, such as the ratio of the inductance-to-resistance densities. Exploring the space of the media and control parameters allows us to test and juxtapose different measures of the system performance, in particular expressed in terms of the voltage drop along the feeder, power import/export from the feeder line as the whole, power losses within the feeder, and critical (with respect to possible voltage collapse) length of the feeder. Our most surprising funding relates to performance of a feeder rich on PhotoVoltaic (PV) systems during a sunny day. We observe that if the feeder is sufficiently long the DistFlow-ODEs may have multiple stable solutions. The multiplicity may mean troubles for successful recovery of the feeder after a very short, few periods long, fault at the head of the line. United States. Dept. of Energy Los Alamos National Laboratory (Contract No. DE-AC52- 06NA25396) United States. Defense Threat Reduction Agency (DTRA/DOD grant BRCALL06-Per3-D-2-0022) National Science Foundation (U.S.) New Mexico Consortium 2013-11-21T18:39:12Z 2013-11-21T18:39:12Z 2012-12 Article http://purl.org/eprint/type/ConferencePaper 978-1-4673-2066-5 978-1-4673-2065-8 978-1-4673-2063-4 978-1-4673-2064-1 0743-1546 INSPEC Accession Number: 13288687 http://hdl.handle.net/1721.1/82525 Wang, Danhua, Konstantin Turitsyn, and Michael Chertkov. DistFlow ODE: Modeling, Analyzing and Controlling Long Distribution Feeder. In 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 5613-5618. Institute of Electrical and Electronics Engineers, 2012. https://orcid.org/0000-0002-7997-8962 en_US http://dx.doi.org/10.1109/CDC.2012.6426054 2012 IEEE 51st IEEE Conference on Decision and Control (CDC) Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Institute of Electrical and Electronics Engineers arXiv |
| spellingShingle | Wang, Danhua Turitsyn, Konstantin Chertkov, Michael DistFlow ODE: Modeling, analyzing and controlling long distribution feeder |
| title | DistFlow ODE: Modeling, analyzing and controlling long distribution feeder |
| title_full | DistFlow ODE: Modeling, analyzing and controlling long distribution feeder |
| title_fullStr | DistFlow ODE: Modeling, analyzing and controlling long distribution feeder |
| title_full_unstemmed | DistFlow ODE: Modeling, analyzing and controlling long distribution feeder |
| title_short | DistFlow ODE: Modeling, analyzing and controlling long distribution feeder |
| title_sort | distflow ode modeling analyzing and controlling long distribution feeder |
| url | http://hdl.handle.net/1721.1/82525 https://orcid.org/0000-0002-7997-8962 |
| work_keys_str_mv | AT wangdanhua distflowodemodelinganalyzingandcontrollinglongdistributionfeeder AT turitsynkonstantin distflowodemodelinganalyzingandcontrollinglongdistributionfeeder AT chertkovmichael distflowodemodelinganalyzingandcontrollinglongdistributionfeeder |