# Systems and methods for optimal power flow on a radial network

## Abstract

Node controllers and power distribution networks in accordance with embodiments of the invention enable distributed power control. One embodiment includes a node controller including a distributed power control application; a plurality of node operating parameters describing the operating parameter of a node and a set of at least one node selected from the group consisting of an ancestor node and at least one child node; wherein send node operating parameters to nodes in the set of at least one node; receive operating parameters from the nodes in the set of at least one node; calculate a plurality of updated node operating parameters using an iterative process to determine the updated node operating parameters using the node operating parameters that describe the operating parameters of the node and the set of at least one node, where the iterative process involves evaluation of a closed form solution; and adjust node operating parameters.

- Inventors:

- Publication Date:

- Research Org.:
- California Institute of Technology, Pasadena, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1436178

- Patent Number(s):
- 9,954,362

- Application Number:
- 14/722,075

- Assignee:
- California Institute of Technology (Pasadena, CA) ARPA-E

- DOE Contract Number:
- AR0000226

- Resource Type:
- Patent

- Resource Relation:
- Patent File Date: 2015 May 26

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 24 POWER TRANSMISSION AND DISTRIBUTION

### Citation Formats

```
Low, Steven H., and Peng, Qiuyu.
```*Systems and methods for optimal power flow on a radial network*. United States: N. p., 2018.
Web.

```
Low, Steven H., & Peng, Qiuyu.
```*Systems and methods for optimal power flow on a radial network*. United States.

```
Low, Steven H., and Peng, Qiuyu. Tue .
"Systems and methods for optimal power flow on a radial network". United States. https://www.osti.gov/servlets/purl/1436178.
```

```
@article{osti_1436178,
```

title = {Systems and methods for optimal power flow on a radial network},

author = {Low, Steven H. and Peng, Qiuyu},

abstractNote = {Node controllers and power distribution networks in accordance with embodiments of the invention enable distributed power control. One embodiment includes a node controller including a distributed power control application; a plurality of node operating parameters describing the operating parameter of a node and a set of at least one node selected from the group consisting of an ancestor node and at least one child node; wherein send node operating parameters to nodes in the set of at least one node; receive operating parameters from the nodes in the set of at least one node; calculate a plurality of updated node operating parameters using an iterative process to determine the updated node operating parameters using the node operating parameters that describe the operating parameters of the node and the set of at least one node, where the iterative process involves evaluation of a closed form solution; and adjust node operating parameters.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Tue Apr 24 00:00:00 EDT 2018},

month = {Tue Apr 24 00:00:00 EDT 2018}

}

Works referenced in this record:

##
Dynamic Network Energy Management via Proximal Message Passing

journal, January 2014

- Kraning, Matt; Chu, Eric; Lavaei, Javad
- Foundations and Trends® in Optimization, Vol. 1, Issue 2, p. 73-126

##
Distributed methods for solving the security-constrained optimal power flow problem

conference, January 2012

- Phan, Dzung; Kalagnanam, Jayant
- 2012 IEEE PES Innovative Smart Grid Technologies (ISGT)

##
A fast distributed implementation of optimal power flow

journal, January 1999

- Baldick, R.; Kim, B. H.; Chase, C.
- IEEE Transactions on Power Systems, Vol. 14, Issue 3, p. 858-864

##
Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers

book, January 2011

- Boyd, Stephen; Parikh, Neal; Chu, Eric

##
Distributed Optimal Power Flow for Smart Microgrids

journal, September 2013

- Dall'Anese, Emiliano; Zhu, Hao; Giannakis, Georgios B.
- IEEE Transactions on Smart Grid, Vol. 4, Issue 3, p. 1464-1475

##
Stability and convergence of distributed algorithms for the OPF problem

conference, December 2013

- Devane, Eoin; Lestas, Ioannis
- 52nd IEEE Conference on Decision and Control

##
Branch Flow Model: Relaxations and Convexification—Part II

journal, August 2013

- Farivar, Masoud; Low, Steven H.
- IEEE Transactions on Power Systems, Vol. 28, Issue 3, p. 2565-2572

##
Branch Flow Model: Relaxations and Convexification—Part I

journal, August 2013

- Farivar, Masoud; Low, Steven H.
- IEEE Transactions on Power Systems, Vol. 28, Issue 3, p. 2554-2564

##
Exact Convex Relaxation of Optimal Power Flow in Radial Networks

journal, January 2015

- Gan, Lingwen; Li, Na; Topcu, Ufuk
- IEEE Transactions on Automatic Control, Vol. 60, Issue 1, p. 72-87

##
Optimal power flow in direct current networks

conference, December 2013

- Gan, Lingwen; Low, Steven H.
- 52nd IEEE Conference on Decision and Control

##
Coarse-grained distributed optimal power flow

journal, May 1997

- Kim, B. H.; Baldick, R.
- IEEE Transactions on Power Systems, Vol. 12, Issue 2, p. 932-939

##
Distributed algorithms for optimal power flow problem

conference, December 2012

- Lam, Albert Y. S.; Zhang, Baosen; Tse, David N.
- 2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

##
Demand response in radial distribution networks: Distributed algorithm

conference, November 2012

- Li, Na; Chen, Lijun; Low, Steven H.
- 2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers

##
Convex Relaxation of Optimal Power Flow—Part II: Exactness

journal, June 2014

- Low, Steven H.
- IEEE Transactions on Control of Network Systems, Vol. 1, Issue 2, p. 177-189

##
Convex Relaxation of Optimal Power Flow—Part I: Formulations and Equivalence

journal, March 2014

- Low, Steven H.
- IEEE Transactions on Control of Network Systems, Vol. 1, Issue 1, p. 15-27

##
Distributed algorithm for optimal power flow on a radial network

conference, December 2014

- Peng, Qiuyu; Low, Steven H.
- 53rd IEEE Conference on Decision and Control

##
Feeder Reconfiguration in Distribution Networks Based on Convex Relaxation of OPF

journal, July 2015

- Peng, Qiuyu; Tang, Yujie; Low, Steven H.
- IEEE Transactions on Power Systems, Vol. 30, Issue 4, p. 1793-1804

##
HERB: a home exploring robotic butler

journal, November 2009

- Srinivasa, Siddhartha S.; Ferguson, Dave; Helfrich, Casey J.
- Autonomous Robots, Vol. 28, Issue 1, p. 5-20

##
Fully decentralized AC optimal power flow algorithms

conference, January 2013

- Sun, Andy X.; Phan, Dzung T.; Ghosh, Soumyadip
- 2013 IEEE Power & Energy Society General Meeting