Methods and systems for determining a linear power flow for a distribution network

Abstract

Methods and systems are disclosed for determining active and/or reactive power flows in a distribution line of a distribution network. The determined power flows may be linear in nature, and they may further be used to determine an overall network power flow for the distribution network. Further, the network power flow can be used to determine a voltage magnitude for any distribution bus in the distribution network. The methods and systems are capable of considering a plurality of sensitivity factors that may affect one or more distribution buses.

1 . A method comprising:
 receiving, by a computing device, from a distribution network, voltage data associated with a plurality of buses;   determining, based on the voltage data, a first power flow and a second power flow;   determining, based on the first power flow and the second power flow, a network power flow;   determining, based the network power flow, a relationship between a voltage magnitude at each bus of the plurality of buses in the distribution network and nodal injections at each bus in the distribution network; and   causing, based on the relationship between the voltage magnitude at each bus and the nodal injections at each bus, the distribution network to perform voltage and reactive power management.   
     
     
         2 . The method of  claim 1 , wherein the distribution network comprises at least three buses. 
     
     
         3 . The method of  claim 1 , wherein the distribution network comprises a three-phase unbalanced distribution network. 
     
     
         4 . The method of  claim 1 , wherein the voltage data is indicative of a voltage magnitude for one or more of a point of interest, a first bus, and a second bus. 
     
     
         5 . The method of  claim 1 , wherein the voltage data is indicative of a voltage angle for one or more of a point of interest, a first bus, and a second bus. 
     
     
         6 . The method of  claim 1 , wherein at least one of the first power flow and the second power flow comprises an active power flow and a reactive power flow associated with a distribution line between a first bus of the distribution network and a second bus of the distribution network. 
     
     
         7 . The method of  claim 1 , wherein determining, based on the voltage data, the first power flow and the second power flow comprises:
 determining, based on the voltage data, a first difference between a voltage magnitude and a voltage angle at a point of interest and a voltage magnitude and a voltage angle at a first bus and a second difference between the voltage magnitude and the voltage angle at the point of interest and a voltage magnitude and a voltage angle at a second bus; and   determining, based on the first difference and the second difference, the first power flow and the second power flow for a distribution line between the first bus and the second bus.   
     
     
         8 . The method of  claim 7 , wherein the point of interest comprises a position in the distribution network at which the distribution network is coupled to an upstream subtransmission network. 
     
     
         9 . The method of  claim 7 , wherein the first difference and the second difference are assumed to be zero. 
     
     
         10 . The method of  claim 7 , further comprising:
 determining, based on the voltage data, a voltage magnitude and a voltage angle for a third bus in the distribution network.   
     
     
         11 . An apparatus comprising:
 one or more processors; and   a memory storing processor-executable instructions that, when executed by the one or more processors, cause the apparatus to:
 receive, from a distribution network, voltage data associated with a plurality of buses; 
 determine, based on the voltage data, a first power flow and a second power flow; 
 determine, based on the first power flow and the second power flow, a network power flow; 
 determine, based the network power flow, a relationship between a voltage magnitude at each bus of the plurality of buses in the distribution network and nodal injections at each bus in the distribution network; and 
 cause, based on the relationship between the voltage magnitude at each bus and the nodal injections at each bus, the distribution network to perform voltage and reactive power management. 
   
     
     
         12 . The apparatus of  claim 11 , wherein the distribution network comprises at least three buses. 
     
     
         13 . The apparatus of  claim 11 , wherein the distribution network comprises a three-phase unbalanced distribution network. 
     
     
         14 . The apparatus of  claim 11 , wherein the voltage data is indicative of a voltage magnitude for one or more of a point of interest, a first bus, and a second bus. 
     
     
         15 . The apparatus of  claim 11 , wherein the voltage data is indicative of a voltage angle for one or more of a point of interest, a first bus, and a second bus. 
     
     
         16 . The apparatus of  claim 11 , wherein at least one of the first power flow and the second power flow comprises an active power flow and a reactive power flow associated with a distribution line between a first bus of the distribution network and a second bus of the distribution network. 
     
     
         17 . The apparatus of  claim 11 , wherein the processor-executable instructions that, when executed by the one or more processors, cause the apparatus to determine, based on the voltage data, the first power flow and the second power flow, further cause the apparatus to:
 determine, based on the voltage data, a first difference between a voltage magnitude and a voltage angle at a point of interest and a voltage magnitude and a voltage angle at a first bus and a second difference between the voltage magnitude and the voltage angle at the point of interest and a voltage magnitude and a voltage angle at a second bus; and   determine, based on the first difference and the second difference, the first power flow and the second power flow for a distribution line between the first bus and the second bus.   
     
     
         18 . The apparatus of  claim 17 , wherein the point of interest comprises a position in the distribution network at which the distribution network is coupled to an upstream subtransmission network. 
     
     
         19 . The apparatus of  claim 17 , wherein the first difference and the second difference are assumed to be zero. 
     
     
         20 . The apparatus of  claim 17 , wherein the processor-executable instructions, when executed by the one or more processors, further cause the apparatus to:
 determine, based on the voltage data, a voltage magnitude and a voltage angle for a third bus in the distribution network.