Method for determining power flow in an electrical distribution system

1. A method for determining a power flow in an electrical distribution network comprising:

determining respective feeder apparent powers of a plurality of electrical distribution network feeders receiving electrical power from a supply node of an electrical distribution network responsive to respective feeder currents in the feeders and a node voltage of the supply node;

generating a system of node equations having feeder power factor angles of each of the feeders as variables and relating the feeder apparent powers with respect to a supply node active power, and a supply node reactive power, wherein the system of node equations is defined as follows:

P inj =S 1 cos φ 1 +S 2 cos φ 2 +S 3 cos φ 3 + . . . +S n cos φ n,

Q inj =S 1 sin φ 1 +S 2 sin φ 2 +S 3 sin φ 3 + . . . +S n sin φ n

wherein n is a positive integer that represents a number of feeders, φ n represents a power factor angle for an n th feeder, S n represents apparent power for the n th feeder with respect to injected active power P inj and injected reactive power Q inj ;

solving the system of node equations for at least one of the feeder power factor angles; and

using the feeder power factor angle for determining a power flow in the electrical distribution network.

2. The method of claim 1 , further comprising calculating at least one of a feeder active power and a feeder reactive power responsive to a corresponding feeder apparent power and a corresponding feeder power factor angle.

3. The method of claim 2 , further comprising generating a load scaling factor responsive to at least one of the feeder active powers and the feeder reactive powers.

4. The method of claim 3 , further comprising using the load scaling factor to determine a load allocation among the feeders.

5. The method of claim 1 , wherein solving the system of node equations comprises using an iterative technique.

6. A method for determining a power flow in an electrical distribution network comprising:

determining respective feeder apparent powers of electrical power feeders connected at a supply node of an electrical distribution network;

relating the feeder apparent powers with respect to a supply node active power and a supply node reactive power, wherein the relating is defined by the following system of equations:

P inj =S 1 cos φ 1 +S 2 cos φ 2 +S 3 cos φ 3 + . . . +S n cos φ n

Q inj =S 1 sin φ 1 +S 2 sin φ 2 +S 3 sin φ 3 + . . . +S n sin φ n,

wherein n is a positive integer that represents a number of feeders, φ n represents a power factor angle for an n th feeder, S n represents apparent power for the n th feeder with respect to injected active power P inj and injected reactive power Q inj ;

determining a feeder power factor angle of at least one of the feeders responsive to the feeder apparent powers, the supply node active power, and the supply node reactive power; and

using at least one of the feeder power factor angles for determining a power flow in the electrical distribution network.

7. The method of claim 6 , wherein determining a feeder power factor angle comprises generating a system of node equations having feeder power factor angles of each of the feeders as variables and relating feeder apparent powers, a supply node active power, and a supply node reactive power.

8. The method of claim 7 , further comprising solving the system of node equations for at least one of the feeder power factor angles.

9. The method of claim 8 , wherein solving the system of node equations comprises using an iterative technique.

10. The method of claim 6 , further comprising calculating at least one of a feeder active power and a feeder reactive power responsive to a corresponding feeder apparent power and a corresponding feeder power factor angle.

11. The method of claim 10 , further comprising generating a load scaling factor responsive to at least one of the feeder active powers and the feeder reactive powers.

12. The method of claim 11 , further comprising using the load scaling factor to determine load allocation among the feeders.

13. Computer readable medium for determining a power flow in an electrical distribution network, said computer readable medium comprising computer program code that when executed by a processor causes the processor to make a determination of electrical power flow in the electrical distribution network, the computer readable medium when executed by the processor is configured:

to determine respective feeder apparent powers of electrical power feeders connected at a supply node of an electrical distribution network;

to relate the feeder apparent powers with respect to a supply node active power and a supply node reactive power based on the following system of equations:

P inj =S 1 cos φ 1 +S 2 cos φ 2 +S 3 cos φ 3 + . . . +S n cos φ n

Q inj =S 1 sin φ 1 +S 2 sin φ 2 +S 3 sin φ 3 + . . . +S n sin φ n,

wherein n is a positive integer that represents a number of feeders, φ n represents a factor angle for an n th feeder, S n represents apparent power for the n th feeder with respect to injected active power P inj and in injected reactive power Q inj ;

to determine a feeder power factor angle of at least one of the feeders responsive to the feeder apparent powers, the supply node active power, and the supply node reactive power; and

to process at least one of the feeder power factor angles for determining a power flow in the electrical distribution network.

14. The computer readable medium of claim 13 , further comprising a computer program code for generating a system of node equations having feeder power factor angles of each of the feeders as variables and relating feeder apparent powers, a supply node active power, and a supply node reactive power.

15. The computer readable medium of claim 14 , further comprising a computer program code for solving the system of node equations for at least one of the feeder power factor angles.

16. The computer readable medium of claim 15 , further comprising a computer program code for solving the system iteratively.

17. The computer readable medium of claim 13 , further comprising a computer program code for calculating at least one of a feeder active power and a feeder reactive power responsive to a corresponding feeder apparent power and a corresponding feeder power factor angle.

18. The computer readable medium of claim 17 , further comprising a computer program code for generating a load scaling factor responsive to at least one of the feeder active powers and the feeder reactive powers.

19. The computer readable medium of claim 18 , further comprising a computer program code for using the load scaling factor to determine load allocation between the feeders.