Measurement-based dynamic modeling of an electrical network

A non-transitory computer-readable medium having computer-executable instructions stored thereon which, when executed by a computer, will cause the computer to perform the following steps, in the management of an electrical grid distribution feeder line responsively to characterized electrical parameters thereat, the line having a first line node being a substation associated with a voltage controller adapted to control the voltage thereat, and, downstream thereof, a second line node that is electrically coupled to a customer's energy resource (that generates or consumes electrical power), to characterizing the voltage phasor at the second line node for a period of time, the steps comprising:

• (i) coupling a first μPMU at said first line node that is adapted to timestamp measure the electrical voltage and current waveforms thereat;
• (ii) (a) coupling a voltage transformer between said second line node and said customer's energy resource with drop lines, and (b) coupling a second μPMU on the drop between the transformer and said customer's energy resource, that is adapted to timestamp measure the electrical voltage and current waveforms thereat;
• (iii) making said first μPMU timestamped measurements and making said second μPMU timestamped measurements and time-synchronizing one of said first μPMU timestamped measurements with one of said second μPMU timestamped measurements;
• (iv) determining, for the period, the impedances of said drop lines and said transformer between said second line node and said customer's energy resource;
• (v) determining, for the period, the voltage at the second line node based on said drop line impedances and said transformer impedance and said second μPMU measurements;
• and
• (vi) informing said determined second line node voltage, to said voltage controller.

For the management of an electrical grid distribution feeder line responsively to characterized electrical parameters thereat, the line having a first line node being a substation with an associated voltage controller adapted to control the voltage thereat, and, downstream thereof, a second line node that is electrically coupled to a customer's energy resource (that generates or consumes electrical power), a system for characterizing the voltage phasor at the second line node for a period of time, the system comprising:

• (i) a first μPMU at said first line node that takes timestamped measurements of the electrical voltage and current waveforms thereat;
• (ii) (a) a voltage transformer coupled between said second line node and said customer's energy resource with drop lines, and (b) a second μPMU coupled on the drop between the transformer and said customer's energy resource, that is adapted to timestamp measure the electrical voltage and current waveforms thereat;
• (iii) a common time source that is communicatively shared by said first μPMU and said second μPMU to act as a common reference to said timestamps;
• (iv) to determine, for the period, the impedances of said drop lines between said transformer and said customer's energy resource;
• (v) to determine, for the period, the voltage at the second line node based on said drop line impedances and said transformer impedance and said second μPMU measurements;
• and
• (vi) to inform said determined second line node voltage, to substation voltage controller.