Measurement-based dynamic modeling of an electrical network
A system and a method for locally controlling delivery of electrical power along the distribution feeder by measuring certain electricity parameters of a distribution feeder line using a substation phasor measurement unit (PMU) electrically coupled to a substation distribution bus at a first node on the feeder line, and at least one customer site PMU electrically coupled to a low voltage end of a transformer at a customer site, wherein the transformer is coupled by a drop line to a second node on the distribution feeder line and the customer site is coupled by another drop line to the transformer, and by controlling at least one controllable reactive power resource and optionally a real power resource connected to the second node or at the customer site. Related apparatus, systems, articles, and techniques are also described.
1. A method for controlling delivery of electric power along a distribution feeder line, the method comprising:
receiving first measurements from a first node on the distribution feeder line, wherein the first measurements include measurements of electrical voltage and current waveforms at the first node;
receiving second measurements from a second node on the distribution feeder line, wherein the second measurements include measurements of the electrical voltage and current waveform at the second node;
determining, using the first measurements and the second measurements, a target voltage phasor for the second node; and
sending the target voltage phasor to the second node.
2. The method of claim 1 , wherein the first measurements and the second measurements are timestamped measurements.
3. The method of claim 2 , further comprising time-synchronizing the timestamped measurements.
4. The method of claim 1 , wherein:
receiving the first measurements comprises receiving the first measurements from a first micro phasor measurement unit (μPMU) at the first node; and
receiving the second measurements comprises receiving the second measurements from a second μPMU at the second node.
5. The method of claim 1 , wherein:
sending the target voltage phasor to the second node comprises sending the target voltage phasor to a resource controller at the second node, the resource controller operable to control a resource using the target voltage phasor.
6. The method of claim 1 , wherein determining the target voltage phasor comprises:
calculating a real power loss and a reactive power loss of the distribution feeder line;
determining a first real power flow and a first reactive power flow at the first node using the first measurements;
determining a second real power flow and a second reactive power flow at the second node using the second measurements;
determining a minimum distribution feeder line power loss using the first real power flow, the first reactive power flow, the second real power flow, and the second reactive power flow; and
calculating the target voltage phasor for the second node based on the minimum distribution feeder line power loss.
7. The method of claim 6 , further comprising:
determining electrical parameters of the distribution feeder line, wherein calculating the real power loss and the reactive power loss of the distribution feeder line comprises using the electrical parameters to calculate the real power loss and the reactive power loss.
8. The method of claim 1 , wherein:
the first node is an upstream node and the second node is a downstream node; and
determining the target voltage phasor comprises:
determining an admittance of the distribution feeder line between the first node and the second node,
calculating a real power at the first node using the admittance, the first measurements, and the second measurements, and
calculating the target voltage phasor for the second node using the admittance and the real power at the first node.
9. The method of claim 8 , wherein determining the admittance comprises:
determining a resistance and a reactance of the distribution feeder line; and
determining the admittance using the resistance and the reactance.
10. The method of claim 9 , wherein:
determining the resistance and the reactance of the distribution feeder line comprises using any one of (a) transformer properties, (b) drop line properties, (c) sensor measurements, or (d) any combination of (a)-(c) to determine the resistance and the reactance.
11. The method of claim 1 , wherein:
the first node is an upstream node and the second node is a downstream node; and
determining the target voltage phasor comprises:
calculating a power flow between the first node and the second node using the first measurements and the second measurements,
calculating the target voltage phasor for the second node using the power flow, the first measurements, and the second measurements,
determining whether the target voltage phasor is withing a voltage limit, and
when the target voltage phasor is not withing the voltage limit, adjusting the target voltage phasor to be within the voltage limit.
12. The method of claim 11 , wherein determining the target voltage phasor comprises:
determining an admittance of the distribution feeder line between the first node and the second node, wherein calculating the power flow comprises using the admittance to calculate the power flow.
13. The method of claim 11 , wherein the voltage limit has a lower limit of 0.95 pu and an upper limit of 1.05 pu.
14. A system for controlling delivery of electric power along a distribution feeder line, the system comprising:
a first micro phasor measurement unit (μPMU) at a first node of the distribution feeder line, wherein the first μPMU is operable to take first measurements of electrical voltage and current waveforms at the first node;
a second μPMU at a second node of the distribution feeder line, wherein the second μPMU is operable to take second measurements of the electrical voltage and current waveforms at the second node;
a resource controller at the second node operable to control an energy resource at the second node; and
a computer operable to:
receive the first measurements from the first μPMU;
receive the second measurements from the second μPMU;
determine a target voltage phasor for the second node using the first measurements and the second measurements; and
send the target voltage phasor to the resource controller.
15. The system of claim 14 , wherein to determine the target voltage phasor comprises to:
calculate a real power loss and a reactive power loss of the distribution feeder line;
determine a first real power flow and a first reactive power flow at the first node using the first measurements;
determine a second real power flow and a second reactive power flow at the second node using the second measurements;
determine a minimum distribution feeder line power loss using the first real power flow, the first reactive power flow, the second real power flow, and the second reactive power flow; and
calculate the target voltage phasor for the second node based on the minimum distribution feeder line power loss.
16. The system of claim 15 , wherein the computer is further operable to:
determine electrical parameters of the distribution feeder line, wherein calculating the real power loss and the reactive power loss of the distribution feeder line comprises using the electrical parameters to calculate the real power loss and the reactive power loss.
17. The system of claim 14 , wherein to determine the target voltage phasor comprises to:
determine an admittance of the distribution feeder line between the first node and the second node;
calculate a real power at the first node using the admittance, the first measurements, and the second measurements; and
calculate the target voltage phasor for the second node using the admittance and the real power at the first node.
18. The system of claim 17 , wherein to determine the admittance comprises to:
determine a resistance and a reactance of the distribution feeder line; and
determine the admittance using the resistance and the reactance.
19. The system of claim 14 , wherein to determine the target voltage phasor comprises to:
calculate a power flow between the first node and the second node using the first measurements and the second measurements;
calculate the target voltage phasor for the second node using the power flow, the first measurements, and the second measurements;
determine whether the target voltage phasor is withing a voltage limit; and
when the target voltage phasor is not withing the voltage limit, adjust the target voltage phasor to be within the voltage limit.
20. The system of claim 19 , wherein the voltage limit has a lower limit of 0.95 pu and an upper limit of 1.05 pu.