Ripple-type control of networked physical systems

A method comprising iteratively:

• determining, by a computing device comprising at least one processor, based on a measurement of an output voltage at a first controllable device in a power system and a minimum output voltage value for the first controllable device, an output voltage violation value for the first controllable device;
• receiving, by the computing device, an assistance requisition value from a second device in the power system, wherein the second device is communicatively coupled to the first controllable device;
• determining, by the computing device, based on a present input reactive power value for the first controllable device, the output voltage violation value, and the assistance requisition value, a target input reactive power value for the first controllable device;
• and
• modifying, by the computing device, operation of the first controllable device based on the target input reactive power value and a maximum input reactive power value for the first controllable device,
• wherein determining the target input reactive power value comprises determining (t+1)=un (t)+η1,nfn(t)+η2,nAnλ(t), wherein:
• n denotes the first controllable device;
• (t+1) denotes the target input reactive power value for the first controllable device;
• un(t) denotes the present input reactive power value for the first controllable device;
• η1,n denotes a first positive scaling factor for the first controllable device;
• fn (t) denotes the output voltage violation value for the first controllable device;
• η2,n, denotes a second positive scaling factor for the first controllable device;
• An denotes an adjacency matrix for the first controllable device, the adjacency matrix indicating devices in the power system that are communicatively coupled to the first controllable device;
• and
• λ(t) denotes a vector of assistance requisition values, including the assistance requisition value that corresponds to the second device.

A system comprising:

• a plurality of devices in a power system, wherein each device in the plurality of devices comprises at least one processor configured to:
• determine, based on a respective measurement of an output voltage at the respective device and a respective minimum output voltage value, a respective output voltage violation value;
• receive an assistance requisition value from another device in the plurality of devices communicatively coupled to the respective controllable device;
• and
• determine, based on a respective present input reactive power value, the respective output voltage violation value, and the assistance requisition value, a respective target input reactive power value;
• and
• wherein the at least one processor of at least one device in the plurality of devices is further configured to:
• modify its operation based on the respective target input reactive power value and a respective maximum input reactive power value,
• wherein determining the respective target input reactive power value comprises determining (t+1)=un (t)+η1,nfn(t)+η2,nAnλ(t), wherein:
• n denotes the respective device;
• (t+1) denotes the respective target input reactive power value for the respective device;
• un(t) denotes the respective present input reactive power value for the respective device;
• η1,n denotes a respective first positive scaling factor for the respective device;
• fn(t) denotes the respective output voltage violation value for the respective device;
• η2,n denotes a respective second positive scaling factor for the respective device;
• An denotes a respective adjacency matrix for the respective device, the respective adjacency matrix indicating devices in the plurality of devices that are communicatively coupled to the respective device;
• and
• λ(t) denotes a respective vector of assistance requisition values, including the assistance requisition value that corresponds to the other device.