A method estimates an optimal power flows (OPF) in a power grid, which is represented as a graph partitioned into virtual sub-graphs, each including at least one bus, and associated with agents that measure local variables and updates consensus variables (CV). The consensus variables of adjacent virtual sub-graphs are exchanged and updated using the agents. An OPF problem is solved for the virtual sub-graphs using the agents based on the CV and the local variables. The exchanging and the solving are iterated until a termination condition is satisfied, when the optimal OPF is outputted for each virtual sub-graph.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method for estimating optimal power flows (OPF) in a power grid, wherein the power grid includes generators and loads connected by buses, comprising steps: representing the power grid as a graph partitioned into virtual sub-graphs, wherein each virtual sub-graphs includes at least one generator, and load and one bus; associating an agent with each virtual sub-graph, wherein the agent includes computation and communication capabilities; measuring local variables and obtaining consensus variables (CV) in each virtual sub-graph by the agent, wherein the local and consensus variables include voltage and power variables subject to power balance constraints in the virtual sub-graph; exchanging and updating the CV of adjacent virtual sub-graphs using the agents; solving an OPF problem for each virtual sub-graph using the agent based on the measured local variables and the exchanged consensus variables; iterating the exchanging and the solving until a termination condition is satisfied; and outputting the optimal OPF for each virtual sub-graph. 2. The method of claim 1, wherein each agent includes computation and communication capabilities and a memory. 3. The method of claim 2, further comprising: storing the graph and sub-graphs in the memory. 4. The method of claim 1, wherein vertices in the sub-graphs represent virtual generators and virtual loads. 5. The method of claim 1, wherein the OPF problem is min P i G , Q i G , e i , f i , i ∈   Σ i ∈  G  F i  ( P i G ) , wherein active and reactive generation power at bus i are PiG and QiG, a complex voltage of bus i is Vi=ei+jfi with ei being a real part of the voltage, fi an imaginary part, and j=√{square root over (−1)}, and PiG, QiG, ei, fi are the local variables. 6. The method of claim 1, wherein the OPF problem is nonconvex due to quadratic relations between voltages of adjacent buses. 7. The method of claim 1, further comprising: penalizing deviations between the local variables and the consensus variables using a penalty function. 8. The method of claim 1, wherein the updating uses a consensus filter. 9. The method of claim 1, wherein the exchanging only occurs among adjacent buses. 10. The method of claim 7 wherein the penalty function is formulated using an 1-norm. 11. The method of claim 1, wherein each virtual sub-graphs includes only one bus. 12. The method of claim 1, wherein each virtual sub-graphs includes two buses. 13. The method of claim 12, wherein the two buses are a generator bus and a load bus. 14. The method of claim 12, wherein the two buses are generator buses. 15. The method of claim 12, wherein the two buses are load buses. 16. The method of claim 15, wherein the one of the load buses is represented in the sub-graph as a real load bus and a virtual generator bus.