Reverse and forward engineering of frequency control in power networks

We reverse-engineer the frequency dynamics with general primary frequency control and show that it is a distributed algorithm to solve a well-defined optimization problem. We further investigate the role of deadband in control, and show that if the aggregated uncontrolled load deviation is nonzero the frequencies will be synchronized, and if however it is zero the frequencies may oscillate but within the deadband. The optimization model does not only provide a way to characterize the equilibrium and establish the convergence of the frequency dynamics, but also suggests a principled way to engineer frequency control. By leveraging the optimization problem and insights from reverse engineering, we propose a distributed realtime frequency control scheme that does not only maintain the frequency to the nominal value but also achieves economic efficiency. This is drastically different from the current hierarchical control approach that addresses frequency regulation and economic efficiency at different timescales and with centralized control, and is what is needed for future power system to cope with rapid and large fluctuations in supply/demand and manage a huge number of control points. This work presents a step towards developing a new foundation - network dynamics as optimization algorithms - for distributed realtime control and optimization of future power networks.