Using clock accuracy to guide model synthesis in distributed systems: An application in power grid control

Practical implementations in distributed model based control face a fundamental trade-off between model complexity and the number of modeled nodes. For linear systems, higher order models better capture the behavior of the system at higher frequencies, but the effective operating frequency range is limited during implementation due to sensor/actuator bandwidth limits, control algorithm limits and, in the case of wide scale distribution, communication bandwidth limits. The optimal choice for model order is the intersection of increasing model fidelity and the increasing generalized cost. Using existing methods for optimal model synthesis we present an evaluation of this cost in terms of clock synchronization accuracy. We show through illustrative example in the domain of large scale power transmission that there is a growing performance penalty as model order is increased in the presence of uncertain time-stamps. We discuss how this penalty can be framed as a design parameter for automated model deduction. As a corollary, we also show that the choice of a network based clock synchronization method can be formalized by using the same performance metric used for model synthesis.