Optimal Time-Varying Flows on Congested Networks

The increasing variability in power plant load, in response to a wildly uncertain electricity market and the need to to mitigate CO2 emissions, lead power plant operators to explore advanced options for efficiency optimization. Model-based, system-scale dynamic simulation and optimization are useful tools in this effort, and the subject of the work presented here. In prior work, a dynamic model validated against steady-state data from a 605 MW subcritical power plant was presented. This power plant model is used as a test-bed for dynamic simulations, in which the coal load is regulated to satisfy a varying power demand. Plant-level control regulates plant load to match an anticipated trajectory of the power demand. The efficiency of the power plant operating at varying load is optimized through a supervisory control architecture that performs set point optimization on the regulatory controllers. Dynamic optimization problems are formulated to search for optimal time-varying input trajectories that satisfy operability and safety constraints during the transition between plant states. An improvement in time-averaged efficiency of up to 1.8% points is shown feasible with corresponding savings in coal consumption of 184.8 tons/day and carbon footprint decrease of 0.035 kg/kWh.

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Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

Algorithms ◽

10.3390/a13090228 ◽

2020 ◽

Vol 13 (9) ◽

pp. 228

Author(s):

Rasoul Shafipour ◽

Gonzalo Mateos

Keyword(s):

Inverse Problem ◽

Covariance Matrix ◽

A Priori ◽

Dynamic Network ◽

Streaming Data ◽

Optimal Time ◽

Time Varying ◽

Graph Learning ◽

Topology Inference ◽

Diffusion Dynamics

We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and affect memory and computational savings by processing the data on-the-fly as they are acquired. The setup entails observations modeled as stationary graph signals generated by local diffusion dynamics on the unknown network. Moreover, we may have a priori information on the presence or absence of a few edges as in the link prediction problem. The stationarity assumption implies that the observations’ covariance matrix and the so-called graph shift operator (GSO—a matrix encoding the graph topology) commute under mild requirements. This motivates formulating the topology inference task as an inverse problem, whereby one searches for a sparse GSO that is structurally admissible and approximately commutes with the observations’ empirical covariance matrix. For streaming data, said covariance can be updated recursively, and we show online proximal gradient iterations can be brought to bear to efficiently track the time-varying solution of the inverse problem with quantifiable guarantees. Specifically, we derive conditions under which the GSO recovery cost is strongly convex and use this property to prove that the online algorithm converges to within a neighborhood of the optimal time-varying batch solution. Numerical tests illustrate the effectiveness of the proposed graph learning approach in adapting to streaming information and tracking changes in the sought dynamic network.

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