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Inertia Placement in Power Grids with Dynamic Loads

As a greater number of nuclear, coal, and gas based power plants are retired in favour of power electronic-interfaced cleaner renewable sources, the apprehensions over its impact on the operation of power grids too has steadily increased. A widely employed remedy is the emulation of inertia (mimicking the operation of synchronous machines) via storage elements. Recent research [1] suggests that “placement” of this inertia across the grid greatly characterises the system performance (H2 norm based performance metrics [2]). The resulting optimisation problem to determine the locally optimal allocations is however non-convex and involves non-trivial gradient computation techniques.

The goal of this student project is to examine the effects of dynamic load models, and realistic state-space models of synchronous machines, on inertia “placement” and compare it’s performance vis-à-vis the linearised model with static loads in [1]. The main steps of the project are as follows:

1. Replace static loads with dynamic first/second order load models and analyse the “inertia placement problem” (i.e. without Kron reduction [3]) for different disturbance heuristics.
2. Consider higher order models for synchronous machines and re-formulate the problem incorporating the new states.
3. Perform a systematic parallel analyses of the allocation problem in terms of performance metric, time domain response, and resulting inertia profiles for both the cases.

Requirements for this project: experience in MATLAB, a basic course in Optimization/Convex Optimization.

[1] Poolla, Bala Kameshwar, Saverio Bolognani, and Florian Dorfler. "Placing Rotational Inertia in Power Grids." arXiv preprint arXiv:1510.01497 (2015).

[2] Bamieh, Bassam, and Dennice F. Gayme. "The price of synchrony: Resistive losses due to phase synchronization in power networks." American Control Conference (ACC), 2013. IEEE, 2013.

[3] Dorfler, Florian, and Francesco Bullo. "Kron reduction of graphs with applications to electrical networks." Circuits and Systems I: Regular Papers, IEEE Transactions on 60.1 (2013): 150-163.