# (679f) Stability-Preserving Economic Optimization of Microgrids

- Conference: AIChE Annual Meeting
- Year: 2018
- Proceeding: 2018 AIChE Annual Meeting
- Group: Computing and Systems Technology Division
- Session:
- Time:
Thursday, November 1, 2018 - 2:05pm-2:24pm

The main control objective in a microgrid is to maintain voltages and frequencies at desired levels given steady-state set-points provided by a high-level energy management system. The energy management system is responsible for transacting and transporting power within the microgrid, with other microgrids, and with the power grid. This layer computes an economic-optimal steady-state by solving an AC power flow problem. The steady-state is usually updated every 5-10 min [3]. Due to the extremely fast dynamics of microgrids, the use of optimization-based control techniques such as model predictive control (MPC) for voltage and frequency stabilization is technically challenging. As a result, stabilization of microgrids usually relies on high-frequency low-level controllers such as droop control [2,4,5]. Droop controllers are highly robust controllers that can reliably stabilize the system in the face of high-frequency disturbances. This is because droop-controlled (closed-loop) microgrid dynamics have the key property that they form a Hamiltonian (dissipative) system around a stable equilibrium (steady-state) point [5]. Unfortunately, computing stable steady-states using AC power flow formulations is not straightforward [6]. In particular, the AC power flow layer might provide an economic-optimal point that is not a strict minimum of the Hamiltonian function (and therefore it is not a stable steady-state).

In this work, we propose modified AC power flow formulations to compute economic-optimal and stable equilibrium points for droop-controlled microgrids. We first consider a bilevel formulation in which we optimize an economic objective subject to the minimization of the Hamiltonian function. This formulation has the key advantage that the dynamics of the system do not need to be taken into consideration (it is entirely a steady-state problem). On the other hand, nonconvex bilevel problems are difficult to solve in general, because the inner problem needs to satisfy second order conditions. Motivated by this, we propose a stochastic optimal control formulation that seeks to stabilize the microgrid under a range of random perturbations of the economic-optimal equilibrium point [7,8]. This approach requires capturing the dynamics of the system and solving high-dimensional nonlinear programs (NLPs) but the NLPs are structured and can be handled in a scalable manner with existing tools [9,10]. We demonstrate the developments using a (343-bus) microgrid system, designed by Hart, Lasseter, and Jahns [11]. The proposed framework can be applied to various applications where finding economically-optimal and stable points for controllers is necessary.

References:

[1] Lasseter, R.H. Microgrids, in Power Engineering Society Winter Meeting, 2002. IEEE, vol. 1. IEEE, pp. 305â€“308, 2002.

[2] DÃ¶rfler, F., Simpson-Porco J.W., and Bullo, F. Breaking the hierarchy: Distributed control and economic optimality in microgrids. IEEE Transactions on Control of Network Systems 3, no. 3, pp. 241-253, 2016.

[3] Kundur, P., Balu, N.J., and Lauby, M.G. Power system stability and control. McGraw-hill New York, vol. 7, 1994.

[4] Simpson-Porco, J. W., DÃ¶rï¬‚er, F., and Bullo, F. Synchronization and power sharing for droop-controlled inverters in islanded microgrids, Automatica, vol. 49, no. 9, pp. 2603â€“2611, 2013.

[5] Schiï¬€er, J., Ortega, R., Astolï¬, A., Raisch, J., and Sezi, T. Conditions for stability of droop-controlled inverter-based microgrids, Automatica, vol. 50, no. 10, pp. 2457â€“2469, 2014.

[6] Frank, S., Steponavice, I., and Rebennack, S. Optimal power ï¬‚ow: a bibliographic survey, Energy Systems, vol. 3, no. 3, pp. 221â€“258, 2012.

[7] Biegler, L.T. Nonlinear programming: concepts, algorithms, and applications to chemical processes. Vol. 10. Siam, 2010.

[8] Nemirovski, A. and Shapiro, A. Scenario approximations of chance constraints. In Probabilistic and randomized methods for design under uncertainty, pages 3â€“47. Springer, 2006.

[9] Chiang, N., Petra, C.G., Zavala, V.M. Structured Nonconvex Optimization of Large-Scale Energy Systems Using PIPS-NLP. 18th IEEE Power Systems Computations Conference, 2014.

[10] Shin, S., Hart, P., Jahns, T., and Zavala, V.M. A Hierarchical Optimization Architecture for Large-Scale Power Networks, Under Review, 2017.

[11] Hart, P.J., Lasseter, R., and Jahns, T. Reduced-order harmonic modeling and analysis of droop-controlled distributed generation networks, in Power Electronics for Distributed Generation Systems (PEDG), 2016 IEEE 7th International Symposium on. IEEE, pp. 1â€“9, 2016.