Managing Uncertainties in Grid-Integration of Distributed Energy Resources: Safety, Stability, and Optimality

Abstract

Distributed energy resources (DERs), in particular renewable resources, are witnessing substantial technology improvements and cost reductions. Large-scale integration of DERs into electric power systems is therefore becoming technically and economically viable. Various critical challenges must be addressed, however, to achieve a successful transition to a clean energy future. Meanwhile, safety, stability, and optimality are of paramount importance for power systems.

The uncertainties introduced by renewable DERs, such as solar photovoltaic (PV) and wind generation, require careful treatments for achieving safe system operation. In the first part of this dissertation, theoretical results and efficient algorithms are developed to analyze the impacts of uncertainties and external disturbances on system dynamics. First, theoretical results for characterizing the second-order trajectory sensitivities for general nonlinear hybrid systems are established. Then, rigorous bounds are developed to quantify all possible system behaviors for general nonlinear systems, by constructing the second-order trajectory sensitivities and exploiting the mathematical tool of the logarithmic norm. Efficient algorithms are proposed for computing the reach-set, which enables safety verification by checking if the reach-set intersects any unsafe region.

Furthermore, DERs are typically connected to power systems through inverter interfaces, whose dynamics are dominated by the enforced control law. This dissertation proposes a control scheme for inverters that can achieve autonomous switch between grid-connected operation and islanded operation. A detailed dynamic model for inverter-based power systems is presented. Discussions on system behavior at steady state and system stability are provided. It is recognized that the fast dynamics introduced by inverter-based resources add another layer of complexity for ensuring system safety. In this dissertation, a barrier-function-based method is extended to construct distributed control laws for inverters in microgrids, which can explicitly certify safety constraints for the overall system. Algorithmic constructions of these control laws are proposed using sum-of-squares optimization.

With the critical issues of safety and stability handled, the second part of this dissertation explores opportunities offered by renewable DERs. First, the collective reactive power capability of multiple DERs such as solar PVs is exploited to balance voltages across the distribution network. Distributed and decentralized Steinmetz-based controllers are proposed, and the interactions and convergence of the controllers are analyzed. Rigorous convergence guarantees are established for the overall system using the Banach fixed-point theory. The convergence guarantee is essential to ensure robustness of the proposed control algorithms in realistic settings where parameters are uncertain, disturbances are prevalent, and control and measurement signals are prone to delays.

Second, the local energy supply from DERs enables off-grid energy systems, such as renewable-only microgrids and community-based energy hub systems that incorporate multiple energy carriers. Designing the system to achieve a balanced trade-off between economic cost and operational reliability is increasingly important. In this dissertation, the design problem is formulated as a stochastic chance-constrained optimization to explicitly address the uncertainty induced by renewable resources and load. An original cluster-based multi-policy formulation is proposed and incorporated in the chance-constrained formulation, which achieves much more flexible storage dispatches. A novel iterative optimization-validation algorithm is devised to efficiently solve the design problem, where a scalar auxiliary parameter is dynamically adjusted for tuning the robustness level. To achieve reliable and economic real-time operation, a two-level control strategy is proposed, and several energy hubs are interconnected to exploit energy sharing capability through electrical and gas networks.