Research Projects

My research focuses on the development and application of advanced computational methods to power and energy systems, with recent emphasis on the development of novel control and optimization methods to enable high penetration of distributed energy resources and renewable energy sources in power systems.

Characterization of aggregate flexibility of distributed energy resources

The high penetration of distributed energy resources (DERs) provides unprecedented aggregate flexibility for an active distribution network to reduce, shape, shift, and modulate its aggregate power consumption/injection at the substation level. Such aggregate flexibility enables aggregated DERs to provide grid services at the bulk power system level and facilitates their grid integration. In this research, we try to quantify the aggregate flexibility of DERs given the flexibility of individual device, their intertemporal coupling constraints, and network constraints.

Specifically, given a description of the feasible region of the DER output ( $p^{mathrm{DER}}$ ) and the aggregate power at the substation ( $p^{mathrm{agg}}$ ) as $(p^{mathrm{agg}}, p^{mathrm{DER}}) in mathcal{F}^+$ , we are interested in the characterization of the set such that for any $p^{mathrm{agg}} in mathcal{F}$ , there exists a vector of $p^{mathrm{DER}}$ such that $(p^{mathrm{agg}}, p^{mathrm{DER}}) in mathcal{F}^+$ . In other words, the projection of $mathcal{F}^+$ onto the $p^{mathrm{agg}}$ -space. It is well known that even in the simple case where $mathcal{F}^+$ is a polytope, finding a general projection in mathcal{H} -representation from $mathcal{F}^+$ in -representation is NP-hard. Our research focuses on developing tractable approximation algorithms using advanced optimization and data-driven approaches to find high-quality approximation of $mathrm{Proj}_{p^{mathrm{agg}}}(mathcal{F}^+)$ .

Relevant publications:
[AF1] B. Cui, A. Zamzam, and A. Bernstein, Network-Cognizant Time-Coupled Aggregate Flexibility of Distribution Systems Under Uncertainties, IEEE Control Systems Letters, vol. 5, no. 5, pp. 1723–1728, Nov. 2021.
[AF2] Q. Li, J. Liu, B. Cui, W. Song, and J. Ye, Distribution System Flexibility Characterization: A Network-Informed Data-Driven Approach, IEEE Transactions on Smart Grid, to be published.
[AF3] S. Wang, B. Cui, L. Du, An Efficient Power Flexibility Aggregation Framework via Coordinate Transformation and Chebyshev Centering Optimization, IEEE Power & Energy Society General Meeting, Denver, CO, 2022.

Market integration of virtual power plants

In this project, we are interested in the development of optimal bidding strategies of virtual power plants to bid into the day-ahead electricity market under a multistage stochastic programming formulation. We develop a policy that determines the optimal offering quantity of a virtual power plant as a function of the price given a Markovian forecast of the day-ahead market price. We develop tailored algorithms based on stochastic dual dynamic programming to improve the computational efficiency of the method.

Relevant publications:
[MI1] L. Chen, B. Xu, S. Zhang, and B. Cui, Optimal Offering Strategy of a Price-Taking Virtual Power Plant, Power System Computation Conference (PSCC), Paris, France, 2024 (submitted).
[MI2] B. Cui, A. Zamzam, and A. Bernstein, Enabling Grid-Aware Market Participation of Aggregate Flexible Resources, 11th Bulk Power Systems Dynamics and Control Symposium (IREP 2022), Banff, Canada, 2022.

Power flow analysis

I'm interested in the explicit characterization of the properties of power flow solutions such as their existence, uniqueness within a specified subset of state space, and convergence of iterative algorithms to the solutions. Such analysis provides theoretical guarantees on the existence and rigorous bounds on power flow solutions given network parameters and loading conditions, without explicitly solving for the power flow equations. The deep understanding of the interplay between power flow solutions and the topological and parametric properties of the power networks provides new insights and tools for the solution of many emerging problems in power systems such as the stability of converter-based networks and power system optimization under uncertainties, which we are actively exploring.

Relevant publications:
[PF1] B. Cui and X. A. Sun, Securing Voltage Stability in Power Grids via Holomorphic Dynamics (submitted).
[PF2] B. Ou, B. Wang, B. Cui, and D. Wu, Updated Impedance Power Flow, Power System Computation Conference (PSCC), Paris, France, 2024 (submitted).
[PF3] B. Cui, A. Zamzam, G. Cavraro, and A. Bernstein, Efficient Region of Attraction Characterization for Control and Stabilization of Load Tap Changer Dynamics, IEEE Transactions on Control of Network Systems, vol. 9, no. 3, pp. 1506–1517, Sep. 2022.
[PF4] J. Liu, B. Cui, D. K. Molzahn, C. Chen, and X. Lu, Optimal Power Flow for DC Networks with Robust Feasibility and Stability Guarantees, IEEE Transactions on Control of Network Systems, vol. 9, no. 2, pp. 904–916, Jun. 2022.
[PF5] B. Li, B. Cui, F. Qiu, and D. K. Molzahn, Balancibility: Existence and Uniqueness of Power Flow Solutions Under Voltage Balance Requirements, Electric Power Systems Research, vol. 190, Jan. 2021.
[PF6] B. Cui, R. Yao, and F. Qiu, Certification and Prediction of Post-Disturbance States in Dynamic Security Assessment, Electric Power Systems Research, vol. 189, Dec. 2020.