Changhong Zhao

Zhaojian Wang, Feng Liu, Steven H. Low et al.

This paper addresses the distributed optimal frequency control of multi-area power system with operational constraints, including the regulation capacity of individual control area and the power limits on tie-lines. Both generators and controllable loads are utilized to recover nominal frequencies while minimizing regulation cost. We study two control modes:the per-node balance mode and the network balance mode. In Part I of the paper, we only consider the per-node balance case, where we derive a completely decentralized strategy without the need for communication between control areas. It can adapt to unknown load disturbance. The tie-line powers are restored after load disturbance, while the regulation capacity constraints are satisfied both at equilibrium and during transient. We show that the closed-loop systems with the proposed control strategies carry out primal-dual updates for solving the associated centralized frequency optimization problems. We further prove the closed-loop systems are asymptotically stable and converge to the unique optimal solution of the centralized frequency optimization problems and their duals. Finally, we present simulation results to demonstrate the effectiveness of our design. In Part II of the paper, we address the network power balance case, where transmission congestions are managed continuously.

Zhaojian Wang, Feng Liu, Steven H. Low et al.

In Part I of this paper we propose a decentralized optimal frequency control of multi-area power system with operational constraints, where the tie-line powers remain unchanged in the steady state and the power mismatch is balanced within individual control areas. In Part II of the paper, we propose a distributed controller for optimal frequency control in the network power balance case, where the power mismatch is balanced over the whole system. With the proposed controller, the tie-line powers remain within the acceptable range at equilibrium, while the regulation capacity constraints are satisfied both at equilibrium and during transient. It is revealed that the closed-loop system with the proposed controller carries out primal-dual updates with saturation for solving an associated optimization problem. To cope with discontinuous dynamics of the closed-loop system, we deploy the invariance principle for nonpathological Lyapunov function to prove its asymptotic stability. Simulation results are provided to show the effectiveness of our controller.

Jinyan Su, Changhong Zhao, Di Wang

In this paper, we revisit the problem of Differentially Private Stochastic Convex Optimization (DP-SCO) in Euclidean and general $\ell_p^d$ spaces. Specifically, we focus on three settings that are still far from well understood: (1) DP-SCO over a constrained and bounded (convex) set in Euclidean space; (2) unconstrained DP-SCO in $\ell_p^d$ space; (3) DP-SCO with heavy-tailed data over a constrained and bounded set in $\ell_p^d$ space. For problem (1), for both convex and strongly convex loss functions, we propose methods whose outputs could achieve (expected) excess population risks that are only dependent on the Gaussian width of the constraint set rather than the dimension of the space. Moreover, we also show the bound for strongly convex functions is optimal up to a logarithmic factor. For problems (2) and (3), we propose several novel algorithms and provide the first theoretical results for both cases when $1<p<2$ and $2\leq p\leq \infty$.

Swaroop S. Guggilam, Changhong Zhao, Emiliano Dall'Anese et al.

We propose a framework to engineer synthetic-inertia and droop-control parameters for distributed energy resources (DERs) so that the system frequency in a network composed of DERs and synchronous generators conforms to prescribed transient and steady-state performance specifications. Our approach is grounded in a second-order lumped-parameter model that captures the dynamics of synchronous generators and frequency-responsive DERs endowed with inertial and droop control. A key feature of this reduced-order model is that its parameters can be related to those of the originating higher-order dynamical model. This allows one to systematically design the DER inertial and droop-control coefficients leveraging classical frequency-domain response characteristics of second-order systems. Time-domain simulations validate the accuracy of the model-reduction method and demonstrate how DER controllers can be designed to meet steady-state-regulation and transient-performance specifications.