Changhong Zhao’s research while affiliated with Chinese University of Hong Kong and other places

The integration of intermittent renewable energy sources into distribution networks introduces significant uncertainties and fluctuations, challenging their operational security, stability, and efficiency. This paper considers robust distribution network reconfiguration (RDNR) with renewable generator resizing, modeled as a two-stage robust optimization (RO) problem with decision-dependent uncertainty (DDU). Our model optimizes resizing decisions as the upper bounds of renewable generator outputs, while also optimizing the network topology. We design a mapping-based column-and-constraint generation (C&CG) algorithm to address the computational challenges raised by DDU. Sensitivity analyses further explore the impact of uncertainty set parameters on optimal solutions. Case studies demonstrate the effectiveness of the proposed algorithm in reducing computational complexity while ensuring solution optimality.

The concept of dispatchable region plays a pivotal role in quantifying the capacity of power systems to accommodate renewable generation. In this paper, we extend the previous approximations of the dispatchable regions on direct current (DC), linearized, and nonlinear single-phase alternating current (AC) models to unbalanced three-phase radial (tree) networks and provide improved outer and inner approximations of dispatchable regions. Based on the nonlinear bus injection model (BIM), we relax the non-convex problem that defines the dispatchable region to a solvable semidefinite program (SDP) and derive its strong dual problem (which is also an SDP). Utilizing the special mathematical structure of the dual problem, an SDP-based projection algorithm is developed to construct a convex polytopic outer approximation to the SDP-relaxed dispatchable region. Moreover, we provide sufficient conditions to guarantee the exact SDP relaxation by adding the power loss as a penalty term, thereby providing a theoretical guarantee for determining an inner approximation of the dispatchable region. Through numerical simulations, we validate the accuracy of our approximation of the dispatchable region and verify the conditions for exact SDP relaxation.

Solving power flow is a fundamental problem in power systems. The normally radial (tree) topology of a distribution network induces a spatially recursive structure in AC power flow, which enables a class of efficient solution methods—backward/forward sweep (BFS). In this paper, we revisit BFS from the perspective of its convergence, which was rarely addressed before. We introduce three variants of BFS algorithms: the first one calculates voltages and line currents in a single-phase network model; the second algorithm extends the first one to an unbalanced three-phase network with Y and $\Delta$ configurations; the third one calculates voltages and line power flows in the classical dist-flow model. We prove a sufficient condition, under which the first algorithm is a contraction mapping on a closed set of voltages and thus converges geometrically to a unique solution. This proof is extended to the second algorithm for three-phase networks. We then use the monotone convergence theorem to prove convergence of the third algorithm. We verify the convergence conditions, solution accuracy, and computational efficiency of BFS algorithms, through simulations in IEEE test systems.

This paper proposes two novel paradigms of approximately adaptive distributionally robust optimization (AADRO) for the energy and reserve dispatch with wind uncertainty. The piecewise linear policy-based AADRO (PLP-AADRO) approximates the adaptive optimization-based recourse decision as piecewise affine adjustment, while the piecewise value function-based AADRO (PVF-AADRO) approximates the quadratic recourse problem as piecewise linear recourse problems. Moreover, an equal probability principle is developed to achieve a high-quality segmentation of the wind power ambiguity set. Consequently, the distributionally robust quadratic cost constraint can be decomposed into decoupled piecewise constraints, allowing the dispatch problem to be formulated as a less-iterative or even non-iterative program. The two-stage AADROs with polyhedron supported uncertainties are first recast precisely as tractable forms with semidefinite constraints, by employing duality theory and S-lemma. Then, the distributionally robust cost constraint in PVF-AADRO is handled by dual vertex generation, and the bilinear terms in both AADROs are addressed by alternating optimization. Numerical simulations verify the efficiency of AADROs in approximating the strict adaptive distributionally robust optimization, and their adaptability in different cases is discussed.

This paper proposes a novel distributionally robust energy and reserve dispatch model with distributed renewable predictions. Through leveraging the prediction information from both the system operator and renewable energy sources, the renewable energy can be predicted more precisely, and hence the dispatch decision is improved. The proposed model captures the relationship between the expectation, variance, covariance of renewable energy and the predictive decision, leading to the formulation of a less conservative moment-based ambiguity set for renewable energy. To solve the distributionally robust dispatch with predictive decision-dependent uncertainty, we first relax the second-stage recourse value function with dual vertices, and then transform the dispatch model to a tractable form using duality theory and S-lemma. A tailored two-layer iterative algorithm is finally developed to solve the tractable model, where the outer-layer iteration solves the master and sub problems alternately to update dual vertices, while the inner-layer iteration convexifies the master problem with nonlinear constraints using alternate optimization and difference-of-convex optimization. Moreover, two acceleration strategies are developed to improve the convergence of the solution. Simulations in three testing systems validate the efficiency of the proposed model and solution algorithm.

Linear approximation commonly used in solving alternating-current optimal power flow (AC-OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal-dual type gradient algorithms converge to solutions with voltage violation. In this paper, we improve a recent hierarchical OPF algorithm that rested on primal-dual gradients evaluated with a linearized distribution power flow model. Specifically, we propose a more accurate gradient evaluation method based on an unbalanced three-phase nonlinear distribution power flow model to mitigate the errors arising from linearization. The resultant gradients feature a blocked structure that enables our development of an improved hierarchical primal-dual algorithm to solve the OPF problem. Numerical results on the IEEE 123-bus test feeder and a 4,518-node test feeder show that the proposed method can enhance voltage safety at comparable computational efficiency with the linearized algorithm.