arXiv subjects

Libao Shi

Publications and source records attributed to Libao Shi.

10 recordsLinked to original sources

arXiv2026

Data-Driven Contextual-Aware Uncertainty Set for Robust Dispatch of Power Systems

Both the level of conservativeness and the computational burden in robust optimization are critically influenced by uncertainty set design. However, contextual side information is rarely exploited in robust dispatch of power systems characterized by irregular data distributions, which hinders the explicit characterization of the relationship between covariates and uncertain parameters. To address this issue, a data-driven method for constructing contextual-aware uncertainty set is proposed in this letter. Based on a conditional Gaussian mixture model, a set of covariates is leveraged as side information to design uncertainty sets tailored to historical data exhibiting irregular distributions. The resulting set is formulated as a union-of-subsets formulation, and a mixed integer linear reformulation is adopted to describe the worst-case realization across all subsets. Finally, the effectiveness of the proposed method is demonstrated through numerical experiments applied to robust unit commitment.

math.OC↗

arXiv2025

Theoretical Analysis on the Ability of Particle Swarm Optimization to Escape from Local Optimum

As one of the most prominent swarm intelligence algorithms, particle swarm optimization (PSO) has been extensively applied to solve global optimization problems. The theoretical analysis on the ability of PSO to escape from local optimum (LO) is deeply intertwined with its global optimization performance, making it highly significant to investigate the underlying mechanisms that enable PSO to escape from LO and achieve global optimization. In this study, a rigorous mathematical analysis is presented to explore the ability and mechanisms of PSO to escape from LO. By modelling each search agent as a Markov chain, the probability of PSO escaping from LO within a finite number of iterations is calculated, and the behavior of agents prior to escaping from LO is analyzed. Through this theoretical analysis, two necessary and sufficient conditions are proposed to ensure that PSO escapes from LO in finite iterations with a probability 1: (a) the personal best (pbest) and global best (gbest) positions stagnate around different local optima, and (b) the inertial weight in PSO is equal to one. Upon these conditions, two potential behaviors of agents, namely inertial motion and oscillation, are proposed, and a state transition chain of the agent toward the global optimum is constructed. Additionally, the theoretical analysis reveals that increasing the distance between pbest and gbest, as well as the values of the learning factors in PSO, enhances the speed at which PSO escapes from LO. Finally, the conclusions drawn from the theoretical analysis are corroborated through numerical experiments.

math.OC↗

arXiv2025

Efficient and accurate solution of wind-integrated optimal power flow based on enhanced second-order cone relaxation with rolling cutting plane technique

The integration of large-scale renewable energy sources, such as wind power, poses significant challenges for the optimal operation of power systems owing to their inherent uncertainties. This paper proposes a solution framework for wind-integrated optimal power flow (OPF) that leverages an enhanced second-order cone relaxation (SOCR), supported by a rolling cutting plane technique. Initially, the wind generation cost, arising from discrepancies between scheduled and actual wind power outputs, is meticulously modeled using a Gaussian mixture model based on historical wind power data. This modelled wind generation cost is subsequently incorporated into the objective function of the conventional OPF problem. To achieve the efficient and accurate solution for the wind-integrated OPF, effectively managing the constraints associated with AC power flow equations is essential. In this regard, a SOCR, combined with a second-order Taylor series expansion, is employed to facilitate the convex approximation of the AC power flow equations. Additionally, a warm-start strategy, grounded in a proposed rolling cutting plane technique, is devised to reduce relaxation errors and enhance computational efficiency. Finally, the effectiveness and efficiency of the proposed solution framework are demonstrated across various case studies. Specifically, the influence of wind power cost is also examined, further highlighting the practical implications of the proposed solution framework.

eess.SY↗

arXiv2025

Resilience assessment framework for cyber-physical distribution power system based on coordinated cyber-physical attacks under dynamic game

Owing to the advanced communication networks and intelligent electronic devices, the cyber-physical distribution systems (CPDSs) possess the capability to perform flexible economic dispatch and achieve rapid self-healing from extreme events. Meanwhile, the deep integration of cyber and physical systems makes CPDS vulnerable to coordinated cyber-physical attacks. In this paper, a resilience assessment framework for the CPDS under coordinated cyber-physical attacks is proposed to investigate the impact of the coordinated attacks on load loss and service restoration in CPDS. First, a three-stage defender-attacker-defender dynamic game model considering fake base station (FBS) and physical attacks for CPDS is established, aiming at seeking the optimal defense resource deployment strategy to enhance the resilience of the CPDS. The physical attack is launched to cause faults on the power lines, and the FBS attack is employed to interrupt the service of wireless cellular network to hinder the self-healing process of the CPDS. The lognormal shadowing model and search theory are applied to quantitatively describe the process of the coordinated cyber-physical attacks. Further, the constructed three-stage dynamic game model is equivalently recast as a tri-level max-min-max optimization model, which is solved using column-and-constraint generation combined with enumeration method. Finally, the effectiveness of the proposed resilience assessment framework and solution strategy is demonstrated by conducting simulation analysis on the modified IEEE 33-node CPDS and a real-world 47-node CPDS in China.

eess.SY↗

arXiv2024

An Enhanced Semidefinite Relaxation Model Combined with Clique Graph Merging Strategy for Efficient AC Optimal Power Flow Solution

Semidefinite programming (SDP) is widely acknowledged as one of the most effective methods for deriving the tightest lower bounds of the optimal power flow (OPF) problems. In this paper, an enhanced semidefinite relaxation model that integrates tighter {\lambda}-based quadratic convex relaxation, valid inequalities, and optimality-based bound tightening algorithms derived in accordance with the branch thermal limit boundary surface into the SDP framework is presented to further tighten the lower bounds of the feasible region of OPF problems, effectively combining the advantages of these recent advancements. Additionally, the utilization of chordal decomposition in the complex matrix formulation of SDP can significantly accelerate the solution time. Notably, for the same SDP problem, different chordal decompositions can result in varying solution time. To address this problem, this paper proposes a clique graph merging strategy within the complex matrix SDP framework, which assesses clique sizes and the computational burden on interior-point solvers, as well as reducing the need for hyperparameter tuning and further enhancing the solution efficiency. Finally, the proposed hybrid relaxation model is evaluated using MATPOWER and PGLib-OPF test cases, demonstrating its effectiveness in reducing the optimality gap and validating its computational performance on test cases with up to 13659-node.

eess.SY↗

arXiv2022

A theoretical framework and some promising findings of grey wolf optimizer, part I: analytical model of sampling distribution and stability analysis

This paper proposes a theoretical framework of the grey wolf optimizer (GWO) based on several interesting theoretical findings, involving sampling distribution, order-1 and order-2 stability, and global convergence analysis. In the part I of the paper, the characteristics of the sampling distribution of the new solution and the probabilistic stability of the GWO are carefully discussed based on the well-known stagnation assumption for simplification purposes. Firstly, the characteristics of the sampling distribution of the new solution, mainly related to the shape of the joint probability density function (PDF), are discussed under the assumption that the original solution before updating is constant. Then, the assumption that the original solution is constant is eliminated to perform the sampling distribution analysis, based on which several characteristics of the new solution are provided, containing the shape of the joint PDF and central moments of any positive integer order. Finally, the order-1 and order-2 stability of the GWO under stagnation assumption is introduced and proved as the inference of conclusions above, which are all verified by numerical simulations.

math.OC↗

arXiv2022

A theoretical framework and some promising findings of grey wolf optimizer, part II: global convergence analysis

This paper proposes a theoretical framework of the grey wolf optimizer (GWO) based on several interesting theoretical findings, involving sampling distribution, order-1 and order-2 stability, and global convergence analysis. In the part II of the paper, the global convergence analysis is carried out based on the well-known stagnation assumption for simplification purposes. Firstly, the global convergence property of the GWO under stagnation assumption is abstracted and modelled into two propositions, corresponding to global searching ability analysis and probability-1 global convergence analysis. Then, the global searching ability analysis is carried out. Next, based on a characteristic of the central moments of the new solution of the GWO under stagnation assumption, the probability-1 global convergence property of the GWO under stagnation assumption is proved. Finally, all conclusions are verified by numerical simulations, and the corresponding discussions that the global convergence property can still be guaranteed in the original GWO without stagnation assumption are given.

math.OC↗

arXiv2021

A Bare Bones Grey Wolf Optimizer for Global Numerical Optimization

In order to better understand and analyze the currently widely used population-based metaheuristic optimization algorithms, , this paper proposes a novel computational intelligence algorithm called bare bones grey wolf optimizer (BBGWO) inspired by a bare bones mechanism. In the BBGWO, the complex updating mechanism of solutions is replaced by a random vector that obeys a normal distribution, whose mean and variance are derived by theoretically studying the probability distribution of the new solution of the original GWO. The corresponding theoretical analysis and simulation results verify the good optimization performance of the proposed BBGWO algorithm.

math.OC↗

arXiv2020

A Solution Strategy to the Unit Commitment Problem Incorporating Manifold Uncertainties

The widespread uncertainties have made the interaction between wind power and power grid more complicated and difficult to model and handle. This paper proposes an approach for the solution of unit commitment (UC) problem incorporating multiple uncertainties that exist in both wind power and power grid inherently, consisting of probability, possibility, and interval measures. To handle the manifold uncertainties in a comprehensive and efficient manner, the evidence theory (ET) is applied to fuse these uncertain variables into Dempster-Shafer structure. Moreover, the power loss is introduced into power balance constraints, and the extended affine arithmetic (EAA) is employed to evaluate the uncertainty of power loss caused by the propagation of the aforementioned uncertainties. Regarding the mix-discrete nonlinear characteristics of the established optimization model, an enhanced grey wolf optimizer (GWO) algorithm is developed to solve the proposed model. Specifically, the corresponding commitment schedule is determined by a kind of binary grey wolf optimizer (BGWO), and the economic dispatch (ED) is settled by GWO. Finally, the IEEE 30-bus test system and a real-sized 183-bus China power system are studied to demonstrate the validity and scalability of the proposed model and method.

eess.SY↗

arXiv2019

An Analytical Probabilistic Expression for Modeling Sum of Spatial-dependent Wind Power Output

Applying probability-related knowledge to accurately explore and exploit the inherent uncertainty of wind power output is one of the key issues that need to be solved urgently in the development of smart grid. This letter develops an analytical probabilistic expression for modeling sum of spatial-dependent wind farm power output through introducing unit impulse function, copulas, and Gaussian mixture model. A comparative Monte Carlo sampling study is given to illustrate the validity of the proposed model.

eess.SY↗