Search Results (5)

This paper addresses the optimal management of photovoltaic (PV) systems and distribution static synchronous compensators (D-STATCOMs) in modern electrical distribution networks. A mixed-integer nonlinear programming (MINLP) model is formulated which co-optimizes device placement, sizing, and multi-period dispatch to minimize the total annualized system costs while satisfying AC power flow and operational constraints. To solve this challenging problem, a decomposition methodology is proposed, wherein the binary location decisions for the PVs and D-STATCOMs are treated as predefined inputs, upon the basis of site selections commonly reported in the literature. With the integer variables fixed, the problem is reduced to a continuous nonlinear programming (NLP) subproblem for optimal capacity sizing and operational scheduling, which is solved using the interior point optimizer (IPOPT) via the Julia/JuMP environment. The core contribution of this work lies in its comprehensive demonstration of the economic superiority of variable reactive power injection over conventional fixed compensation schemes. Through numerical validation on standard 33- and 69-bus test systems, it is shown that a variable D-STATCOM operation yields substantial and consistent economic gains. Compared to optimized fixed-injection solutions, variable injection provides additional annual savings averaging USD 120,516 (33-bus feeder) and USD 125,620 (69-bus grid), corresponding to a further 3.4% reduction in total costs. These benefits prove robust across different device location sets identified by various metaheuristic algorithms, and they scale effectively to larger network topologies. The results demonstrate that transitioning to variable power injection is not merely an incremental improvement but a fundamental advancement for achieving techno-economic optimality in distribution system planning. The proposed methodology provides utilities with a computationally efficient framework for determining near-optimal PV and D-STATCOM management strategies by first fixing deployment locations based on established planning insights and then rigorously optimizing sizing and dispatch, in order to maximize economic returns while ensuring reliable network operation. Full article

This paper investigates the fractal dynamical behavior of a discrete Caputo fractional-order hepatitis C virus model. First, we analyze the stability of the system by using spectral radius and design the fractional-order controller based on coordinate transformation. Then, a nonlinear coupling controller is constructed to achieve synchronization between two fractional-order models with different parameters and different fractional orders, and the synchronization is supported by rigorous mathematical proof. Numerical simulations are used to verify the effectiveness of control and synchronization. Full article

When aiming to achieve consistency in fractal characteristics between different models, it is crucial to consider the synchronization of Julia sets. This paper studies the synchronization of Julia sets in three-dimensional discrete financial models. First, three-dimensional discrete financial models with different model parameters are proposed and their Julia sets are presented. According to the model forms, two kinds of synchronous couplers that can achieve synchronization of Julia sets between different models are designed by changing the synchronization parameters. The proposed synchronization method is theoretically derived and the efficiency of different synchronous couplers are compared. Finally, the effectiveness is verified by Julia sets graphics. This method has reference value for theoretical research into financial models in the field of fractals. Full article

In this paper, we introduce a generalized complex discrete fractional-order cosine map. Dynamical analysis of the proposed complex fractional order map is examined. The existence and stability characteristics of the map’s fixed points are explored. The existence of fractal Mandelbrot sets and Julia sets, as well as their fractal properties, are examined in detail. Several detailed simulations illustrate the effects of the fractional-order parameter, as well as the values of the map constant and exponent. In addition, complex domain controllers are constructed to control Julia sets produced by the proposed map or to achieve synchronization of two Julia sets in master/slave configurations. We identify the more realistic synchronization scenario in which the master map’s parameter values are unknown. Finally, numerical simulations are employed to confirm theoretical results obtained throughout the work. Full article

The Julia set is one of the most important sets in fractal theory. The previous studies on Julia sets mainly focused on the properties and graph of a single Julia set. In this paper, activated by the consensus of multi-agent systems, the consensus of Julia sets is introduced. Moreover, two types of the consensus of Julia sets are proposed: one is with a leader and the other is with no leaders. Then, controllers are designed to achieve the consensus of Julia sets. The consensus of Julia sets allows multiple different Julia sets to be coupled. In practical applications, the consensus of Julia sets provides a tool to study the consensus of group behaviors depicted by a Julia set. The simulations illustrate the efficacy of these methods. Full article