Capacitor planning for large distribution systems with wind generators using successive fuzzy MILP

Day-ahead unit commitment (UC) solution methods seek to determine the status and output of all available generators. In a world with an increasing integration of renewable energy sources such as wind electric generators (WEG), the UC solution process must model and include WEGs too in the decision-making process. Power output of WEGs in a day-ahead decision-making process are usually modeled using a short-term probabilistic forecast. Inclusion of WEGs introduces uncertainty in the solution that may be quantified through an imbalance risk function. Thus a UC solution method should seek a solution to minimize cost and risk in schedule. Two strategies are proposed in this paper to minimize costs and handle risks introduced due to WEGs. These formulations are posed as fuzzy optimization models and are solved using the mixed integer linear programming (MILP) technique. The proposed strategies are tested on a 26- and a 100-generator systems with associated transmission networks that have three and six wind generators each. The results with two strategies of handling WEGs are discussed.

In this paper, an mixed integer linear programming (MILP) method is proposed for calculating the optimal power flow in a multicarrier energy system. A state variable-based linear energy hub model is developed, which avoids the introduction of dispatch factor variables applied traditionally to the optimal power flow problem. The multidimensional piecewise linear approximation method is proposed for representing nonconvex natural gas transmission constraints in which the approximation error is further analyzed. Accordingly, the optimal power flow is reformulated as an MILP problem. Compared with the nonlinear models, the proposed model can be solved by the existing optimization techniques, which can be easily implemented in the optimal power system planning problem. The proposed method is verified by case studies applied to the modified six-bus and the IEEE-118 systems. The test results show that the proposed method can provide a fast solution for the optimal power flow which can be applied to large scale hub systems with sufficient accuracy. The results also demonstrate that the proposed method outperforms the existing MILP methods in calculation time especially in large scale hub applications.

To attain the highest performance of energy supply systems, it is necessary to rationally determine design specifications in consideration of operational strategies corresponding to energy demands. Mixed-integer linear programming (MILP) approaches have been applied widely to such optimal design problems. A MILP method utilizing the hierarchical relationship between design and operation variables have been proposed to solve them efficiently. However, it cannot necessarily be effective to multi-objective optimal design problems because of the existence of a large number of competing design candidates. In this paper, the hierarchical MILP method is revised from the viewpoint of computation efficiency so that it can be applied practically to multi-objective optimal design problems. At the lower level, the order of the optimal operation problems to be solved is changed based on incumbents obtained previously to increase a lower bound for the optimal value of the combined objective function and reduce the number of the optimal operation problems to be solved. At the upper level, a lower bound for the optimal value of the combined objective function is incorporated into the solution method to reduce the number of the design candidates to be generated. This revised hierarchical MILP method is applied to a multiobjective optimal design of a gas turbine cogeneration plant, and its validity and effectiveness are clarified.

The necessity for Renewable Energy Resources (RES) has become a major issue due to the shortage of adequate fossil fuels recently. In addition to fossil fuel shortages, global warming is also an anxiety for a lot of countries and companies. These problems have led to the addition of a large number of renewable energy sources to modern distribution systems. However, due to the high integration of RES to these systems and the intermittent characteristic of sources such as wind and solar, it causes variable production and uncertainty in the power system. It is proposed as a solution to gather these resources together in order to solve the problems caused by the changeable outputs of these resources. Virtual Power Plant (VPP) is described as the management of distributed generation facilities, energy storage systems and controllable loads by an Energy Management System (EMS). In this study, the VPP model consists of renewable energy sources such as wind power plant (WPP), solar power plant (SPP), biogas power plant (BPP) and pumped hydro storage plant (PHSP) as an energy storage system (ESS). The aim of the VPP is to maximize the net daily profit in a 24 h time interval. The proposed mixed integer linear programming (MILP) optimization problem is modeled in GAMS software and solved using CPLEX.

Summary form only given. Important research effort has been devoted to the topic of optimal planning of distribution systems. However, in general it has been mostly referred to the design of the primary network, with very modest considerations to the effect of the secondary network in the planning and future operation of the complete grid. Relatively little attention has been paid to the optimization of the secondary grid and to its effect on the optimality of the design of the complete electrical system, although the investment and operation costs of the secondary grid represent an important portion of the total costs. Appropriate design procedures have been proposed separately for both the primary and the secondary grid, however in general both planning problems have been presented and treated as different, almost isolated problems, setting aside with this approximation some important factors that couple both problems, such as the fact that they may share the right of way, use the same poles, etc., among other factors that strongly affect the calculation of the investment costs. The main purpose of this work is the development and initial testing of a model for the optimal planning of a distribution system that includes both the primary and the secondary grids, so that a single optimization problem is stated for the design of the integral primary-secondary distribution system that overcomes these simplifications. The mathematical model incorporates the variables that define both the primary as well as the secondary planning problems and consists of a mixed integer-linear programming problem that may be solved by means of any suitable algorithm. Results are presented of the application of the proposed integral design procedure using conventional mixed integer-linear programming techniques to a real case of a residential primary-secondary distribution system consisting of 75 electrical nodes.

This paper presents results of research associated with the development of a fuzzy set based approach to improving the efficiency of distribution system operational planning on indices of service quality and economic feasibility. To reach this goal the problem of operational planning is formulated and solved within the framework of a fuzzy mixed integer linear programming model. An example illustrating the validity of the approach is considered.

Tremendous number of renewable energy sources (RES) and distributed generators integrated into distribution system, power generation uncertainty and massive decision variables bring about significant challenges to distribution system operator (DSO). Benefiting from advanced information technologies, distribution system evolves into cyber-physical distribution system (CPDS), and effective countermeasures can be made under distributed control framework to achieve optimality and resiliency of CPDS. For this purpose, fully distributed robust control strategy is specifically explored in this paper. Firstly, a two-stage robust optimization (RO) model is developed for each sub-area in CPDS, which takes uncertainty of wind power into consideration. After that, based on Consensus-ADMM algorithm, a fully distributed solution strategy of combined Consensus-ADMM and RO model is proposed. Results of study case verify that by adopting our method, accurate robust solution under different uncertainty budge can be obtained adaptively under diverse cyber or physical topologies, which guarantees optimality and resiliency of CPDS.

The generalized lock scheduling problem (GLSP) is a mixed integer optimization problem which consists of a ship placement (SP) and a lockage operation scheduling (LOS) sub-problem. In previous research, the GLSP is solved by different exact and heuristic methods, which are confirmed inferior with respect to computation time and solution quality. Consequently, none of those methods is efficient for handling practical large-scale GLSP. For the first time, we show that high-quality solutions of GLSP can be efficiently obtained by using an innovative approach proposed in this paper. Specifically, an ingenious solution structure of GLSP is designed, by which the GLSP is converted to a combinatorial optimization problem. Furthermore, an adaptive large neighborhood search (ALNS) heuristic based on the principle of destruction and reconstruction of solutions is proposed for solving the GLSP. Test results using a large number of instances reported in the literature are compared with those obtained by two exact methods, the mixed integer linear programming (MILP) and combinatorial Benders' decomposition (CBD) method. The results show that our ALNS achieves optimal solutions within less time in terms of most of the small-scale instances. Much better solutions are obtained by the ALNS within a few minutes for those large-scale instances that cannot be solved to optimality by exact methods within 2 h. Especially, the advantage of the proposed method is more remarkable when there is no specific chronological rules forced, which indicates that the proposed method is capable of handling the GLSP in a broader scope of situations.

In diffusion MRI (dMRI), a good sampling scheme is important for efficient acquisition and robust reconstruction. Diffusion weighted signal is normally acquired on single or multiple shells in q-space. Signal samples are typically distributed uniformly on different shells to make them invariant to the orientation of structures within tissue, or the laboratory coordinate frame. The Electrostatic Energy Minimization (EEM) method, originally proposed for single shell sampling scheme in dMRI, was recently generalized to multi-shell schemes, called Generalized EEM (GEEM). GEEM has been successfully used in the Human Connectome Project (HCP). However, EEM does not directly address the goal of optimal sampling, i.e., achieving large angular separation between sampling points. In this paper, we propose a more natural formulation, called Spherical Code (SC), to directly maximize the minimal angle between different samples in single or multiple shells. We consider not only continuous problems to design single or multiple shell sampling schemes, but also discrete problems to uniformly extract sub-sampled schemes from an existing single or multiple shell scheme, and to order samples in an existing scheme. We propose five algorithms to solve the above problems, including an incremental SC (ISC), a sophisticated greedy algorithm called Iterative Maximum Overlap Construction (IMOC), an 1-Opt greedy method, a Mixed Integer Linear Programming (MILP) method, and a Constrained Non-Linear Optimization (CNLO) method. To our knowledge, this is the first work to use the SC formulation for single or multiple shell sampling schemes in dMRI. Experimental results indicate that SC methods obtain larger angular separation and better rotational invariance than the state-of-the-art EEM and GEEM. The related codes and a tutorial have been released in DMRITool.

Bit-based division property was first proposed to find integral for SIMON32 by Todo \(et al.\) at FSE 2016. Xiang \(et al.\) improved the work with aid of Mixed Integer Linear Programming(MILP) method and applied the method to block ciphers with wider block size. Later on, Sun \(et al.\) applied division property to ARX block ciphers. Todo \(et al.\) proposed a more precise division property using three subsets method to describe integral propagation at FSE 2016, which can not be applied to wide state ARX block ciphers. In this paper, we extend bit-based division property using three subsets and propose an automatic method for finding integral distinguishers for ARX block ciphers with SAT/SMT solvers. Firstly, we study bit-based division property using three subsets through three basic operations (Copy, AND, XOR). Then, we model division property using three subsets through Addition Modulo function. Finally, by constructing and solving division property using three subsets propagation system, we find integral distinguishers for round reduced ARX block cipher. As a result, we propose 15 round integral distinguishers for SIMON32 automatically and verify the secure margins Todo \(et al.\) proposed for \(\hbox {SIMON}48,64,96,128\). Also, we can find one more 6 round integral distinguishers for SPECK32, which can not be found with conventional division property without using three subsets. It is interesting that no more integral distinguishers are found for SPECK48,64,96,128. Moreover, we apply to SIMECK, HIGHT, LEA, TEA and XTEA \(et al.\) Unfortunately, we find no more new results than conventional division property can do.

Deoxys-BC is the internal tweakable block cipher of Deoxys, a third-round authenticated encryption candidate at the CAESAR competition. In this study, by adequately studying the tweakey schedule, we seek a six-round related-tweakey impossible distinguisher of Deoxys-BC-256, which is transformed from a 3.5-round single-key impossible distinguisher of AES, by application of the mixed integer linear programming (MILP) method. We present a detailed description of this interesting transformation method and the MILP-modeling process.Based on this distinguisher, we mount a key-recovery attack on 10 (out of 14) rounds of Deoxys-BC-256.Compared to previous results that are valid only when the key size $>204$ and the tweak size $<52$, our method can attack 10-round Deoxys-BC-256 as long as the key size $\\geq174$ and the tweak size $\\leq82$. For the popular setting in which the key size is 192 bits, we can attack one round more than previous studies.Note that this paper only gives a more accurate security evaluation and does not threaten the security of full-round Deoxys-BC-256.

Uncertainty has always been a significant yet unresolved issue in geography. Uncertainty in spatial optimization models, particularly in coverage maximization problems, stems from the limitations of binary coverage metrics for areal-based demand units. Traditional models classify units as either fully covered or not, ignoring partial coverage scenarios. This binary approach creates discrepancies between modeled and actual service demand, as even marginally covered units may count as fully serviced. The propagation of such errors is amplified by variations in the unit size and coverage thresholds, leading to suboptimal solutions in urban planning tasks such as urban greenway planning. To address these limitations, we proposed a deep reinforcement learning (DRL)-driven optimization framework that quantifies the optimality gap caused by spatially induced uncertainty and provides superior solutions. By employing a three-module structure that incorporates a graph neural network (GNN)-driven agent for data representation, a policy and a value network for decision-making, and a stochastic environment for simulating individual-level demand distributions, our model dynamically adapts to spatial uncertainty and generates robust solutions. We tested our framework in solving the maximal covering location problem for lines (MCLP-Line) for urban greenway route planning. The experimental results demonstrated that traditional mixed integer linear programming (MILP) methods yielded highly variable outcomes with different coverage metrics, whereas our proposed model consistently outperformed MILP across diverse scenarios. Our findings underscore the potential of modern AI-driven approaches in mitigating spatial uncertainty and achieving optimized solutions in geographic applications.

A hierarchical optimization approach to robust design of energy supply systems based on a mixed-integer linear model

Leakage power consumption is an increasingly serious problem in very large-scale integration circuits, especially for portable applications. Two novel approaches to leakage power minimization in static complementary metal-oxide-semiconductor circuits that employ input vector control (IVC) are investigated. The authors model leakage effects by means of pseudo-Boolean functions. These functions are linearized and incorporated into an exact (optimal) integer linear programming (ILP) model, called virtual-gate ILP, which analyzes leakage variation with respect to a circuit's input vectors. A heuristic mixed-integer linear programming (MLP) method is also proposed, which has several advantages: it is faster, its accuracy can be quickly estimated, and tradeoffs between runtime and optimality can easily be made. Furthermore, the MLP model also provides a way to estimate a lower bound on circuit leakage current. The proposed methods are used to generate an extensive set of experimental results on leakage reduction. It is shown that average leakage currents are usually 1.25 times the minimum, confirming the effectiveness of IVC. The heuristic MLP approach is shown to be approximately 13.6 times faster than the exact ILP method, whereas finding input vectors whose power consumption is only a few percent above the optimum. In addition, the lower bound estimated by the MLP model is also within a few percent of the optimal value

A resilience-oriented optimal planning of energy storage systems in high renewable energy penetrated systems