mixed integer linear programming

This paper presents a new formulation and algorithm for the problem of unit commitment with security constraints, which can obtain the worst case of transmission network line outage and solve the problem under such conditions. Optimal charging and discharging of electric vehicles, optimal charging and discharging of energy storage systems, and flexible loads along with renewable energy resources are considered in the problem of unit commitment. Uncertainty of energy resources is modeled as a scenario-based method. In this paper, a multi-objective function that includes reduction of operating cost, no-load and unit start-up/shutdown, load shedding costs, load shifting, unit pollution, optimal charging and discharging of storages, and the power cut of renewable energy resources is considered. The proposed formulation is a mixed integer linear programming (MILP) model whose absolute optimal solution is guaranteed by powerful Gurobi solvers. To validate the proposed formulation, several study cases and test 6- and 24-bus networks are analyzed. The simulation results show that the proposed algorithm is effective in identifying the worst possible line exit of the transmission network so that the objective function of the problem increases by about 8% after the worst-case line exit from the network.

Electric vehicle charging in the distribution network is one of the common techniques for technical and economic management of energy distribution, which, if implemented properly, will bring several benefits such as reducing network peak load, charging costs reduction, loss minimization, and etc. In most traditional charging methods, the constraints of fully charging electric vehicles at departure time from the parking lot have always been considered, while, in fact, it is not necessary to fully charge electric vehicles. Instead, it is better for each vehicle to be charged smartly based on its required energy for daily trips. In order to implement this smart method, electric vehicle owners provide information about the number of trips and the length of their route for the parking charge management unit. Then, the desired charge calculation is done according to the vehicle's specifications and their initial state of charge of the battery at arrival time to the parking lot. Finally, the charge manager will schedule charging based on the time of use tariff, the limitation of the distribution transformers, the charging level (normal or fast), etc. to so minimize the charging cost in compliance with the technical and economic constraints. The result of smart charging is compared in normal and fast charging mode and several limitations of the distribution network in the presence/absence of the demand response program. YALMIP and MOSEK software have been applied as solvers of the mixed-integer linear programming model.

Resilience characteristics in power systems refer to the system's ability to withstand against severe disturbances with a low probability of occurrence. As extreme dust storms in the south and southwest in recent years have caused heavy damage to the IRAN's electricity industry, in this paper, a bi-level planning model is proposed to simultaneous hardening of distribution lines and substations against this phenomenon. In the first and second levels of the proposed model, the investment costs of distribution system hardening and total expected operating costs are minimized subject to financial and operational constraints, respectively. The planning results in different case studies have shown that the simultaneous hardening planning of substations and distribution lines can, in addition to reducing operating costs in the emergency conditions, play a significant role in reducing investment costs. The proposed model is implemented on a large-scale power distribution system in Khuzestan province, and the simulation results confirm the efficiency of the proposed scheme at different budget levels.

Charging electric vehicles in the distribution network is one of the most basic solutions for technical and economic management of energy distribution. In many traditional charging methods, the condition of fully charging cars when leaving the parking lot has always been a problem. But in this article, each car is intelligently charged only based on the amount of energy required to travel its daily journeys. In order to implement this smart method, owners of electric vehicles provide information about the number of trips and the length of their route to the parking charge management, and based on the specifications of the vehicles and the initial energy level of their battery when entering the parking lot, the amount The charge required for them is determined. Then, the charging manager plans the charging based on the tariff of energy consumption time, limitation of distribution network transformers, type of charge level selected (normal or fast) so that charging costs are minimized by observing technical and economic constraints. . The result of intelligent car charging in normal and fast charging conditions and in different limitations of the distribution network and in the presence or absence of load response program is compared with each other. YALMIP and MOSEK software have been used to solve the mixed integer linear programming model.

The issue of unit commitment (UC) is one of the most important issues in the electricity market, and with the smartening and restructuring of networks which its goals and variables have undergone changes. In this paper, solving and modeling the problem of unit commitment by considering smart networks is proposed. As we know, in smart grids, there are new issues such as demand side management and energy storage systems (batteries) as well as new goals such as reducing the environmental pollution of the units that must be considered. In this paper, the issue of unit commitment with demand side management modeling along with optimal charging and discharging of battery storage system with the aim of minimizing the economic costs of units and batteries and environmental pollution is presented. The proposed model is a Mixed Integer Linear Programming (MILP) model that is solved using powerful commercial software such as Gurobi and guarantees optimal global solutions. The proposed model is implemented on two standard IEEE 6 and 118 bus networks, the results of which show the efficiency of the proposed model.

Due to the progress of renewable energy technologies and the intention of energy policymakers to use these clean and cheap resources, many studies have focused on ways to take advantage of these energies. Limitations, such as low capacity, output power uncertainty, and sustainability problems, make the use of distributed energy resources costly and difficult. Among distributed generation resources, renewable energy resources such as wind energy and solar energy are more environmentally friendly and are used more than other technologies. Despite the many advantages of these resources, their output power depends on such factors as wind speed and solar intensity, which cannot be accurately predicted. For this reason, the infiltration[MSH1]  of high levels of these resources into power systems increases system uncertainty and can reduce reliability while system reliability is very important for power system designers and operators, as well as energy consumers. To solve these problems, a new concept, named virtual power plant, is proposed. A virtual power plant is a collection of distributed energy resources that come together to participate in the market. Virtual power plants can efficiently coordinate, aggregate, and manage different distributed energy resources such as distributed generation, energy storage systems, and controllable loads. These plants are flexible agents for a range of distributed energy sources that can be used in wholesale markets to provide services to system operators. The energy management system is the heart of a virtual power plant that coordinates the flow of power from generators, controllable loads, and energy storage devices. This paper proposes a full model for optimal planning of a virtual power plant if uncertainties of distributed generation sources such as wind and solar energy, as well as electrical vehicles, are considered. To prevent the negative effects of the presence of electric vehicles on electricity networks, especially in virtual power plants, it is necessary to charge these vehicles in a controlled manner and with careful planning. In addition, the demand response whose modeling is based on price-based demand response for non-users and encouragement-based for electric vehicles is optimized on two scenarios, and a 32-bus network is studied. The main goal of the research is to maximize the profit of the virtual power plant for the simultaneous use of load response and electric vehicles with the capability of connecting to the grid.

The problem of unit commitment (UC) or in other words, the issue of placing the units in orbit is a very important optimization problem, the exact solution of which can lead to a significant reduction in operation costs. In general, UCchr('39')s goal is to minimize the total cost of production units by considering the constraints of the units and the system during the intended period. In fact, UC is divided into two issues. First, there is the issue of determining the on or off mode of production units for each hour, which is usually 24 hours, and the second is the distribution of economic dispatch between production units. Considering both problems at the same time will complicate the solution. It should also be noted that the difficulty of the problem also increases in proportion to the number of production units as well as the constraints considered. As mentioned, unit cost is typically the primary goal of minimizing UC issues. This paper considers smart grids, one of whose goals is reducing environmental pollution in addition to reducing costs. Therefore, this paper considers UC problem-solving in smart grids by considering the pollution of production units, so a multi-objective function is selected for minimization. On the other hand, with the introduction of smart grids, the existence of energy storage systems (ESS) in the network is also considered. This paper suggests optimal charging and discharging of energy storage systems, too. Another issue modeled in this paper is the issue of demand response in smart grids. Demand response program modeling allows grid demands to be shifted within the specified range at different times of the day. The proposed model is a mixed integer linear programming model (MILP) that has been tested to validate the performance of the proposed model, i.e., 4-unit and 10-unit systems with storage resources. To solve the proposed model, a powerful Gurobi solver is used. This solver also guarantees optimal global solutions and can get optimal solutions in the shortest time. In the end, the simulation results showed that modeling the problem of optimizing the charge and discharge of the energy storage system, along with the problem of demand-response management in the issue of unit participation, is very effective in reducing operating costs and reducing pollution. On the other hand, due to the linear nature of the problem, the proposed model can be solved in larger dimensions of the power systems.

This research addresses a simultaneous jobs scheduling and worker assignment problem in flow shop environment in which there are some workers with different skills who can operate the jobs with different speed. The primary aim of the research is to schedule the jobs and assign the worker so that maximum completion time (Cmax) is minimized. To tackle this problem, a mixed integer linear programming model is introduced and is coded in CPLEX software so that it can obtain the optimal solutions in reasonable time. Due to NP-hardness of the research problem, CPLEX cannot achieve the optimal solutions for large-scale problems. Thus, two metaheuristic approaches based on particle swarm optimization (PSO) is proposed here. In order to trapping the PSO algorithm in local optima with high probability, the performance of the PSO algorithm is improved by simulated annealing (SA) algorithm (IPSO). The experimental results show that the IPSO algorithm can generate better results in entire scales and the superiority of the IPSO is significant in the large scale.