Mixed Integer Linear Programming Algorithm Research Articles

Analysis of Electrical Distribution Network Voltage Configuration with Mixed Integer Linear Programming Algorithm and Genetic Algorithm I Terms of Energy Cost

Analysis of Electrical Distribution Network Voltage Configuration with Mixed Integer Linear Programming Algorithm and Genetic Algorithm I Terms of Energy Cost

Integrated approach for optimal techno-economic planning for high renewable energy-based isolated microgrid considering cost of energy storage and demand response strategies

To realize an efficient energy supply system for an isolated microgrid, a joint design framework that considered the capacity sizing alongside operational planning is essential. In this work, an integrated planning model was developed to investigate the techno-economic performances of a high renewable energy-based standalone microgrid. The approach combines capacity sizing and operation scheduling, considering demand-side management strategies for different system design scenarios. The evaluated scenarios involved the combination of wind turbine, photovoltaic system, diesel generator, with either battery energy storage or pumped thermal energy storage. A demand response program based on instantaneous renewable energy availability is proposed with dynamic pricing economic model for improving the overall system flexibility. Mixed-integer linear programming algorithm on MATLAB® is deployed as the optimization solver. The minimization of the sum of system costs which includes equivalent annual costs of the investments, running costs and costs based on demand-side management strategies is the objective function. The combination of photovoltaic, wind turbine and pumped thermal energy storage is found to be the most techno-economically efficient system configuration for the considered microgrid. More so, the proposed demand response strategy minimizes the mismatch between the generation and the load demand profile effectively, thereby increasing the system flexibility.

Novel Heuristic ToD-Block Rate Tariff for DSM Initiation in Domestic Sector: A Study Analysis

Effectiveness of demand side management practice is studied with low-tension domestic sector load data of a south Indian district using tariff as load scheduling tool. A suggestion regarding the impact of proposed novel hybrid Time of Day-Block rate tariff on energy consumption cost calculation is made to initiate load management. Three different combinations of peak-off peak pricing strategy are introduced and optimized to induce future implementation of suggested tariff for welfare of consumer and utility as well. A preference-adaptive load management algorithm is proposed and testified for power flow under two schemes of priority-based load shifting namely, all-time and off-peak time shifting. Genetic algorithm confirms the suggestion being modeled as an initiative work of unidirectional power flow domain from utility to consumer and also ensures its implementation for billing. Mixed integer linear programming algorithm approves the hourly consumption cost calculation for monthly/bimonthly billing over existing block rate billing. Five-year (2014–2018) load data is analyzed with nine different scenarios. Study declares its necessity in replacing existing tariff under all seasonal conditions.

MILP-PSO Combined Optimization Algorithm for an Islanded Microgrid Scheduling with Detailed Battery ESS Efficiency Model and Policy Considerations

This paper presents the optimal scheduling of a diesel generator and an energy storage system (ESS) while using a detailed battery ESS energy efficiency model. Optimal scheduling has been hampered to date by the nonlinearity and complexity of the battery ESS. This is due to the battery ESS efficiency being a multiplication of inverter and battery efficiency and the dependency of an inverter and any associated battery efficiencies on load and charging and discharging. We propose a combined mixed-integer linear programming and particle swarm optimization (MILP-PSO) algorithm as a novel means of addressing these considerations. In the algorithm, MILP is used to find some initial points of PSO, so that it can find better solution. Moreover, some additional algorithms are added into PSO to modify and, hence, improve its ability of dealing with constraint conditions and the local minimum problem. The simulation results show that the proposed algorithm performs better than MILP and PSO alone for the practical microgrid. The results also indicated that simplification or neglect of ESS efficiency when applying MILP to scheduling may cause a constraint violation.

A MILP algorithm for the optimal sizing of an off-grid​ hybrid renewable energy system in South Tyrol

The exploitation of renewable energy sources through sustainable energy technologies are taking the field to decrease the pollutions’ emissions into the Earth’s environment. To offset the limitations of such resources, hybrid energy systems are becoming fundamental in grid-connected applications as well as in off-grid ones. However, the unsteady behavior of renewable sources, such as Sun and Wind, complicates the prediction of the energy production’s trend. The main factors and components involved in the design of hybrid energy systems are: (i) type of generators, (ii) their optimal number, (iii) storage systems and (iv) optimal management strategies. All of them have to be considered simultaneously to develop the optimal solution aimed at either reducing the dependence from fossil fuels or granting the supply of energy. In this paper, a methodology based on the Mixed Integer Linear Programming (MILP) is presented and adopted to meet the electric demand of a mountain lodge located in a remote area in South-Tyrol (Italy). The methodology has been developed implementing an algorithm through the Matlab ©software. The algorithm is capable of evaluating the optimal size of a hybrid off-grid Solar–Wind system with battery storage in order to replace an Internal Combustion Engine (ICE) fueled by diesel.

Energetic and economic optimization of the yearly performance of three different solar assisted heat pump systems using a mixed integer linear programming algorithm

This paper presents a yearly energetic and economic assessment of three different solar assisted heat pump concepts integrated with electrical and thermal storages and applied to a single-family house. The three heat pump-based systems are (i) a conventional air-to-water heat pump plus photovoltaic solar modules, (ii) a water-to-water heat pump coupled to hybrid photovoltaic-thermal solar modules and (iii) a dual source heat pump integrated with hybrid photovoltaic-thermal solar modules. The energetic and economic analysis is performed using physically-based models of each component for different numbers of solar modules and sizes of the electric storage. The maximum economic saving of these highly integrated systems is determined through an optimization algorithm based on the mixed integer linear programming technique. The results show that the dual source heat pump system with the largest battery size is the system that achieves the highest energetic performance, i.e. 77% primary energy saving with respect to traditional boiler-based system, whereas the lowest operating cost and the highest economic saving are obtained using the conventional air-to-water heat pump without any electric storage since it achieves 31% economic saving compared with the baseline system.

A Novel MILP Model for N-vehicle Exploration Problem

The N-vehicle exploration problem (NVEP) is a nonlinear discrete scheduling problem, and the complexity status remains open. To our knowledge, there is no literature until now employing mixed integer linear programming (MILP) technology to solve this problem except for Wang (J Oper Res Soc China 3(4):489–498, 2015). However, they did not give numerical experiments since their model existed strictly inequalities and the number of constraints was up to $$O(n^3)$$, which was inefficient to solve practical problems. This paper establishes a more concise MILP model, where the number of constraints is just $$O(n^2)$$. Therefore, the existing efficient MILP algorithms can be used to solve NVEP. Secondly, we provide some properties of N-vehicle problem and give three methods for cutting plane construction, which can increase the solving speed significantly. Finally, a numerical experiment is provided to verify the effectiveness and robustness for different instances and scales of acceleration techniques.

Solver-Based Mixed Integer Linear Programming (MILP) Based Novel Approach for Hydroelectric Power Generation Optimization

In Pakistan, hydroelectric power is one of the reliable sources of electricity with a capacity of 8,713 MW, which is 29% of the total energy mix. Hence, with such a vast resource capacity of hydroelectric power, its optimization and dispatch planning will have a great significance. This research work discusses the importance of hydroelectric power generation planning for both storage and run-of-river (ROR) hydropower plants, as well a; a solver-based optimization technique is proposed for the first time to resolve the intricate job of generation planning for hydroelectric power plants in MATLAB. A mathematical-optimization model is also developed, which uses a Mixed-Integer Linear-Programming (MILP) algorithm, based on the objective function of profit maximization, which considers a random varying revenue plan as model input. Three hydropower generators of different capacities and efficiencies are considered for the optimization problem. MILP based solution is proposed for both storage and ROR hydropower plants with two dispatch schedules, i.e., Normal dispatch schedule and optimum dispatch schedule. The objective functions are solved, and the profit (in dollars) from each dispatch schedule is calculated and compared. The preliminary optimization results show an increase of $22,000 and $29,130 in the profit for storage and ROR hydropower plants, respectively, which is 19% more than average income. Hence, ensuring the credibility of the proposed algorithm for maximizing the revenue ($), is aimed to facilitate and assist better planning for electric power producers.

Methodology to support the flexibility maximisation for multi-energy systems to provide services to the electrical distribution system

This study proposes the energy-lattice methodology designed to model and analyse multi-energy systems (MESs) as energy transformation flows. A mixed-integer linear programming algorithm supports the methodology to set short-term planning for MES to satisfy the multi-energy demand, and the provision of services, like ancillary services to the power system. The methodology is based on the notion of energy layers associated with energy carriers. An energy layer represents the provision of services and the satisfaction of the external demand, by the operation of suitable devices, like generators, storages and loads related to an energy carrier. Energy layers are related to each other by conversion nodes. This work was partially carried out in the European project H2020 MANGNITUDE (n. 774309). This study illustrates the main features of the energy-lattice methodology and the underlying algorithm that models the behaviour of the MES in the short term. This algorithm is a mathematical mixed-integer linear programming composed of two stages. The former copes with the energy demand and the latter, according to the results of the first one, verifies the economic convenience to provide ancillary services according to the identified flexibility margins.

Development of a responsive optimisation framework for decision-making in precision agriculture

Emerging digital technologies and data advances (e.g. smart machinery, remote sensing) not only enable Agriculture 4.0 to envisage interconnected agro-ecosystems and precision agriculture but also demand responsive decision-making. This study presents a mathematical optimisation model to bring real-time data and information to precision decision-support and to optimise short-term farming operation. To achieve responsive decision-support, we proposed two meta-heuristic algorithms i.e. a tailored genetic algorithm and a hybrid genetic-tabu search algorithm for solving the deterministic optimisation. The developed responsive optimisation framework has been applied to a hypothetical case study to optimise sugarcane harvesting in the KwaZulu Natal region in South Africa. In comparison with the optimal solutions derived from the exact algorithm, the proposed meta-heuristic methods lead to near optimal solutions (less than 5% from optimality) and significantly reduced computational time by over 95%. Our results suggest that the tailored genetic algorithm enables rapid solution searching but the solution quality on sugarcane harvesting cannot compete with the exact method. The hybrid genetic-tabu search algorithm achieved a good trade-off between computational time reduction and solution optimality, demonstrating the potential to enhance responsive decision making in precision sugarcane farming. Our research highlights the development of the responsive optimisation framework combining mixed integer linear programming and hybrid meta-heuristic search algorithms and its applications in real-time decision-making under Agriculture 4.0 vision.

Optimal Configuration of Island Microgrid Considering Wind/Photovoltaic/Line/Storage and Seawater Desalination Load

Safe and reliable power supply is the basic guarantee for the development and construction of the island. Aimed at the problem of lack of electricity and water on the island, the paper proposes an optimal configuration method of island microgrid considering wind/photovoltaic/line/storage and seawater desalination loads. Firstly, the paper analyzes the load demand and the characteristics of renewable resources on the island, and proposes a grid-connected island microgrid system with multiple energy types and seawater desalination load. On this basis, an optimization model with the minimum annual cost as the objective function is established. The mixed integer linear programming(MILP) algorithm is used to optimize the capacity configuration and operation mode of the island microgrid system simultaneously. Finally, taking an island in the eastern coast of China as an example, the effectiveness of the optimal configuration method is verified through scenario analysis.

Planning Method for Power-Gas-Heat-Steam Integrated Energy System in Industrial Park Considering Annual Comprehensive Cost

The current energy system in industrial parks have the problem of poor investment efficiency and low energy utilization rate. A planning method for the park’s power-gas-heat-steam integrated energy system(IES) considering annual comprehensive cost is proposed. Firstly, based on the uncertainty of renewable energy and the characteristics of energy supply and consumption in the park, the structure of the integrated energy system is established. Papersets the minimum annual comprehensive cost including investment, operation, maintenance cost and environmental protection cost as the optimization goal. The mixed integer linear programming(MILP) algorithm is used to optimize the equipment selection, capacity planning and equipment operation mode at the same time. Through the example simulation, the planning scheme under different scenarios is given, and the effectiveness of the method is verified.

Flexibility Services to Minimize the Electricity Production from Fossil Fuels. A Case Study in a Mediterranean Small Island

The design of multi-carrier energy systems (MESs) has become increasingly important in the last decades, due to the need to move towards more efficient, flexible, and reliable power systems. In a MES, electricity, heating, cooling, water, and other resources interact at various levels, in order to get optimized operation. The aim of this study is to identify the optimal combination of components, their optimal sizes, and operating schedule allowing minimizing the annual cost for meeting the energy demand of Pantelleria, a Mediterranean island. Starting from the existing energy system (comprising diesel generators, desalination plant, freshwater storage, heat pumps, and domestic hot water storages) the installation of solar resources (photovoltaic and solar thermal) and electrical storage were considered. In this way, the optimal scheduling of storage units injections, water desalination operation, and domestic hot water production was deduced. An energy hub model was implemented using MATLAB to represent the problem. All equations in the model are linear functions, and variables are real or integer. Thus, a mixed integer linear programming algorithm was used for the solution of the optimization problem. Results prove that the method allows a strong reduction of operating costs of diesel generators also in the existing configuration.

Increase of flight operations effectiveness using automated control over a fleet of various UAS

ABSTRACTFollowing paper presents a research aiming to increase the efficiency of an Unmanned Aerial System (UAS) fleet during mission execution. The developed system allows to reduce the mission time by considering the fleet diversity. System is based on a multilevel optimization, applying an innovative trajectory generation method. The Mixed Integer Linear Programming (MILP) algorithm was adopted, so the trajectories for individual platform were optimal (shortest). The developed solution considers not only the area but also the UASs performance and sensors capabilities. The mission operator with the dedicated GUI could control and designate the platforms for various tasks. The method was tested on various platforms with different performance. The method proved its efficiency reducing the mission time up to 15%. Finally, the system was successfully tested in real environment with the use of three various platforms.

Optimal capacity planning of combined renewable energy source-pumped storage and seawater desalination systems

As water scarcity is becoming a growing threat to human development, finding effective solutions has become an urgent need. To make better use of water resources, seawater desalination and storage systems using renewable energy sources (RES) are designed and implemented around the world. In this paper, an optimal capacity planning method for RES-pumped storage-seawater desalination (RES-PS-D) system is introduced. The configuration of the RES-PS-D system is clarified first, after which a cost-benefit analysis is performed using all cost and benefit components. A function for determining maximum economic benefits of the RES-PS-D system is then established, and the constraints are proposed based on various limitations. The mixed-integer linear programming algorithm is applied to solve the optimal function. A case study is introduced to validate the feasibility and effectiveness of the method. The conclusion shows that the strategy is suitable for solving the configuration optimization problem, and finally both merits and defects of the method are discussed.

Real-Time Energy Management for a Small Scale PV-Battery Microgrid: Modeling, Design, and Experimental Verification

A new energy management system (EMS) is presented for small scale microgrids (MGs). The proposed EMS focuses on minimizing the daily cost of the energy drawn by the MG from the main electrical grid and increasing the self-consumption of local renewable energy resources (RES). This is achieved by determining the appropriate reference value for the power drawn from the main grid and forcing the MG to accurately follow this value by controlling a battery energy storage system. A mixed integer linear programming algorithm determines this reference value considering a time-of-use tariff and short-term forecasting of generation and consumption. A real-time predictive controller is used to control the battery energy storage system to follow this reference value. The results obtained show the capability of the proposed EMS to lower the daily operating costs for the MG customers. Experimental studies on a laboratory-based MG have been implemented to demonstrate that the proposed EMS can be implemented in a realistic environment.

A Resilient and Optimal Microgrid Scheduling Portfolio in Linear Programming Platform

In recent year, alarming rate of natural disasters around the world have demanded the need for operative solution in field of power generation, to control polluted energy sources which are major cause of global warming. Microgrid facilitates penetration of renewable energy sources into the existing distribution systems to reduce the overall carbon footprint of the globe by reducing the dependency on the main grid. Efficient but linear microgrid resource scheduling algorithms are gaining interest in present time due to its simplicity and fast computation. This research paper aims to serve the purposes by designing a mixed integer linear programming based microgrid scheduling problem while various types of scenario, minimize the electricity cost for the utilities also maintain the generation and load balance. The strategy is implemented on a small microgrid to prove its efficacy .In this paper mainly optimal scheduling of microgrid has been done in various scenario, and obtained there global minimum electricity cost to the help of mixed integer linear programming (MILP) algorithm. Microgrid is a small scale type of power grid, which provides the energy locally, its offers integration between distributed energy resources and the locally connected loads. Microgrid able to be operated with the main grid and in standalone mode also ability to transitions between these two modes, the mode of operation of microgrid is depends on the system operating condition. The reliability of power grid is improving more when it’s integrated with the Microgrid and works together. Power exchange with the upper stream grid is done through the point of common coupling (PCC). Microgrid having renewable energy resources i.e. PV, Wind and non-renewable energy resources, DG, FC, and MC connected with the Battery storage type system and locally connected loads. So it is a very reliable scenario, main grid with the microgrid, it is more beneficial, economy and stable types of system. Keywords : Optimal Microgrid Scheduling, Linear Programming DOI : 10.7176/APTA/76-05 Publication date :March 31 st 2019

A Branch-and-Cut Benders Decomposition Algorithm for Transmission Expansion Planning

The emergence of a great number of regional planning projects worldwide has considerably increased the complexity and relevance of transmission expansion planning, prompting intensive research and investigation on the formulation and solution. In this paper, the security constrained transmission expansion planning problem is addressed by a branch-and-cut Benders decomposition (BCBD) algorithm. It is a deterministic method where the global optimal solution can be guaranteed in a finite number of iterations. Based on this implementation framework, four acceleration strategies have been employed to enhance the performance. For the validation of accuracy and efficiency, the commercial solver Cplex running on the same platform is introduced for comparison, where four types of mixed-integer linear programming algorithms are discriminated by specifying two pairs of key settings, including dynamic searching and parallel implementation. The superiority of BCBD over Cplex has been validated by case studies, where five benchmark systems ranging from 6 to 300 buses are employed. In addition, performance analysis between BCBD and classical Benders decomposition has also been carried out to distinguish the contribution of branch-and-cut framework and acceleration strategies.

An Integrated Design and Operation Optimal Method for CCHP System

Abstract As a CCHP (combined cooling, heating and power) system becomes more and more complicated, the optimization of capacity configuration and operation strategy turns into a critical issue. In this paper, we put forward a two-layer programming approach which can solve the optimal design and dispatch problem simultaneously. On the first layer, stochastic selection algorithm (SSA) and non-dominated sorting genetic algorithm-II (NSGA-II) are both used to solve the design problem including the optimization of equipment type and capacity, with the goal of minimizing the total lifecycle cost and the pollutant emissions. On the second layer, mixed-integer linear programming (MILP) algorithm is applied to explore a dynamic optimal scheduling scheme, and achieve the lowest operating costs, based on hourly analysis of load characteristics through a whole year. The first layer optimization is based on the optimal results of the second layer. A modelling analysis case of a hospital CCHP system in Chongqing, China is carried out. The economic and environmental goals of Pareto optimality are achieved by applying the two-layer optimization method. The results comparison between SSA and NSGA-II indicates that the former algorithm is much easier and faster, and proofs that the proposed method is reliable.

Risk-Based Allocation of Automation Devices in Distribution Networks With Performance-Based Regulation of Continuity of Supply

This paper presents a risk-based procedure for obtaining the best network automation scenario in the presence of uncertainty in distribution networks where performance-based regulation of continuity of supply is used. The proposed approach takes into account the uncertainty in loads, failure rates, and interruption duration. It employs fuzzy sets, fuzzy mixed integer linear programming algorithm, and a tool for managing risk to determine the optimal number, type and location of different types of automation devices in the presence of the aforementioned uncertainty. The presented approach considers performance-based (reward/penalty) schemes for an extended group of network reliability indices (SAIFI, SAIDI, MAIFI, and ASIDI) along with the cost of new automation devices and cost of relocation of the existing devices.