General Mixed Integer Linear Programming Research Articles

Mixed-Integer-Linear-Programming-Based Energy Management System for Hybrid PV-Wind-Battery Microgrids: Modeling, Design, and Experimental Verification

Microgrids are energy systems that aggregate distributed energy resources, loads, and power electronics devices in a stable and balanced way. They rely on energy management systems to schedule optimally the distributed energy resources. Conventionally, many scheduling problems have been solved by using complex algorithms that, even so, do not consider the operation of the distributed energy resources. This paper presents the modeling and design of a modular energy management system and its integration to a grid-connected battery-based microgrid. The scheduling model is a power generation-side strategy, defined as a general mixed-integer linear programming by taking into account two stages for proper charging of the storage units. This model is considered as a deterministic problem that aims to minimize operating costs and promote self-consumption based on 24-hour ahead forecast data. The operation of the microgrid is complemented with a supervisory control stage that compensates any mismatch between the offline scheduling process and the real time microgrid operation. The proposal has been tested experimentally in a hybrid microgrid at the Microgrid Research Laboratory, Aalborg University.

A capacity expansion planning model for integrated water desalination and power supply chain problem

Cogeneration of water and power in integrated cogeneration production plants is a common practice in the Middle East and North Africa (MENA) countries. There are several combinations of water desalination and power technologies which give significant adverse environmental impact. Renewable and alternative energy technologies have been recently proposed as alternative power production paths in the water and power sector. In this study, we examine the optimal capacity expansion of water and power infrastructure over an extended planning horizon. A generic mixed integer linear programming model is developed to assist in the decision making process on: (1) optimal installation of cogeneration expansion capacities; (2) optimal installation of renewable and alternative power plants; (3) optimal operation of the integrated water and power supply chain over large geographical areas. Furthermore, the model considers the installation of carbon capture methods in fossil-based power plants. A case study will be presented to illustrate the mathematical programming application for the Emirate of Abu Dhabi (AD) in the United Arab Emirates (UAE). The case study is solved reflecting different scenarios: base case scenario, integration of renewable and alternative technologies scenario, and CO2 reduction targets scenario. The results show that increased carbon tax values up to 150$/ton-CO2 gives a maximum 3% cost increase for the supply chain net present value. The installation of carbon capture methods is not an economical solution due to its high operation energy requirements in the order of 370kWh per ton of captured CO2. Thus, the Cplex solver in GAMS chooses optimal solutions without installation of carbon capture processes. In addition, higher degree of alternative and renewable energy technologies penetration within the energy mix reduces the overall net present value of the network, and the carbon emissions by 40%, and 12%, respectively.

Investment planning of residential energy supply systems using dual dynamic programming

The residential sector contributes significantly to primary energy consumption. Energy efficiency measures in this sector consequently play a key role in the transformation towards a more sustainable energy system. There are a multitude of options available to increase the energy efficiency, e.g. the installation of various electricity and heat supply systems or retrofitting of the building stock. Due to the availability of all these options, the investment planning decision for residential energy supply systems is very complex and requires the support of mathematical optimization methods. However, existing works in this field often use simplifications with regard to the considered portfolio of measures or the considered time resolution in order to maintain computational feasibility. These simplifications lead to sub-optimal or incomplete decisions for residential energy system investments. In this paper, a novel optimization model for the integrated investment and operation planning decision for residential energy supply systems is presented. Instead of using simplifications, the presented model uses a dual dynamic programming approach to reduce computational complexity. Due to this efficient solution strategy, additional decision variables can be integrated into the optimization without meeting computational limits. The functionality and mathematical structure of the decomposition approach are presented and compared to a general mixed-integer linear programming model. An exemplary case study is conducted for both a single family and an apartment building.

Generation Applications Package for Combined Heat Power in On-Grid and Off-Grid Microgrid Energy Management System

A microgrid can be operated in on-grid or off-grid mode using distributed energy resources (DER), among which combined heat power (CHP) can play an important role in increasing the total energy efficiency. This paper reports the total solutions to the problem of scheduling DER, including CHP and their dispatch, called a generation application package. To increase the accuracy of forecasting, this paper proposes the methods of electrical or heat load forecasting and photovoltaic forecasting using a pattern recognition algorithm by ${k}$ -means clustering. In response of the forecasted data, the formulation and solution of generation scheduling and the dispatch of DER are provided in two operation modes of a microgrid. The formulation of generation scheduling is linearized for a general mixed integer linear programming solver. The formulation and the detailed solution of the economic dispatch of the DER are presented. Finally, the field tests of the generation application package in two demonstration sites were performed and the results showed that the proposed solutions are very effective in the real fields.

Optimal design and operation of integrated wind-hydrogen-electricity networks for decarbonising the domestic transport sector in Great Britain

Abstract This paper presents the optimal design and operation of integrated wind-hydrogen-electricity networks using the general mixed integer linear programming energy network model, STeMES (Samsatli and Samsatli, 2015). The network comprises: wind turbines; electrolysers, fuel cells, compressors and expanders; pressurised vessels and underground storage for hydrogen storage; hydrogen pipelines and electricity overhead/underground transmission lines; and fuelling stations and distribution pipelines. The spatial distribution and temporal variability of energy demands and wind availability were considered in detail in the model. The suitable sites for wind turbines were identified using GIS, by applying a total of 10 technical and environmental constraints (buffer distances from urban areas, rivers, roads, airports, woodland and so on), and used to determine the maximum number of new wind turbines that can be installed in each zone. The objective is the minimisation of the total cost of the network, subject to satisfying all of the demands of the domestic transport sector in Great Britain. The model simultaneously determines the optimal number, size and location of each technology, whether to transmit the energy as electricity or hydrogen, the structure of the transmission network, the hourly operation of each technology and so on. The cost of distribution was estimated from the number of fuelling stations and length of the distribution pipelines, which were determined from the demand density at the 1 km level. Results indicate that all of Britain's domestic transport demand can be met by on-shore wind through appropriately designed and operated hydrogen-electricity networks. Within the set of technologies considered, the optimal solution is: to build a hydrogen pipeline network in the south of England and Wales; to supply the Midlands and Greater London with hydrogen from the pipeline network alone; to use Humbly Grove underground storage for seasonal storage and pressurised vessels at different locations for hourly balancing as well as seasonal storage; for Northern Wales, Northern England and Scotland to be self-sufficient, generating and storing all of the hydrogen locally. These results may change with the inclusion of more technologies, such as electricity storage and electric vehicles.

A multi-period, multi-regional generation expansion planning model incorporating unit commitment constraints

This work presents a generic mixed integer linear programming (MILP) model that integrates the unit commitment problem (UCP), i.e., daily energy planning with the long-term generation expansion planning (GEP) framework. Typical daily constraints at an hourly level such as start-up and shut-down related decisions (start-up type, minimum up and down time, synchronization, soak and desynchronization time constraints), ramping limits, system reserve requirements are combined with representative yearly constraints such as power capacity additions, power generation bounds of each unit, peak reserve requirements, and energy policy issues (renewables penetration limits, CO2 emissions cap and pricing). For modelling purposes, a representative day (24h) of each month over a number of years has been employed in order to determine the optimal capacity additions, electricity market clearing prices, and daily operational planning of the studied power system. The model has been tested on an illustrative case study of the Greek power system. Our approach aims to provide useful insight into strategic and challenging decisions to be determined by investors and/or policy makers at a national and/or regional level by providing the optimal energy roadmap under real operating and design constraints.

A risk management approach to the economic and environmental strategic design of ethanol supply chains

A general Mixed Integer Linear Programming modelling framework supporting strategic design and planning decisions for multi-period and multi-echelon ethanol supply chains is developed and implemented. Multiple biomass and technology options involving both first and second generation production are addressed for paving the way towards sustainable and feasible energy infrastructures. The ethanol supply chain is optimised according to a comprehensive mathematical framework where multiple decision criteria are simultaneously considered in an uncertain market scenario. In particular, the economic and environmental performances are both optimised also considering the decision makers' risk mitigation preferences. Carbon cost emissions allowances trading scheme, crop management and technology learning issues are encompassed, too. A demonstrative case study is proposed involving the potential future Italian biomass-based ethanol production. Results show the effectiveness of the modelling framework as a decision making-tool to steer decisions and investments in the long term horizon among different ethanol fuel configurations.

Thermal-Aware Post Layout Voltage-Island Generation for 3D ICs

To reduce the interconnect delay and improve the chip performance, three-dimensional (3D) chip emerged with the rapid increasing of chip integration and chip power density. Therefore, thermal issue is one of the critical challenges in 3D IC design due to the high power density. Multiple Supply Voltages (MSV) technique provides an efficient way to optimize power consumption which in turn may alleviate the hotspots. But the voltage assignment is limited not only by the performance constraints of the design, but also by the physical layout of circuit modules since the modules with the same voltage should be gathered to reduce the power-network routing resource. Especially in 3D designs, the optimization using MSV technique becomes even more complicated since the high temperature also influences the power consumption and delay on paths. In this paper, we address the voltage-island generation problem for MSV designs in 3D ICs based on a mixed integer linear programming (MILP) model. First, we propose a general MILP formulation for voltage-island generation to optimize thermal distribution as well as power-network routing resources while maintaining the whole chip performance. With the thermal-power interdependency, an iterative optimization approach is proposed to obtain the convergence. Experimental results show that our thermal-aware voltage-island generation approach can reduce the maximal on-chip temperature by 23.64 % with a reasonable runtime and save the power-network routing resources by 16.71 %.

Energy and Environmental Systems Planning with Recourse: Inexact Stochastic Programming Model Containing Fuzzy Boundary Intervals in Objectives and Constraints

AbstractIn this study, a feasibility-analysis-based inexact fuzzy multistage model (FA-IFMSM) was developed for supporting the planning of energy and environmental systems under multiform uncertainties. In FA-IFMSM, methods of feasibility-analysis-based fuzzy linear programming (FA-FLP) and inexact multistage stochastic programming (IMSP) with recourse were integrated into a general mixed-integer linear programming framework, such that the developed model could tackle uncertainties described in terms of probability distributions, interval values, fuzzy sets, and their hybrid and mixture. Moreover, it could reflect dynamic features of facility-capacity expansions and energy supplies over a multistage context. It could also quantify constraint violation degrees through the adoption of various acceptable degree levels. Then the proposed model was applied to a regional energy and environmental system to illustrate its applicability, where conventional and renewable energy resources and their economic and envi...

Optimal control of a residential microgrid

We propose a generic mixed integer linear programming model to minimize the operating cost of a residential microgrid. We model supply and demand of both electrical and thermal energy as decision variables. The modeled microgrid is operated in grid-connected mode. It covers solar energy, distributed generators, energy storages, and loads, among them controllable load jobs released by home appliances and electric vehicles. We propose a model predictive control scheme to iteratively produce a control sequence for the studied microgrid. Our case study reveals the performance of minimum cost control by comparison with benchmark control policies. We consider three price scenarios in our analyses which include two market-based scenarios. Numerical results from our study indicate savings in annual operating cost between 3.1 and 7.6 percent.

On the global solution of multi-parametric mixed integer linear programming problems

This paper deals with the global solution of the general multi-parametric mixed integer linear programming problem with uncertainty in the entries of the constraint matrix, the right-hand side vector, and in the coefficients of the objective function. To derive the piecewise affine globally optimal solution, the steps of a multi-parametric branch-and-bound procedure are outlined, where McCormick-type relaxations of bilinear terms are employed to construct suitable multi-parametric under- and overestimating problems. The alternative of embedding novel piecewise affine relaxations of bilinear terms in the proposed algorithmic procedure is also discussed.

Planning and Sequencing Product Distribution in a Real-World Pipeline Network: An MILP Decomposition Approach

In the oil industry, any improvement in the planning and execution of the associated operations (e.g., production, storage, distribution) can generate considerable profits. To achieve this, the related activities need to be optimized. Within these activities, planning and scheduling occur at the different levels of the oil supply chain, from the strategic to the operational levels looking from global networks to sets of individual resources. This work looks into the planning, namely the assignment/sequencing of activities that occur in a multiproduct, multipipeline system. The aim is to contribute to the definition of generic models that can help the decision-making process characterized by a high level of complexity. An approach formed by two mixed integer linear programming (MILP) formulations that act in sequence is proposed. The first generic MILP planning model calculates volumes for attending the necessary requirements on inventory management of the producer and consumer areas. As a result, this mod...

Solving the quadratic assignment problem by means of general purpose mixed integer linear programming solvers

The Quadratic Assignment Problem (QAP) can be solved by linearization, where one formulates the QAP as a mixed integer linear programming (MILP) problem. On the one hand, most of these linearizations are tight, but rarely exploited within a reasonable computing time because of their size. On the other hand, Kaufman and Broeckx formulation (Eur. J. Oper. Res. 2(3):204–211, 1978) is the smallest of these linearizations, but very weak. In this paper, we analyze how the Kaufman and Broeckx formulation can be tightened to obtain better QAP-MILP formulations. As shown in our numerical experiments, these tightened formulations remain small but computationally effective to solve the QAP by means of general purpose MILP solvers.

The extended resource task network: a framework for the combined scheduling of batch processes and CHP plants

The issue of energy has emerged as one of the greatest challenges facing mankind. In an industrial perspective, the development of site utility systems (generally combined heat and power (CHP) systems) for the generation and management of utilities provides a great potential source for energy savings. However, in most industrial sites, a master–slave relationship usually governs this kind of system and limits the potential operating capacity of CHP. To improve the decision-making process, Agha et al. (2010. Integrated production and utility system approach for optimising industrial unit operation. Energy, 35, 611–627) have proposed an integrated approach that carries out simultaneous and consistent scheduling of batch production plants and site utility systems. The modelling of the problem relies on a mixed integer linear programming (MILP) formulation. Nevertheless, although it is a powerful mathematical tool, it still remains difficult to use for non-expert engineers. In this framework, a graphical formalism based on existing representations (STN, RTN) has been developed: the extended resource task network (ERTN). Combined with an efficient and generic MILP formulation, it permits various kinds of industrial problems, including production and consumption of utility flows to be modelled homogenously. This paper focuses on the semantic elements of the ERTN formalism and illustrates their use through representative examples.

A New Approach to the Feasibility Pump in Mixed Integer Programming

The feasibility pump is a recent, highly successful heuristic for general mixed integer linear programming problems. We show that the feasibility pump heuristic can be interpreted as a discrete ver...

Integrated Electricity Planning Comprise Renewable Energy and Feed-In Tariff

Problem statement: Mitigation of global warming and energy crisis has called upon the need of an efficient tool for electricity planning. This study thus presents an electricity planning tool that incorporates RE with Feed in-Tariff (FiT) for various sources of Renewable Energy (RE) to minimize grid-connected electricity generation cost as well as to satisfy nominal electricity demand and CO2 emission reduction target. Approach: In order to perform these tasks, a general Mixed Integer Linear Programming (MILP) model was developed and implemented in General Algebraic Modeling System (GAMS). The RE options considered including landfill gas, municipal solid waste, palm oil residue and hydro power. While the model presents a general approach for electricity planning, Iskandar Malaysia is applied as a case study in this research. Results: By considering the cost, FiT, availability of the Renewable Energy Source (RES) and limit of RE fund for FiT remuneration in Malaysia. The optimization result indicates that Iskandar Malaysia can satisfy the set target of 40% carbon emission reduction by 2015 by implementing biomass RE. Conclusion: It’s revealed that a total of 875 MW of RE is required from Biomass Bubbling Fluidized Bed (BBFB) using various palm oil biomass fuel (mesofiber-215 MW, Empty Fruit Bunch (EFB)-424 MW and kernel-236 MW). However, this increases the Cost Of Electricity (COE) by 69-6.5% cents/kWh.

A comprehensive approach to the design of ethanol supply chains including carbon trading effects

The optimal design of biofuels production systems is a key component in the analysis of the environmental and economic performance of new sustainable transport systems. In this paper a general mixed integer linear programming modelling framework is developed to assess the design and planning of a multi-period and multi-echelon bioethanol upstream supply chain under market uncertainty. The optimisation design process of biofuels production systems aims at selecting the best biomass and technologies options among several alternatives according to economic and environmental (global warming potential) performance. A key feature in the proposed approach is the acknowledgement of an economic value to the overall GHG emissions, which is implemented through an emissions allowances trading scheme. The future Italian biomass-based ethanol production is adopted as a case study. Results show the effectiveness of the model as a decision making-tool to steer long-term decisions and investments.

A computational study of the cutting plane tree algorithm for general mixed-integer linear programs

The cutting plane tree algorithm provides a finite procedure for solving general mixed-integer linear programs with bounded integer variables. The computational evidence provided in this work illustrates that this algorithm is powerful enough to close a significant fraction of the integrality gap for moderately sized MIPLIB instances.

Finite Disjunctive Programming Characterizations for General Mixed-Integer Linear Programs

In this paper, we give a finite disjunctive programming procedure to obtain the convex hull of general mixed-integer linear programs (MILP) with bounded integer variables. We propose a finitely convergent convex hull tree algorithm that constructs a linear program that has the same optimal solution as the associated MILP. In addition, we combine the standard notion of sequential cutting planes with ideas underlying the convex hull tree algorithm to help guide the choice of disjunctions to use within a cutting plane method. This algorithm, which we refer to as the cutting plane tree algorithm, is shown to converge to an integral optimal solution in finitely many iterations. Finally, we illustrate the proposed algorithm on three well-known examples in the literature that require an infinite number of elementary or split disjunctions in a rudimentary cutting plane algorithm.

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Contributors