Mixed Integer Linear Programming Optimization Research Articles

Techno-economic, environmental, and safety assessment of hydrogen powered community microgrids; case study in Canada

This paper proposes a comprehensive design of a renewable hydrogen powered microgrid that can provide backup power to a community in Cornwall, Ontario when disconnected from the power grid. The work employs the implementation of the energy hub concept to optimally design and operate energy generation systems to meet energy loads of a community. Solar PVs, wind turbines, electrolysers, hydrogen tanks, fuel cells and fuel cell vehicles are considered as the components that make up the entire system providing energy within the community. Failure mode and effect analysis (FMEA) is done to assess the safety of hydrogen based microgrid.The major load centers include a fresh food distribution center and a residential complex, where the peak demand is ∼5410 kW. The results of a mixed integer linear programming optimization problem show that a renewable energy generation system size of 2000 kW (400 kW-solar Photovoltaic and 1600 kW-wind turbine) is required. In addition to this, a backup fuel cell generation system of 3000 kW is also needed for the two-day blackout period. One of the positive attributes of implementing vehicle to grid services during islanded operation mode is that it enables the community to offset investment in fuel cell backup generation capacity by 1000 kW. Thirty-eight Toyota Mirai have been used to provide the vehicle to grid service. Due to the scale of the system, it is observed that even after proposing the use of existing market pricing mechanisms for the services offered by the microgrid, the energy system does not have a positive net present value at the end of its project life. Therefore, further economic incentives in the form of bundling costs need to be sanctioned for cleaner microgrid energy systems to be developed. This submission was the Grand Prize Winner of the Hydrogen Education Foundation's 2016 Hydrogen Student Design Contest.

Partitioning of Intelligent Buildings for Distributed Contaminant Detection and Isolation

Intelligent buildings are responsible for ensuring indoor air quality for their occupants under normal operation as well as under possibly harmful contaminant events. An emerging environmental application involves the monitoring of intelligent buildings against harmful events by incorporating various sensing technologies and using sophisticated algorithms to detect and isolate such events. In this context, both centralized and distributed approaches have been proposed, with the latter having significant benefits in terms of complexity, scalability, reliability, and performance. This paper considers the automatic partitioning of the building into subsystems, which enables the distributed simulation, modeling, analysis, and management of the intelligent building while ensuring the effective detection and isolation of contaminants in the building interior. Specifically, we develop both a high-quality heuristic algorithm and an optimal mixed integer linear programming (MILP) formulation for the building partitioning problem. The MILP formulation is based on graph partitioning techniques, while the heuristic is based on matrix clustering techniques. Both approaches partition the building into subsystems while ensuring 1) maximum decoupling between the various subsystems, 2) strong connectivity between the zones of each subsystem, and 3) control of the size of the subsystems with respect to the number of allocated zones. A combination of the two approaches is also proposed for reconfiguring an initial partitioning composition in real time in order to accommodate partitioning needs that arise from dynamic system changes.

Impacts of Operational Variability and Uncertainty on Distributed Generation Investment Planning: A Comprehensive Sensitivity Analysis

This paper presents a comprehensive sensitivity analysis to identify the uncertain parameters which significantly influence the decision-making process in distributed generation (DG) investments and quantify their degree of influence. To perform the analysis, a DG investment planning model is formulated as a novel multistage and multiscenario optimization problem. Moreover, to ensure tractability and make use of exact solution methods, the entire problem is kept as a mixed-integer linear programming optimization. A real-world distribution network system is used to carry out the analysis. The results of the analysis generally show that uncertainty as well as operational variability of the considered parameters have meaningful impacts on investment decisions of DG. The degree of influence varies from one parameter to another. But, in general, ignoring or inadequately considering uncertainty and variability in model parameters has a quantifiable cost. Hence, the analysis made in this paper can be very useful to identify the most relevant model parameters that need special attention in planning practices.

New Multistage and Stochastic Mathematical Model for Maximizing RES Hosting Capacity—Part I: Problem Formulation

This two-part work presents a new multistage and stochastic mathematical model, developed to support the decision-making process of planning distribution network systems (DNS) for integrating large-scale “clean” energy sources. Part I is devoted to the theoretical aspects and mathematical formulations in a comprehensive manner. The proposed model, formulated from the system operator's viewpoint, determines the optimal sizing, timing, and placement of distributed energy technologies (particularly, renewables) in coordination with energy storage systems and reactive power sources. The ultimate goal of this optimization work is to maximize the size of renewable power absorbed by the system, while maintaining the required/standard levels of power quality and system stability at a minimum possible cost. From the methodological perspective, the entire problem is formulated as a mixed integer linear programming optimization, allowing one to obtain an exact solution within a finite simulation time. Moreover, it employs a linearized ac network model which captures the inherent characteristics of electric networks and balances well accuracy with computational burden. The IEEE 41-bus radial DNS is used to test validity and efficiency of the proposed model, and carry out the required analysis from the standpoint of the objectives set. Numerical results are presented and discussed in Part II of this paper to unequivocally demonstrate the merits of the model.

Energy flow modeling and optimal operation analysis of the micro energy grid based on energy hub

The energy security and environmental problems impel people to explore a more efficient, environment friendly and economical energy utilization pattern. In this paper, the coordinated operation and optimal dispatch strategies for multiple energy system are studied at the whole Micro Energy Grid level. To augment the operation flexibility of energy hub, the innovation sub-energy hub structure including power hub, heating hub and cooling hub is put forward. Basing on it, a generic energy hub architecture integrating renewable energy, combined cooling heating and power, and energy storage devices is developed. Moreover, a generic modeling method for the energy flow of micro energy grid is proposed. To minimize the daily operation cost, a day-ahead dynamic optimal operation model is formulated as a mixed integer linear programming optimization problem with considering the demand response. Case studies are undertaken on a community Micro Energy Grid in four different scenarios on a typical summer day and the roles of renewable energy, energy storage devices and demand response are discussed separately. Numerical simulation results indicate that the proposed energy flow modeling and optimal operation method are universal and effective over the entire energy dispatching horizon.

Service agent–transport agent task planning incorporating robust scheduling techniques

As the use of cooperative, heterogeneous teams of autonomous robots to perform tasks such as autonomous package delivery and long-duration ocean sampling becomes more prevalent, the is a quickly-emerging need to study the high-level interaction of specialized robotic agents that perform service tasks, and specialized transport agents that transport the service agents between service areas. If the service routes, docking, and deployment schedules are not carefully planned, the overall schedule is inefficient at best, and possibly even infeasible due to fuel limitations at worst. We introduce a new problem in the area of scheduling and route planning operations called the service agent transport problem (SATP). Within the SATP, autonomous service agents must perform tasks at a number of locations. The agents are free to move between locations, however, the agents may also be transported throughout the region by a limited number of faster-moving transport agents. The goal of the SATP is to plan a schedule of service agent and transport agent actions such that all locations are serviced in the shortest amount of time. We believe the SATP formulation is unique because there is strong coupling between vehicle constraints as well as between the task allocation component of the problem and the scheduling component of the problem. We present a solution to the problem using a mixed-integer linear programming optimization framework and compare several complexity reduction heuristics to full optimization. Additionally, we include methods to account for relative uncertainty in the duration of planned tasks in such a manner as to balance the risk of schedule slips (conflicts) to the risk of creating an overly conservative and sub-optimal schedule.

Mix-mode energy management strategy and battery sizing for economic operation of grid-tied microgrid

This paper presents a novel ‘mix-mode’ energy management strategy (MM-EMS) and its appropriate battery sizing method for operating the microgrid at the lowest possible operating cost. The MM-EMS is developed by combining three proposed operating strategies, namely “continuous run mode”, “power sharing mode” and “ON/OFF mode” for a 24 h time period. The objective functions for the proposed strategies are solved using linear programming (LP) and mixed integer linear programming (MILP) optimization methods. A sizing method using the particle swarm optimization (PSO) technique to determine the optimal energy capacity of battery energy storage (BES) in kWh is also presented. Since the size of the BES influences the microgrid's operating cost, the energy management strategy (EMS) and BES capacity are simultaneously optimized. The proposed MM-EMS and battery sizing method were first validated. Then, the variation of optimal battery capacity for different battery state of charge (SOC) levels is analyzed. The variation of microgrid's associated costs for different battery's initial state of charge (SOC) levels is analyzed as well. Finally, a recommendation on the choice of initial SOC level during the start of the day for the economic operation of microgrid is also suggested.

An integrated optimization-simulation framework for vehicle and personnel relocations of electric carsharing systems with reservations

One-way electric vehicle carsharing systems are receiving increasing attention due to their mobility, environmental, and societal benefits. One of the major issues faced by the operators of these systems is the optimization of the relocation operations of personnel and vehicles. These relocation operations are essential in order to ensure that vehicles are available for use at the right place at the right time. Vehicle availability is a key indicator expressing the level of service offered to customers. However, the relocation operations, that ensure this availability, constitute a major cost component for the provision of these services. Therefore, clearly there is a trade-off between the cost of vehicle and personnel relocation and the level of service offered. In this paper we are developing, solving, and applying, in a real world context, an integrated multi-objective mixed integer linear programming (MMILP) optimization and discrete event simulation framework to optimize operational decisions for vehicle and personnel relocation in a carsharing system with reservations. We are using a clustering procedure to cope with the dimensionality of the operational problem without compromising on the quality of the obtained results. The optimization framework involves three mathematical models: (i) station clustering, (ii) operations optimization and (iii) personnel flow. The output of the optimization is used by the simulation in order to test the feasibility of the optimization outcome in terms of vehicle recharging requirements. The optimization model is solved iteratively considering the new constraints restricting the vehicles that require further charging to stay in the station until the results of the simulation are feasible in terms of electric vehicles’ battery charging levels. The application of the proposed framework using data from a real world system operating in Nice, France sheds light to trade-offs existing between the level of service offered, resource utilization, and certainty of fulfilling a trip reservation.

A mixed integer linear programming optimization approach for multi-cloud capacity allocation

Abstract The large success of the Cloud computing, its strong impact on the ICT world and on everyday life testifies the maturity and effectiveness this paradigm achieved in the last few years. Presently, the Cloud market offers a multitude of heterogeneous solutions. However, despite the undeniable advantages, Cloud computing introduced new issues and challenges. In particular, the heterogeneity of the available Cloud services and their pricing models makes the identification of a configuration that minimizes the operating costs of a Cloud application, guaranteeing at the same time the Quality of Service, a challenging task. This situation requires new processes and models to design software architectures and predict costs and performance considering together the large variability in price models and the intrinsic dynamism and multi-tenancy of the Cloud environments. This work aims at providing a novel mathematical approach to this problem presenting a queuing theory based Mixed Integer Linear Program (MILP) to find a promising multi-cloud configuration for a given software architecture. The effectiveness of the proposed model has been favorably evaluated against first principle heuristics currently adopted by practitioners. Furthermore, the configuration returned by the model has been also used as initial solution for a local-search based optimization engine, which exploits more accurate but time-consuming performance models. This combined approach has been shown to improve the quality of the returned solutions by 37% on average and reducing the overall search time by 50% with respect to state-of-the-art heuristics based on tiers utilization thresholds.

Stochastic coordinated operation of wind and battery energy storage system considering battery degradation

Grid-scale battery energy storage systems (BESSs) are promising to solve multiple problems for future power systems. Due to the limited lifespan and high cost of BESS, there is a cost-benefit trade-off between battery effort and operational performance. Thus, we develop a battery degradation model to accurately represent the battery degradation and related cost during battery operation and cycling. A linearization method is proposed to transform the developed battery degradation model into the mixed integer linear programming (MILP) optimization problems. The battery degradation model is incorporated with a hybrid deterministic/stochastic look-ahead rolling optimization model of wind-BESS bidding and operation in the real-time electricity market. Simulation results show that the developed battery degradation model is able to effectively help to extend the battery cycle life and make more profits for wind-BESS. Moreover, the proposed rolling look-ahead operational optimization strategy can utilize the updated wind power forecast, thereby also increase the wind-BESS profit.

Assessing the economic value of co-optimized grid-scale energy storage investments in supporting high renewable portfolio standards

Worldwide, environmental regulations such as Renewable Portfolio Standards (RPSs) are being broadly adopted to promote renewable energy investments. With corresponding increases in renewable energy deployments, there is growing interest in grid-scale energy storage systems (ESS) to provide the flexibility needed to efficiently deliver renewable power to consumers. Our contribution in this paper is to introduce a unified generation, transmission, and bulk ESS expansion planning model subject to an RPS constraint, formulated as a two-stage stochastic mixed-integer linear program (MILP) optimization model, which we then use to study the impact of co-optimization and evaluate the economic interaction between investments in these three asset classes in achieving high renewable penetrations. We present numerical case studies using the 24-bus IEEE RTS-96 test system considering wind and solar as available renewable energy resources, and demonstrate that up to $180million/yr in total cost savings can result from the co-optimization of all three assets, relative to a situation in which no ESS investment options are available. Surprisingly, we find that co-optimized bulk ESS investments provide significant economic value through investment deferrals in transmission and generation capacity, but very little savings in operational cost. Finally, we observe that planning transmission and generation infrastructure first and later optimizing ESS investments—as is common in industry—captures at most 1.7% ($3million/yr) of the savings that result from co-optimizing all assets simultaneously.

Strategic mining options optimization: Open pit mining, underground mining or both

Near-surface deposits that extend to considerable depths are often amenable to both open pit mining and/or underground mining. This paper investigates the strategy of mining options for an orebody using a Mixed Integer Linear Programming (MILP) optimization framework. The MILP formulation maximizes the Net Present Value (NPV) of the reserve when extracted with (i) open pit mining, (ii) underground mining, and (iii) concurrent open pit and underground mining. Comparatively, implementing open pit mining generates a higher NPV than underground mining. However considering the investment required for these mining options, underground mining generates a better return on investment than open pit mining. Also, in the concurrent open pit and underground mining scenario, the optimizer prefers extracting blocks using open pit mining. Although the underground mine could access ore sooner, the mining cost differential for open pit mining is more than compensated for by the discounting benefits associated with earlier underground mining.

Interfacing renewable energy sources to the ac grid by a 43-level CMLI with many advantages

This paper proposes a 43-level asymmetric cascaded multilevel inverter (CMLI) as an interface between renewable energy sources and the grid, that has the following advantages:1.The CMLI consists of only four H-bridges per phase, with separate dc sources. Renewable energy sources of different types are treated as the dc sources of the CMLI (e.g., dc voltage from PV panels, rectified ac voltage from wind turbines, etc.).2.It can interface different types of renewable energy sources instantaneously to feed the ac grid with a nearly sinusoidal voltage with very low total harmonic distortion (THD).3.It can accommodate natural fluctuations in the renewable energy sources and provide output voltage regulation against many fluctuations in these sources while keeping very low value of the THD for its output voltage.An approach using a mixed integer linear programming (MILP) optimization model is applied to determine the switching angles of the power switches of this CMLI to minimize the values of the undesired low order harmonics. A mathematical model is proposed, that can be applied for uniform step CMLIs, and this is applied for normal operation cases. Then a modification to this model is given that can be applied for some disturbance cases in the dc sources These models are applied for the single phase and three phase cases. For each case, an output voltage amplitude is selected first for normal operation at the nominal values of the dc sources, whose harmonics absolute values agree with the IEEE Standards 519-1992 for voltage distortion limits. Then the following disturbance cases are analyzed:1.Fluctuations of all the dc sources within ±20% of their nominal values.2.Dropping some dc sources below 80% of their nominal values.The models are applied under the required value of the output voltage with an allowed deviation within ±5%. Solutions are obtained that give the switching angles of the inverter at these disturbances in the dc sources while keeping low values of the output voltage THD, and still satisfying the IEEE standards for voltage distortion limits up to 59kV for single phase case and up to 161kV for three phase case.

A robust optimization approach for cash flow management in stationery companies

This paper proposes an effective optimization approach based on mixed integer linear programming and robust optimization to support decisions in the cash management problem of stationery companies. The approach represents the problem by means of network flows with gains and losses in an environment with uncertainty in the parameters that define financial flows over time. A case study was conducted in the cash flow of a typical company in the stationery sector with different grace periods and piecewise linear yields. Several results and analysis are presented by applying this robust optimization approach to support the decision maker in relation to the trade-off between risk and return, showing that the approach is able to generate solutions as good as, or better than, the ones of the treasury of the stationery company. It is in these conditions of uncertainty that the motivation of this research can be found, addressing how financial managers project their cash flows in order to maximize their uncertain monetary resources in a given multi-period and finite planning horizon.

Constrained pre-equalization accounting for multi-path fading emulated using large RC networks: applications to wireless and photonics communications

Multi-path propagation is modelled assuming a multi-layer RC network with randomly allocated resistors and capacitors to represent the transmission medium. Due to frequency-selective attenuation, the waveforms associated with each propagation path incur path-dependent distortion. A pre-equalization procedure that takes into account the capabilities of the transmission source as well as the transmission properties of the medium is developed. The problem is cast within a Mixed Integer Linear Programming optimization framework that uses the developed nominal RC network model, with the excitation waveform customized to optimize signal fidelity from the transmitter to the receiver. The objective is to match a Gaussian pulse input accounting for frequency regions where there would be pronounced fading. Simulations are carried out with different network realizations in order to evaluate the sensitivity of the solution with respect to changes in the transmission medium mimicking the multi-path propagation. The proposed approach is of relevance where equalization techniques are difficult to implement. Applications are discussed within the context of emergent communication modalities across the EM spectrum such as light percolation as well as emergent indoor communications assuming various modulation protocols or UWB schemes as well as within the context of space division multiplexing.

Robust design and planning of microalgae biomass-to-biodiesel supply chain: A case study in Iran

Microalgae have emerged as one of the most promising sources for biodiesel production because they yield a substantial amount of oil. In order to accelerate the commercialization of microalgal biodiesel, this paper proposes a two-stage model for the design and planning of a microalgae-based biodiesel supply chain. The macro-stage performs a spatial filtering using GIS and AHP to identify the most suitable candidate locations to establish biodiesel production facilities. These potential locations are later applied in the supply chain design model of the micro-stage. Consequently, the macro-stage obviates the need to consider a large set of candidate locations which is the main reason for the computational complexity of the supply chain optimization problems. In the micro-stage, a robust mixed-integer linear programming (RMILP) optimization model, which provides a trade-off between system cost and reliability, is elaborated to determine the strategic and tactical supply chain decisions that remain optimal for almost all possible realizations of the uncertain parameters. The applicability of the proposed framework is demonstrated through a case study considering different uncertainty settings. The results show that the proposed model outperforms the traditional supply chain design models in terms of solution robustness and computational time.

Incorporating price-responsive customers in day-ahead scheduling of smart distribution networks

Demand response and real-time pricing of electricity are key factors in a smart grid as they can increase economic efficiency and technical performances of power grids. This paper focuses on incorporating price-responsive customers in day-ahead scheduling of smart distribution networks under a dynamic pricing environment. A novel method is proposed and formulated as a tractable mixed integer linear programming optimization problem whose objective is to find hourly sale prices offered to customers, transactions (purchase/sale) with the wholesale market, commitment of distribution generation units, dispatch of battery energy storage systems and planning of interruptible loads in a way that the profit of the distribution network operator is maximized while customers’ benefit is guaranteed. To hedge distribution network operator against financial risk arising from uncertainty of wholesale market prices, a risk management model based on a bi-level information-gap decision theory is proposed. The proposed bi-level problem is solved by recasting it into its equivalent single-level robust optimization problem using Karush–Kuhn–Tucker optimality conditions. Performance of the proposed model is verified by applying it to a modified version of the IEEE 33-bus distribution test network. Numerical results demonstrate the effectiveness and efficiency of the proposed method.

Handover and SINR Optimized Deployment of LTE Femto Base Stations in Enterprise Environments

The data rates for indoor users can be boosted using low power consuming nodes like Femtos base stations (FBSs) in long term evolution networks. The manner in which Femtos are deployed inside a building environment, with large number of users, can significantly affect the throughput and number of handovers among Femtos. In our system model, we take into account the following parameters: co-channel interference between FBS and macro BSs, wall attenuation factor and user density in the enterprise building environment. In this work, we formulate two mixed integer linear programming (MILP) optimization models: optimal constant threshold signal to interference plus noise ratio (OptCTSINR) which guarantees a certain minimum SINR and also minimizes the number of Femtos needed for the coverage of enterprise buildings and optimal handover (OptHO) which reduces the number of handovers when the user passes through a certain portion (i.e., within a room or corridor) of the building. We solve these MILP models by utilizing branch and cut framework of CPLEX solver using General Algebraic Modeling System (GAMS) tool. When compared to K-means clustering based placement scheme, for a given number of Femtos, proposed OptCTSINR scheme results in an average SINR improvement of 28 %. Similarly, our proposed OptHO scheme reduces 30 % of the unnecessary handovers when compared to OptCTSINR scheme.

Automatic Generation of Model for Building Energy Management

This paper proposes a model transformation ap-proach for model-based energy management in buildings. Indeed, energy management is a large area that covers a wide range of applications such as simulation, mixed integer linear pro-gramming optimization, simulated annealing optimization, model parameter estimation, diagnostic analysis,. . . Each application re-quires a model but in a specific formalism with specific additional information. Up to now, application models are rewritten for each application. In building energy management, because the optimization problems may be dynamically generated, model transformation should be done dynamically, depending on the problem to solve. For this purpose, a model driven engineering approach combined with the use of a computer algebra system is proposed. This paper presents the core specifications of the transformation of a so-called high level pivot model into applica-tion specific models. As an example, transformations of a pivot model into both an acausal linear model for mixed integer linear programming optimization and a causal non-linear model for simulated annealing optimization are presented. These models are used for energy management of a smart building platform named Monitoring and Habitat Intelligent located at PREDIS/ENSE3 in Grenoble, France.

Benchmarks for Current Linear and Mixed Integer Optimization Solvers

Linear programming (LP) and mixed integer linear programming (MILP) problems belong among very important class of problems that find their applications in various managerial consequences. The aim of the paper is to discuss computational performance of current optimization packages for solving large scale LP and MILP optimization problems. Current market with LP and MILP solvers is quite extensive. Probably among the most powerful solvers GUROBI 6.0, IBM ILOG CPLEX 12.6.1, and XPRESS Optimizer 27.01 belong. Their attractiveness for academic research is given, except their computational performance, by their free availability for academic purposes. The solvers are tested on the set of selected problems from MIPLIB 2010 library that contains 361 test instances of different hardness (easy, hard, and not solved).