General Algebraic Modeling System Research Articles

Wide area monitoring and measurements using mixed integer linear programming in deregulated power system for smart grid

This paper deals with different methods involved in the determination of complete observability of power system under wide area monitoring using Phasor Measurement Unit (PMU). There are numerous methods available in literature for the determination of optimal locations of PMU for complete system observability, but out of all those methods, fast selection of best suitable with minimum number of PMUs at optimal location for complete observability, is still a challenge to power engineers for applying online in Smart Grid under deregulation environment. After detail analysis with various methods, this paper proposes an algorithm for selecting best possible method for determining optimal locations of PMUs. The analysis compares performance of the available methods, e.g., Binary Integer Linear Programming, Admittance Bus Matrix Method and Mixed Integer Linear Programing using General Algebraic Modelling System. To investigate the effectiveness of the proposed method for complete observability using system observability redundancy index (SORI), Indian Northern Regional Power Grid (NRPG-246 bus system) has also been considered here.

Multi-objective Optimization Approach Based on Deterministic and Metaheuristic Techniques to Resource Management in Health Crisis Scenarios Under Uncertainty

This paper presents an optimization strategy based on mathematical programming to solve resource management problems regarding hospitalization of sick patients, considering emergency scenarios, such as those that can occur in a pandemic. This optimization strategy is based on the use of efficient optimization tools in solving complex problems in which other strategies are not efficient. The mathematical modeling of epidemiological phenomena is a useful tool to predict the direction of a disease, as well as to adequately and timely manage the available resources and thus save as many lives as possible. This work uses a mathematical model formulation based on deterministic optimization developed in general algebraic modeling system (GAMS) environment. The main user interface has been developed in a Microsoft™ (MS) Excel worksheet, which is familiar to many users. The linking code to send values from MS Excel to GAMS has been programmed in visual basic for applications (VBA) and it uses GAMS data exchange (GDX) files. The proposed optimization methodology is applied to case studies based on data obtained from affected people by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which is the virus that causes coronavirus disease 2019 (COVID-19). The distances were taken as example from severely affected cities in the USA. The obtained results offer attractive alternatives for the specified objective function in an acceptable computation time.

Research on logistics management layout optimization and real-time application based on nonlinear programming

Abstract To solve the problem of long logistics delivery time in supply chain, a Mixed Integer Non-linear Program (MINLP) model is built by using Mixed Integer nonlinear programming theory. Firstly, the General algebraic modeling system (GAMS) is used to build the model to fully integrate each parameter of logistics transportation, the total distribution time of the supply chain network, the coverage radius of the logistics base, the number of users, the total capacity of the logistics base, the mode of railway and road transportation, the nonlinear programming model is built and solved by DICOPT solver in GAMS. The cost of logistics can be decreased, transportation time can be reduced, and the logistics system's operating efficiency can be increased in the long term with the help of this algorithm. The proper operation of the logistics system is critical in encouraging the supply chain circulation of various industries and has a direct impact on the society's economic development. The optimal logistics distribution plan with 5 logistics bases covered users of 18 and railway capacity of 2. With the same railway capacity and the same total budget, the larger the number of covered users, the greater the total distribution time increases, but the larger the total budget, the growth of the total distribution time slows down significantly. Experiments show that MINLP model can solve the problem of logistics-based layout optimization in nonlinear logistics management.

Data Driven Stochastic Energy Management for Isolated Microgrids Based on Generative Adversarial Networks Considering Reactive Power Capabilities of Distributed Energy Resources and Reactive Power Costs

This paper proposes a two-stage stochastic energy management (EM) in an isolated microgrid (MG) to decide for the day-ahead optimal dispatch. The dispatch aims to effectively manage the MG power sources, including intermittent renewable energy sources (RESs), battery energy storage systems (BESSs), and diesel generators such that the expected operation costs, reactive power costs, spinning reserve, and load shedding are minimized. The Generative Adversarial Networks (GANs) is utilized in this paper as a data driven scenario generation method to model the uncertainties in the output power of the RESs to be used in the stochastic programming formulation. Then, the fast forward scenario reduction algorithm is used to reduce the number of scenarios with the help of SCENRED/GAMS software. Usually, fuel consumption costs of diesel generators are considered to be dependent on active power generation only. However, neglecting the related reactive power costs might result in increased operation costs and deviations in the dispatches from the optimal solutions. Hence, this paper co-optimizes the costs related to both active and reactive powers of diesel generators. In addition, this study considers the reactive power capability of inverter-interfaced distributed energy resources (DERs). Moreover, the detailed models for the different resources are presented, especially for diesel generators where the actual capability curves are used instead of the widely used box constraints. The problem is formulated as a nonlinear programming problem in the General Algebraic Modeling System (GAMS) software and is solved by the CONOPT solver.

A CVaR-Robust-Based Multi-Objective Optimization Model for Energy Hub Considering Uncertainty and E-Fuel Energy Storage in Energy and Reserve Markets

The increasing demand for energy carriers has expanded the use of energy hubs that employ distributed demand response programs to improve power system reliability and efficiency. Moreover, the unstable behavior of renewable resources, as well as the indeterminate electrical and thermal demands, create major problems for energy hub operation. Inspired by this, this paper presents a day-ahead scheduling framework for energy hubs (EH) in energy and reserve markets considering two main objectives of economy and pollution emission. The studied energy hub consists of a novel hybrid energy storage facility based on a fuel cell, wind power, photovoltaic energy, and a particular fuel cell unit in the presence of elastic demand. This multi-component system participates in energy and reserve markets as a single entity to optimize energy hub operation. The proposed method also models the uncertainty of wind speed, photovoltaic irradiance, and load using the Mont-Carlo method. The energy hub risk level is analyzed using the conditional value at risk (CVaR) approach to increase the EH operation and efficiency. The proposed multi-objective energy hub model is solved using the MINLP method in General Algebraic Modeling System (GAMS) to minimize operation cost and pollution emission. Finally, to prove the effectiveness of adding a new E-fuel energy storage system and considering uncertainties on energy hub operation, the proposed method is compared with other reported models.

User-Defined Dual Setting Directional Overcurrent Relays with Hybrid Time Current-Voltage Characteristics-Based Protection Coordination for Active Distribution Network

With the penetration of renewable energy sources based distributed generation (RES-DG) in the distribution network (DN), the operating time of protection relays becomes a major concern to avoid the mis-coordination and nuisance tripping of RES-DG. It is due to the bidirectional flow of current, variance in the fault current level, i.e. high fault current in case of Squirrel cage induction generator (SCIG) based RES-DG, and low fault current for an inverter-based RES-DGs. This paper proposes a novel User-defined dual setting direction overcurrent relay with hybrid time current-voltage (UDDOR-TCV) characteristics to intensify the proposed scheme’s flexibility without any communication assistance for radial DN. The proposed model is formulated in a constrained non-linear optimization fashion and solved with the MINLP solver of general algebraic modelling system(GAMS) software to determine the optimal relay settings. The propounded protection scheme is simulated on IEEE-33 bus radial distribution system and a local 40-bus system hosting the multiple SCIG and PV based RES-DGs at optimal locations. Detailed numerical studies are carried out to show the performance of the proposed scheme. 66.848% and 68.26% reduction in relay operation time with zero mis-coordination is achieved with SCIG-WTG case and PV-units case for the IEEE-33 bus system and a similar reduction in operation time is 68.937% and 66.563% for Local-40 bus system. Moreover, the relays numbers are reduced by 32.692% and 39.7% for IEEE-33 and Local-40 bus systems, respectively, due to the forward/reverse characteristics capability of the proposed UDDOR-TCV. The performance of the proposed scheme is also evaluated on IEEE-8 bus meshed DN. The results are compared with the existing protection schemes in recent literature.

Application of BARON Solver for Solution of Cost Based Unit Commitment Problem

This paper presents the solution to cost-based unit commitment (CBUC) problem with and without ramp rate limits of thermal power plants using general algebraic modelling system (GAMS) with BARON solver. The BARON solver in GAMS environment takes care of different units and system constraints to find an optimal solution. To validate the effectiveness of the proposed GAMS solution, simulations have been performed on six different systems consisting of 10-units, 20-units, 40-units, 60-units, 80-units and 100-units, respectively. The analysis also includes the valve-point loading along with the ramp rate limits of thermal units. Results obtained with BARON solver in GAMS have been compared with other approaches available in literature. Comparative analysis shows that the performance of GAMS is better as compared to other existing techniques in terms of operating cost obtained and satisfaction level of constraints.

Coordinated Operational Optimization Approach for PV Inverters and BESSs to Minimize the Energy Loss of Distribution Networks

The article presents a coordinated operational optimization approach for PV inverters and battery energy storage systems (BESSs) to minimize the energy loss in distribution networks with time-varying load demand and PV generation. PV inverters are modeled to inject available PV generation into a network during PV generation hours and to provide VAr compensation during rest of the time. BESSs are modeled to store surplus PV power during high penetration of PV generation and to discharge stored energy during no/low PV generation hours. An optimization problem is formulated to determine the optimal VAr compensation setpoints for PV inverters and optimal charge/discharge schedule for the BESSs. The maximization of PV hosting capacity and the minimization of energy loss are the objective functions for the first and second stages, respectively. The limits on bus voltage magnitude, line flow, state-of-charge (SOC) of BESSs, charging and discharging of BESSs, PV inverter capacity, etc., are considered to be the operational constraints. The CONOPT solver of general algebraic modeling system software is used for solving the optimization problem. The contribution of the proposed approach is to show that significant energy loss reduction can be obtained with the optimal time-varying setpoints of PV inverters and BESSs.

Optimal Selection and Location of BESS Systems in Medium-Voltage Rural Distribution Networks for Minimizing Greenhouse Gas Emissions

This paper explores a methodology to locate battery energy storage systems (BESS) in rural alternating current (AC) distribution networks fed by diesel generators to minimize total greenhouse gas emissions. A mixed-integer nonlinear programming (MINLP) model is formulated to represent the problem of greenhouse gas emissions minimization, considering power balance and devices capabilities as constraints. To model the BESS systems, a linear relationship is considered between the state of charge and the power injection/consumption using a charging/discharging coefficient. The solution of the MINLP model is reached through the general algebraic modeling system by employing the BONMIN solver. Numerical results in a medium-voltage AC distribution network composed of 33 nodes and 32 branches operated with 12.66 kV demonstrate the effectiveness of including BESS systems to minimize greenhouse gas emissions in diesel generators that feeds rural distribution networks.

Stochastic Unit Commitment Problem, Incorporating Wind Power and an Energy Storage System

This paper presents a modified formulation for the wind-battery-thermal unit commitment problem that combines battery energy storage systems with thermal units to compensate for the power dispatch gap caused by the intermittency of wind power generation. The uncertainty of wind power is described by a chance constraint to escape the probabilistic infeasibility generated by classical approximations of wind power. Furthermore, a mixed-integer linear programming algorithm was applied to solve the unit commitment problem. The uncertainty of wind power was classified as a sub-problem and separately computed from the master problem of the mixed-integer linear programming. The master problem tracked and minimized the overall operation cost of the entire model. To ensure a feasible and efficient solution, the formulation of the wind-battery-thermal unit commitment problem was designed to gather all system operating constraints. The solution to the optimization problem was procured on a personal computer using a general algebraic modeling system. To assess the performance of the proposed model, a simulation study based on the ten-unit power system test was applied. The effects of battery energy storage and wind power were deeply explored and investigated throughout various case studies.

An optimal water regeneration, reuse and resource recovery network integrating domestic and industrial sources

Implementation of reduce, reuse, recycle strategies are pertinent to ensure sustainability. There are studies to minimize freshwater reduction via mathematical modelling method. However, study to explore possibilities of combining both domestic and industrial wastewater regeneration, reuse, and resource recovery in a centralised facility is yet to be made. This study develops a mathematical model that could provide optimal water regeneration and reuse network that also be capable to produce biogas from the selected wastewater streams. The main objective is to maximize profit from the network established. A superstructure that consists of sources, outsource, freshwater, mixers-demands, and biogas systems is developed. A combination of the sources, regenerated sources, outsource water, and freshwater is performed in the mixers. The multi integer non-linear programming (MINLP) model is optimized by BARON solver in General Algebraic Modelling System (GAMS) software. The case study result shows that freshwater water saving is 42% and 377 kW of electricity can be generated from the biogas produced. This offers possibilities to consider the idea of the centralised wastewater facility that considers water regeneration, reuse, and resource recovery for both domestic and industrials sources, as the Eco-Industrial Park (EIP) may serve as the suitable platform.

Optimal Operation of Electrified Railways with Renewable Sources and Storage

This paper proposes an approach for the optimal operation of electrified railways by balancing energy flows among energy exchange with the traditional electrical grid, energy consumption by accelerating trains, energy production from decelerating trains, energy from renewable energy resources (RERs) such as wind and solar photovoltaic (PV) energy systems, and energy storage systems. The objective function considered in this work is the minimization of total operating cost of electrified railway system consisting of cost of power generation from the external power system, cost of power obtained from RERs such as wind and solar PV sources, cost of power from storage systems such as battery storage and supercapacitors, and the income obtained by selling excess power back to the main electrical grid. This problem is formulated as an AC optimal power flow problem subjected to various equality and inequality constraints. In this work, the probability distribution functions (PDFs) are used to the uncertainties related to wind and solar PV powers. The proposed optimization problem is solved by using CONOPT solver of generalized algebraic modeling system (GAMS) software, which is a powerful and efficient optimization tool. The simulation results obtained with GAMS/CONOPT solver are also compared with meta-heuristic based differential evolution algorithm (DEA).

Development of a superstructure optimization framework for the design of municipal solid waste facilities

The main objective of this study is to develop a decision-making tool for the design of the optimal municipal solid waste (MSW) facilities based on superstructure optimization. Currently, the disposal of MSW is a major problem due to the lack of awareness of the negative impacts resulting from dumping MSW into the environment. This poses a challenge for the authorities. MSW valorization such as anaerobic digestion, pyrolysis, and gasification has been increasingly focused on as an approach when handling MSW to enhance both economic and environmental sustainability. However, with an increasing array of processing technologies, the design of MSW facilities involving the integration of these technologies is becoming tedious and unmanageable. To deal with this problem, superstructure optimization is proposed. It is an effective tool for the design of several chemical processes because it is able to consider all potential process alternatives including the optimal solution using mathematical models based on mass and energy balances. Uncertainty is incorporated into the optimization framework to enhance the robustness of the solution. The proposed methodology was applied in the design process of the MSW facility in Ubon Rathathani Province, Thailand, with the objective function of maximizing the profit. The optimization problem was developed as Mixed Integer Linear Programming and it was solved using an optimization platform, General Algebraic Modeling System, with CPLEX as the solver related to obtaining the optimal solution. The results show there to be as positive profit that is economically viable compared to the use of landfill technology.

Voltage Regulation and Loss Minimization in Reconfigured Distribution Systems with Capacitors and OLTC in the Presence of PV Penetration

Optimal reactive power management is one of the key operational aspects for efficient planning of distribution system. This study has become more challenging with renewable energy sources integration into the system. Objective of this paper is to address optimal reactive power planning in distribution system using hybrid optimization. This paper presents a comprehensive model for solving capacitor allocation, PV penetration and feeder reconfiguration simultaneously. The objective function considered in this paper includes cost of capacitor, PV and energy loss. The proposed work includes: (i) capacitor allocation using ant lion optimization, (ii) capacitor rating determination using general algebraic modeling system, (iii) reconfiguration of distribution system using genetic algorithm, (iv) investigated different case studies to realize the impact of various load models and load growth factors on reactive power compensation and network reconfiguration, (v) real-time procedure to determine rating of capacitor banks for practical distribution systems, (vi) reactive power dispatch for realistic time-varying load model considering coordination among capacitors, on-load tap changer and photo-voltaic (PV) penetration. The analysis is carried out considering uncertainty of load demand and PV power generation. The proposed methodology is implemented on IEEE 33-bus distribution system and real-time existing Indian distribution network to demonstrate effectiveness of the proposed methodology. It is observed that voltage-dependent load models have a significant impact on system performance and rating of capacitor banks. The proposed strategy ensures optimal solution compared to other existing techniques.

Optimal sub-contractor selection and allocation in a multiple construction project: Project portfolio planning in practice

Subcontracting is known as a global concern in construction industry. Appropriate selection of sub-contractors (SCs) significantly affects scheduling. However, review of the recent literature suggests that the issues of selecting SC and scheduling construction projects are investigated separately. Moreover, general contractors (GCs) usually conduct a number of projects simultaneously, while the literature demonstrates that subcontracting is often studied when the GC is conducting only one project. In order to fill these gaps, the current research study is conducted to investigate the subjects of subcontracting and scheduling construction projects when more than one project must be done at the same time. To this aim, a mixed-integer linear programming model is developed to minimize the cost of the project in two different conditions. In the first condition, the deadline can be postponed by paying a penalty. In contrast, in the second condition, the deadline cannot be postponed under no circumstances. Then, the proposed model is solved by applying the general algebraic modelling system. The findings demonstrate that the proposed model is reliable to provide an optimized schedule when several projects must be conducted at the same time.

A Second-Order Cone Programming Reformulation of the Economic Dispatch Problem of BESS for Apparent Power Compensation in AC Distribution Networks

The problem associated with economic dispatch of battery energy storage systems (BESSs) in alternating current (AC) distribution networks is addressed in this paper through convex optimization. The exact nonlinear programming model that represents the economic dispatch problem is transformed into a second-order cone programming (SOCP) model, thereby guaranteeing the global optimal solution-finding due to the conic (i.e., convex) structure of the solution space. The proposed economic dispatch model of the BESS considers the possibility of injecting/absorbing active and reactive power, in turn, enabling the dynamical apparent power compensation in the distribution network. A basic control design based on passivity-based control theory is introduced in order to show the possibility of independently controlling both powers (i.e., active and reactive). The computational validation of the proposed SOCP model in a medium-voltage test feeder composed of 33 nodes demonstrates the efficiency of convex optimization for solving nonlinear programming models via conic approximations. All numerical validations have been carried out in the general algebraic modeling system.

Optimal emission management of photovoltaic and wind generation based energy hub system using compromise programming

The pollution of fossil fuels uses and low efficiency performance of energy systems are the main issues which threaten the environment and cause extra cost. Many solutions are presented and the one which is performed in this study is using energy hub which is composed of several parts. Sub energy hub and combined cooling, heating and power combining with the renewable energies such as wind turbine and photovoltaic are the component parts of this novel energy hub. The optimum flow of energy plus using energy storage devices brings coordination and reliability to the system. The model proposed is multi-objective and the goal is to investigate the effects of accomplishment real-time based demand response program in reducing operation cost and CO2 emission. The mathematical methods like compromise programming and fuzzy approach are implemented to gain the Pareto solutions and obtain trade-off between economic and environmental performances. Two cases which are investigated in this paper are without and with demand response program. The linear model with mixed-integer programming is implemented in general algebraic modeling system to solve the proposed model. The comparison results illustrate that the operation cost and CO2 emission is decreased 4.05% and 1.52% respectively due to demand response program.

RETRACTED: Risk-constrained scheduling of a CHP-based microgrid including hydrogen energy storage using robust optimization approach

Recently, the integration of various energy resources, including renewable generation and combined heat and power (CHP) units in microgrids, has created the opportunity of off-grid operation with a suitable range of reliability. This paper presents an optimization model to schedule an islanded MG with various resources, including CHP, photovoltaic (PV), and boiler, as the primary energy provision sources besides electric battery storage, thermal storage and hydrogen energy system (HES). The HES has the power-to-hydrogen (P2H) and hydrogen-to-power (H2P) modes, which increases the flexibility of the scheduling. The uncertainty management is the most essential task in the CHP-based MGs scheduling problem, since the power and heat productions are interrelated and can result in economic losses without enough deliberations. Hence, this paper proposes the robust optimization approach (ROA) to cope with the uncertainties associated with the PV production and electric and heat load demands. The robust counterparts are applied to the deterministic problem to create a tractable adjustable robust framework. The problem is structured as a mixed-integer linear programming (MILP) handled by the General Algebraic Modeling System (GAMS) using CPLEX solver. The results verified the effectiveness of the proposed robust counterparts in managing the associated risk. The results illustrated a conscious scheduling strategy under robust conditions. However, the more preserved decisions are taken, the higher operational cost is realized. In this regard, the increment of robustness level from the lowest value (deterministic condition) to the highest value (conservatism condition) increased the operation cost by about 43.29%.

Optimal Selection of Integrated Electricity Generation Systems for the Power Sector with Low Greenhouse Gas (GHG) Emissions

Cheap and clean energy demand is continuously increasing due to economic growth and industrialization. The energy sectors of several countries still employ fossil fuels for power production and there is a concern of associated emissions of greenhouse gases (GHG). On the other hand, environmental regulations are becoming more stringent, and resultant emissions need to be mitigated. Therefore, optimal energy policies considering economic resources and environmentally friendly pathways for electricity generation are essential. The objective of this paper is to develop a comprehensive model to optimize the power sector. For this purpose, a multi-period mixed integer programming (MPMIP) model was developed in a General Algebraic Modeling System (GAMS) to minimize the cost of electricity and reduce carbon dioxide (CO2) emissions. Various CO2 mitigation strategies such as fuel balancing and carbon capture and sequestration (CCS) were employed. The model was tested on a case study from Pakistan for a period of 13 years from 2018 to 2030. All types of power plants were considered that are available and to be installed from 2018 to 2030. Moreover, capacity expansion was also considered where needed. Fuel balancing was found to be the most suitable and promising option for CO2 mitigation as up to 40% CO2 mitigation can be achieved by the year 2030 starting from 4% in 2018 for all scenarios without increase in the cost of electricity (COE). CO2 mitigation higher than 40% by the year 2030 can also be realized but the number of new proposed power plants was much higher beyond this target, which resulted in increased COE. Implementation of carbon capture and sequestration (CCS) on new power plants also reduced the CO2 emissions considerably with an increase in COE of up to 15%.

Risk-averse multi-objective optimal combined heat and power planning considering voltage security constraints

In this paper, a comprehensive model is proposed for long-term planning of various combined heat and power units in an integrated heat and electricity network. The proposed model takes into account the uncertain electric loads, and market price applying the information gap decision theory. Furthermore, the security of the power grid from the voltage stability viewpoint utilizing the L-index approach is considered. The model is based on the risk-averse multi-objective combined heat and power planning methodology, which maximizes the profit of combined heat and power owners and minimizes the system operator costs over the planning horizon in the presence of the environmental emissions cost. The best compromise solution is achieved via a fuzzy logic-based min-max method. The risk-averse strategy of Information gap decision theory is applied to the obtained solution, which demonstrates the impact of data uncertainty. The proposed mixed-integer non-linear programming model is solved using the general algebraic modeling system package and tested on the IEEE 14-bus standard system. The results indicate that the risk-averse strategy improves the robustness of the network against the uncertainty. Also solving the model using the multi-objective framework gives comprehensive results, and shows that the voltage stability constraints affect the planning decisions.