A Multi-Period Optimal Reactive Power Dispatch Approach Considering Multiple Operative Goals

The optimal reactive power dispatch (ORPD) problem plays a key role in daily power system operations. This paper presents a novel multi-period approach for the ORPD that takes into account three operative goals. These consist of minimizing total voltage deviations from set point values of pilot nodes and maneuvers on transformers taps and reactive power compensators. The ORPD is formulated in GAMS (General Algebraic Modeling System) software as a mixed integer nonlinear programming problem, comprising both continuous and discrete control variables, and is solved using the BONMIN solver. The most outstanding benefit of the proposed ORPD model is the fact that it allows optimal reactive power control throughout a multi-period horizon, guaranteeing compliance with the programmed active power dispatch. Additionally, the minimization of maneuvers on reactors and capacitor banks contributes to preserving the useful life of these devices. Furthermore, the selection of pilot nodes for voltage control reduces the computational burden and allows the algorithm to provide fast solutions. The results of the IEEE 118 bus test system show the applicability and effectiveness of the proposed approach.

Evaluación de modelos de programación lineal y no lineal para la planeación de sistemas de transmisión en el software GAMS

Objetivo: Este trabajo analiza el costo óptimo de expansión, el número de líneas a incluir y el tiempo de simulación computacional para dos sistemas transmisión, empleando programación no lineal entera mixta a través de los solver del software GAMS (General Algebraic Modeling System). El objetivo es determinar las diferencias en los costos de expansión cuando se emplea el modelo de transporte, DC, híbrido lineal y lineal disyuntivo. Metodología: Está dividida en cinco etapas: la primera identifica el sistema de transmisión, la segunda establece el problema de planeamiento del sistema de transmisión, la tercera realiza la formulación del sistema de potencia de acuerdo con cada uno de los modelos de optimización, la cuarta aplica la formulación del sistema de potencia en el software GAMS y la última selecciona el costo óptimo. Resultados: Desde el análisis de costo óptimo, el modelo DC y el modelo lineal disyuntivo presentaron el mayor costo óptimo respecto al modelo de transporte y al modelo hibrido lineal. Conclusiones: Los modelos implementados presentaron desempeños equivalentes en el sistema de prueba con el menor número de nodos; al aumentar el número de nodos, el desempeño de los modelos no presenta similitud. Por el contrario, se identifican diferencias importantes en los resultados obtenidos, lo que permite caracterizar solver específicos de acuerdo con el número de nodos. Metodología: Está dividida en 5 etapas, la primera identifica el sistema de transmisión, la segunda establece el problema de planeamiento del sistema de transmisión, la tercera realiza la formulación del sistema de potencia de acuerdo a cada uno de los modelos de optimización, la cuarta aplica la formulación del sistema de potencia en el software GAMS y la última seleccionar el costo óptimo. Resultados: Desde el análisis de costo optimo, el modelo DC y el modelo lineal disyuntivo presento el mayor costo optimo respecto al modelo de transporte y al modelo hibrido lineal. Conclusiones: Los modelos implementados presentaron desempeños equivalente en el sistema de prueba con el menor número de nodos, al aumentar el número de nodos el desempeño de los modelos no presenta similitud, por el contrario se identifican diferencias importantes en los resultados obtenidos, lo que permite caracterizar solver específicos de acuerdo al número de nodos.

A method to solve two-player zero-sum matrix games in chaotic environment

This research article proposes a method for solving the two-player zero-sum matrix games in chaotic environment. In a fast growing world, the real life situations are characterized by their chaotic behaviors and chaotic processes. The chaos variables are defined to study such type of problems. Classical mathematics deals with the numbers as static and less value-added, while the chaos mathematics deals with it as dynamic evolutionary, and comparatively more value-added. In this research article, the payoff is characterized by chaos numbers. While the chaos payoff matrix converted into the corresponding static payoff matrix. An approach for determining the chaotic optimal strategy is developed. In the last, one solved example is provided to explain the utility, effectiveness and applicability of the approach for the problem.Abbreviations: DM= Decision Maker; MCDM = Multiple Criteria Decision Making; LPP = Linear Programming Problem; GAMS= General Algebraic Modeling System.

Auto-correlation robustness of factorial designs and GAMS in studying the effects of process variables in a dual-objective adsorption system

The performance of factorial designs is still limited due to some uncertainties that usually intensify process complexities, hence, the need for inter-platform auto-correlation analyses. In this study, the auto-correlation capabilities of factorial designs and General Algebraic Modeling System (GAMS) on the effects of some pertinent operating variables in wastewater treatment were compared. Individual and combined models were implemented in GAMS and solved with the trio of BARON, CPLEX and IPOPT solvers. It is revealed that adsorbent dosage had the highest effect on the process. It contributed the most effect toward obtaining the minimum silica and TDS contents of 13 mg/L and 814 mg/L, and 13.6 mg/L and 815 mg/L from factorial design and GAMS platforms, respectively. This indicates a concurrence between the results from the two platforms with percentage errors of 4.4% and 0.2% for silica and TDS, respectively. The effects of the mixing speed and contact time are negligible.

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.

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.

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, gasification etc 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.

A Novel Market Clearing and Safety Checking Method for Multi-Type Units That Considers Flexible Loads

Flexible loads have flexibility and variability in time and space, and they have been widely studied by scholars. However, the research on the participation of flexible loads in market clearing and safety checking is still insufficient. We propose a market clearing and safety checking method for multi-type units that considers flexible loads. First, the flexible load is divided into reducible loads, shiftable loads, and convertible loads, and its mathematical model is established. Then, the convertible loads are considered in the market clearing model, and the power management agency executes the market clearing procedure to obtain the clearing result. When the line power exceeds the limit as a result of clearing, the power flow of the branches and sections is eliminated by adjusting the unit output and reducing the flexible load at the same time, and a safety checking model considering load reduction is established. The marginal electricity price of the nodes is obtained by the interior point method, and we solve the model by calling the CPLEX (v12.7.1) solver in GAMS (General Algebraic Modeling System v24.9.1). We use a regional power grid of 220 kV and above as an example for analysis; the results show that the proposed method can reduce the marginal electricity price of the nodes, reduce the cost of safety checking, and improve the safety of the market clearing.

Optimal Location-Reallocation of Battery Energy Storage Systems in DC Microgrids

This paper deals with the problem of optimal location and reallocation of battery energy storage systems (BESS) in direct current (dc) microgrids with constant power loads. The optimization model that represents this problem is formulated with two objective functions. The first model corresponds to the minimization of the total daily cost of buying energy in the spot market by conventional generators and the second to the minimization of the costs of the daily energy losses in all branches of the network. Both the models are constrained by classical nonlinear power flow equations, distributed generation capabilities, and voltage regulation, among others. These formulations generate a nonlinear mixed-integer programming (MINLP) model that requires special methods to be solved. A dc microgrid composed of 21-nodes with existing BESS is used for validating the proposed mathematical formula. This system allows to identify the optimal location or reallocation points for these batteries by improving the daily operative costs regarding the base cases. All the simulations are conducted via the general algebraic modeling system, widely known as the General Algebraic Modeling System (GAMS).