Optimal Operation Problem Research Articles

Multi-objective optimization and multi-attribute decision-making support for optimal operation of multi stakeholder integrated energy systems

To efficiently tackle the optimal operation problem of multi-stakeholder integrated energy systems (IESs), this paper develops a multi-objective optimization and multi-attribute decision-making support method. Mathematically, The optimal operation of IESs interconnected with distributed district heating and cooling units (DHCs) via the power grid and gas network, can be formulated as a multi-objective optimization problem considering both economic, reliability and environment-friendly objectives with numerous constraints of each energy stakeholder. Firstly, a multi-objective group search optimizer with probabilistic operator and chaotic local search (MPGSO) is proposed to balance global and local optimality during the random search iteration. The MPGSO utilizes a crowding probabilistic operator to select producers to explore areas with higher potential but less crowding and reduce the number of fitness function calculations. Moreover, a new parameter selection strategy based on chaotic sequences with limited computational complexity is adopted to escape the local optimal solutions. Consequently, a set of superior Pareto-optimal fronts could be obtained by the MPGSO. Subsequently, a multi-attribute decision-making support method based on the interval evidential reasoning (IER) approach is used to determine a final optimal solution from the Pareto-optimal solutions, taking multiple attributes of each stakeholder into consideration. To verify the effectiveness of the MPGSO, the DTLZ suite of benchmark problems are tested compared with the original GSOMP, NSGA-II and SPEA2. Additionally, simulation studies are conducted on a modified IEEE 30-bus system connected with distributed DHCs and a 15-node gas network to verify the proposed approch. The quality of the obtained Pareto-optimal solutions is assessed using a set of criteria, including hypervolume (HV), generational distance (GD), and Spacing index, among others. Simulation results show that the number of Pareto-optimal solutions (NPS) of MPGSO are higher by about 32.6 %-62.1%, computation time (CT) are lower by about 2.94 %-46.1 % compared with other algorithms. Besides, to further evaluate the performance of the proposed approach in addressing larger-scale issues, the study employs the modified IEEE 118-bus system of greater magnitude. The proposed MPGSO algorithm effectively handles multi-objective and non-convex optimization problems with Pareto sets in terms of better convergence and distributivity.

Coordinated Optimal Operation Method for Snow-Shaped Distribution Networks Based on Game Theory

The snow-shaped distribution network is developed and upgraded from the traditional single-loop network and double-loop network structure. It is composed of three or four groups of single-loop networks in pairs that form a feeder cluster in the form of a ring network. Based on this topology, the coordinated optimization operation problem is studied. First, the game elements are analyzed, and then a cooperative game-based, coordinated optimization operation model is established by taking the minimum network loss and voltage deviation of the system as the utility function. Then, the alternating direction multiplier method (ADMM) is employed in Cplex solver to solve the established optimization model. Finally, a numerical case is given to verify the effectiveness of the proposed model and method. The results show that, by using the complementary difference relationship of source–charge characteristics between different regions in the snow-shaped distribution networks, the cooperative game model can realize the energy interconnection among different regions to improve the operation level.

Optimizing fleet, staff configuration and operational strategies in one-way mixed fleet carsharing systems: a Lagrangian relaxation-based approach

ABSTRACT This study explores enhancing carsharing services by integrating gasoline and electric vehicles into a one-way mixed fleet carsharing system (OMFCS). The focus is on optimizing configurations (fleet and staff size, initial deployment) and operational strategies (vehicle relocation and staff rebalancing) while considering carbon emission costs. Employing a space-time-electricity network modeling approach, we developed an integer linear programming model to tackle the configurations and operational strategies optimization problem. For solving this model, we introduce a Lagrangian relaxation-branch bound approach, which integrates subgradient, dynamic programming and greedy-based heuristics algorithm. An illustrative case and a real-world case are conducted to demonstrate the efficiency of the proposed solution method and the analysis sheds light on the configurations and operational strategies of OMFCS. The sensitive analysis results suggest that OMFCS is more profitable and balances user service quality and carbon emissions better than carsharing systems using only one type of vehicle.

Solving optimization problems in steady operation of regulated asynchronous motor

Solving optimization problems in steady operation of regulated asynchronous motor

Conjunctive optimal operation of water and power networks

Water distribution systems (WDSs) are designed to convey water from sources to consumers. Their operation is a main concern for engineers, researchers, and practitioners and is subject to demand, pressure, and quality constraints. Pumping stations require power to pump water and keep system pressure at a desired level. On the other hand, power is generally supplied through power grids (PGs), which require optimal operation while satisfying operational constraints, such as generation limits, power consumption, and voltage constraints. Since the two infrastructure systems are interconnected, decision-makers could benefit from a holistic approach that would allow solving the two operational optimization problems together as one conjunctive problem. This paper presents the full mathematical formulation of the conjunctive optimization problem, including a novel modelling approach for the operation of a variable speed pump, which does not include integer variables for pump status, thus allowing to solve the model as a non-linear programming (NLP) problem. The formulation is applied to two illustrative case studies, and the results are compared to the optimal operation of the independent WDS. The inclusion of the PG in the optimization problem is observed clearly in the results and influences them quite significantly. WDS operation is shown adjust to the PG constraints, and the application of the conjunctive model results in a cost reduction rate of more than 10 % for both case studies.

Inclusion of water age in conjunctive optimal operation of water and power networks

ABSTRACT Water distribution systems (WDSs) are vital infrastructures designed to deliver water safely to consumers. This complex system necessitates continuous operational decisions, often optimized for efficiency. WDSs rely on power grids (PGs) to operate pumps and treatment facilities. PGs, likewise crucial, require strategic management to meet demand and environmental standards. Integrating the operation of both systems has garnered attention for its potential cost, energy, and environmental benefits. By leveraging the interconnection, trade-offs can be assessed, leading to improved solutions. Past research primarily focused on cost or carbon emissions as well as on hydraulic and voltage constraints. However, this study examines the impact of power systems on water quality, particularly water age, a key operational concern. Incorporating PGs into the optimal operation problem may alter flow directions, thereby influencing water age. Through mathematical modelling, this study evaluates these effects and applies them to simple case studies, demonstrating the influence of PG operation on water quality. Results demonstrate how tank constraints affect water age and show that a conjunctive operation approach, although beneficial for reduction of cost and energy consumption, can be damaging for water quality.

MILP and PSO approaches for solving a hydropower reservoirs intraday economic optimization problem

AbstractShort-term hydropower generation with several water reservoirs requires deciding, for each moment in time, the volume of water (outflow) that is released from every reservoir to be turbined and generate energy. Knowing the price of energy at every time period, the objective is to maximize the income earned from the generated energy. In this paper, we present (1) a Hydropower Reservoirs Operation Optimization problem with a higher level of detail than those found in the literature, encompassing temporal delays, water hammer effects, and increased temporal discretization, among others features, and (2) two distinct approaches for addressing this problem: MILP and PSO. These methods are compared across instances of varying nature to evaluate their performance. We make our code available on GitHub: https://github.com/baobabsoluciones/flowing-basin.

Human-safe and economic operation of renewable hydrogen-based microgrids under plateau conditions

The cold and hypoxic environment threatens the health and quality of people's lives in plateau areas. Appropriate air pressure, oxygen, and temperature are crucial for human-safe aspects in plateau microgrids. Facing extreme scenarios in these areas, we propose a two-stage robust operation strategy for renewable hydrogen-based microgrids considering the reliable supply of hydrogen and oxygen. To cope with rapid weather changes in these areas, the distributionally robust optimization (DRO) model that incorporates first-moment information is employed to depict renewable energy uncertainty. This study focuses on two weakly connected microgrids with distinct characteristics, showcasing their potential for mutual support. In the first stage, the plateau microgrid fulfills demands for electric power, hydrogen, and oxygen, with the power support from the another microgrid. In the second stage, reserves such as hydrogen fuel cells, diesel generators, and hydropower are utilized to mitigate renewable energy uncertainty. The operation optimization problem based on DRO is solved using the alternating direction method of multipliers. Case studies show that the strategy can coordinate complementary operation to enhance reliability, guarantee human safety, and save costs by 39.29 % and 38.73 % for the two microgrids.

Collaborative Pricing Strategy of Distribution Network and Electric Vehicle Aggregator Based on Integral System

Scaled EVs as a new type of load have great potential to participate in the standby market. However, the uncertainty of EV users' participation in aggregator regulation affects the optimal strategy for aggregators to participate in the market. Aiming at the uncertainty of users' willingness and the conflict of interest between aggregators and the distribution network, this paper proposes an optimal scheduling strategy of master-slave game for EV aggregators to improve users' willingness with a point system. First, the second-order cone optimal current model of the distribution network is established, and then the distribution network node marginal tariff is obtained. Second, the aggregator revenue model with energy storage is established, and the price-guided demand response model is proposed, while the aggregator point system is established to guide the charging behavior of EV users, so that the cooperative operation optimization problem between the distribution grid and the aggregator can be solved, and the economic interests among EV users, EV aggregators and distribution grid operators can be effectively balanced.

Comparison of different optimization techniques applied to optimal operation of energy storage systems in standalone and grid-connected direct current microgrids

This study addresses the problem of optimal operation and functioning of lithium-ion batteries in direct current (DC) microgrids with photovoltaic generators, in both urban and rural settings, under an approach that considers three mathematical models as objective functions: reduction of operational costs, reduction of power losses associated with energy transport, and reduction of CO2 emissions produced by conventional generators. After defining the objective functions, six optimization algorithms are integrated as solution methodologies: Equilibrium Optimizer (EO), Salp Swarm Algorithm (SSA), Particle Swarm Optimization (PSO), Sine and Cosine Algorithm (SCA), Black Hole Optimizer (BHO), and the Generalized Normal Distribution Optimizer (GNDO) algorithm. These methodologies are used to determine the hourly power flow through successive approximations, thus evaluating each of the objective functions with the system’s constraints in order to achieve reductions of each objective function and thereby confirm the quality of the solutions applied to the problem under analysis. Where, for the urban case of Medellín, the optimization achieved minimum reductions of 0.163% in fixed costs, 1.436% in variable costs, 7.160% in power losses, and 0.165% in CO2 emissions. In the rural case of Capurganá, the results showed minimum reductions of 0.095% in energy costs and 10.938% in power losses. These numerical results confirm the effectiveness of the applied optimization algorithms in reducing operational costs, power losses, and emissions, thereby validating the quality of the solutions for the analyzed problem.

Stochastic modeling for the aggregated flexibility of distributed energy resources

This paper proposes an uncertainty modeling method for the aggregated power flexibility of DERs. Basically, both outer and inner approximated power-energy boundary models are utilized to describe the aggregated flexibility of controllable DERs. These power and energy boundary parameters are uncertain because the availability of controllable devices, such as electric vehicles and thermostatically controlled loads, cannot be precisely predicted. The optimal operation problem of the aggregator is thus formulated as chance-constrained programming (CCP). Then, a flexibility envelope searching algorithm based on the ALSO-X+ method is proposed to solve the CCP, the result of which is a conservative approximation of the original CCP but not as conservative as the Conditional Value-at-Risk approximation. After optimizing the aggregated power of the group of DERs, the decision at the aggregator level is disaggregated into the flexibility regions of individual DERs. Finally, the numerical test demonstrates the effectiveness and robustness of the proposed method.

Phased optimization of active distribution networks incorporating distributed photovoltaic storage system: A multi-objective coati optimization algorithm

In this study, a phased operation optimization method for active distribution network with energy storage system is proposed for the operation optimization problem of active distribution network. The proposed model considers the PV and storage system output, the number of regulation equipment action, network loss and node voltage deviation for multi-objective optimization of the active distribution network. To achieve multi-objective optimization of the proposed optimal model, this study proposes a multi-objective coati optimization algorithm based on integrated crowding distance ranking, Bernoulli chaotic mapping, external archiving and non-dominated ranking mechanism. The proposed algorithm exhibits good performance as tested by ZDT and UF test functions, and obtaining optimal values in 75 % of the results. In the test of the improved IEEE30 and IEEE33 node system, the proposed method is improved by 21.55 %, 56.10 % and 4.12 % in the three aspects of network loss, node voltage deviation and minimum voltage of the whole network compared with the unoptimized case. Therefore, the proposed method in this study has a good application value for the optimization of active distribution network operation and can support the grid-connected operation of distributed new energy sources.

Data-Driven Modeling and Operation Optimization With Inherent Feature Extraction for Complex Industrial Processes

In response to the tenets of Industry 4.0, operation optimization in industrial processes has become a significant research topic. However, the uncertainties prevailing in the process pose challenges to production operations, especially the feedstock properties. In this work, the operation optimization study is performed on a distillation unit (DU), a typical plant in the industrial process. To enhance production performance, a modeling and operation optimization strategy based on feedstock property and production features is presented. One of the difficulties is how to uncover features from high-dimensional and imperfect data, where imperfect data refers to product quality data that is unavailable online. In the strategy, we inject the inherent characteristic of the process into the data-driven method to extract the feedstock property in a data-based and knowledge-oriented manner. Further, optimal feature representation and process modeling can be achieved by customizing the network structure. The operation optimization problem is formulated to adjust the top temperature of the distillation column (TTDC) to achieve satisfactory production under varying feedstock properties. Experimental results illustrate that the process model based on feedstock property and production features (PM-FP-PF) can better fit the physical process mechanism even based on incomplete information in industrial data. Industrial experiments have shown the proposed strategy has advanced generalization ability to the different feedstock properties. The proposed operation optimization strategy (OOS) improves the product qualification rate and has broad application prospects in industrial processes with similar features. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Industrial processes suffer from a variety of disturbances that interrupt the smooth operation of the system, such as varying feedstock properties. How to deal with them is the key to improve the product qualification rate. In this work, we propose a data-driven modeling and operation optimization framework to improve product quality under varying feedstock properties. The dynamic variation characteristics of the feedstock properties can be obtained by analyzing the physical properties of the production unit. This is used as a basis for representing and extracting feedstock properties in a data-driven way. Further, a process model based on feedstock property and production features (PM-FP-PF) is built to predict product quality. An operation optimization strategy with production capacity consideration is established. It can determine the optimal operation action required by the current system, mitigating the uncertainty of feedstock property. This operation optimization system has been applied to a distillation unit in the hydrofining process. The application results show that the process model achieves satisfactory estimation accuracy, and the operation optimization strategy has improved production performance.

A Novel Dynamic Operation Optimization Method Based on Multiobjective Deep Reinforcement Learning for Steelmaking Process.

This article studies a dynamic operation optimization problem for a steelmaking process. The problem is defined to determine optimal operation parameters that bring smelting process indices close to their desired values. The operation optimization technologies have been applied successfully for endpoint steelmaking, but it is still challenging for the dynamic smelting process because of the high temperature and complex physical and chemical reactions. A framework of deep deterministic policy gradient is applied to solve the dynamic operation optimization problem in the steelmaking process. Then, an energy-informed restricted Boltzmann machine method with physical interpretability is developed to construct the actor and critic networks in reinforcement learning (RL) for dynamic decision-making operations. It can provide a posterior probability for each action to guide training in each state. Furthermore, in terms of the design of neural network (NN) architecture, a multiobjective evolutionary algorithm is used to optimize the model hyperparameters, and a knee solution strategy is designed to balance the model accuracy and complexity of neural networks. Experiments are conducted on real data from a steelmaking production process to verify the practicability of the developed model. The experimental results show the advantages and effectiveness of the proposed method compared with other methods. It can meet the requirements of the specified quality of molten steel.

An Estimation of Distribution Algorithm With Resampling and Local Improvement for an Operation Optimization Problem in Steelmaking Process

An Estimation of Distribution Algorithm With Resampling and Local Improvement for an Operation Optimization Problem in Steelmaking Process

Multiobjective multihydropower reservoir operation optimization with transformer-based deep reinforcement learning

The paper introduces a transformer-based deep reinforcement learning (T-DRL) approach designed to address the multiobjective multihydropower reservoir operation optimization (MMROO) problem. Unlike existing literature that primarily focuses on maximizing power generation from individual reservoirs, the MMROO model in this study considers the broader context of multiple reservoirs, encompassing total power generation, ecological protection, and residential area water supply. The computational challenges posed by the numerous constraints and nonlinearities of multiple reservoirs render conventional multiobjective evolutionary algorithms both expensive and lacking in generalization capabilities for solving the MMROO problem. To overcome these challenges, the paper proposes a T-DRL approach that leverages the multihead attention mechanism within the encoder module to adeptly extract complex information from reservoirs and residential areas. The two-stage encoder effectively processes diverse information separately. The multireservoir network of the decoder then generates optimal decisions based on contextual information. The case study focusing on Lake Mead and Lake Powell in the Colorado River Basin demonstrates the efficacy of the T-DRL approach, producing operation strategies that outperform a state-of-the-art method. Specifically, the proposed approach yields a 10.11% increase in electricity generation, a 39.69% reduction in amended annual proportional flow deviation, and a 4.10% rise in water supply revenue. Overall, the T-DRL approach emerges as an effective method for the multiobjective operation of multihydropower reservoir systems.

Implementation of an Optimal Energy Management within Islanded Microgrid

This paper proposes an optimal Energy Management System (EMS) based on Mixed Integer Linear Programming (MILP) optimization technique for an islanded Microgrid (MG). A local energy market (LEM) platform is employed which attempts to obtain the best electricity market price and to maximize the utilization of existing distributed energy resources. Besides, a single side auction market structure is used for the LEM which takes the offer prices from all microsources to calculate market clearing price. Simulation and experimental results from the proposed method over a real MG are compared with those from a Modified Conventional EMS (MCEMS). The proposed algorithm is flexible, extendable and too fast to be utilized for different MG structures with various capacities. The results demonstrate the effectiveness of the proposed method to solve the optimal operation problem in an isolated MG with 25% reduction in the cost of operation.

A hybrid butterfly algorithm in the optimal economic operation of microgrids.

With the increasing capacity of renewable energy generators, microgrid (MG) systems have experienced rapid development, and the optimal economic operation is one of the most important and challenging issues in the MG field. To reduce the overall generation cost of microgrids, a hybrid butterfly algorithm (HBOA) is proposed to address the optimal economic operation problem in MG systems. This algorithm uses adaptive switching thresholds to balance the global exploration capability and local exploitation capability of the algorithm. It introduces a diversity learning mechanism to enhance information exchange among populations to improve the algorithm's accuracy and proposes an elite-guided guidance strategy to accelerate the convergence speed of the algorithm. Numerical simulation experiments on 10 standard test functions validate that the HBOA algorithm has higher optimization accuracy and faster convergence speed. Simulation experiments are conducted on two operation modes of microgrids: Islanded and grid-connected, and compared with other algorithms. In islanded and grid-connected modes, HBOA can reduce operating costs by up to 11.7% and 17.7%, respectively. The experimental results confirm the applicability and superiority of the proposed algorithm for solving the optimal economic operation problem in microgrids.

Multi-Criteria Decision Making in Optimal Operation Problem of Unbalanced Distribution Networks Integrated With Photovoltaic Units

Multi-Criteria Decision Making in Optimal Operation Problem of Unbalanced Distribution Networks Integrated With Photovoltaic Units

Research on the Operation Optimization of Aggregate Resources under the Dual Factors of Power Grid and Economy

Under the influence of power grid and economy, the operation optimization of aggregate resources has high practical value and significance. For the problems of the existing aggregate resource operation optimization methods, this paper presents a completely new optimization method, considering the economic factors of power output, grid line transmission, grid stability, transformer capacity, energy storage charging and discharge loss, grid transmission loss, transformer loss and production arrangement of adjustable resource aggregate, and combined with the idea of electric power translation in the operation of the load device. By adopting a mixed-integer linear programming model (Mixed-Integer Linear Programming, MILP), the operation optimization problem of the aggregate resource is transformed into a mathematical planning problem to be solved, which effectively avoids the start-stop delay of the load device, and shortens the time taken to adjust power supply and demand, reduces the construction cost and operation and maintenance cost of the aggregate, and realizes the optimal allocation of electric power resources, improves the sustainable energy utilization rate and the stability of the power system, and provides a new direction for the continuous development and progress of the power system.