Minimum Generation Cost Research Articles

Assessment of a Multiperiod Optimal Power Flow for Power System Operation

The optimal power flow is an important tool for power system planning and power system operation. It is used in a 24-hour period to find an economic dispatch of generating units considering network restrictions. The optimal power flow provides valuable information about the operation cost, the transmission flows, the generation and the congestion in the system. This information is used by generators, planners, operators and regulators in order to analyze and take decisions about the system at short and long term. The first one corresponds to the information for the operation. The second one corresponds to the information for the planning. This paper proposes a detailed optimal power flow formulation looking for a minimum cost of generation considering wind generation. Five solvers (CBC, CLP, CPLEX, Gurobi and GLPK.) have been used in order to compare differences between them. These solvers are commonly used to solve the multiperiod DC optimal power flow. An IEEE-24 test system is used to compare the solutions provided by the solvers. The findings reveal significant differences between the solvers when they are used to solve the IEEE-24 test system. Additionally, the computing time for each solver is reported. The solvers CPLEX and Gurobi show the lowest computational time to find a solution.

Solution to the economic dispatch problem of the Nigerian power system using genetic algorithm

This paper aims to solve the economic dispatch problem of the 28-bus Nigerian power system using genetic algorithm. The power flow solution of the network is first obtained using Newton-Raphson technique; the solution thus obtained is used to determine the loss coefficients of the network. For this study, a forecasted load demand of 2000MW will be considered, MATLAB's genetic algorithm optimization toolbox is used to obtain the optimum generation level of each unit. The optimal power output of each scheduled generating units was obtained after 200 iterations at a minimal generation cost of ₦136,370.205/hr. A power loss of 11.32MW in the network was also obtained using Kron's loss formula. Keywords: Genetic Algorithm, Economic Dispatch, loss coefficient, Optimization, Constraint

A Probabilistic Optimal Power Flow in Wind-Thermal Coordination Considering Intermittency of the Wind

This article specifically aims to prove the superiority of the proposed moth swarm algorithm (MSA) in view of wind-thermal coordination. In the present article, a probabilistic optimal power flow (POPF) problem is formulated to reflect the probabilistic nature of wind. Modelling of doubly fed induction generator (DFIG) is included in the proposed POPF to represent the wind energy conversion system (WECS). To reduce DFIG imposed deviation of bus voltage ancillary reactive power support is considered. Moreover, three different optimization techniques, namely, MSA, biogeography-based optimization (BBO), and particle swarm optimization (PSO) are independently applied for the minimization of active power generation cost for wind-thermal coordination, considering different instances in case of IEEE 30-bus and IEEE 118-bus system. From the simulation results, it is confirmed and validated that the proposed MSA performs considerably better than BBO and PSO.

Power generation cost minimization of the grid-connected hybrid renewable energy system through optimal sizing using the modified seagull optimization technique

A hybrid renewable power system is studied in this paper. This system is composed of PV panels, wind turbines, inverter, rectifier, electrolyzer, and fuel cell such that it prioritizes storing excess energy by converting it to hydrogen and using it later in the fuel cell. Additional extra generation power is sold to the main electricity network. The system generates power from clean sources and has zero emission. To achieve minimum power generation cost, the optimal size of each component is obtained using the proposed modified seagull optimization technique. The cooperative generation of wind and PV and energy storage mitigate the uncertain behavior of renewable energy sources. The proposed hybrid power system and optimization are implemented in a real-world case study in Qingdao, China. The consumption and meteorological data of the year 2018 are used as input to the system. To prove the superiority of the proposed optimization method in terms of accuracy and computation time, it is compared to two other optimization methods, namely original seagull optimization algorithm (SOA) and modified farmland fertility algorithm (MFFA), which are used in similar applications. The proposed method has achieved 2.02% and 2.78% better results and converged 69.36% and 47.07% faster compared to conventional SOA and MFFA methods, respectively. In addition, the hybrid system is able to operate with high reliability and loss of power supply probability well below the threshold of 8.96e20.

Synthesis of wastewater treatment plant based on minimal waste generation cost: A material flow cost accounting (MFCA) approach

Wastewater treatment (WWT) is a mandatory process to ensure wastewater quality meets legislation requirements and to reduce environmental impacts. Many established WWT technologies are available in the market and the selection of such technologies is usually based on heuristics. However, technologies selected using heuristics may not be able to guarantee optimal economic performance. In this respect, it is important for manufacturing companies to synthesise a WWT process with minimum investment cost while meeting legislation requirements. Most manufacturing companies face issues to achieve this goal. Among these issues, is the fact that part of the investment invested into a WWT process will be lost to waste (sludge cake) generation. The generated waste (sludge cake) will require additional high waste disposal costs. Therefore, to reduce the loss of investment in a WWT process, the waste generation cost and waste disposal cost must be minimised. This can be addressed via Material Flow Cost Accounting (MFCA), a management tool that quantifies material flows across physical and monetary values in a production process. Previous works had adapted the concept of MFCA for prioritisation of waste streams for waste recovery and minimisation of investment cost in processes with revenue streams. Thus, the objective of this paper is to extend the use of MFCA as a preliminary decision-making tool in the selection of WWT technologies with minimum waste generation cost. To illustrate the developed approach, a case study on sago-based WWT process is solved in this work. Based on the results, the synthesised WWT process from the developed model is capable of recovering as much as 93.3 % of the total operating cost back into the manufacturing process while minimising the waste generation cost to 6.7 % of the operating investment cost.

Real-Time Dispatch of Coupled Transmission and Distribution Systems within a Distributed and Cooperative Framework

This paper presents a real-time dispatch strategy for coupled transmission and distribution systems within a distributed and cooperative control framework to maintain reliable and secure operation with minimum generation costs and maximum renewable energy consumption. The presented strategy transforms each distribution system into a dispatchable active source via an average-consensus-based active power control of renewable distributed energy resources (DERs) at the distribution level and then dispatches the active power reference of conventional generators as well as the distribution systems in a measurement-based way at a transmission level. The voltage fluctuation caused by the DER active power control is smoothened with a distributed voltage control method, which can also reduce the active power loss in the distribution systems. Compared to existing real-time dispatch strategies, the proposed strategy can eliminate security issues in the transmission system in a short time by regulating large amounts of DERs at a distribution level in a simple and easy controlled structure, in which the differences in the communication conditions and privacy requirements between the distribution and transmission systems are adequately considered.

A novel disruption based symbiotic organisms search to solve economic dispatch

Economic dispatch (ED) is one of the vital prospects in the energy management system for determining the optimal power generation distribution among several committed power generating units. The objective of ED is to generate the electric power to meet the load demand by minimizing the total operating cost subjected to various equality and inequality constraints. This ED problem is generally solved using conventional techniques such as a gradient method by assuming the objective function as linear and convex. However, in general, the ED problem is constrained, non-convex, large scale, multimodal and highly nonlinear optimization problem. In order to overcome this drawback, various heuristic techniques have been introduced in the literature. Symbiotic organism search (SOS) is one of the emerging nature-inspired meta-heuristic algorithms. Due to simple in implementation and free from algorithm-specific control parameters, the SOS algorithm has gained a reputation among the researchers. The SOS technique mimics the biological interaction between two distinct species to survive and proliferate in the ecosystem. To evade the suboptimal solution and to enhance the exploration and exploitation of the SOS algorithm, the disruption operator is integrated with the basic SOS to form a novel disruption based SOS (DSOS) algorithm. The disruption strategy is originated from astrophysics and has the ability to shift between exploration and exploitation during the process of finding an optimum solution. To illustrate the effectiveness of the proposed method, it is applied on various test systems such as 3-unit, 5-unit, 6-unit, 13-unit, 20-unit, 38-unit, and 110-unit systems to solve different ED problems, namely, without transmission losses (TL), with transmission losses, by simultaneously considering valve point loading (VPL) effect along with TL, by simultaneously considering the effect of ramp rate limits (RRLs), prohibited operating zones (POZs) and TLs, and dynamic economic load dispatch by considering RRLs, POZs, VPL, and TL. The comparison of DSOS based simulation results with other methods reveal the efficiency and robustness of the proposed method to provide minimum total generation cost in all the cases with better convergence rate and less computational time.

Optimal power scheduling for economic dispatch using moth flame optimizer

<p>This paper proposes the optimal generator allocation to solve Economic Dispatch (ED) problem in power system using Moth Flame Optimizer (MFO). With this approach, the optimum power for each unit generating in the system will be searched based on the power constraints per unit and the amount of power demand. The objective function of this study is to minimize the total cost of generation. The amount of power loss is measured to determine the effectiveness of the proposed technique. The performance of the MFO technique is also compared to the evolutionary programming (EP) and Particle Swarm Optimization (PSO) methods. Five- and thirty-bus power system networks are selected as test systems and simulated using MATLAB. Based on simulation results, MFO provides better results in regulating the optimum power generation with minimum generation cost and power loss, compared to EP and PSO.</p>

Multiverse optimisation based technique for solving economic dispatch in power system

Economic dispatch (ED) is one of the many important components in a power system operation. It is designed to calculate the exact amount of power generation needed to ensure a minimum cost of generation. A power system with multiple generators should be running under an economic condition. The operating cost has to be minimised for any feasible load demand. The increase of power demand is getting higher throughout the year. Economic dispatch is used to schedule and control all output of the fossil-fuel or coal-generators to satisfy the system load demand at a minimum cost. This paper presents the Multiverse Optimisation (MVO) for solving the economic dispatch in a power system. The proposed Multiverse optimisation engine developed in this study is implemented on the IEEE 30-Bus Reliability Test System (RTS). It has five generators, all of which are denoted as the control variables for the optimisation process. To reveal the superiority of MVO, a similar process was conducted using Evolutionary Programming (EP). Results from both techniques were compared, and it was revealed that MVO had outperformed EP in terms of reduced cost of generation for the system.

Optimal economic dispatch of power generation solution using lightning search algorithm

Economic dispatch (ED) is the power demand allocating process for the committed units at minimum generation cost while satisfying system and operational constraints. Increasing cost of fuel price and electricity demand can increase the cost of thermal power generation. Therefore, robust and efficient optimization algorithm is required to determine the optimal solution for ED problem in power system operation and planning. In this paper the lightning search algorithm (LSA) is proposed to solve the ED problem. The system constraints such as power balance, generator limits, system transmission losses and valve-points effects (VPE) are considered in this paper. To verify the effectiveness of LSA in terms of convergence characteristic, robustness, simulation time and solution quality, the two case studies consists of 6 and 13 units have been tested. The simulation results show that the LSA can provide optimal cost than many methods reported in literature. Therefore, it has potential to solve many optimization problems in power dispatch and power system applications.

Distributed cooperative control strategy for islanded microgrids

In this paper, a distributed cooperative control strategy for islanded microgrids (MGs) is proposed, to minimize the total generation cost of distributed generators (DGs), and maintain the state of charge (SoC) balancing of battery energy storage systems (BESSs). First, a consensus-based economic dispatch (ED) strategy is proposed, to achieve the minimum total generation cost of DGs, while the aggregated power output of DGs meets the power dispatch command from the supervisory control system. Further, an SoC-based droop control strategy is developed for BESSs, to maintain the SoC balancing and power balance in the islanded MG simultaneously. Compared with the centralized control schemes, the proposed cooperative control strategy is fully distributed such that it simply requires local information exchange without the necessity of a central controller. More importantly, the proposed cooperative control strategy is able to achieve multiple control objectives in a unified framework. Finally, the simulation results in an islanded MG with renewable energy and time-varying load demands are presented, to demonstrate the effectiveness of the proposed distributed cooperative control strategy.

Optimal current flow technique for distribution systems with renewable energy generation

This article presents an optimal current flow (OCF) technique for analyzing distribution systems with renewable energy generation. The overall aim of this study is to reduce the complexity of the traditional nonlinear models by representing the problem as a quadratic optimization network flow model with linear constraints. The objective of the OCF method is minimization of renewable generation costs with or without consideration of transmission losses. Taking advantage of the topological characteristic of the distribution system, the network constraints are represented by Kirchhoff current and voltage laws. In addition, the model considers the capacity limits of the distribution components (renewable generators, transformers and lines current flow). The robustness and fastness of the OCF method is tested on 34-bus, 69-bus, and 400-bus systems under balanced and unbalanced, conditions and in radial or meshed distribution systems under different load scenarios. The results demonstrate the accuracy, and efficiency of the proposed approach in determining the optimal operation of a distribution system with renewable energy generation.

Optimal power flow using hybrid firefly and particle swarm optimization algorithm.

In this paper, a novel, effective meta-heuristic, population-based Hybrid Firefly Particle Swarm Optimization (HFPSO) algorithm is applied to solve different non-linear and convex optimal power flow (OPF) problems. The HFPSO algorithm is a hybridization of the Firefly Optimization (FFO) and the Particle Swarm Optimization (PSO) technique, to enhance the exploration, exploitation strategies, and to speed up the convergence rate. In this work, five objective functions of OPF problems are studied to prove the strength of the proposed method: total generation cost minimization, voltage profile improvement, voltage stability enhancement, the transmission lines active power loss reductions, and the transmission lines reactive power loss reductions. The particular fitness function is chosen as a single objective based on control parameters. The proposed HFPSO technique is coded using MATLAB software and its effectiveness is tested on the standard IEEE 30-bus test system. The obtained results of the proposed algorithm are compared to simulated results of the original Particle Swarm Optimization (PSO) method and the present state-of-the-art optimization techniques. The comparison of optimum solutions reveals that the recommended method can generate optimum, feasible, global solutions with fast convergence and can also deal with the challenges and complexities of various OPF problems.

Voltage-Based Distributed Optimal Control for Generation Cost Minimization and Bounded Bus Voltage Regulation in DC Microgrids

In conventional DC microgrid control schemes, optimization and real-time control are usually performed at different time scales. It is hard for such control schemes to achieve real-time optimization. Even a small disturbance can result in deviations of bus voltages and output currents from their optimal operating points. In addition, most real-time controllers cannot guarantee the satisfaction of pre-defined constraints on individual bus voltages due to the disconnection between steady-state optimization and real-time control. In this paper, a distributed optimal control scheme is presented for DC microgrid. The objectives are to simultaneously realize generation cost minimization and individual bus voltage regulation. First, the optimal control problem is formulated, based on which a necessary and sufficient optimality condition is derived that characterizes the optimal operating points. The distributed optimal controller is then proposed to dynamically drive the system to operate at the optimality condition. Convergence to the optimal operating points that minimizes generation cost under constraints is guaranteed through rigorous Lyapunov synthesis. Each individual bus voltage can also be maintained within bounds in both transient- and steady-state. The performance of the proposed controller is validated through simulations based on a switch-level microgrid model.

Achieving Acceleration for Distributed Economic Dispatch in Smart Grids Over Directed Networks

In this paper, the economic dispatch problem (EDP) in smart grids is investigated over a directed network, which concentrates on allocating the generation power among the generators to satisfy the load demands with minimal total generation cost while complying with all constraints of local generation capacity. Each generator possesses its own local generation cost, and the total generation cost is the sum of all local generation costs. To deal with EDP, most of the existing methods, such as strategy based on push-sum, surmount the unbalancedness induced by the directed network via employing column-stochastic weights, which might be infeasible in distributed implementation. In contrast, in order to be suitable for the directed network with row-stochastic weights, we develop a novel directed distributed Lagrangian momentum algorithm, named as D-DLM, which integrates distributed gradient tracking method with two types of momentum terms and utilizes non-uniform step-sizes with respect to the updates of Lagrangian multipliers. If the largest step-size and the maximum momentum coefficient are positive and sufficiently small, D-DLM can linearly allocate the optimal dispatch on condition that the generation costs are smooth and strongly convex. Finally, a variety of studies on EDP in smart grids are simulated.

Adaptive Droop Control of Multi-Terminal HVDC Network for Frequency Regulation and Power Sharing

This paper proposes a novel adaptive droop control strategy for multi-terminal HVDC (MTHVDC) network to provide frequency support and power sharing via a distributed consensus algorithm. The droop coefficient is adaptively tuned by an effective integration of optimization algorithms and frequency consensus method. The optimization control aims to minimize generation cost, frequency deviation cost, and converter losses. Furthermore, the coordination between the consensus-based droop controller and the optimization technique is established by a feedback loop of coupling gain solution method, which is based on coupling gain matrix. The proposed control is successfully applied to a four-terminal MTHVDC system and modified New England 39-bus system on PSCAD. Power sharing is further improved by adding an adjustment factor based on frequency deviation with coupling gain matrix, which redirects power flow in ac and dc sub-grids. In addition, the loss reduction of voltage source converters is presented to demonstrate the proposed control performance.

OPF for large scale power system using ant lion optimization: a case study of the Algerian electrical network

<span lang="EN-US">This paper presents a study of the optimal power flow (OPF) for a large scale power system. A metaheuristic search method based on the Ant Lion Optimizer (ALO) algorithm is presented and has been confirmed in the real and larger scale Algerian 114-bus system for the OPF problem with and without static VAR compensator (SVC) devices. To get the highest impact of SVC devices in terms of improving the voltage profile, minimize the total generation cost and reduction of active power losses, the ALO algorithm was applied to determine the optimal allocation of SVC devices. The results obtained by the ALO method were compared with other methods in the literature such as DE, GA-ED-PS, QP, and MOALO, to see the efficiency of the proposed method. The proposed method has been tested on the Algerian 114-bus system with objective functions is the minimization of total generation cost (TGC) with two different vectors of variables control.</span>

A Privacy Preserving Distributed Optimization Algorithm for Economic Dispatch Over Time-Varying Directed Networks

The economic dispatch problem (EDP) plays a fundamental and significant role in smart grids. Its purpose is to decide the output power of every generator in smart grids for achieving the minimal generation cost. With advantages in flexibility, robustness, and scalability, it is desirable to apply distributed optimization methods to solve EDPs. In most existing distributed optimization approaches, all generators explicitly exchange their states with neighbors to obtain the optimal solution, which may result in disclosing the privacy information of generators. This problem becomes worse if there are some adversaries aimed at inferring privacy information from the communication network for nefarious purposes. For privacy preservation, a privacy preserving distributed optimization algorithm over time-varying directed communication networks is proposed in this article by adding conditional noises to the exchanged states. It is proved that this proposed algorithm is able to solve the EDP. Moreover, the convergence rate and privacy analysis of the proposed algorithm are also shown in this article. An example is provided to confirm the effectiveness of this proposed algorithm.

The Economic Dispatch of Wind Integrated Power System based on an Improved Differential Evolution Algorithm

Background: As more and more renewable energy such as wind energy is connected to the power grid, the static economic dispatch in the past cannot meet its needs, so the dynamic economic dispatch of the power grid is imperative. Methods: Hence, in this paper, we proposed an Improved Differential Evolution algorithm (IDE) based on Differential Evolution algorithm (DE) and Artificial Bee Colony algorithm (ABC). Firstly, establish the dynamic economic dispatch model of wind integrated power system, in which we consider the power balance constraints as well as the generation limits of thermal units and wind farm. The minimum power generation costs are taken as the objectives of the model and the wind speed is considered to obey the Weibull distribution. After sampling from the probability distribution, the wind speed sample is converted into wind power. Secondly, we proposed the IDE algorithm which adds the local search and global search thoughts of ABC algorithm. The algorithm provides more local search opportunities for individuals with better evolution performance according to the thought of artificial bee colony algorithm to reduce the population size and improve the search performance. Results: Finally, simulations are performed by the IEEE-30 bus example containing 6 generations. By comparing the IDE with the other optimization model like ABC, DE, Particle Swarm Optimization (PSO), the experimental results show that obtained optimal objective function value and power loss are smaller than the other algorithms while the time-consuming difference is minor. The validity of the proposed method and model is also demonstrated. Conclusion: The validity of the proposed method and the proposed dispatch model is also demonstrated. The paper also provides a reference for economic dispatch integrated with wind power at the same time.

A heuristic benders-decomposition-based algorithm for transient stability constrained optimal power flow

Security Constrained Optimal Power Flow (SCOPF) is traditionally performed to obtain the optimal generation levels to achieve the minimum generation cost under operational constraints in normal and contingency conditions. In this paper the SCOPF problem with DC load flow equations is extended to consider the transient stability margin of the generating units as a heuristic decomposition algorithm. However, the proposed algorithm is compatible with any SCOPF formulation. Due to computational complexities of security constraints and transient stability assessment, Benders decomposition algorithm is utilized to handle the transient stability margin of generating units as separate sub-problems. A transient energy function is developed to assess the transient stability of generating units under credible faults using the cut-set energy function criterion. In case of violation of the required transient stability margin, Benders cuts are constructed and added to the master problem. The proposed decomposed Transient Stability Constrained OPF (TSCOPF) is converged in few iterations. The developed TSCOPF algorithm is implemented on the IEEE 39-bus dynamic test system to validate its accuracy and efficiency.