Constrained Economic Dispatch Research Articles

Dynamic Voltage Unbalance Constrained Economic Dispatch for Electrified Railways Integrated Energy Storage

The cophase traction power supply system (CTPSS) is a promising solution in the smart electrified railways to effectively eliminate the neutral section, improve regeneration braking energy (RBE) utilization and mitigate voltage unbalance (VU). It works by coordinating the power flow distribution (PFD) among the energy storage (ES), power flow controller, and traction transformer. However, the conventional dispatch considering VU mitigation may result in increasing extra operation costs and accelerating ES aging. Therefore, driven by the day-ahead forecasted information, a dynamic VU regulation strategy is proposed to draw up the VU compensation schedule (VU-CS), which can satisfy the probabilistic limitations of power quality standards. Consequently, a Copula-based VU dependence model is developed to transform the VU-CS into the PFD constraint set of CTPSS. Meanwhile, an ES degradation model is introduced to quantify the system operation cost within different scenarios. Taking the PFD as a VU regulation constraint, an economic dispatch scheme of CTPSS is established to obtain a minimum operation cost and maximum RBE utilization. Finally, case study tests verify the efficiency of the proposed approach. The results show that scheme can improve ES cycle life and decrease cost under the probabilistic limitations of VU.

On the development of organized nodal local energy markets and a framework for the TSO-DSO coordination

In this paper we propose a market design for implementing organized nodal electricity markets for the distribution grid. Distribution System Operators (DSOs) are expected to manage a massive penetration of Distributed Energy Resources (DERs), such as Renewable Energy Resources (RES), Electric Vehicles (EVs), Storage and Demand response. A Day Ahead Market (DAM) and a Real-Time Market (RTM) is proposed to optimize and clear offers and bids submitted by the DERs. A Mixed Integer Programming (MIP) Security Constrained Unit Commitment (SCUC) and a Security Constrained Economic Dispatch (SCED) iterates with a detailed asymmetric and unbalanced three-phased Distribution Power Flow (DPF) to enforce all constraints in the distribution grid. The solution produces Distribution Locational Marginal Prices (DLMPs) for all phases at every node of the distribution grid. A general framework for the coordination of the DSO with the ISO/TSO markets is also presented as an integral part of the proposed multi-level energy market design. The proposed new methodology has been applied to an actual large-scale distribution system. Numerous simulation scenarios have been executed to prove the validity of the proposed approach. In this paper a simple small subset of the actual distribution system is selected to illustrate the proposed methodology.

Application of Genetic Algorithm to Solve Emission Constrained Economic Dispatch Problems

Application of Genetic Algorithm to Solve Emission Constrained Economic Dispatch Problems

A hybrid multi-objective improved bacteria foraging algorithm for economic load dispatch considering emission

In this paper, a hybrid multiobjective improved bacterial foraging algorithm with fuzzy dominance sorting FSIBF is proposed and used to solve environmental friendly economic load dispatch problem. The fuzzy dominance-based sorting procedure is used to select the non-dominated solutions in the Pareto front. The proposed algorithm is applied to nonlinear constrained multiobjective environmental friendly economic load dispatch problem. In the proposed work, we have considered the standard IEEE 30-bus six-generator test system with fuel cost and emission as two conflicting objectives to be optimised simultaneously satisfying the system's operational constraints. The constraints imposed from the operation point of view are the limits on generator real power and reactive power outputs, bus voltages and power flow in the transmission lines. The proposed work also includes the effect of having non-smooth cost characteristics of the thermal generators which arises because of the valve point loading effect. The practical generator constraints such as ramp rate limits and prohibited operating zones are also incorporated in this work suitably.

Risk Reserve Constrained Economic Dispatch of Wind Power Penetrated Power System Based on UPSMC and SAGA Algorithms

A short-term Economic Dispatch (ED) model with risk constraint for wind penetrated power systems was built to face the challenge of scheduling spinning reserves brought from wind energies. The proposed model utilizes the probability of spinning reserve shortage as measurement of system risk and evaluates the risk by an Unequal Probabilities Sampling based Monte Carlo (UPSMC) method. A Genetic Algorithm (GA) improved with Simulated Annealing (SA) strategy is presented as SAGA to solve the problem. By comparing simulation results under different wind penetrations and risk constraints, coal consumptions will not always decrease with wind penetration and risk constraint but for most times. In addition, unit risk benefit has a trend to increase with wind penetration and decrease with risk constraint while contribution of unit wind generation has the contrary character. Simulation results also show that the proposed sampling method could improve the sampling efficiency and the SAGA method had better performance than traditional GA.

Refined augmented Lagrange Hopfield network-based Lagrange relaxation for hydrothermal scheduling

This paper proposes a refined augmented Lagrange Hopfield network-based Lagrange relaxation (ALHN-LR) for solving short term hydrothermal scheduling (HTS) problem with pumped-storage hydro units. ALHN-LR consists of improved Lagrange relaxation (ILR) and augmented Lagrange Hopfield network (ALHN). For solving the HTS problem, the proposed method applies enhanced ILR for finding thermal unit scheduling, ALHN for solving constrained economic dispatch (CED), and heuristic search-based algorithms in earlier papers for committing hydro and pumped-storage units, repairing ramp rate, emission, and transmission constraint violations, and refining the obtained result. The proposed ALHN which is a continuous Hopfield network with its energy function based on augmented Lagrangian function can properly handle both equality and inequality constraints in CED problem. The proposed ALHN-LR is tested on a hydrothermal system with 17 thermal, two hydro and two pumped-storage units, and the IEEE 24-bus reliability test system over the 168-hour schedule time horizon. Test results indicate that the proposed method can obtain less total costs than those from augmented Hopfield network (AHN), hybrid enhanced Lagrangian relaxation and quadratic programming (hybrid LRQP), and augmented Lagrangian relaxation (ALR).

宁夏电网日前调度计划编制系统的开发与应用

本文所开发的宁夏电网日前调度计划编制系统，对于提高调度计划管理的精益化水平与智能化水平具有重要意义。该系统结合宁夏电网日前调度计划编制工作的业务流程，实现了智能的数据检测、边界参数的灵活配置、电网模型自适应、以及算法流程可感知等重要的功能目标，全面提高了电网调度运行计划编制的最优性、灵活性和高效性。该系统基于宁夏电网EMS的实际电网模型，考虑发输变电设备检修计划的影响，可以自动匹配生成未来态的96点电网模型，能够在日前调度计划决策的同时，对系统的机组开停方案和检修计划进行安全校核，并考虑基态、断面、N-1、故障集等校核要求，实现内嵌式闭环化的安全校核计算。本文将对宁夏电网日前调度计划编制系统的功能框架与计划编制流程进行分析与梳理；在此基础上，重点介绍该系统在约束配置、算法支撑、安全校核等方面的功能特点，并介绍该系统在宁夏电网的应用效果。 This paper introduced the development and application of day-ahead generation scheduling (DAGS) system in Ningxia Provincial Power Grid. The system is designed considering the actual work process of generation scheduling in Ningxia Provincial Power Grid, towards the target of efficiency, flexibility and optimality. In the DAGS system, the input-output data would be automatically examined, operation parameters could be set flexibly, a self-adaptive grid model is embedded, and the process of algorithm could be incepted by the operators. The grid model for the planned day would be built based on the EMS module considering the impacts of equipment maintenance, with 96 periods and 15 minutes as interval. The generation scheduling problem would be then transferred into a standard security con-strained economic dispatch (SCED) problem, considering static and N-1 security correction embedded. This paper would introduce the function framework and work process of the DAGS system. And the function module of constraint setting, algorithm configuration and security correction would be described in detail. Finally, application effects of the DAGS system in Ningxia Provincial Power Grid would be introduced.

Fuzzified Particle Swarm Optimization Algorithm for Multi-area Security Constrained Economic Dispatch

This article presents a new computationally efficient fuzzified particle swarm optimization algorithm for solving the security-constrained multi-area economic dispatch of an interconnected power system. The core objective of the security-constrained multi-area economic dispatch is to determine the generation allocation of each committed unit in the system and the power exchange between areas so as to minimize the total generation cost without violating the tie-line constraint. The proposed fuzzified particle swarm optimization algorithm is based on the combined application of fuzzy logic strategy incorporated in the particle swarm optimization algorithm. The proposed method was tested on a system of three interconnected areas. The investigation reveals that the proposed method can provide an accurate solution with fast convergence and has the potential to be applied to other power system optimization problems.

New SCED Based on Minimum Bias Objective for Large-Scale Wind Integrated Power Systems

AbstractThe necessity of minimum bias control is discussed in this paper, especially for the power system with large-scale wind power integration. Three minimum bias SCED (Security Constrained Economic Dispatch) models: sum-bias, minmax-bias and sum-penalty bias, are presented, and the linear programming algorithm is proposed to solve the optimization problem. Based on actual power system simulation, the proposed models are analyzed and compared. The result shows the efficiency sum-penalty bias model. This model can equably distribute load deviation into available generators even considering the power network constraints. As a result, the proposed sum-penalty bias model has been applied in actual power scheduling in a province power system in China.

Risk Reserve Constrained Economic Dispatch Model with Wind Power Penetration

This paper develops a modified economic dispatch (ED) optimization model with wind power penetration. Due to the uncertain nature of wind speed, both overestimation and underestimation of the available wind power are compensated using the up and down spinning reserves. In order to determine both of these two reserve demands, the risk-based up and down spinning reserve constraints are presented considering not only the uncertainty of available wind power, but also the load forecast error and generator outage rates. The predictor-corrector primal-dual interior point (IP) method is utilized to solve the proposed ED model. Simulation results of a system with ten conventional generators and one wind farm demonstrate the effectiveness of the proposed method.

Reserve Constrained Multi-Area Economic Dispatch Employing Evolutionary Approach

The objective of Multi-area economic dispatch (MAED) is to determine the generation levels and the interchange power between areas that minimize fuel costs, while satisfying power balance and generating limit and transmission constraints. If an area with excess power is not adjacent to a power deficient area, or the tie-line between the two areas is at transmission limit, it is necessary to find an alternative path between these two areas to transmit additional power. When a MAED problem is solved with spinning reserve constraints, the problem becomes further complicated. The power allocation to each unit is done in such a manner that after supplying the total load, some specified reserve is left behind. In this paper, the authors compare classic PSO and DE strategies and their variants for reserve constrained MAED. The superior constraint handling capability of these techniques enables them to produce high quality solutions. The performance is tested on a 2-area system having 4 generating units and a 4-area, 16-unit system.

Improved merit order and augmented Lagrange Hopfield network for short term hydrothermal scheduling

This paper proposes an improved merit order (IMO) combined with an augmented Lagrangian Hopfield network (ALHN) for solving short term hydrothermal scheduling (HTS) with pumped-storage hydro plants. The proposed IMO-ALHN consists of a merit order based on the average production cost of generating units enhanced by heuristic search algorithm for finding unit scheduling and a continuous Hopfield neural network with its energy function based on augmented Lagrangian relaxation for solving constrained economic dispatch (CED). The proposed method is applied to solve the HTS problem in five stages including thermal, hydro and pumped-storage unit commitment by IMO and heuristic search, constraint violations repairing by heuristic search and CED by ALHN. The proposed method is tested on the 24-bus IEEE RTS with 32 units including 4 fuel-constrained, 4-hydro, and 2 pumped-storage units scheduled over a 24-h period. Test results indicate that the proposed IMO-ALHN is efficient for hydrothermal systems with various constraints.

Application of Exponential Evolutionary Programming to Security Constrained Economic Dispatch with FACTS Devices

Application of Exponential Evolutionary Programming to Security Constrained Economic Dispatch with FACTS Devices

Application of pattern search method to power system security constrained economic dispatch with non-smooth cost function

Direct search methods are evolutionary algorithms used to solve optimization problems. (DS) methods do not require any information about the gradient of the objective function at hand while searching for an optimum solution. One of such methods is Pattern Search (PS) algorithm. This paper presents a new approach based on a constrained pattern search algorithm to solve a security constrained power system economic dispatch problem (SCED) with non-smooth cost function. Operation of power systems demands a high degree of security to keep the system satisfactorily operating when subjected to disturbances, while and at the same time it is required to pay attention to the economic aspects. Pattern recognition technique is used first to assess dynamic security. Linear classifiers that determine the stability of electric power system are presented and added to other system stability and operational constraints. The problem is formulated as a constrained optimization problem in a way that insures a secure-economic system operation. Pattern search method is then applied to solve the constrained optimization formulation. In particular, the method is tested using three different test systems. Simulation results of the proposed approach are compared with those reported in literature. The outcome is very encouraging and proves that pattern search (PS) is very applicable for solving security constrained power system economic dispatch problem (SCED). In addition, valve-point effect loading and total system losses are considered to further investigate the potential of the PS technique. Based on the results, it can be concluded that the PS has demonstrated ability in handling highly nonlinear discontinuous non-smooth cost function of the SCED.

Emission Constrained Economic Dispatch—A New Recursive Approach

The purpose of this article is to present a dynamic programming recursive approach for the emission constrained economic dispatch (ECED). A multiobjective, multistage decision making problem has been solved analytically without the familiar Lambda (λ) iteration method. The optimization algorithm has been developed with a sequential dynamic programming model. The salient feature of this technique is that all the former conventional procedures have been avoided completely. This method has boundless applications for economic generation studies with different constraints. An accurate solution is made available on par with other conventional results. The validity of the proposed method is demonstrated with the help of two standard test systems.

Parallel tabu search algorithm for constrained economic dispatch

A parallel tabu search (PTS) algorithm for solving ramp rate constrained economic dispatch (CED) problems for generating units with non-monotonically and monotonically increasing incremental cost (IC) functions is proposed. To parallelise tabu search (TS) algorithms efficiently, the neighbourhood decomposition is used to balance the computing load, whereas competitive selection is used to update the best solution reached among subneighbourhoods. The proposed PTS is implemented on a 32-processor Beowulf cluster with an Ethernet switching network on a generating unit system size in the range 10-80 units over the entire dispatch periods. With different subneighbourhood sizes, the proposed PTS compromises the experimental speedup and solution quality for the best performance. PTS is potentially viable for the online implementation of CED because of the substantial generator fuel cost savings and high speedup upper bounds.

Constrained Economic Dispatch by Combined Genetic and Simulated Annealing Algorithm

This article proposes a combined genetic and simulated annealing algorithm (CGSA) to solve ramp rate constrained economic dispatch (ED) problems for generating units with non-monotonically and monotonically increasing incremental cost (IC) functions. The developed CGSA method is tested on the systems with the number of generating units in the range of 10 to 80 over the entire dispatch periods. The obtained solutions are near the optimal solutions of zoom brute force (ZBF) and zoom dynamic programming (ZDP), and are less expensive than those obtained from local search (LS), simulated annealing (SA), genetic algorithm (GA), GA based on SA solutions (GA-SA) and merit order loading (MOL) methods, thereby leading to substantial generator fuel cost savings. The proposed CGSA is effective in solving constrained ED problem in terms of the quality of solutions.

Power generation scheduling through use of generalised network flow programming

The economic dispatch problem is important in both power system planning and operation. Although there have been major advances in defining and solving more complete optimal power flow (OPF) problems, there exists a need for constrained economic dispatch (CED) techniques which, though not as rigorous or as exact as an OPF, are fast enough to be used on desktop computers. The authors present a CED formulation that is based upon generalised network flow programming (GNFP). The methodology for applying GNFP to the CED problem is developed and illustrated in this paper using four examples: 5, 39, 264, and 515-bus systems. Starting with a solved loadflow case, execution times for the CED are shown to be about the same as for a Newton-Raphson loadflow, and memory requirements are approximately 75% of the loadflow. Salient features of the CED-GNFP method include the ability to minimise generation cost while meeting constraints on line flows and area interchange. Network location of loads and generators is automatically considered without need of penalty factors, and transmission line flow limits do not affect solution times significantly. The authors believe that, owing to its simplicity of application, robustness, and ease of implementation on desktop computers, the CED-GNFP procedure is an important adjunct to the group of techniques and algorithms currently available for solving the overall economic dispatch/OPF problem.

A Penalty Function-Linear Programming Method for Solving Power System Constrained Economic Operation Problems

The use of a non-conventional linear programming technique, involving a piecewise differentiable penalty function minimization, is presented in this paper in connection with power system Constrained Economic Dispatch (CED) problems.