Transient Stability Constrained Optimal Power Flow Problem Research Articles

Fitness-distance balance based artificial ecosystem optimisation to solve transient stability constrained optimal power flow problem

ABSTRACT The Transient Stability Constrained Optimal Power Flow (TSCOPF) has become an important tool for power systems today. TSCOPF is a nonlinear optimisation problem, making its solution difficult, especially for small power systems. This paper presents a new optimisation method that incorporates Fitness-Distance Balance (FDB) with the Artificial Ecosystem Optimisation (AEO) algorithm to improve the solution quality in multi-dimensional and nonlinear optimisation problems. The proposed method, named the Fitness-Distance Balance Artificial Ecosystem Optimisation (FDBAEO), also has the capacity to solve the TSCOPF problem efficiently. In order to evaluate the proposed algorithm, it was tested on IEEE CEC benchmarks and on an IEEE 30-bus test system for the TSCOPF problem. Simulation results were compared with the basic AEO algorithm and other current meta-heuristic methods reported in the literature. The results showed that the proposed method was more effective in converging at the global optimum point in solving the TSCOPF problem compared to the other algorithms. This situation indicates that the design changes made in the decomposition phase of the AEO were more suitable for simulating the operation of the algorithm in the real world. The FDBAEO has exhibited a promising performance in solving both single-objective optimisation and constrained real-world engineering design problems.

Information‐gap decision theory based transient stability constrained optimal power flow considering the uncertainties of wind energy resources

Studies on transient stability constrained optimal power flow (TSCOPF) have become crucial for power systems to guarantee their dynamic securities against credible contingencies, while their optimum operations are to be continuously projected under changing conditions. However, the current approach to the TSCOPF problem is not sufficient to meet the expectations of a modern power system because it suffers from uncertainties mainly due to the rapid and large integration of distributed energy sources. This study proposes a novel method using the information-gap decision theory (IGDT) technique to solve the TSCOPF problem in the presence of uncertainties due to the penetration of wind farms. The IGDT is a non-probabilistic decision-making method that can be easily implemented to handle uncertainty in optimisation problems. While presenting applicable strategies, it does not require any information about the historical data, probability density function or membership function of the uncertain parameters. The proposed method offers an analysis for the economic dispatch in a power system with wind energy resources while providing robustness against transient instabilities and uncertainties in power generation. To demonstrate the effectiveness of the proposed method, it is implemented on New England 39-bus and IEEE 118-bus test systems.

Parallel Transient Stability-Constrained Optimal Power Flow Using GPU as Coprocessor

Graphics processing unit (GPU) has significantly increased the computing capacity of state-of-the-art high performance computing systems. This paper presents a novel GPU acceleration approach for transient stability-constrained optimal power flow (TSCOPF), which is one of the most computational challenging tasks in large-scale power system applications. Enabled by the revealed two-level decomposition parallelism in reduced-space interior point method, GPUs serve as plug-and-play coprocessors for time-consuming linear algebra operations in TSCOPF solving. Enhanced by multi-GPU processing and mixed-precision iterative refinement technique, the efficiency of solving TSCOPF is greatly improved without redesigning and reimplementing the existing algorithm framework. Numerical studies based on a series of test cases with up to 12 951 buses indicate the effectiveness of the proposed GPU-based approach for large-scale TSCOPF problems.

Transient Stability Constrained Optimal Power Flow Based on Multi-time Scale Power System Models

This paper is focused on the transient stability constrained optimal power flow (TSC-OPF) problem and its application for determining the optimal dispatch of active and reactive powers of distributed synchronous generators. In order to relieve the mathematical complexity of the TSC-OPF problem with respect to its dimensionality, this paper proposes a decomposition of the power system model in a two-time scale model which is constituted by two smaller-order subsystems denoted by the fast and slow subsystems, where only the equations of the fast subsystem are transformed in algebraic equations by means of the implicit trapezoidal technique and incorporated in the TSC-OPF formulation. The TSC-OPF is then solved by considering in its formulation the lowest amount of time steps in post-fault period that guarantee the rotor angle first swing (FS) stability of the fast subsystem, and this aspect also contributes for reducing the dimensionality of the TSC-OPF problem. Tests were made for a 31-bus distribution network with two synchronous generators and for a 51-bus distribution network with nine synchronous generators.

Self‐adaptive differential approach for transient stability constrained optimal power flow

A new transient stability-constrained optimal power flow (TSCOPF) model for power system optimal operations is presented in this study. The proposed model is a non-linear, non-convex, discrete, and non-differentiable optimisation problem, and very difficult to be solved by classic programming algorithms. In this study, an effective optimisation framework is developed to address the TSCOPF problem. The self-adaptive differential evolution (SaDE) algorithm is employed in the framework, which can effectively eliminate the needs for the strategy selection process and at the same time improve the robustness of the DE search process. The benchmark New England 10-generator, 39-bus system is used to verify the efficacy of this algorithm. The simulation result obtained using SaDE is compared with both conventional mathematical method and the recently published heuristic methods for OPF problems. The simulation results reveal that the SaDE optimisation technique outperforms other algorithms in both terms of robustness and solution quality.

Transient stability constrained optimal power flow using oppositional krill herd algorithm

Transient stability constrained optimal power flow (TSCOPF) is becoming an effective tool for many problems in power systems since it simultaneously considers economy and dynamic stability of system operations. It is increasingly important because modern power systems tend to operate closer to the stability boundaries due to the rapid increase of electricity demand and the deregulation in power sector. TSCOPF is, however, a nonlinear optimization problem with both algebraic and differential equations which is difficult to solve even for small power network. In order to solve the TSCOPF problem efficiently, a relatively new optimization technique, named as krill herd algorithm (KHA), is employed in this paper. KHA simulates the herding behavior of krill swarms in response to specific biological and environmental processes to solve multi-dimensional, linear and nonlinear problems with appreciable efficiency. To accelerate the convergence speed and to improve the simulation results, opposition based learning (OBL) is also incorporated in the basic KHA method. The simulation results, obtained by the basic KHA method and the proposed oppositional KHA (OKHA) algorithm, are compared to those obtained by using some other recently developed methods available in the literature. In this paper, case studies conducted on 10 generator New England 39-bus system and 17 generator 162-bus system indicate that the proposed OKHA approach is much more, computationally, efficient than the other reported popular state-of-the-art algorithms including the basic KHA and the proposed method is found to be a promising tool to solve the TSCOPF problem of power systems.

A two stage model for rotor angle transient stability constrained optimal power flow

Abstract Transient stability constrained optimal power flow (TSCOPF) is a nonlinear optimization problem with both algebraic and differential equations. This paper utilizes the Imperialist Competitive Algorithm (ICA) as an evolutionary optimization algorithm and Artificial Neural Network (ANN) to develop a robust and efficient two stages scheme to solve TSCOPF problem. In the first stage an Artificial Neural Network is constructed to predict the rotor-angle transient stability margin, and is then incorporated in the TSC-OPF as the transient stability estimator. To solve the proposed TSC-OPF problem the ICA is used as the optimizer. The performance of the proposed method is verified over the WSCC three-machine, nine-bus system under different loading conditions and fault scenarios.

Transient Stability Constrained Optimal Power Flow Using Teaching Learning Based Optimization

Transient stability constrained optimal power flow (TSC-OPF) is a non-linear optimization problem which is not easy to deal directly because of its huge dimension. In order to solve the TSC-OPF problem efficiently, a relatively new optimization technique named teaching learning based optimization (TLBO) is proposed in this paper. TLBO algorithm simulates the teaching–learning phenomenon of a classroom to solve multi-dimensional, linear and nonlinear problems with appreciable efficiency. Like other nature-inspired algorithms, TLBO is also a population-based method and uses a population of solutions to proceed to the global solution. The authors have explained in detail, the basic philosophy of this method. In this paper, the authors deal with the comparison of other optimization problems with TLBO in solving TSC-OPF problem. Case studies on IEEE 30-bus system WSCC 3-generator, 9-bus system and New England 10-generator, 39-bus system indicate that the proposed TLBO approach is much more computationally efficient than the other popular methods and is promising to solve TSC-OPF problem.

Transient Stability Constrained Optimal Power Flow Using Teaching Learning-Based Optimization

Transient stability constrained optimal power flow (TSC-OPF) is a non-linear optimization problem which is not easy to deal directly because of its huge dimension. In order to solve the TSC-OPF problem efficiently, a relatively new optimization technique named teaching learning based optimization (TLBO) is proposed in this paper. TLBO algorithm simulates the teaching–learning phenomenon of a classroom to solve multi-dimensional, linear and nonlinear problems with appreciable efficiency. Like other nature-inspired algorithms, TLBO is also a population-based method and uses a population of solutions to proceed to the global solution. The authors have explained in detail, the basic philosophy of this method. In this paper, the authors deal with the comparison of other optimization problems with TLBO in solving TSC-OPF problem. Case studies on IEEE 30-bus system WSCC 3-generator, 9-bus system and New England 10-generator, 39-bus system indicate that the proposed TLBO approach is much more computationally efficient than the other popular methods and is promising to solve TSC-OPF problem.

Fast approach for transient stability constrained optimal power flow based on dynamic reduction method

The main challenge to solve the transient stability constrained optimal power flow (TSC-OPF) problem is its huge dimension due to numerous discretised transient variables and constraints. This problem becomes more serious when large power systems are considered. This study presents a fast approach to realise a global TSC-OPF based on dynamic reduction method, which decomposes the power system into several coherent areas and represents the original system by a reduced equivalent system. In this approach, the single transient stability constraint is obtained by simulating the reduced system instead of the full system. The new approach reduces the simulation execution time and thus increases the efficiency of the TSC-OPF. Two case studies indicate that the proposed approach can remarkably reduce the CPU time of the TSC-OPF procedure, compared with the TSC-OPF based on the full-system simulation. The new approach is very practical in solving the TSC-OPF problem in large power systems where numerous machines are coherent.

Contingency filtering technique for transient stability constrained optimal power flow

Transient stability constrained optimal power flow (TSCOPF) is an important and difficult problem. When multiple contingencies are considered, a reliable contingency filtering technique should be used to reduce the scale of TSCOPF problem. This study brings in the concepts of active contingency and critical contingency, and develops a novel contingency filtering strategy. Based on time-domain numerical simulations, the proposed contingency filtering strategy first screens all the considered contingencies and identifies active contingencies whose severe indices violate the pre-defined threshold of transient stability, then further finds out the critical contingencies in which some generators are most severely disturbed according to the severe indices trajectories. The severe indices can be such as maximal relative rotor angles, maximal transient generator voltage dips and so on. Taking only the critical contingencies into account, the scale of TSCOPF problem is reduced significantly. Interior point method is used to solve the reduced TSCOPF problem. Numerical results on several cases indicate that the proposed contingency filtering technique is reliable and efficient. Compared with the conventional TSCOPF approach, which involves all the contingencies, the proposed contingency filtering strategy possesses overwhelming advantages in CPU time and memory consumption, and is hopeful to solve TSCOPF problems with many contingencies.

A novel margin sensitivity based method for transient stability constrained optimal power flow

Transient stability constrained optimal power flow (TSCOPF) is still a difficult but important problem in power system planning and operation. In this paper, the challenging TSCOPF problem is divided into optimal power flow (OPF) and stability analysis processes, and solved iteratively by the interior point method (IPM). The novelty of the proposed approach is that the transient stability constraints for each contingency are incorporated into the OPF model as a single stability constraint derived from the minimum kinetic energy for normal unstable case or the minimum accelerating power distance for extreme unstable case using the time domain simulation based single machine equivalent (SIME) method. The proposed constraint is robust and scalable for large power systems as well as applicable to multi-swing unstable, normal unstable and extreme unstable cases. In addition, this stability constraint is further refined to overcome the issue of over-stabilization by guiding the solution gradually across the stability boundary. As a whole, a complete solution method capable to solve multi-contingency TSCOPF problems is presented in this paper. The effectiveness and computation performance of the proposed approach have been fully studied and extensively validated using the New England 10-generator system and the IEEE 50-generator 145-bus system.

An improved micro-particle swarm optimization algorithm and its application in transient stability constrained optimal power flow

SUMMARY In this paper, an improved micro-particle swarm optimization (μPSO) algorithm is proposed and applied to the development of a computational method for solving Transient Stability Constrained Optimal Power Flow (TSCOPF) problem. The improvement includes two novel intelligent strategies: the dynamic space adjustment and the selective re-initialization. The first strategy is designed to accelerate the convergence speed by confining the search in a reduced space, while the second strategy is to reduce the possible overabundance by re-initializing the particles only in a non-overlapping space. The simulation results demonstrate the superiority of the improved μPSO algorithm over both the original μPSO algorithm and the standard PSO algorithm. The proposed method is validated through case studies for solving TSCOPF problems on IEEE 39-bus system and IEEE 162-bus system. The results show that the algorithm can utilize a small population to obtain an equally good or better optimization outcomes compared to those of the original μPSO algorithm and the standard PSO algorithm. Copyright © 2012 John Wiley & Sons, Ltd.

A Two-Level Parallel Decomposition Approach for Transient Stability Constrained Optimal Power Flow

Transient stability constrained optimal power flow (TSCOPF) is able to reduce costs while keeping the operation point away from the stability boundary. While especially useful in modern power system operations, TSCOPF problems are practically very hard to solve; unacceptable computational time is considered to be one of the largest barriers in applying TSCOPF-based solutions. Based on the reduced-space interior point method (RIPM)-which takes advantage of the relatively few degrees of freedom and shows promising potential for solving large-scale TSCOPF problems-this paper introduces a parallel RIPM algorithm with high computing efficiency for multi-contingency TSCOPF problems. A two-level parallelism is developed to fully utilize the computing power of a Beowulf cluster equipped with multi-core CPUs. First, several compute-intensive steps of the TSCOPF algorithm are decomposed according to different contingencies with mathematical equivalent transformations, the corresponding computing tasks are assigned, stored, and processed on different nodes. Second, the distributed computing task is accelerated using elemental decomposition on Jacobian matrices, and then high performance multithreaded mathematical libraries are employed to fully exploit the multi-core CPUs on each node. The effectiveness of the proposed parallel algorithm is benchmarked on a Beowulf cluster with 16 computing nodes with 128 CPU cores using a series of test cases including up to 2746 buses and 16 contingencies. The results of the case studies indicate that the proposed parallel decomposition approach inherits the optimal solution and convergence properties of the original serial interior point method (IPM) approach and shows great capacity in accelerating TSCOPF solution.

Application of Differential Evolution Algorithm for Transient Stability Constrained Optimal Power Flow

Consideration of transient stability constraints in optimal power flow (OPF) problems is increasingly important because modern power systems tend to operate closer to stability boundaries due to the rapid increase of electricity demand and the deregulation of electricity markets. Transient stability constrained OPF (TSCOPF) is however a nonlinear optimization problem with both algebraic and differential equations, which is difficult to be solved even for small power systems. This paper develops a robust and efficient method for solving TSCOPF problems based on differential evolution (DE), which is a new branch of evolutionary algorithms with strong ability in searching global optimal solutions of highly nonlinear and nonconvex problems. Due to the flexible properties of DE mechanism, the hybrid method for transient stability assessment, which combines time-domain simulation and transient energy function method, can be employed in DE so that the detailed dynamic models of the system can be incorporated. To reduce the computational burden, several strategies are proposed for the initialization, assessment and selection of solution individuals in evolution process of DE. Numerical tests on the WSCC three-generator, nine-bus system and New England ten-generator, 39-bus system have demonstrated the robustness and effectiveness of the proposed approach. Finally, in order to deal with the large-scale system and speed up the computation, DE is parallelized and implemented on a Beowulf PC-cluster. The effectiveness of the parallel DE approach is demonstrated by simulations on the 17-generator, 162-bus system.

Transient stability constrained optimal power flow using particle swarm optimisation

A novel approach based on the particle swarm optimisation (PSO) technique is proposed for the transient-stability constrained optimal power flow (TSCOPF) problem. Optimal power flow (OPF) with transient-stability constraints considered is formulated as an extended OPF with additional rotor angle inequality constraints. For this nonlinear optimisation problem, the objective function is defined as minimising the total fuel cost of the system. The proposed PSO-based approach is demonstrated and compared with conventional OPF as well as a genetic algorithm based counterpart on the IEEE 30-bus system. Furthermore, the effectiveness of the PSO-based TSCOPF in handling multiple contingencies is illustrated using the New England 39-bus system. Test results show that the proposed approach is capable of obtaining higher quality solutions efficiently in the TSCOPF problem.