Optimal load shedding to prevent voltage instability based on multi-objective optimization using modal analysis and PSO

In this paper, a hybrid method is proposed for reducing the amount of load shedding and voltage collapse. The hybrid method is the combination of particle swarm optimisation (PSO) algorithm and artificial bee colony (ABC) algorithm. Both algorithms equally contribute in the paper to determine the optimal load shed values for improving the voltage stability of the power system. Here, PSO is used to determine the weak buses in the system whereas ABC computes the optimal amount of load shed value to be cut for voltage stability purpose. They work on different fitness functions as per the requirements of their purpose. The appropriate buses for load shedding are selected based on the sensitivity of minimum eigenvalue of load flow Jacobian with respect to the load shed. The proposed method based on PSO and ABC is implemented in MATLAB working platform and its performance is tested with six bus and IEEE 14 bus bench mark test systems. From the simulations, the performance of the proposed method is analysed and compared with various techniques in terms of sensitivity of minimum eigenvalues, voltage profile and load power. Through comparison performance, it is showed that the proposed method ensures voltage stability with minimum load shedding.

A novel approach to find optimal real power generation pattern will be introduced in this study. This has been achieved by maximizing the power system voltage stability margin and minimizing generation cost. The loadability limit index is used to assess static voltage stability security margin. Based on proposed algorithm, a Toolbox has been developed to recognize the loadability limit by using Lagrangian method. The mentioned problem has been modeled as a non-linear and multi objective optimization problem along with Hybrid Genetic Algorithm Particle Swarm Optimization (HGAPSO) method to reach the optimal generation pattern. The method has been performed as a hierarchical optimization problem. In the first stage, HGAPSO method has been used to reach the securest pattern of real power. Also, mentioned voltage stability toolbox has been executed to evaluate the voltage stability margin respectively each real power generation pattern during HGAPSO search. These simulations are performed on IEEE 30 bus test system. To validation of proposed method, obtained results have been compared with Particle Swarm Optimization (PSO) results.

In this study, an efficient approach is proposed to find best real power generation participation for improving static voltage stability and reducing total generation cost. Therefore, loadability limit index is used to assess static voltage stability security margin, which is associated to the point of voltage collapse. Based on it, a toolbox is developed to recognize the loadability margin by using Lagrangian method. Finally, the mentioned problem is modeled as a non-linear and multiobjective optimization problem. In this paper, Hybrid Genetic Algorithm Particle Swarm Optimization (HGAPSO) and Particle Swarm Optimization (PSO) algorithms are applied to find out best generation direction. This problem is performed as a hierarchical optimization problem. In first stage, an algorithm is used to search possible solution area and reach tradeoff between secure and economic direction of real power generations. In second stage of proposed approach, respectively to each generation pattern, power system voltage stability margin and generation cost are evaluated during search algorithm. The simulations are performed on IEEE 14 and IEEE 30 bus test systems to find best generation direction.

Preventive and corrective control applications in power systems via Big Bang–Big Crunch optimization

In a real life situation, due to the complexity of the industrial systems and non-linearity of their behavior, it is very difficult to achieve optimum performance of system for desired industrial goals using uncertain, vague and imprecise data. Herein, an approach has been proposed through which the behavior of the system is analyzed in the form of well- known six reliability indices by using triangular fuzzy numbers which allow the consideration of expert opinions, linguistic variables, operating conditions in reliability information. Using their behavior analysis a fuzzy multi-objective optimization problem (FMOOP) has been formulated. Due to the conflicting nature of the multiple objectives, the decision making is difficult and it leads to the Pareto optimal solutions instead of single optimal solutions. Many evolutionary algorithms (EAs) already exist in the literature for solving a multi-objective optimization problem (MOOP), and are termed as multi-objective evolutionary algorithms (MOEAs). Particle swarm optimization (PSO) is one of such MOEA which demonstrates the ability to identity a Pareto-optimal front efficiently. Here, a crisp optimization problem is reformulated from FMOOP by taking into account the preference of decision maker (DM) and then PSO is applied to solve the resulting fuzzified MOOP. The presented approach is applied in order to solve the multi-objective series-parallel system reliability optimization problem for a crystallization unit of a urea plant.

To enhance the operational security of a multi-energy microgrid (MEMG) under contingency events, this paper proposes a new method to robustly coordinate preventive control (PC) and corrective control (CC) actions with multiple demand response (DR) participation. Firstly, a coordination framework is designed for pre-contingency and emergency DR of multi-energy loads and other PC and CC measures across day-ahead, intra-day normal and contingency stages. Then, a robust optimization (RO) model is formulated to determine the optimal coordination between those PC and CC actions under uncertainties, while minimizing the security control costs. To better characterize the effect of the thermal carrier in multi-energy coupling and supply changes during failures, an energy flow-based thermal network model with association matrix modification is proposed. For space heating loads with thermal inertia, temperature regulation is employed in pre-contingency DR considering consumer comfort. Further, a ladder-type emergency load control model is developed to exploit the response potential of incentive-based DR and load shedding. Finally, a contingency screening method and a column-and-constraint generation-embedded sequential contingency augmentation (CCG-SCA) solution algorithm are designed. The effectiveness and robustness of the proposed method are verified on a MEMG system with 33 electric buses and 24 thermal nodes.

Voltage instability and voltage collapse have been considered as a major threat to present power system networks due to their stressed operation. It is very important to do the power system analysis with respect to voltage stability. Flexible AC Transmission System (FACTS) is an alternating current transmission system incorporating power electronic-based and other static controllers to enhance controllability and increase power transfer capability. A FACTS device in a power system improves the voltage stability, reduces the power loss and also improves the load ability of the system. FACTS have made the power systems operation more flexible and secure. Amongst the several FACTS controllers, the Unified Power Flow Controller (UPFC) is most effective to improve the enhancement of voltage stability and reduces the power loss. This study investigates the application of Particle Swarm Optimization (PSO) to find sizing of Unified Power Flow Controller (UPFC) device to minimize the voltage stability index, total power loss, load voltage deviation, and cost of FACTS devices to improve voltage stability in the power system. A new model is proposed in this thesis to improve existing power-based model by using the Norton Equivalent Theorem. The proposed model can be integrated with the Equivalent Current Injection (ECI) power flow model easily. By ECI algorithm, it is much quickly and precisely to implement power flow calculations. Finally It is observed from the results that the voltage stability margin is improved, the voltage profile of the power system is increased and real power losses also reduced by optimally sizing UPFC device in the power system. Index Terms: Voltage stability, Unified Power Flow Controller (UPFC), Equivalent -Current Injection (ECI), Modified particle swarm optimization (MPSO)

A reactive power planning method based on improved particle swarm optimization (IPSO) is presented. This method can improve the quality of initial particles and eliminate the boundary oscillation in traditional particle swarm optimization. The voltage stability margin index (VSI) is used to rank the load buses. Then reactive power compensators are installed on the buses with weak voltage stability. The maximization of voltage stability margin is included in the objective function of reactive power planning to improve system voltage stability. Its application in IEEE 30‐bus system illustrates that the real power loss is depressed with voltage stability margins increased simultaneously. Copyright © 2009 John Wiley & Sons, Ltd.

Enhanced Genetic Algorithm based computation technique for multi-objective Optimal Power Flow solution

Voltage stability is an important issue in power system operation. Flexible AC transmission systems, so-called FACTS devices, help to improve voltage stability and minimize real power losses. The effectiveness of FACTS devices depend on their proper location and rating. This paper presents a method, based on line flow sensitivity factors such as bus voltage stability index and line voltage stability index, to find suitable locations of multi-type FACTS devices. Also this paper proposes an application of particle swarm optimization (PSO) and harmony search algorithm (HSA) in optimizing the rating of FACTS devices. The proposed approaches are evaluated with three different objective functions namely, minimization of real power loss, improvement of voltage profile and enhancement of voltage stability. The performance of proposed methods is analyzed on IEEE 14 bus system by implementing FACTS devices such as static var compensator (SVC), thyristor controlled series capacitor (TCSC) and unified power flow controller (UPFC).The analysis shows that there is a reduction in real power loss and improvement in voltage stability and voltage profile of the system after employing FACTS devices. It also shows that both real power loss and bus voltage stability index (BVSI) have been reduced more with FACTS ratings obtained from PSO than with that from HSA.

The goal of the multi-objective optimization algorithm is to quickly and accurately find a set of trade-off solutions. This paper develops a clustering-based competitive multi-objective particle swarm optimizer using the enhanced grid for solving multi-objective optimization problems, named EGC-CMOPSO. The enhanced grid mechanism involved in EGC-CMOPSO is designed to locate superior Pareto optimal solutions. Subsequently, a hierarchical-based clustering is established on the grid for improving the accuracy rate of the grid selection. Due to the adaptive division of clustering centers, EGC-CMOPSO is applicable for solving MOPs with various Pareto front (PF) shapes. Particularly, the inferior solutions are discarded and the leading particles are identified by the comprehensive ranking of particles in each cluster. Finally, the selected leading particles compete against each other, and the winner guides the update of the current particle. The proposed EGC-CMOPSO and the eight latest multi-objective optimization algorithms are performed on 21 test problems. The experimental results validate that the proposed EGC-CMOPSO is capable of handling multi-objective optimization problems (MOPs) and obtaining superior performance on both convergence and diversity.

The multi-objective portfolio optimization is regarded as an multi-objective optimization problem which is complicated and hard to find a satisfactory solution in a limited time. It is more complex and difficult to use the conventional method to solve this problem. In this paper, we first establish a mean-CVaR-entropy model with transaction costs and investment weight restrictions, and then propose a Multi-objective Optimization Algorithm for BeetleSearch(MOBSO), a meta-heuristic optimization algorithm, and a variant of Beetle Antennae Search (BAS) algorithm, which is applied into portfolio optimization to solve this constraint multi-objective optimization problem. Finally, we use the 20 stocksfrom January 2017 to December 2021 in the US stock market to do case studyand compare the results with other meta-heuristic optimization algorithms. It shows that the MOBSO outperforms swarm algorithms such as the particle swarm optimization (PSO) and the genetic algorithm(GA). KeywordsMulti-objective portfolio optimizationBeetle Antennae Search (BAS)Particle Swarm Optimization (PSO)Meta-heuristic optimizationFinance problem

A multi-objective particle swarm optimization (MOPSO) approach for multi-objective economic load dispatch problem in power system is presented in this paper. The economic load dispatch problem is a non-linear constrained multi-objective optimization problem. The proposed MOPSO approach handles the problem as a multi-objective problem with competing and non-commensurable fuel cost, emission and system loss objectives and has a diversity-preserving mechanism using an external memory (call “repository”) and a geographically-based approach to find widely different Pareto-optimal solutions. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed MOPSO approach were carried out on the standard IEEE 30-bus test system. The results revealed the capabilities of the proposed MOPSO approach to generate well-distributed Pareto-optimal non-dominated solutions of multi-objective economic load dispatch. Comparison with Multi-objective Evolutionary Algorithm (MOEA) showed the superiority of the proposed MOPSO approach and confirmed its potential for solving multi-objective economic load dispatch.

In this paper, a new technique based on particle swarm optimization (PSO) is proposed to incorporate voltage stability limits into traditional optimal power flow (OPF) formulations. Two objective functions such as fuel cost and voltage stability margin (loadability) are considered to be optimized. In proposed method systempsilas maximum loading margin (loadability) is calculated by continuation power flow (CPF). Particle swarm optimization (PSO) is employed to solve the proposed multi-objective OPF problem. The proposed method allows system operators in order to control the desired level of system security via adjusting the weighting factors of the different objective functions directly. Simulation results for the IEEE 30-bus test system demonstrate the effectiveness of the PSO in solving multi-objective OPF problems.

Particle swarm optimization (PSO) and differential evolution (DE) are meta-heuristics which have been found to be successful in a wide variety of optimization tasks. The high speed of convergence and the relative simplicity of PSO make it a highly viable candidate to be used in multi-objective optimization problems (MOPs). Therefore, several PSO approaches capable to handle MOPs (MOPSOs) have appeared in the past. There are some problems, however, where PSO-based algorithms have shown a premature convergence. On the other hand, multi- objective DEs (MODE) have shown lower speed of convergence than MOPSOs but they have been successfully used in problems where MOPSO have mistakenly converged. In this work, we have developed experiments to observe the convergence behavior, the online convergence, and the diversity of solutions of both meta-heuristics in order to have a better understanding about how particles and solutions move in the search space. To this end, MOPSO and MODE algorithms under (to our best effort) similar conditions were used. Moreover, the ZDT test suite was used on all experiments since it allows to observe Pareto fronts in two-dimensional scatter plots (more details on this are presented on the experiments section). Based on the observations found, modifications to two PSO-based algorithms from the state of the art were proposed resulting in a rise on their performance. It is concluded that MOPSO presents a poor distributed scheme that leads to a more aggressive search. This aggressiveness showed to be detrimental for the selected problems. On the other hand, MODE seemed to generate better distributed points on both decision and objective space allowing it to produce better results.