Improving power system damping using a combination of optimal control theory and differential evolution algorithm

Discrete-time optimal control problems with time delay argument: New discrete-time Euler-Lagrange equations with delay

Discrete-time optimal control problems are a crucial type of control problems that deal with a dynamic system evolving in discrete time-steps. This paper introduces a new technique for solving linear discrete-time optimal control problems with state delays, applicable to both finite and infinite time horizons. Our method employs a Riccati matrix equation, optimizing control strategies and ensuring system stability through bounded control inputs. We adopt a Bolza problem for the performance index, which guides the classification of control issues. The technique simplifies problems into manageable Riccati matrix equations using the Euler-Lagrange equations and Pontryagin maximum principle, ensuring stability and necessary condition compliance. The paper validates the approach with numerical examples from quantum mechanics and classical physics, demonstrating its practicality and potential for broader application.

Improved chaotic Bat algorithm for optimal coordinated tuning of power system stabilizers for multimachine power system

Power systems exhibit nonlinearity. causing dynamic instability and complex power oscillations. This research proposes an innovative strategy using the Novel Bat Algorithm (NBA) to achieve ideal Power System Stabilizers (PSSs) in a multimachine power system. The approach shifts electromechanical modes to specific areas in the s-plane. Enhancing the multi-machine power system and establishing stabilizer parameters for dynamic performance. The study examines the designed approach aptitude for standard lead-lag PSSs configurations. In order to elevate the global search problem and transfer some static operators for the optimum optimization process. the chaos mapping. also known as CNBA. is introduced into NBA. Four different forms of chaos maps are compared in experiments to resolve unconstrained mathematical issues in order to illustrate CNBA performance. In any other case. the challenge of designing PSS under a wide range of loading situations is transformed into an optimization challenge with the damping ratio of electromechanical modes with low damping as the target function. The optimal stabilizers' gains are gotten by employing the CNBA algorithm. Second plan. an effective technique is astutely established to delineate the PSS location and quantity using CNBA and another side using participation factor. To examine the efficacy of the proposed CNBA-based PSS on a large system; it is tested on the interconnected of New-England/New-York (16 generators and 68 buses) power grid. and verified by comparative study with NBA through eigenvalue analysis and nonlinear simulation to provide evidence the algorithmic competence of CNBA. The CNBA approach yields a minimum damping ratio of 37%. which is consistent with the its eigenvalue. In contrast, the NBA approach achieves a minimum damping ratio of 31%. The simulation results reveal the fine performance of the proposed CNBA-PSS in a convincing manner and its capacity to provide an excellent damping for inter-area and local oscillations under diverse operating cases compared to NBA-PSS then in the case of PSS location.

Linear quadratic regulator design via metaheuristics applied to the damping of low-frequency oscillations in power systems

This paper proposes the application of control by state feedback using the linear quadratic regulator (LQR) optimized by metaheuristics to damp low-frequency electromechanical oscillations in electrical power systems. The current sensitivity model was used to represent the single machine infinite bus (SMIB) system in the time domain. The weighting matrices of the LQR were adjusted using four different algorithms: (i) the genetic algorithm, (ii) the differential evolution algorithm, (iii) the particle swarm optimization algorithm, and (iv) the gray wolf optimization (GWO) algorithm. In the cases considered, disturbances were applied to the electrical power system and, then, performances comparisons associated with each metaheuristic were statistically analyzed, in which the number of iterations, error, and time to achieve convergence of each algorithm were compared. From the results, it was possible to conclude that the algorithms were efficient in adjusting the weighting matrices of the LQR, providing additional damping to the poles of interest of the system. It was also possible to conclude that the GWO algorithm presented the best performance, accrediting it as a powerful tool in the study of small-signal stability for the analyzed case.

Controller optimization using data-driven constrained bat algorithm with gradient-based depth-first search strategy

The meta-heuristic algorithms have aroused great attention for controller optimization. However, most of them are inseparable from the explicit system models when addressing a constrained optimization problem (COP). In this paper, we propose a data-driven constrained bat algorithm via a gradient-based depth-first search (GDFS) strategy. In the proposed scheme, the GDFS strategy can predetermine a search space that satisfies some strict constraints (e.g., stability requirements) of the optimized system. Meanwhile, an improved boundary constraint handling method is proposed to limit the exploration process to the predetermined space. In this way, the proposed algorithm can solve the COP by utilizing experimental data from real scenes, thereby relieving the dependence on precisely modeling the complex system. Together with an ɛ-constraint-handling method, the bat algorithm is employed to seek the global optimum of the COP. The search performance is enhanced by the designed linear-varying elite layer-based local search and a social learning-based walk mechanism to dynamically balance exploration and exploitation. The convergence is ensured based on the criteria of the stochastic optimization algorithm. Experimental results on a servo drive system and benchmark test functions verify the effectiveness of the proposed algorithm.

Optimal damping for generalized unified power flow controller equipped single machine infinite bus system for addressing low frequency oscillation

Low frequency oscillation (LFO) is one of the major concerns for reliable operation of the power system. This LFO occurs due to the failure of the rotor to supply sufficient damping torque to compensate the imbalance between mechanical input and electrical output. Hence, in this paper, we adopt a third generation flexible AC transmission system (FACTS) device named generalized unified power flow controller (GUPFC) based damping controller in order to investigate its effect for mitigating LFO for an single machine infinite bus (SMIB) system. To find an effective damping controller-optimizer pair, we integrate proportional-integral (PI) or lead-lag as a controller and grey wolf optimizer (GWO), differential evolution (DE), particle swarm optimization (PSO), whale optimization algorithm (WOA), and chaotic whale optimization algorithm (CWOA) as an optimizer. Later, we investigate the performances for the above mentioned controller-optimizer pairs through time domain simulation, eigenvalue analysis, nyquist stability test, and quantitative analysis. Moreover, we carry out two non-parametric statistical tests named as one sample Kolmogorov-Smirnov (KS) test and paired sample t-test to identify statistical distribution as well as uniqueness of our optimization algorithms. Our analyses reveal that the GWO tuned lead-lag controller surpasses all other controller-optimizer combinations.

Comparing strategies to damp electromechanical oscillations through STATCOM with multi-band controller

This paper aims to compare two strategies for damping low-frequency electromechanical oscillations in multi-machine power systems through Static Synchronous Compensators (STATCOM) with a multi-band controller. STATCOM is represented by a controllable voltage source behind an impedance and the multi-band controller acts as a power oscillation damper that modulates parameters of the voltage source in the transient period. In the first strategy, the multi-band controller acts on the voltage-control loop through the voltage modulation. In the second one, the controller acts on the real power-control loop to modulate the phase angle of the voltage source. The coordinated design of multi-band controllers and power systems stabilizers is performed through an optimization approach taking into account several operation conditions.

Application of Neuro-Fuzzy Controller to Replace SMIB and Interconnected Multi-Machine Power System Stabilizers

In this research, an effective application and performance assessment of the Neuro-Fuzzy Controller (NFC) damping controller is designed to replace a single machine infinite bus (SMIB) power system stabilizer (PSS), and coordinated multi PSSs in large interconnected power systems are presented. The limitation of the conventional PSSs on SMIB and interconnected multi-machine test power systems are exposed and disclosed by the proposed NFC stabilizer. The NFC is a nonlinear robust controller which does not require a mathematical model of the test power system to be controlled, unlike the conventional PSSs’ damping controller. The Proposed NFC is designed to improve the stability of SMIB, an interconnected IEEE 3-machine, 9-bus power system, and an interconnected two-area 10-machine system of 39-bus New England IEEE test power system under multiple operating conditions. The proposed NFC damping controller performance is compared with the conventional PSS damping controller to confirm the capability of the proposed stabilizer and realize an improved system stability enhancement. The conventional PSSs’ design problem is transformed into an optimization problem where an eigenvalue-based objective function is developed and applied to design the SMIB-PSS and the interconnected multi-machine PSSs. The time-domain phasor simulation was done in the SIMULINK domain, and the simulation results show that the transient responses of the system rise time, settling time, peak time, and peak magnitude were all impressively improved by an acceptable amount for all the test system with the proposed NFC stabilizer. Thus, the NFC was able to effectively control the LFOs and produce an enhanced performance compared to the conventional PSS damping controller. Similarly, the result validates the effectiveness of the proposed NFC damping controller for LFO control, which demonstrates more robustness and efficiency than the classical PSS damping controller. Therefore, the application and performance of the NFC has appeared as a promising method and can be considered as a remarkable method for the optimal design damping stabilizer for small and large power systems.

Evolutionary extreme learning machine with sparse cost matrix for imbalanced learning

Extreme learning machine is a popular machine learning technique for single hidden layer feed-forward neural network. However, due to the assumption of equal misclassification cost, the conventional extreme learning machine fails to properly learn the characteristics of the data with skewed category distribution. In this paper, to enhance the representation of few-shot cases, we break down that assumption by assigning penalty factors to different classes, and minimizing the cumulative classification cost. To this end, a case-weighting extreme learning machine is developed on a sparse cost matrix with a diagonal form. To be more actionable, we formulate a multi-objective optimization with respect to penalty factors, and optimize this problem using an evolutionary algorithm combined with an error bound model. By doing so, this proposed method is developed into an adaptive cost-sensitive learning, which is guided by the relation between the generalization ability and the case-weighting factors. In a broad experimental study, our method achieves competitive results on benchmark and real-world datasets for software bug reports identification.