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Comparative Analysis of Power System Model Reduction
Abstract
This paper presents the modal truncation and singular value decomposition (SVD) technique as two main algorithms for dynamic model reduction of the power system. The significance and accuracy of the proposed methods are investigated with their detailed formulation derived for a constrained linear system. The full linearized model of the original nonlinear system is determined and used as the input of the dynamic reduction technique. Therefore, the variables of a synchronous machine in a multi-machine system is studied and replaced with a much simpler dynamic model. This equivalent dynamic model should behave similarly to what is observed from the system under study. The capability of each technique in keeping dominant oscillation modes after dynamic reduction is utilized as the comparison criteria. The reduction techniques are simulated over the dynamic 39-bus New England test system for validation.
... The Imperialistic Competitive Algorithm (ICA) is used in [27] as a singleobjective optimization to minimize losses in the system. The Plant Growth Simulation Algorithm (PGSA) has been used in [28][29][30] to determine the unit capacity and the loss sensitivity factor in choosing optimal DG location. Firefly Algorithm (FA) is used in [21,31] to optimize singleobjective DGs with the goal of reducing power losses. ...
The use of renewable solar and wind resources as distributed generation sources in distribution networks has been welcomed by network operators. In order to exploit the maximum benefits of using these distributed products, the location of installation and their capacity should be determined optimally in the distribution network. In this paper, in order to optimize the placement of solar panels and wind turbines in the distribution network with the aim of reducing losses and improving reliability based on Energy Not Supplied subscribers (ENS), a multi-objective evolutionary algorithm based on fuzzy decision method, called the Multi-Objective Hybrid Training Learning Based Optimization-Grey Wolf Optimizer (MOHTLBOGWO) proposed that has a High optimization speed and not trapped at all in the optimal local. At first, the candidate buses are set for the installation of renewable resources using the Loss Sensitivity Factor (LSF). Then the proposed method is used to determine the location and optimal capacity of renewable resources through the candidate bases. Proposed issues have been implemented in a single-objective and multi-objective manner on a 33 bus IEEE radial distribution network. Also, in this paper, the effect of distributing renewable resources on the characteristics of the distribution network is evaluated. The results obtained from the proposed algorithm are compared with the results of other algorithms to demonstrate the superiority of the proposed method in reducing losses, improving reliability, and increasing the financial profit of the network. Simulation results show the better performance of the proposed method in comparison with Teaching–Learning Based Optimization (TLBO) and Grey Wolf Optimiser (GWO) methods and past studies to achieve optimal results. Also, the results show that distributing of the capacity and location of distributed renewable generation leads to a further reduction in losses and a better improvement of the reliability criterion.
In this study, the problem of fault zone detection of distance relaying in FACTS-based transmission lines is analyzed. Existence of FACTS devices on the transmission line, when they are included in the fault zone, from the distance relay point of view, causes different problems in determining the exact location of the fault by changing the impedance seen by the relay. The extent of these changes depends on the parameters that have been set in FACTS devices. To solve the problem associated with these compensators, two instruments for separation and analysis of three-line currents, from the relay point of view at fault instance, have been utilized. The wavelet transform was used to separate the high-frequency components of the three-line currents, and the support vector machine (using methods for multi-class usage) was used for classification of fault location into three protection regions of distance relay. Besides, to investigate the effects of TCSC location on fault zone detection of distance relay, two places, one in fifty percent of line length and the other in seventy-five percent of line length, have been considered as two scenarios for confirmation of the proposed method. Simulations indicate that this method is effective in the protection of FACTS-based transmission lines.
The productions quality has become one of the essential issues in the modern manufacturing industry and several techniques have introduced for control and monitoring the production process. Control charts are the most practical and popular tools for continuously monitoring and, if required, make adjustments to the product or process. A new automatic method based on deep learning and optimization algorithms for nine control chart patterns (CCPs) recognition are proposed in this paper. This method has two principal parts: the classification part and the tuning part. In the last few years, a convolutional neural network (ConvNet) has led to an excellent performance on various tasks, like image processing, speech recognition, and signal processing. Therefore, in the classification part, ConvNet is used as the intelligent classifier for CCPs recognition. One significant difficulty of ConvNet is that it requires considerable proficiency to select suitable parameters like a number of kernels and their spatial sizes, learning rate, etc. The ConvNet parameters have domestic dependencies which make the tuning of these parameters a challenging task. According to these issues, in the tuning part of the proposed method, the Harris hawks optimization (HHO) algorithm is used for optimal tuning of ConvNet parameters. Contrasting the common CCPs recognition methods, the proposed method takes unprocessed data and passes to more than one hidden layer for extracting the optimal feature representation instead of relying on any feature engineering mechanisms. The quantitative and simulation results show the superiority of the proposed method over the previous techniques in terms of its performance.
This article describes the model development and preliminary progress of an ongoing research study on the effects of nonlinearities in ocean wave input and power-takeoff (PTO) control on wave energy conversion system dynamics and efficiency. The model system employed and progress on recent developments are: (1) nonlinear wave modeling in the ocean, generation and propagation in a wave basin, and (2) nonlinear PTO control algorithm. An overview of the holistic analytical, numerical and experimental research approach/work plan is presented. To provide a simple means for analysis, comparison and performance evaluation, the WEC-Sim numerical platform is used for model implementation and system dynamic simulation. Analytical and numerical predictions of the nonlinear wave fields in a wave basin using the nonlinear Fourier analysis (NLFA) technique and corresponding nonlinear wavemaker theory and a plan for future validation using a comprehensive series of experimental test data as well as ocean wave measurements are described. Efficiency of the nonlinear PTO control and a future evaluation work plan by comparing numerical simulations with results of WEC model test data under corresponding wave conditions of the experimental studies without the presence of the WEC system are also presented.
An image may be influenced by noise during capturing and transmitting process. Removing the possible noise from the image has been always challenging issue due to this fact that further processing will not be possible unless by diminishing the noise from images. Many researchers attempted to remove the noise to improve the qualitative and also the quantitative results but these methods could not preserve the quality of images after applying de-noising techniques. In this paper, in the first stage, we utilized the most recent nature inspired meta-heuristic optimization algorithm to get the optimal solutions for the parameters of thresholding function. Using Harris Hawk Optimization (HHO) algorithm results in obtaining the optimized thresholded wavelet coefficients before applying the inverse wavelet transform. In the second stage, we proposed improved adaptive generalized Gaussian distribution (AGGD) threshold which is a data driven function with an adaptive threshold value. This function can be fitted to any kind of images without using any shape tuning parameter. It is clear that calculation of the threshold value does not require any optimization and LMS learning algorithm. Qualitative and quantitative results validate the superiority of the proposed method.
Since electric vehicles have gained more and more popularities in the current research area, there is need to design a circuit and converter for charging these electric vehicles by means of the excess amount of electricity produced by the grid. Since they should compete in the market with their traditional counterparts, their efficiency is the winning point in their competence with respect to the traditional ones. Thus, there is a need to design using DC/DC converter to increase the efficiency. In this paper, Forward converter followed by a boost converter is designed and their elements are selected in order to meet the design criteria. Eventually, the converter is simulated in PLECS to get a validation of the calculations.
The control chart patterns are the most commonly used statistical process control (SPC) tools to monitor process changes. When a control chart produces an out-of-control signal, this means that the process has been changed. In this study, a new method based on optimized radial basis function neural network (RBFNN) is proposed for control chart patterns (CCPs) recognition. The proposed method consists of four main modules: feature extraction, feature selection, classification and learning algorithm. In the feature extraction module, shape and statistical features are used. Recently, various shape and statistical features have been presented for the CCPs recognition. In the feature selection module, the association rules (AR) method has been employed to select the best set of the shape and statistical features. In the classifier section, RBFNN is used and finally, in RBFNN, learning algorithm has a high impact on the network performance. Therefore, a new learning algorithm based on the bees algorithm has been used in the learning module. Most studies have considered only six patterns: Normal, Cyclic, Increasing Trend, Decreasing Trend, Upward Shift and Downward Shift. Since three patterns namely Normal, Stratification, and Systematic are very similar to each other and distinguishing them is very difficult, in most studies Stratification and Systematic have not been considered. Regarding to the continuous monitoring and control over the production process and the exact type detection of the problem encountered during the production process, eight patterns have been investigated in this study. The proposed method is tested on a dataset containing 1600 samples (200 samples from each pattern) and the results showed that the proposed method has a very good performance.
Signalized intersections act as one of the main elements to control the traffic flow at transportation systems in urban areas. However intersections as nodes impose more delays to vehicles. Creating maximum efficiency in transportation systems in urban areas and maintaining the optimal performance of these intersections always have been the main concern of traffic engineers. Furthermore, recently, the various kinds of programs and techniques are presented to help to traffic engineers to find optimized timing of signalized intersections. In this study, a new method based on kinematic wave theory is used through genetic algorithm technique to optimize the timing of three signalized intersections in the most crowded city in the north of Iran (Rasht city) to minimize travel time, delays and create better performing crossings at a dense transportation systems. The applied algorithm indicated that after the signal timing optimization, the average vehicle delay time can be reduced at the intersection in a.m. peak, noon peak, and p.m. peak by 31, 22 and 22 percent, respectively.
Numerical simulation of large-scale dynamical systems plays a fundamental role in studying a wide range of complex physical phenomena; however, the inherent large-scale nature of the models often leads to unmanageable demands on computational resources. Model reduction aims to reduce this computational burden by generating reduced models that are faster and cheaper to simulate, yet accurately represent the original large-scale system behavior. Model reduction of linear, nonparametric dynamical systems has reached a considerable level of maturity, as reflected by several survey papers and books. However, parametric model reduction has emerged only more recently as an important and vibrant research area, with several recent advances making a survey paper timely. Thus, this paper aims to provide a resource that draws together recent contributions in different communities to survey the state of the art in parametric model reduction methods. Parametric model reduction targets the broad class of problems for which the equations governing the system behavior depend on a set of parameters. Examples include parameterized partial differential equations and large-scale systems of parameterized ordinary differential equations. The goal of parametric model reduction is to generate low-cost but accurate models that characterize system response for different values of the parameters. This paper surveys state-of-the-art methods in projection-based parametric model reduction, describing the different approaches within each class of methods for handling parametric variation and providing a comparative discussion that lends insights to potential advantages and disadvantages in applying each of the methods. We highlight the important role played by parametric model reduction in design, control, optimization, and uncertainty quantification - settings that require repeated model evaluations over different parameter values.
In image guided radiotherapy, in order to reach a prescribed uniform dose in dynamic tumors at thorax region while minimizing the amount of additional dose received by the surrounding healthy tissues, tumor motion must be tracked in real-time. Several correlation models have been proposed in recent years to provide tumor position information as a function of time in radiotherapy with external surrogates. However, developing an accurate correlation model is still a challenge. In this study, we proposed an adaptive neuro-fuzzy based correlation model that employs several data clustering algorithms for antecedent parameters construction to avoid over-fitting and to achieve an appropriate performance in tumor motion tracking compared with the conventional models. At first step of this work, a comparative assessment is done between seven nuero-fuzzy correlation models each constructed using a unique data clustering algorithm. Then, all these constructed models are combined within an adaptive sevenfold synthetic model since our tumor motion database has high degrees of variability and that each model has its intrinsic properties at motion tracking. In the proposed sevenfold synthetic model, best model is selected adaptively at pre-treatment. The model also updates the steps for each patient using an automatic model selectivity subroutine. We tested the efficacy of the proposed synthetic model on twenty patients (divided equally into two control and worst groups) treated with CyberKnife synchrony system. Compared to Cyberknife model, the proposed synthetic model resulted in 61.2% and 49.3% reduction in tumor tracking error in worst and control group, respectively. These results suggest that the proposed model selection program in our synthetic neuro-fuzzy model can significantly reduce tumor tracking errors. Numerical assessments confirmed that the proposed synthetic model is able to track tumor motion in real time with high accuracy during treatment.
© The Author(s) 2015.
Increased penetration of distributed generation
(DG) in recent years has a significant impact on operation
and control of power systems. One of the main issues with the
increased penetration of DGs is the effect of voltage rise. This
paper investigates integration of coordinated voltage regulator
(VRs) operation with cooperative distributed inverter control to
maintain voltages in appropriate limits in distribution systems
with high penetration of DGs. The coordinated VR control
is used to optimize the settings of multiple nested VRs while
the cooperative distributed control optimally dispatches reactive
power of the DGs. The integrated approach is compared with
the case without coordinated VRs control (uncoordinated local
control). Simulation results illustrate the effective performance
of the proposed method to achieve unified voltage profile.
In this paper, estimation of optimal capacity and location of installation of wind, solar and fuel cell sources in distribution systems to reduce loss and improve voltage profile, by considering load changes, is carried out with Lightning Search Algorithm (LSA). Studies have been conducted on the standard IEEE 33 bus power system in two scenarios. In the first scenario, study is done with the assumption that the load remains constant throughout the project period and in the second scenario with the load growth. The results of the simulation, indicated that the puissance of load changes on distributed generations (DGs) placement studies. Also, the results confirm the performance of the proposed algorithm in reducing the objective function.
Energy harvesting from low amplitude vibrating sources is a challenging problem. To overcome this problem there is a requirement to design and optimize a harvester device to amplify the vibration to access a considerable amount of harvested energy. In this paper, a new diamond frame design for piezoelectric energy harvesting is purposed and compared with a single frame conventional design of piezoelectric harvesters to amplify the vibration amplitude to harvest more energy. Also, a linear optimization function is obtained to optimize the frame shape which means with different values of input displacement to the device, an optimum angle of frame is obtained. To show the versatility of the novel design, it is used in both flat and round structures. Based on the results with the new design in a flat and round structure, 35% and 70% improvement in energy harvesting is obtained, respectively.
With increased penetration of solar energy sources, solar power forecasting has become more crucial and challenging. This paper proposes a copula-based Bayesian approach to improve probabilistic solar power forecasting by capturing the joint distribution between solar power and ambient temperature. A prior forecast distribution is first obtained using different underlying point forecasting models. Parametric and empirical copulas of solar power and temperature are then developed to update the prior distribution to the posterior forecast distribution. A public solar power database is used to demonstrate effectiveness of the proposed method. Numerical results show that the copula-based Bayesian method outperforms the forecasting method that directly uses temperature as a feature. The Bayesian method is also compared with persistent models and show improved performance. This article includes supplementary material (data and code) for reproducibility.
This paper introduces the application of an iterative SVD-Krylov algorithm for dynamic model reduction of power systems. The method is a two-sided projection combining advantages of the singular value decomposition based and the Krylov-based model reduction methods. The significance and accuracy of the method are numerically investigated. The full linearized dynamic model of the original nonlinear power system is determined and used as the input of dynamic reduction technique. The capability of this technique in keeping dominant oscillation modes after reduction is utilized as the comparison criteria. Physical relationship between the reduced and the original system is also discussed by mean of coherency in power systems.
In this paper, three algorithms for dynamic model reduction of power systems are compared. The significance and accuracy of approximate bi-simulation, balance truncation, and modal truncation technique are investigated. While the bi-simulation method is applied to power systems for the first time, its detailed formulation is derived for a constrained linear system. The full linearized dynamic model of a nonlinear system is determined and used as the input of the dynamic model reduction techniques. The capability of each technique in keeping dominant oscillation modes after dynamic reduction is utilized as the comparison criterion. As a result, this reduced model led to faster analysis and control of the power system. All three reduction techniques are simulated over the dynamic 39-bus New England test system.
An improved modal truncation method with arbitrarily high order accuracy is developed for calculating the second- and third-order eigenvalue derivatives and the first- and second-order eigenvector derivatives of an asymmetric and non-defective matrix with repeated eigenvalues. If the different eigenvalues λ 1 , λ 2 ,⋯,λ r of the matrix satisfy |λ 1 |⩽⋯⩽|λ r | and |λ s |<|λ s+1 |(s⩽r-1), then associated with any eigenvalue λ i (i⩽s), the errors of the eigenvalue and eigenvector derivatives obtained by the qth-order approximate method are proportional to |λ i /λ s+1 | q+1 , where the approximate method only uses the eigenpairs corresponding to λ 1 , λ 2 ,⋯,λ s . A numerical example shows the validity of the approximate method. The numerical example also shows that in order to get the approximate solutions with the same order accuracy, a higher order method should be used for higher order eigenvalue and eigenvector derivatives.
In interconnected power systems, dynamic model reduction can be applied to generators outside the area of interest (i.e., study area) to reduce the computational cost associated with transient stability studies. This paper presents a method of deriving the reduced dynamic model of the external area based on dynamic response measurements. The method consists of three steps, namely dynamic-feature extraction, attribution, and reconstruction (DEAR). In this method, a feature extraction technique, such as singular value decomposition (SVD), is applied to the measured generator dynamics after a disturbance. Characteristic generators are then identified in the feature attribution step for matching the extracted dynamic features with the highest similarity, forming a suboptimal “basis” of system dynamics. In the reconstruction step, generator state variables such as rotor angles and voltage magnitudes are approximated with a linear combination of the characteristic generators, resulting in a quasi-nonlinear reduced model of the original system. The network model is unchanged in the DEAR method. Tests on several IEEE standard systems show that the proposed method yields better reduction ratio and response errors than the traditional coherency based reduction methods.
This paper proposes a new approach to reduction of power system dynamic models based on approximate bisimulation relations. Advantages of these relations for time domain analysis over the model reduction techniques commonly used in system theory are pointed out. The approach is applied to the transient stability analysis in power systems. We propose an algorithm that identifies whether the power system is able to maintain the synchronism after a disturbance, based on linearization and approximate bisimulation relations. During the time simulation, the linearized model is transformed into the appropriate form and reduced using the approximate bisimulation relations. This reduced (and linear) model is used in the numerical integration instead of the original nonlinear one, while the accuracy criterion is satisfied. The New England benchmark power system is used to verify the described algorithm.
This paper deals with obtaining accurate eigenvector derivatives in damped vibration systems with modal truncation method only by system matrices and a few available lower modes. A numerical example shows that the method of this paper is correct and efficient.
The problem of approximating a multivariable transfer function G(s) of McMillan degree n, by Ĝ(s) of McMillan degree k is considered. A complete characterization of all approximations that minimize the Hankel-norm is derived. The solution involves a characterization of all rational functions Ĝ(s) + F(s) that minimize where Ĝ(s) has McMillan degree k, and F(s) is anticavisal. The solution to the latter problem is via results on balanced realizations, all-pass functions and the inertia of matrices, all in terms of the solutions to Lyapunov equations. It is then shown that where σk+1(G(s)) is the (k+l)st Hankel singular value of G(s) and for one class of optimal Hankel-norm approximations. The method is not computationally demanding and is applied to a 12-state model.
This paper is aimed to propose an optimization problem, solved to estimate parameters of fictitious generators that represent a dynamic equivalent of an external subsystem; such generators are located on frontier nodes, linking the external and the studied subsystem. The problem is based on preserving closely those modes highly related with the studied subsystem's dynamic. Different operating conditions can be taken into account; besides, Power System Stabilizers can be included. Time simulations are carried out to compare signals obtained from the full and reduced power system, whose proximity is evaluated through an RMS difference. Results show the feasibility of the methodology.
The general applicability of the modal approach for model reduction is restricted by the lack of guaranteed bounds for approximation errors and of a satisfactory modal dominance analysis proce- dure. Functional and computational enhancements of this approach are proposed. Functional enhance- ments arise by combining the modal techniques with other methods and by using improved dominance analysis techniques. The computational enhance- ments are the results of employing numerically reli- able algorithms for both dominance analysis as well as for model reduction.
The notion of bisimulation in theoretical computer science is one of the main complexity reduction methods for the analysis and synthesis of labeled transition systems. Bisimulations are special quotients of the state space that preserve many important properties expressible in temporal logics, and, in particular, reachability. In this paper, the framework of bisimilar transition systems is applied to various transition systems that are generated by linear control systems. Given a discrete-time or continuous-time linear system, and a finite observation map, we characterize linear quotient maps that result in quotient transition systems that are bisimilar to the original system. Interestingly, the characterizations for discrete-time systems are more restrictive than for continuous-time systems, due to the existence of an atomic time step. We show that computing the coarsest bisimulation, which results in maximum complexity reduction, corresponds to computing the maximal controlled or reachability invariant subspace inside the kernel of the observations map. These results establish strong connections between complexity reduction concepts in control theory and computer science.
A general notion of bisimulation is defined for linear input-state-output systems, using analogies with the theory of concurrent processes. A characterization of bisimulation and an algorithm for computing the maximal bisimulation relation is derived using geometric control theory. Bisimulation is shown to be a notion which unifies the concepts of state-space equivalence and state-space reduction, and which allows to study equivalence of systems with nonminimal state-space dimension. The notion of bisimulation is especially powerful for "nondeterministic" dynamical systems, and leads in this case to a notion of equivalence which is finer than equality of external behavior. For abstractions of systems it is shown how the results specialize to previously obtained results by other authors. Extensions of the main results to the nonlinear case are provided.
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Controller Design of Voltage Source Converter Using Nyquist Array
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