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When it comes to estimating dynamics (modes) of interconnected power systems through transient (ringdown) data, one can expect more realistic estimates for the compound system if multiple signals distributed over different locations can be used simultaneously during modal estimation. In this context, the contributions of this paper are twofold. First, it is proposed a multi-signal ringdown time-domain Vector Fitting method (‘multi-signal RTD-VF’) which is capable of modeling multiple ringdown signals simultaneously. This method appropriately generalizes the ‘single-signal RTD-VF’ method, which processes ringdown signals independently, i.e., one at a time. Second, it is proposed an instrumental variable (IV) extension of multi-signal RTD-VF. By guaranteeing local optimums after algorithm convergence, such a ‘multi-signal IV-RTD-VF’ formulation may be used for further refining estimates provided by regular multi-signal RTD-VF. Two numerical examples are used to validate the proposed methods. The first example considers actual ringdown data sets extracted from North American Eastern Interconnection (NAEI) and Brazilian Interconnected Power (BIP) systems, whereas the second one considers mode identification of a synthetic signal corrupted by colored noise.

This paper addresses the problem of obtaining optimal black-box models of n-terminal power transformers for transient studies. We use actual transformer data to demonstrate that a transformer model endowed with both passivity and symmetry can be optimally achieved only if the corresponding constraints are formulated and simultaneously included in the parameter estimation problem as opposed to enforcing them independently as two distinct post-processing model adjustments.

This paper proposes an optimal and unifying instrumental variable (IV)-based Vector Fitting (VF) method for frequency-domain (FD) identification of models formed by rational basis function (RBF) expansions. The proposed method is denoted by IV-FD-VF and can be similarly applied for estimating models formed by both continuous- and discrete-time RBF sets. The key advantage of IV-FD-VF lies in the fact that, differently from standard FD-VF approaches, it guarantees an optimal solution after convergence. This important optimality property is proved to be independent of the nature of the noise that corrupts the data (for instance, if it is white or coloured). Two case studies are used to validate the proposed IV-FD-VF method. One of these case studies considers actual frequency-domain data sets extracted from two different single-phase power transformers.

In this paper, a methodology using Differential Evolution algorithm is proposed for the definition of the discourse universe of the fuzzy PID controller structure variables, for the load/frequency control in power systems, with this eliminating the need of the expert in systems speed control of hydraulic turbines. This controller uses the fuzzy system to tune the PID controller in real time. A mathematical model, based upon constructive information and where nonlinearities are taken into account, of a hydroelectric plant belonging to the Brazilian Interconnected System is presented as a test benchmark to analysis the proposed controller performance under various loading conditions. Simulation results are introduced to show the performance of the developed controller in comparison with a PID controller tuned by a Differential Evolution Algorithm and with a PID algorithm similar to the one actually used in the field. These results denote that the proposed controller offer better performance over others in terms of settling times and oscillation of the frequency.

This paper proposes a novel method, called Ringdown Time-Domain Vector Fitting (RTD-VF), for estimating electromechanical modes in interconnected power systems. Such a method authentically extends, to the context of ringdown analysis, the well known Time-Domain Vector Fitting (TD-VF) method, which has already been successfully applied within other power systems areas. The proposed method is based on a state-space discretization framework which enables ringdown events to be effectively estimated when described as artificial unit impulse responses. Moreover, RTD-VF completely avoids the necessity to perform discrete Fourier transforms (DFTs) of ringdown data sequences. Three case studies are used to validate the proposed method. One of the examples considers a synthetic test signal, whereas the other two case studies consider actual ringdown data sets extracted from the North American Eastern Interconnection (NAEI) system and from the Brazilian Interconnected Power (BIP) system.

This paper proposes a general and unifying method for constructing rational basis functions (RBFs). The proposal is specifically designed for finding characterizing matrices of linear RBF state equations. Analytic expressions for the realization of such state-space matrices are also developed. As will be shown, the construction method here proposed can be easily applied (but is not limited) to several RBF sets which have been successfully adopted in both linear and nonlinear system identification areas.

Vector fitting (VF) algorithms have become popular and powerful tools for estimating models formed by rational basis function (RBF) expansions. In this paper, we first translate the well-known continuous time-domain VF method (cTD-VF) to a discrete time-domain framework. We denote this new domain VF method by dTD-VF. Differently from the cTD-VF, the dTD-VF formulation does not rely on a numerical approximation of convolution integrals and, as a result, it can be easily implemented with a variety of RBF sets. The second part of this paper shows that the proposed dTD-VF can also be transformed into a novel instrumental variable (IV)-dTD-VF technique, which is shown to have a guaranteed optimal solution at convergence. Moreover, this important optimality property does not depend on the nature of the noise that corrupts the data (for instance, if it is white or colored). Two case studies highlight the advantages of using the proposed methods. One of these examples consists of modeling the admittance characteristics of a power system implemented as a frequency-dependent network equivalent (FDNE).

This paper introduces the setup of a Distributed Generation Microgrid (DGM) focused onto research on monitoring (electrical and environmental), controling and operating microgrids. This network is located at the Polytech Center Campus of the Federal University of Parana (UFPR), in Curitiba, Brazil. It consists of nine 13.8 kV feeders, three Distributed Generation (DG) sources and is connected to the main utility through a 69 kV distribution substation of the state electricity company named as Copel DIS. In addition to the electrical configuration, all components of the microgrid are presented, such as power generation, electrical and environmental meters, $\mu \mathrm{PMU}$ and the system monitoring computing environment.

This paper presents the results of an ongoing project involving the monitoring of micro phasor measurement units (micro-PMU) at Universidade Federal do Parana (UFPR). The infrastructure for receiving, processing and storing data from micro-PMUs, energy meters and power quality analysers was deployed. Free software were tested for data storage and visualization. We modified an existing open-source Energy Monitoring System (EMS) for proper use with PMUs. The software native communication protocol was adapted from hypertext protocol (HTTP) to direct reception of user datagram protocol (UDP) in IEEE Std. C37.118.2-2011 format to receive micro-PMUs transmission at 120 phasor per second. We modified data storage format to efficiently deal with time information allowing reduction of 60% of storage space in comparison to commonly used phasor data concentrator (openPDC).

Procedures for modeling potential/ power transformers and reactors in order to support electromagnetic transients analysis have been addressed by many recent researchers. Among all methods for obtaining black-box models, the Frequency Domain Vector Fitting (FD-VF) or, simply VF, has several successful application reports in electrical power systems. This article is two purpose: first to describe a procedure that combines instrumental variables to the VF method, called the Instrumental Variable VF (IV-VF). The main advantage of the IV-VF is the fact that if the iterative procedure converged, an optimal local solution is obtained. Also to present a case study based on actual single-phase transformer measurements (Benchmark JWG A2/C4.52 for Power Transformers) and a GIS installation, where IV-VF is used for evaluating internal resonances in power transformers due to high frequency transients. The knowledge of external and internal winding response to these transients contribute to insulation design and reliability in field operation.

This paper presents a nonlinear model for a hydraulic amplifier, a component of the governor in the speed control loop of hydroelectric power plants. The amplifier transforms the electrical signal of the controller into mechanical movement of the turbine components, including the switching characteristics. This model is used to propose, on the one hand, a Piecewise Affine (PWA) representation for the hydraulic amplifier, and, on the other hand, a methodology for estimating the model parameters using field measurements, which facilitates its practical implementation. This representation is referred to as semi-physical because the model parameters are closely related with the physical construction of the hydraulic amplifier components. Among the advantages of this PWA representation are the appropriate structuring for use in system identification methods, for estimating its parameters, and the existence of advanced control techniques that use this structure in controller design, thereby improving the load-frequency control performance. The paper concludes with a description of the results, including the parameters that were estimated by using the hydraulic amplifier model with PWA structure.

The passivity enforcement problem is always a key issue when estimating passive black-box models. Passivity has been broadly scrutinized in the literature and is known to yield stable time-domain simulation; thus, passivity is a much-desired model property which cannot remain an unmodeled effect. Many successful algorithms exist that accomplish the enforcement task by model parameter perturbation, with the caveat that the passivity violations to be suppressed are not large. This paper proposes a novel approach to address this issue. We propose four different mathematical formulations to preprocess the measurement of admittance parameters. Preprocessed data serve as inputs to parameter estimation algorithms to obtain passive models for power system applications. This approach is particularly adequate to use with model parameter perturbation methods. Three examples containing data of actual measurements illustrate the advantage of using the proposed methodology.

Power system transient analysis relies on the deployment of models with ever-increasing accuracy that represents the system's frequency-dependent components with respect to the phenomena being scrutinized. A key issue in this context is the construction of a model yielding passive properties for each system component. Such properties are commonly compromised by corrupting noise in measurements that serve as input to the computation of blackbox models. In addition, model passivity could be further compromised during parameter estimation. This paper undertakes the task of developing a proposal to build an optimization methodology based on linear matrix inequalities (LMI-based) which is intended for obtaining an optimal, passive, blackbox model for a $n$ -terminal power transformer. The resulting model can be further realized as a circuit representation in order to simulate the transformer dynamics in an Eletromagnetic Transient program (EMT type). The results derived from two operating power transformers are later provided to confirm how effective the procedure herein proposed is.

In this paper, a Takenaka---Malmquist---Volterra (TMV) model structure is employed to improve the approximations in the low-pass equivalent behavioral modeling of radio frequency (RF) power amplifiers (PAs). The Takenaka---Malmquist basis generalizes the orthonormal basis functions previously used in this context. In addition, it allows each nonlinearity order in the expanded Volterra model to be parameterized by multiple complex poles (dynamics). The state-space realizations for the TMV models are introduced. The pole sets for the TMV model and also for the previous Laguerre---Volterra (LV) and Kautz---Volterra (KV) models are obtained using a constrained nonlinear optimization approach. Based on experimental data measured on a GaN HEMT class AB RF PA excited by a WCDMA signal, it is observed that the TMV model reduces the normalized mean-square error and the adjacent channel error power ratio for the upper adjacent channel (upper ACEPR) by 1.6 dB when it is compared to the previous LV and KV models under the same computational complexity.

The wireless power transfer can be useful in applications where the use of cables for powering remote devices are not suitable or even feasible. However, the transferred power is highly dependent on the relative position between the transmitter and receiver coils as well as other circuit parameters. The use of adaptive matching network in wireless power transfer system allows to track the maximum power transferred to the load while changing the magnetic coupling between the coils. By controlling both, the excitation frequency and matching capacitor at the primary side of the inductive link, the output power can be hold approximately constant over a large range of magnetic coupling coefficient. This paper presents an automatic compensation method for an inductive power transfer system. The proposed method monitors the magnitude and phase of the input current of the inductive link. Thus, the data is processed by a fuzzy logic controller actuating on the working frequency and on the matching capacitor in order to maximize the power transferred to the load. The proposed method can tolerate the movement of remote devices while charging processes.