F. de Leon

Complete transformer model for electromagnetic transients

A complete, three phase transformer model for the calculation of electromagnetic transients is presented. The model consists of a set of state equations solved with the trapezoidal rule of integration in order to obtain an equivalent Norton circuit at the transformer terminals. Thus the transformer model can be easily interfaced with an electromagnetic transients program. Its main features are: (a) the basic elements for the winding model are the turns; (b) the complete model includes the losses due to eddy currents in the windings and in the iron core; and (c) the solution of the state equations is obtained in decoupled iterations. For validation, the frequency response of the model is compared with tests on several transformers. Applications to the calculation of transients are given for illustration. >

Time domain modeling of eddy current effects for transformer transients

Eddy current effects are included in a model of a power transformer for the study of electromagnetic transients. Existing analytical formulae for the calculation of losses in the windings are evaluated. Various equivalent circuits are fitted to represent in the time domain the damping produced by eddy currents in the windings. A frequency dependent model is derived for the iron core, based on the physical distribution of losses and magnetization effects. The parameters of this model are obtained by optimal discretization of the laminations. Simulation show the effects of eddy current in the damping of transients. >

Optimal Distributed Voltage Regulation for Secondary Networks With DGs

An algorithm for the optimal voltage regulation of distribution secondary networks with distributed generators (DGs) is proposed in the paper. Based on the ε decomposition of the sensitivity matrix (inverse of Jacobian) obtained from the solution of the Newton-Raphson power flow problem, a large secondary network is divided into several small subnetworks. From the ε decomposition, the range of influence of each DG on the voltage of the entire network is determined. When voltage at particular nodes exceeds normal operating limits, the nearest DGs can be located and commanded to control the voltage. The control action can be coordinated using communications in a small-size subnetwork. The voltage regulation is achieved by solving a small linear programming optimization problem with an objective function that makes every DG to optimize its generation. The algorithm is tested with a model of a real heavily-meshed secondary network. The results show that the algorithm proposed in this paper can effectively control the voltage in a distributed manner. It is also discussed in the paper how to choose the value of ε for the system decomposition.

Efficient calculation of elementary parameters of transformers

Very efficient procedures for computing elementary parameters (turn leakage inductances and capacitances) in a transformer are presented. The turns are used as a calculation base to permit modeling at very high frequencies. Turn-to-turn (or loop) leakage inductances are obtained by an image method. The charge simulation method is used for finding the capacitances between turns and from turns to ground. The new methods are very efficient compared with the use of the technique of finite elements and are also remarkably accurate. Thus, the short circuit (or test) leakage inductance can be obtained from turn-to-turn information. Examples of calculated parameters are given for illustration. For validation, the results are compared with the parameters obtained using finite elements and tests. The elementary parameters can be used to create reduced-order computational models for the calculation of transient phenomena. >

Reduced order model for transformer transients

A complete model for transformers is derived on the basis of very efficiently calculated elementary (turn-to-turn) parameters. A high-order turn-to-turn model is constructed for the windings. This model is reduced to a lower order by operating on the resulting matrices. An electric equivalent circuit for the core is obtained from the principle of duality. By the use of test turns the winding model is interfaced with the iron-core. For validation, the frequency response of the model has been compared with test results. The model for the calculation of transients has the form of a Norton equivalent circuit and it can easily be incorporated in a power system transients program such as the EMTP. Examples of calculated transients are given for illustration and further validation. >

Analysis of Voltage Profile Problems Due to the Penetration of Distributed Generation in Low-Voltage Secondary Distribution Networks

This paper presents a comprehensive analysis of the possible impacts of different penetration levels of distributed generation (DG) on voltage profiles in low-voltage secondary distribution networks. Detailed models of all system components are utilized in a study that performs hundreds of time-domain simulations of large networked distribution systems using the Electromagnetic Transients Program (EMTP). DGs are allocated in a probabilistic fashion to account for the uncertainties of future installations. The main contribution of this paper is the determination of the maximum amount of DG that secondary distribution networks can withstand without exhibiting undervoltage and overvoltage problems or unexpected load disconnections. This information is important for network planning engineers to facilitate the extension of the maximum penetration limit. The results show that depending on the location, type, and size of the installed DGs, small amounts of DG may cause overvoltage problems. However, large amounts of DG may not cause any voltage problems when properly selected.

A simple representation of dynamic hysteresis losses in power transformers

The paper describes a procedure for the representation of hysteresis in the laminations of power transformers in the simulation of electromagnetic transient phenomena. The model is based on the recognition that in todays iron cores the hysteresis loops are narrow and therefore the modeling details are only important in relation to the incurred losses and the associated attenuation effects. The resultant model produces losses proportional to the square of the flux density, as expected from measurement data. It is formulated as a simple, linear relationship between the variation B-B/sub re/spl nu, of the magnetic flux density B after a reversal point B/sub re/spl nu and the resulting additional field intensity H/sub hyst/. This idea can be easily implemented in existing transformer models with or without frequency dependent modeling of eddy currents in the laminations. It has been found that in simulation tests the representation of hysteresis is not necessary those situations have been described where the modeling of hysteresis appears to be more meaningful. >

Effects of Backfilling on Cable Ampacity Analyzed With the Finite Element Method

Expressions for computing the external thermal resistance (T4) of buried cables, in both the IEEE and the IEC standards, are applicable to a limited number of installation geometries. In this paper, a method for the computation of T4 using the finite element approach is presented. With this method, a parametric study on how cable ampacity is affected by different configurations of the backfills is performed. The obtained results are compared with those of the IEC and IEEE standards (Neher-McGrath) and published extensions by El-Kady and Horrocks. Important differences can be observed for nonstandardized situations.

Dual Three-Winding Transformer Equivalent Circuit Matching Leakage Measurements

An equivalent circuit for the leakage inductance of three-winding transformers is presented. The model is derived from the principle of duality (between electric and magnetic circuits) and matches terminal leakage inductance measurements. The circuit consists of a set of mutually coupled inductances and does not contain negative inductances. Each inductance can be computed from both: the geometrical information of the windings and from terminal leakage measurements taking two windings at a time. The new model is suitable for steady state, electromechanical transients and electromagnetic transient studies. The circuit can be assembled in any circuit simulation program such as EMTP, PSPICE, etc. programs using standard mutually coupled inductances.

Computation of electromagnetic transients using dual or multiple time steps

When computing transients with the EMTP (electromagnetic transients program) a single time step is selected for the trapezoidal integration all over the system. When this step is small because of the presence of a fast component, the simulation may be significantly slowed down. The authors present a procedure by which the computations at selected fast buses can be performed with smaller time steps than at the rest of the system. The linkage of the variables at two different time steps is achieved in a simple way at the line-bus interface by a small addition to any existing implementation of an electromagnetic transients program. Significant computational savings can be obtained without any loss of accuracy. >