M. Madrigal

Dynamic harmonic evolution using the extended harmonic domain

A novel methodology is presented in this paper for conducting transient and steady-state analysis of electric networks containing nonlinearities and switching plants components. The method is termed the extended harmonic domain (EHD) method as may be seen as an extension of the harmonic domain (HD) method used in steady-state analysis. It is shown in the paper that EHD is a natural approach for conducting dynamic and steady-state studies of the evolution of harmonics in power circuits containing nonlinear components and flexible AC transmission systems (FACTS) devices. It is also shown in the paper that EHD provides a suitable basis for extending the well-known steady-state power quality indices to the transient range. To illustrate the use of the theory, a three-phase linear circuit and a three-phase PWM-STATCOM are modeled using EHD. The results are compared against those provided by industry standard tools as PSCAD/EMTDC and Matlab.

Trends in Power Quality Monitoring

This letter introduces two Pade/spl acute/ approximation schemes that, when combined, enable the ABCD parameters of multiconductor transmission lines to be accurately and efficiently evaluated directly in the phase domain for application to harmonic analysis studies. Since the solution is obtained directly in the phase domain, modal decompositions are completely avoided.

Modelling of custom power equipment using harmonic domain techniques

A new and comprehensive harmonic domain model of a three-phase, six-pulse PWM STATCOM is presented in this paper. The model takes proper account of the DC capacitor effect and it comes in the form of a three-phase Thevenin equivalent expressed in the harmonic domain, where switching functions are used to represent with ease the PWM control firing sequences. The harmonic impedance of the Thevenin equivalent shows high cross-couplings between phases and between harmonics, an effect which is strongly influenced by the STATCOM capacitor size. Results are presented which show that the PWM STATCOM observes quite different harmonic voltage response when it is made to operate as a reactive power source and when it is made to operate as a sink. This effect can not be observed with steady state models that use a voltage source representation to model the STATCOM.

Dynamic harmonic evolution in FACTS via the extended harmonic domain method

The extended harmonic domain (EHD) method is used to obtain the harmonics in the dynamic and steady state response to disturbances for four common FACTS devices. The versatility of this method is demonstrated by applying it to a thyristor-controlled series compensator (TCSC), static reactive power compensator (SVC), static synchronous series compensator (SSSC), and unified power flow controller (UPFC). The derivation of the state-space equations that describe the dynamics of the above devices and their transformation into linear, time-invariant (LTI) systems using EHD is presented. The LTI systems are simulated in the presence of disturbances using MATLAB®, and graphical depictions are used to illustrate the evolution in time of the harmonic coefficients and power quality indices such as RMS voltage and current, apparent power, active power, reactive power, and distortion power. This study shows the usefulness of this methodology in highlighting the sensitivity of the harmonic response of these devices to disturbances.

Operational matrices for the analysis of periodic dynamic systems

This letter presents a methodology for the study of periodical dynamic systems. The method is based on the use of orthogonal series expansions and their operational properties. As opposed to the conventional use of the series expansions, in this work it is considered that the expansion coefficients may slowly vary with time. This salient feature allows for traditional steady-state methods such the harmonic domain to be used in dynamical systems. An important use of the method is the analysis of switched networks. The use of the method is illustrated with simple but of practical value systems.

Harmonic modelling in Hartley's domain with particular reference to three phase thyristor-controlled reactors

The main objectives of this paper are to present a new frame-of-reference based on the use of Hartleys transform and to present a three-phase thyristor controlled reactor (TCR) harmonic model which uses Hartleys domain. Solutions using the new frame-of-reference are between two to four times faster than solutions using an established frame-of-reference based on Fouriers transform because Hartleys transform makes use of the real plane as opposed to the complex plane. Harmonic switching vectors in Hartleys domain have been developed for maximum computer efficiency. Their use, combined with discrete convolution operations, provide cleaner and faster operations than those afforded by the fast Hartley transform. The TCR model is completely general and caters for any kind of plant imbalances, e.g. uneven firing angles and inductances. Network imbalances are accounted for via the excitation voltage. The new frame-of-reference accommodates any number of buses, phases, harmonics and cross-couplings between harmonics. It provides a reliable and efficient means for the iterative solution of power systems harmonic problems through a Newton-Raphson method which exhibits quadratic convergence.

Modeling and Analysis of a TCR-FC Reactive Power Compensator Using the Harmonic Domain

This paper presents a methodology for steady-state and transient analysis in electrical networks, the methodology is applied to reactive power compensation using thyristor-controlled reactor with fixed capacitor (TCR-FC). The method is based on the use of dynamic harmonic domain (DHD) and associated discrete circuit models. The dynamic harmonic domain is a natural approach for conducting dynamic and steady-state studies of the evolution of harmonics in electrical networks. On the other hand, the associated discrete circuit models facilitate the transient analysis of large electrical networks.

A new harmonic power flow method based on the instantaneous power balance

In this paper an instantaneous power flow (IPF) solution method for analysing the harmonic power flow problem is proposed. The IPF uses the instantaneous power balance to formulate the problem. The methodology uses the harmonic domain as a frame-of-reference and the Newton-Raphson method. This method is fully formulated in the frequency domain and applicable to systems which also contain nonlinear elements and FACTS devices. The method also offers a flexible and modular formulation which shows excellent convergence properties. The IPF is developed, implemented and proved with simple examples for linear and nonlinear concentrated loads and the thyristor controlled reactor (TCR) in the control of reactive power.

Single-phase PWM converters array for three-phase reactive power compensation. II. Frequency domain studies

This paper presents a three-phase STATCOM structure based on the use of three single-phase PWM converters. Each single-phase PWM converter is represented by a Thevenin equivalent obtained from analytical expressions based on the operation of the PWM converter. The model is suitable for harmonic propagation studies of large, unbalanced network. The proposed STATCOM structure was used with a particular application to reactive power compensation and phase balancing, where fundamental frequency and harmonics are included in the analysis. The generic model is implemented in the frequency domain using INTAR libraries and proved through time domain simulations via PSCAD/EMTDC. INTAR is a industry grade software for three-phase power flow analysis and harmonic propagation for large networks.

Single-Phase Modeling Approach in Dynamic Harmonic Domain

In this paper, a frequency-based analytical approach is presented for dynamic analysis of three-phase balanced systems in the presence of harmonic distortion based on single-phase analysis. By providing mathematical foundation, this study proves that a three-phase balanced system (linear or non-linear, supplied by periodic balanced sinusoidal or non-sinusoidal sources) is completely balanced during both transient and steady-state conditions. This is done by utilizing Dynamic Harmonic Domain (DHD) and defining a phase-shift matrix in frequency domain. As the most noteworthy application of the proposed methodology, single-phase modeling approach is put forward. Therefore, during the transient period, one can analyze only one phase of a three-phase balanced system and calculate exact quantities of the other phases without performing extra simulations, which is not possible through time domain. The introduced concept has been applied to different test cases including three-phase transformer inrush current. In addition, the proposed approach has been utilized to obtain a single-phase model of VSC-based power electronic devices for dynamic harmonic analysis, followed by discussion on results.