Manuel Castilla

Wavelet and neural structure: a new tool for diagnostic of power system disturbances

The Fourier transform can be used for the analysis of nonstationary signals, but the Fourier spectrum does not provide any time-domain information about the signal. When the time localization of the spectral components is needed, a wavelet transform giving the time-frequency representation of the signal must be used. In this paper, using wavelet analysis and neural systems as a new tool for the analysis of power system disturbances, disturbances are automatically detected, compacted and classified. An example showing the potential of these techniques for diagnosis of actual power system disturbances is presented.

Power Quality Factor for Networks Supplying Unbalanced Nonlinear Loads

A single indicator [i.e., the power quality factor (PQF)] in the range between 0 and 1 is suggested in this paper to integrally reflect the power transfer quality of a general three-phase network feeding unbalanced nonlinear loads. The prominent power quality aspects considered in the paper are the following: 1) the voltage and current harmonic levels; 2) the degree of unbalance; and 3) the phase displacement factor in the different phases at the fundamental frequency. A network that supplies balanced sinusoidal currents at balanced sinusoidal voltages with zero phase displacement between the corresponding currents and voltages yields a PQF of unity. The measurement of the PQF is discussed. Practical examples illustrate the use and relevance of the new quality factor.

Clifford Theory: A Geometrical Interpretation of Multivectorial Apparent Power

In this paper, a generalization of the concept of electrical power for periodic current and voltage waveforms based on a new generalized complex geometric algebra (GCGA) is proposed. This powerful tool permits, in n-sinusoidal/nonlinear situations, representing and calculating the voltage, current, and apparent power in a single-port electrical network in terms of multivectors. The new expressions result in a novel representation of the apparent power, similar to the Steinmetzs phasor model, based on complex numbers, but limited to the purely sinusoidal case. The multivectorial approach presented is based on the frequency-domain decomposition of the apparent power into three components: the real part and the imaginary part of the complex-scalar associated to active and reactive power respectively, and distortion power, associated to the complex-bivector. A geometrical interpretation of the multivectorial components of apparent power is discussed. Numerical examples illustrate the clear advantages of the suggested approach.

Geometric algebra: a multivectorial proof of Tellegen's theorem in multiterminal networks

A generalised and multivectorial proof of Tellegens theorem in multiterminal systems is presented using a new power multivector concept defined in the frequency domain. This approach permits in nonsinusoidal/linear and nonlinear situations formulating Tellegens theorem in a novel complex-multivector representation, similar to Steinmetzs phasor model, based on complex numbers and limited to the purely sinusoidal case. In this sense, a suitable notation of voltage and current complex-vectors, associated to the elements and nodes of the network, is defined for easy development to Kirchhoffs laws in this environment. A numerical example illustrates the clear advantages of the suggested proof.

Voltage quality analyzer

The Voltage Quality Analyzer is a virtual instrument for diagnosing voltage quality of three-phase signals: instantaneous frequency deviations, harmonic spec- trum, total harmonic distortion and instantaneous symmetri- cal components. Accurate measurement of the instantaneous frequency and the harmonic content are obtained and the three-phase electrical waveforms and their symmetrical components are displayed. A voltage quality factor in the range between 0 to 1 is defined and measured.

Power quality factor and line-disturbances measurements in three-phase systems

A power quality meter (PQM) is presented for measuring, as a first objective, a single indicator, designated power quality factor (PQF), in the range between zero to one, which integrally reflect the power transfer quality of a general three phase network feeding unbalanced nonlinear loads. PQF definition is based on the analysis of functions in the frequency domain, separating the fundamental terms from the harmonic terms of the Fourier series. Then, quality aspects considered in the PQF definition can be calculated: a) the voltage and current harmonic levels b) the degree of unbalance and c) the phase displacement factor in the different phases at the fundamental frequency. As a second objective, the PQM has been designed for detecting, classifying and organizes power line disturbances. For monitoring power line disturbances, the PQM is configured as virtual instrument, which automatically classifies and organizes them in a database while they are being recorded. The type of disturbances includes: impulse, oscillation, sag, swell, interruption, undervoltage, overvoltage, harmonics and frequency variation. For amplitude disturbances (impulse, sag, swell, interruption, undervoltage and overvoltage), the PQM permits the measurement of parameters such as amplitude, start time and final time. Measurement of harmonic distortion allows recording and visual presentation of the spectrum of amplitudes and phases corresponding to the first 40 harmonics. Software tools use the database structure to present summaries of power disturbances and locate an event by severity or time of occurrence. Simulated measurements are included to demonstrate the versatility of the instrument.

Instantaneous line-frequency measurement under nonstationary situations

A virtual instrument for the measurement of instantaneous power-system-frequency is proposed. It is based on the frequency estimation of the voltage signal using three equidistant samples. An algorithm is further developed that diminishes the variance of the estimation. The procedure is applied to the case of single and three-phase networks and relative errors in the frequency estimation are obtained. Low cost hardware, consisting of compatible PC, standard data acquisition card and signal conditioning module, has been used in conjunction with a software application developed with LABVIEW/spl trade/. Finally, measurements using single and three-phase signals, simulating severe conditions of signal quality, were performed. A variation of the frequency throughout the measurement time has been assumed, according to a sinusoidal signal of 5 Hz, within a /spl plusmn/1 Hz margin. The developed tool has been proven, with worst case data and relative errors of 0.1% and 0.025% having been obtained for single and three-phase signals, respectively.

Energy Conservation Law in Industrial Architecture: An Approach through Geometric Algebra

Since 1892, the electrical engineering scientific community has been seeking a power theory for interpreting the power flow within electric networks under non-sinusoidal conditions. Although many power theories have been proposed regarding non-sinusoidal operation, an adequate solution is yet to be found. Using the framework based on complex algebra in non-sinusoidal circuit analysis (frequency domain), the verification of the energy conservation law is only possible in sinusoidal situations. In this case, reactive energy turns out to be proportional to the energy difference between the average electric and magnetic energies stored in the loads and its cancellation is mathematically trivial. However, in industrial architecture, apparent power definition of electric loads (non-sinusoidal conditions) is inconsistent with the energy conservation law. Up until now, in the classical complex algebra approach, this goal is only valid in the case of purely resistive loads. Thus, in this paper, a new circuit analysis approach using geometric algebra is used to develop the most general proof of energy conservation in industrial building loads. In terms of geometric objects, this powerful tool calculates the voltage, current, and apparent power in electrical systems in non-sinusoidal, linear/nonlinear situations. In contrast to the traditional method developed by Steinmetz, the suggested powerful tool extends the concept of phasor to multivector-phasors and is performed in a new Generalized Complex Geometric Algebra structure (CGn), where Gn is the Clifford algebra in n-dimensional real space and C is the complex vector space. To conclude, a numerical example illustrates the clear advantages of the approach suggested in this paper.

Analysis of instantaneous NSV&C in polyphase systems

(N-1)-phase N-wire systems are analyzed into an orthonormal-coordinate system using the fundamental laws of polyphase systems and the condition of zero neutral-current. N-dimension voltage vectors are referenced to a virtual star-point and the current vectors are decomposed into three mutually orthogonal components, two of them are responsible of the active power. Without the condition of zero neutral-current, results are modified: the current vector is decomposed into a power-current vector and a complementary current vector. Only the first component transports the instantaneous collective power, the other is useless. The analysis is valid for a general situation and shows the condition of line losses minimization after compensation with active power filters.

Power factor optimization with switched-LC networks

A new reactive power compensator consisting of a set of parallel LC branches, which can be automatically switched, is proposed. This permits operation under nonsinusoidal conditions and time-varying loads. A control system, which measures the equivalent admittance on the load side, and sets the optimal LC configuration to minimize the reactive component of the line current, has been used. Thus, the synthesized compensator presents an equivalent harmonic-susceptance which is approximately equal (as given by its discrete structure) to that of the load (with opposite sign) within the appropriate frequency range. Numerical simulation and experimental results are presented.