Juan-Carlos Bravo

Power System Frequency Measurement Under Nonstationary Situations

A new method for the measurement of the instantaneous power-system frequency is proposed. It is based on the frequency estimation of the voltage signal using three equidistant samples. An algorithm is developed that diminishes the variance of the estimation. The procedure is applied to the case of single- and three-phase networks, and uncertainty in the frequency estimation is obtained with simulated signal and severe conditions of signal quality. A frequency variation has been assumed as plusmn2 Hz around the nominal value, with a maximum rate of change of 1 Hz/s. The uncertainty of 25 mHz and 3.5 mHz has been obtained for single- and three-phase signals, respectively. A low-cost virtual instrument has been developed to make frequency measurements over the actual voltage signal.

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.

Disturbance Ratio for Optimal Multi-Event Classification in Power Distribution Networks

This paper presents an effective approach to identify power quality (PQ) events based on IEEE Std 1159-2009 caused by intermittent power sources like those of renewable energy. An efficient characterization of these disturbances is granted by the use of two useful wavelet-based indices. For this purpose, a wavelet-based global disturbance ratio (GDR) index, defined through its instantaneous precursor [instantaneous transient disturbance ITD(t) index], is used in power distribution networks (PDNs) under steady-state and/or transient conditions. An intelligent disturbance classification is done using a support vector machine (SVM) with a minimum input vector based on the GDR index. The effectiveness of the proposed technique is validated using a real-time experimental system with single event and multi-event signals.

The geometric algebra as a power theory analysis tool

In this paper, a multivectorial decomposition of power equation in single-phase circuits for periodic n-sinusoidal /linear and nonlinear conditions is presented. It is based on a frequency-domain Clifford vector space approach. By using a new generalized complex geometric algebra (GCGA), we define the voltage and current complex-vector and apparent power multivector concepts. First, the apparent power multivector is defined as geometric product of vector-phasors (complex-vectors). This new expression result in a novel representation and generalization of the apparent power similar to complex-power in single-frequency sinusoidal conditions. Second, in order to obtain a multivectorial representation of any proposed power equation, the current vector-phasor is decomposed into orthogonal components. The power multivector concept, consisting of complex-scalar and complex-bivector parts with magnitude, direction and sense, obeys the apparent power conservation law and it handles different practical electric problems where direction and sense are necessary. The results of numerical examples are presented to illustrate the proposed approach to power theory analysis.

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-quality Factor for Electrical Networks

The ever-growing proliferation of power-switching devices for source conditioning and motion control in single-phase and three-phase modern industrial applications has increased the occurrence of unbalanced currents, unacceptable harmonic levels and poor power factor in three-phase distribution systems. The harmful and costly effects of harmonics have been discussed extensively [15, 40] and spurred stringent requirements by international institutions regarding the allowed levels of harmonics at the point of connection to the power supply [19, 24, 32]. Unbalanced loading of the three-phase supply has other no less detrimental effects such as the underutilisation of the power-supply equipment and overloading of neutral conductors with fundamental frequency in addition to harmonic currents. Also, as is well known, a phase displacement between corresponding voltages and currents indicate both a low utilization of the generation and distribution equipment and increased line losses for the same power-consumption level.