scholarly journals Geometric Algebra Framework Applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1259
Author(s):  
Francisco G. Montoya ◽  
Raúl Baños ◽  
Alfredo Alcayde ◽  
Francisco Manuel Arrabal-Campos ◽  
Javier Roldán Roldán Pérez
Keyword(s):  
Geometric Algebra ◽  
Dimensional Euclidean Space ◽  
Active Components ◽  
Electrical Circuits ◽  
Current Harmonics ◽  
Operation Conditions ◽  
Multiple Phase ◽  
Three Phase ◽  
Phase Systems ◽  
Definition Of

This paper presents a new framework based on geometric algebra (GA) to solve and analyse three-phase balanced electrical circuits under sinusoidal and non-sinusoidal conditions. The proposed approach is an exploratory application of the geometric algebra power theory (GAPoT) to multiple-phase systems. A definition of geometric apparent power for three-phase systems, that complies with the energy conservation principle, is also introduced. Power calculations are performed in a multi-dimensional Euclidean space where cross effects between voltage and current harmonics are taken into consideration. By using the proposed framework, the current can be easily geometrically decomposed into active- and non-active components for current compensation purposes. The paper includes detailed examples in which electrical circuits are solved and the results are analysed. This work is a first step towards a more advanced polyphase proposal that can be applied to systems under real operation conditions, where unbalance and asymmetry is considered.

scholarly journals Geometric algebra framework applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply

2020 ◽  
Author(s):  
Francisco Montoya ◽  
Raul Baños ◽  
Alfredo Alcayde ◽  
Francisco M. Arrabal-Campos ◽  
Javier Roldan-Perez
Keyword(s):  
Geometric Algebra ◽  
Dimensional Euclidean Space ◽  
Active Components ◽  
Electrical Circuits ◽  
Current Harmonics ◽  
Three Phase ◽  
Phase Systems ◽  
Definition Of ◽  
Conservation Theorem ◽  
New Framework

This paper presents a new framework based on geometric algebra (GA) for solving and analysing three-phase balanced electrical circuits under sinusoidal and non-sinusoidal conditions. The proposed approach is an application of the geometric algebra power theory (GAPoT) to three-phase systems. Calculations are performed in a multi-dimensional Euclidean space where cross effects between voltage and current harmonics are taken into consideration. A definition of geometric apparent power for three-phase systems that complies with the energy conservation theorem is introduced. By using the proposed framework, the current can be easily decomposed into active- and non-active components for current compensation purposes. The paper includes detailed examples in which electrical circuits are solved and the results are analysed. This work is a first step towards a more advanced polyphase proposal with realistic cases, where unbalance and asymmetry is included.

scholarly journals Vector Geometric Algebra in Power Systems: An Updated Formulation of Apparent Power under Non-Sinusoidal Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1295
Author(s):  
Francisco G. Montoya ◽  
Raúl Baños ◽  
Alfredo Alcayde ◽  
Francisco Manuel Arrabal-Campos ◽  
Javier Roldán-Pérez
Keyword(s):  
Energy Balance ◽  
Power Systems ◽  
Electric Power ◽  
Geometric Algebra ◽  
Single Phase ◽  
Electrical Power ◽  
Electrical Circuits ◽  
Distorted Grid ◽  
Alternative Expression ◽  
Phase Systems

Traditional electrical power theories and one of their most important concepts—apparent power—are still a source of debate, because they present several flaws that misinterpret the power-transfer and energy-balance phenomena under distorted grid conditions. In recent years, advanced mathematical tools such as geometric algebra (GA) have been introduced to address these issues. However, the application of GA to electrical circuits requires more consensus, improvements and refinement. In this paper, electrical power theories for single-phase systems based on GA were revisited. Several drawbacks and inconsistencies of previous works were identified, and some amendments were introduced. An alternative expression is presented for the electric power in the geometric domain. Its norm is compatible with the traditional apparent power defined as the product of the RMS voltage and current. The use of this expression simplifies calculations such as those required for current decomposition. This proposal is valid even for distorted currents and voltages. Concepts are presented in a simple way so that a strong background on GA is not required. The paper included some examples and experimental results in which measurements from a utility supply were analysed.

Suppression of Major Current Harmonics for Dual Three Phase PMSMs by Virtual Multi Three Phase Systems

2021 ◽  
pp. 1-1
Author(s):  
Luocheng Yan ◽  
Z.Q. Zhu ◽  
Ji Qi ◽  
Yuan Ren ◽  
Chengwei Gan ◽  
...  
Keyword(s):  
Current Harmonics ◽  
Three Phase ◽  
Phase Systems

Research the Test Method of the Voltage Transformer Secondary Load in the Three-Phase Three-Wire Electric Energy Metering Device

2014 ◽  
Vol 687-691 ◽  
pp. 3110-3115
Author(s):  
Gu Li ◽  
Zi Ming Fu ◽  
Jie Feng Yan ◽  
Bing Wen Li ◽  
Zhi Rong Cen
Keyword(s):  
Power Supply System ◽  
Electric Energy ◽  
Test Methods ◽  
Test Method ◽  
Testing Methods ◽  
Voltage Transformer ◽  
Secondary Load ◽  
Three Phase ◽  
Energy Metering ◽  
Definition Of

This paper analyzes and studies the definition of the voltage transformer secondary load, examines the practical purposes of the measured values of the voltage transformer secondary load, and presents a variety of testing methods to analyze and compare the differences. This paper gives the test methods of the voltage transformer secondary load when the connection of the voltage transformer is the Y / Y in a three-phase three-wire power supply system, filling the blank of this type of test method in the industry. When other units within the industry carry out such work, the conclusions of this paper are available for reference, and the conclusions of this paper can be referred when drafting relevant regulations in the future.

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