Advantages of Geometric Algebra Over Complex Numbers in the Analysis of Networks With Nonsinusoidal Sources and Linear Loads

作者：Castro Nunez Milton^*; Castro Puche Robinson

来源：IEEE Transactions on Circuits and Systems I-Regular Papers, 2012, 59(9): 2056-2064.

DOI：10.1109/TCSI.2012.2185291

• Compensator design
• harmonics
• power factor
• power flow
• reactive and apparent power

An alternative circuit analysis technique is used to study networks with nonsinusoidal sources and linear loads. In contrast to the technique developed by Steinmetz, this method is supported by geometric algebra instead of the algebra of complex numbers, uses multivectors in place of phasors and is performed in the G(N) domain instead of the frequency domain. The advantages of this method over the present technique involve: determining the flow of current and power quantities in the circuit, validating the results using the principle of conservation of energy, discerning and revealing other forms of reactive power generation, and the ability to design compensators with great flexibility. The power equation is composed of the active power and the CN-power representing the nonactive power. All the CN-power terms are sorted into reactive power terms due to phase shift, reactive power terms due to harmonic interactions and degrading power terms which determine the new quantity called degrading power. This decomposition shows that estimating these quantities is intricate. It also displays the power equation%26apos;s functionality for power factor improvement. The geometric addition of power quantities is not pre-established but results from applying the established norm and yields the new quantity called net apparent power.

• 出版日期2012-9