Algebra for power systems

Can geometric algebra be used in electrical circuits?

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.

Does geometric algebra explain power flows under unbalanced grid conditions?

However, none of them provide a clear overview of power flows under disported and unbalanced grid conditions, and this point is still an open discussion [ 9 ]. Geometric algebra (GA) is a mathematical tool developed by W. K. Clifford and H. Grassmann at the end of the 19th Century.

What is geometric power based on?

Furthermore, the norm of the geometric power was in good agreement with the traditional definition of apparent power based on the product of RMS voltage and current. Circuit theory analysis can also be performed in the steady state for AC circuits using geometric vectors.

What is a geometric product in power flow analysis?

Geometric Algebra for Power Flow Analysis The geometric product was introduced by Clifford at the end of the 19th Century, and it includes the exterior (Grassmann) and interior (dot) products of vectors. Suppose a Euclidean two-dimensional vector space spanned by the basis and elements such as and with .

How do we convert power system DAEs into ordinary differential equations (ODEs)?

We leverage a symbolic programming framework to equivalently convert the power system's DAEs into ordinary differential equations (ODEs) using index reduction methods and then encode their data into qubits using amplitude encoding.

How is complex power determined?

The complex power is determined by the following relation: while its direction is consistent with the direction of active power. The length of this power vector is called the geometric apparent power , which in this example is: ... ... Electric and magnetic field in 2D using geometric algebra.