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All loads will be described in terms of ZIP fractions and represented by voltage and current injections into the powerflow solution. The loads will be connected in a nodal manner so that any combination of wye and delta connected loads can be attached to a single bus.

Parameters

The parameters required to determine the current injections due to a load connected to nodes [math]n[/math] and [math]m[/math] of a bus are listed below.

  • [math]|S_{b,nm}|[/math] The magnitude of the base absolute power of the load connected to nodes [math]n[/math] and [math]m[/math] of a particular bus (VA) at [math]V_{b,nm}[/math].
  • [math]V_{nm}[/math] The variable voltage difference between the node to ground voltages of nodes [math]n[/math] and [math]m[/math] of a particular bus (V).
  • [math]|V_{b,nm}|[/math] The magnitude of the base voltage difference between the node to ground voltages of nodes [math]n[/math] and [math]m[/math] of a particular bus (V).
  • [math]pfr_{p,nm}[/math] The constant power fraction of the load connected to nodes [math]n[/math] and [math]m[/math] of a particular bus (unitless).
  • [math]pf_{p,nm}[/math] The power factor of the constant power fraction of the load connected to nodes [math]n[/math] and [math]m[/math] of a particular bus (-1.0 - 1.0).
  • [math]pfr_{i,nm}[/math] The constant current fraction of the load connected to nodes [math]n[/math] and [math]m[/math] of a particular bus (unitless) at [math]V_{b,nm}[/math].
  • [math]pf_{i,nm}[/math] The power factor of the constant current fraction of the load connected to nodes [math]n[/math] and [math]m[/math] of a particular bus (-1.0 - 1.0) at [math]V_{b,nm}[/math].
  • [math]pfr_{z,nm}[/math] The constant impedance fraction of the load connected to nodes [math]n[/math] and [math]m[/math] of a particular bus (unitless) at [math]V_{b,nm}[/math].
  • [math]pf_{z,nm}[/math] The power factor of the constant impedance fraction of the load connected to nodes [math]n[/math] and [math]m[/math] of a particular bus (-1.0 - 1.0) at [math]V_{b,nm}[/math].

Equations

For the parameters described above the current injections due to each type of load fraction can be found below.

Constant Impedance Loads

The constant impedance of the load can be found by the following equations

[math]\displaystyle{}S_{z,nm}=S_{b,nm}*pfr_{z,nm}*[pf_{z,nm}+j*sign(pf_{z,nm})*(1-pf_{z,nm}^{2})^{\frac{1}{2}}][/math]
[math]\displaystyle{}Z_{nm}=\frac{|V_{b,nm}|^{2}}{S_{z,nm}^{*}}[/math]

The current injection due to the constant impedance can then be found from the equation below.

[math]\displaystyle{}I_{z,nm}=\frac{V_{nm}}{Z_{nm}}[/math]

Constant Current Loads

The constant current of the load can be found by the following equations

[math]\displaystyle{}S_{i,nm}=S_{b,nm}*pfr_{i,nm}*[pf_{i,nm}+j*sign(pf_{i,nm})*(1-pf_{i,nm}^{2})^{\frac{1}{2}}][/math]
[math]\displaystyle{}I_{nm}=(\frac{S_{i,nm}}{|V_{b,nm}|})^{*}[/math]

The current injection due to the constant impedance can then be found from the equation below.

[math]\displaystyle{}I_{i,nm}=I_{nm}[/math]

Constant Power Loads

The constant Power of the load can be found by the following equation

[math]\displaystyle{}S_{p,nm}=S_{b,nm}*pfr_{p,nm}*[pf_{p,nm}+j*sign(pf_{p,nm})*(1-pf_{p,nm}^{2})^{\frac{1}{2}}][/math]

The current injection due to the constant impedance can then be found from the equation below.

[math]\displaystyle{}I_{p,nm}=(\frac{S_{p,nm}}{V_{nm}})^{*}[/math]

Total Current Injection

The total current injection into a node [math]n[/math] due to loads connecting node [math]n[/math] to any number of other nodes on the same bus can be found by the following equation

[math]\displaystyle{}I_{n}=\Sigma (I_{z,nj}+I_{i,nj}+I_{p,nj})[/math]

where [math]j[/math] are the nodes the loads connect node [math]n[/math] to on a bus.