Current loads (I)¶
They represent loads for which the current is considered constant, i.e. the power is proportional to the voltage.
ZIP equation: \(S = 0 \times V^0 + i \times V^1 + 0 \times V^2 \implies S \propto V\)
Equations¶
The equations are the following for star loads given the constant currents \(i_{\mathrm{abc}}\):
\[\begin{split}\left\{
\begin{aligned}
\underline{I_{\mathrm{abc}}} &= i_{\mathrm{abc}} \frac{\underline{V_{\mathrm{abc}}}
-\underline{V_{\mathrm{n}}}}{|\underline{V_{\mathrm{abc}}}-\underline{V_{\mathrm{n}}}|} \\
\underline{I_{\mathrm{n}}} &= -\sum_{p\in\{\mathrm{a},\mathrm{b},\mathrm{c}\}}\underline{I_{p}}
\end{aligned}
\right.\end{split}\]
And the following for delta loads given the constant currents \(i_{\mathrm{ab}}\), \(i_{\mathrm{bc}}\) and \(i_{\mathrm{ca}}\):
\[\begin{split}\left\{
\begin{aligned}
\underline{I_{\mathrm{ab}}} &= i_{\mathrm{ab}} \frac{\underline{V_{\mathrm{a}}}
-\underline{V_{\mathrm{b}}}}{|\underline{V_{\mathrm{a}}}-\underline{V_{\mathrm{b}}}|} \\
\underline{I_{\mathrm{bc}}} &= i_{\mathrm{bc}} \frac{\underline{V_{\mathrm{b}}}
-\underline{V_{\mathrm{c}}}}{|\underline{V_{\mathrm{b}}}-\underline{V_{\mathrm{c}}}|} \\
\underline{I_{\mathrm{ca}}} &= i_{\mathrm{ca}} \frac{\underline{V_{\mathrm{c}}}
-\underline{V_{\mathrm{a}}}}{|\underline{V_{\mathrm{c}}}-\underline{V_{\mathrm{a}}}|}
\end{aligned}
\right.\end{split}\]
Example¶
import functools as ft
import numpy as np
import roseau.load_flow as rlf
# Two buses
bus1 = rlf.Bus(id="bus1", phases="abcn")
bus2 = rlf.Bus(id="bus2", phases="abcn")
# A line
lp = rlf.LineParameters(id="lp", z_line=rlf.Q_(0.35 * np.eye(4), "ohm/km"))
line = rlf.Line(id="line", bus1=bus1, bus2=bus2, parameters=lp, length=rlf.Q_(1, "km"))
# A voltage source on the first bus
un = 400 / np.sqrt(3)
vs = rlf.VoltageSource(id="source", bus=bus1, voltages=rlf.Q_(un, "V"))
# The potential of the neutral of bus1 is fixed at 0V
pref = rlf.PotentialRef(id="pref", element=bus1)
# A balanced constant-current load on the second bus: 5A per phase
load = rlf.CurrentLoad(id="load", bus=bus2, currents=rlf.Q_(5, "A"))
# Create a network and solve a load flow
en = rlf.ElectricalNetwork.from_element(bus1)
en.solve_load_flow()
# Get the current of the load (equal to the one provided)
en.res_loads["current"].transform([np.abs, ft.partial(np.angle, deg=True)])
# | | absolute | angle |
# |:--------------|------------:|-----------:|
# | ('load', 'a') | 5 | 0 |
# | ('load', 'b') | 5 | -120 |
# | ('load', 'c') | 5 | 120 |
# | ('load', 'n') | 1.77636e-15 | -71.5651 |
# Get the voltages of the network
en.res_buses_voltages["voltage"].transform([np.abs, ft.partial(np.angle, deg=True)])
# | | ('voltage', 'absolute') | ('voltage', 'angle') |
# |:---------------|--------------------------:|-----------------------:|
# | ('bus1', 'an') | 230.94 | 0 |
# | ('bus1', 'bn') | 230.94 | -120 |
# | ('bus1', 'cn') | 230.94 | 120 |
# | ('bus2', 'an') | 229.19 | 0 |
# | ('bus2', 'bn') | 229.19 | -120 |
# | ('bus2', 'cn') | 229.19 | 120 |
# Create an unbalanced load with three different current values
load.currents = rlf.Q_(np.array([5.0, 2.5, 0]) * rlf.PositiveSequence, "A")
en.solve_load_flow()
# Get the currents of the loads of the network
en.res_loads["current"].transform([np.abs, ft.partial(np.angle, deg=True)])
# | | absolute | angle |
# |:--------------|-----------:|------------:|
# | ('load', 'a') | 5 | -0.187647 |
# | ('load', 'b') | 2.5 | 119.999 |
# | ('load', 'c') | 0 | -0 |
# | ('load', 'n') | 4.32197 | -150.188 |