Static power flow¶
%matplotlib inline
import matplotlib.pyplot as plt
import matplotlib
import numpy as np
from dem import *
matplotlib.rc("figure", figsize=(7,7))
matplotlib.rc("lines", linewidth=2)
Basic examples¶
Hello world¶
load = FixedLoad(power=100)
gen = Generator(power_max=1000, alpha=0.01, beta=100)
net = Net([load.terminals[0], gen.terminals[0]])
network = Group([load, gen], [net])
network.init_problem()
network.problem.solve()
print network.results.summary()
Terminal Power
-------- -----
FixedLoad[0] 100.0000
Generator[0] -100.0000
Net Price
--- -----
Net 102.0001
Curtailable load¶
load = CurtailableLoad(power=1000, alpha=150)
gen = Generator(power_max=1000, alpha=1, beta=100)
net = Net([load.terminals[0], gen.terminals[0]])
network = Group([load, gen], [net])
network.init_problem()
network.problem.solve()
print network.results.summary()
Terminal Power
-------- -----
CurtailableLoad[0] 25.0026
Generator[0] -25.0026
Net Price
--- -----
Net 150.0000
Two generators, transmission line¶
load = FixedLoad(power=100)
gen1 = Generator(power_max=1000, alpha=0.01, beta=100, name="Gen1")
gen2 = Generator(power_max=100, alpha=0.1, beta=0.1, name="Gen2")
line = TransmissionLine(power_max=50)
net1 = Net([load.terminals[0], gen1.terminals[0], line.terminals[0]])
net2 = Net([gen2.terminals[0], line.terminals[1]])
network = Group([load, gen1, gen2, line], [net1, net2])
network.init_problem()
network.problem.solve()
print network.results.summary()
Terminal Power
-------- -----
FixedLoad[0] 100.0000
TransmissionLine[0] -50.0000
TransmissionLine[1] 50.0000
Gen2[0] -50.0000
Gen1[0] -50.0000
Net Price
--- -----
Net 101.0000
Net 10.1000
Three buses¶
Figure 2.1 from Kraning, et al. without the battery.
Three bus example
load1 = FixedLoad(power=50, name="Load1")
load2 = FixedLoad(power=100, name="Load2")
gen1 = Generator(power_max=1000, alpha=0.01, beta=100, name="Gen1")
gen2 = Generator(power_max=100, alpha=0.1, beta=0.1, name="Gen2")
line1 = TransmissionLine(power_max=50)
line2 = TransmissionLine(power_max=10)
line3 = TransmissionLine(power_max=50)
net1 = Net([load1.terminals[0], gen1.terminals[0], line1.terminals[0], line2.terminals[0]])
net2 = Net([load2.terminals[0], line1.terminals[1], line3.terminals[0]])
net3 = Net([gen2.terminals[0], line2.terminals[1], line3.terminals[1]])
network = Group([load1, load2, gen1, gen2, line1, line2, line3], [net1, net2, net3])
network.init_problem()
network.problem.solve()
print network.results.summary()
Terminal Power
-------- -----
TransmissionLine[1] 50.0000
TransmissionLine[0] -10.0000
Gen2[0] -60.0000
Gen1[0] -90.0000
TransmissionLine[0] 50.0000
TransmissionLine[1] -50.0000
Load2[0] 100.0000
Load1[0] 50.0000
TransmissionLine[1] 10.0000
TransmissionLine[0] -50.0000
Net Price
--- -----
Net 101.8008
Net 196.1907
Net 12.0975
Grouping devices¶
We can wrap up several devices and nets into a single device
solar = Generator(power_max=10, alpha=0, beta=0, name="Solar")
load = FixedLoad(power=13)
line = TransmissionLine(power_max=25)
net = Net([load.terminals[0], solar.terminals[0], line.terminals[0]])
home = Group([solar, load, line], [net], [line.terminals[1]], name="Home")
grid = Generator(power_max=1e6, alpha=0.05, beta=100, name="Grid")
meter = Net([line.terminals[1], grid.terminals[0]], name="Meter")
network = Group([home, grid], [meter])
network.init_problem()
network.problem.solve()
print network.results.summary()
Terminal Power
-------- -----
FixedLoad[0] 13.0000
TransmissionLine[1] 3.0000
Solar[0] -10.0000
Grid[0] -3.0000
TransmissionLine[0] -3.0000
Net Price
--- -----
Net 100.3000
Meter 100.3000
Varying parameters¶
We can modify a single parameter and reoptimize, which is useful for sweeping over a parameter range.
load1 = FixedLoad(power=50, name="Load1")
load2 = FixedLoad(power=100, name="Load2")
gen1 = Generator(power_max=100, alpha=1, beta=10, name="Gen1")
gen2 = Generator(power_max=1000, alpha=0.01, beta=0, name="Gen2")
line1 = TransmissionLine(power_max=100)
line2 = TransmissionLine(power_max=10)
line3 = TransmissionLine(power_max=Parameter(1))
net1 = Net([load1.terminals[0], gen1.terminals[0], line1.terminals[0], line2.terminals[0]])
net2 = Net([load2.terminals[0], line1.terminals[1], line3.terminals[0]])
net3 = Net([gen2.terminals[0], line2.terminals[1], line3.terminals[1]])
network = Group([load1, load2, gen1, gen2, line1, line2, line3], [net1, net2, net3])
network.init_problem()
xs = np.linspace(0, 150, 100)
prices = np.empty((len(xs), 3))
for i, x in enumerate(xs):
line3.power_max.value = x
network.problem.solve()
prices[i,:] = [net.price for net in network.nets]
plt.plot(xs, prices)
plt.xlabel("Line capacity")
plt.ylabel("Price")
plt.legend(["Bus 1", "Bus 2", "Bus 3"])
<matplotlib.legend.Legend at 0x1103feb90>
