Newton-Raphson Power Flow¶

In this example, we are going to create a network with three nodes, three lines, one load, and one generator with given setpoints. We then solve the non-linear power flow equations using the Newton-Raphson method applied in n.pf().

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import numpy as np

import pypsa

n = pypsa.Network()

N_BUSES = 3

import numpy as np import pypsa n = pypsa.Network() N_BUSES = 3

Add three buses:

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for i in range(N_BUSES):
    n.add("Bus", f"My bus {i}", v_nom=20)

n.buses

for i in range(N_BUSES): n.add("Bus", f"My bus {i}", v_nom=20) n.buses

Add three lines in a ring

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for i in range(N_BUSES):
    n.add(
        "Line",
        f"My line {i}",
        bus0=f"My bus {i}",
        bus1=f"My bus {(i + 1) % N_BUSES}",
        x=0.1,
        r=0.01,
    )

n.lines

for i in range(N_BUSES): n.add( "Line", f"My line {i}", bus0=f"My bus {i}", bus1=f"My bus {(i + 1) % N_BUSES}", x=0.1, r=0.01, ) n.lines

Add a generator at bus 0

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n.add("Generator", "My gen", bus="My bus 0", p_set=100, control="PQ")

n.generators

n.add("Generator", "My gen", bus="My bus 0", p_set=100, control="PQ") n.generators

Add a load at bus 1

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n.add("Load", "My load", bus="My bus 1", p_set=100, q_set=100)

n.loads

n.add("Load", "My load", bus="My bus 1", p_set=100, q_set=100) n.loads

Do a Newton-Raphson power flow

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n.pf()

n.pf()

Alright, it converged! Now, what is the active power flow on the lines?

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n.lines_t.p0

n.lines_t.p0

...and what are the voltage angles on the buses?

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n.buses_t.v_ang * 180 / np.pi

n.buses_t.v_ang * 180 / np.pi

...and their mangitudes?

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n.buses_t.v_mag_pu

n.buses_t.v_mag_pu