Note

You can download this example as a Jupyter notebook or start it in interactive mode.

Minimal three node network#

Here, we are going to create a network with three nodes, three lines and one generator. We then solve the non-linear power flow using a Newton-Raphson.

[1]:

import pypsa
import numpy as np

ERROR 1: PROJ: proj_create_from_database: Open of /home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/latest/share/proj failed

[2]:

network = pypsa.Network()

Add three buses

[3]:

n_buses = 3

for i in range(n_buses):
    network.add("Bus", "My bus {}".format(i), v_nom=20.0)

network.buses

[3]:

attribute	v_nom	x	y	carrier	v_mag_pu_set	v_mag_pu_min	v_mag_pu_max	control
Bus
My bus 0	20.0	0.0	0.0	AC	1.0	0.0	inf	PQ
My bus 1	20.0	0.0	0.0	AC	1.0	0.0	inf	PQ
My bus 2	20.0	0.0	0.0	AC	1.0	0.0	inf	PQ

Add three lines in a ring

[4]:

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

network.lines

[4]:

attribute	bus0	bus1	x	r	g	b	s_nom	s_nom_mod	s_nom_extendable	...	v_ang_min	v_ang_max	x_pu	r_pu	g_pu	b_pu	x_pu_eff	r_pu_eff	s_nom_opt
Line
My line 0	My bus 0	My bus 1	0.1	0.01	0.0	0.0	0.0	0.0	False	...	-inf	inf	0.0	0.0	0.0	0.0	0.0	0.0	0.0
My line 1	My bus 1	My bus 2	0.1	0.01	0.0	0.0	0.0	0.0	False	...	-inf	inf	0.0	0.0	0.0	0.0	0.0	0.0	0.0
My line 2	My bus 2	My bus 0	0.1	0.01	0.0	0.0	0.0	0.0	False	...	-inf	inf	0.0	0.0	0.0	0.0	0.0	0.0	0.0

3 rows × 30 columns

Add a generator at bus 0

[5]:

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

network.generators

[5]:

attribute	bus	control	type	p_nom	p_nom_mod	p_nom_extendable	p_nom_min	p_nom_max	p_min_pu	p_max_pu	...	min_up_time	min_down_time	up_time_before	down_time_before	ramp_limit_up	ramp_limit_down	ramp_limit_start_up	ramp_limit_shut_down	weight	p_nom_opt
Generator
My gen	My bus 0	PQ		0.0	0.0	False	0.0	inf	0.0	1.0	...	0	0	1	0	NaN	NaN	1.0	1.0	1.0	0.0

1 rows × 34 columns

[6]:

network.generators.p_set

[6]:

Generator
My gen    100.0
Name: p_set, dtype: float64

Add a load at bus 1

[7]:

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

network.loads

[7]:

attribute	bus	carrier	type	p_set	q_set	sign
Load
My load	My bus 1			100.0	0.0	-1.0

[8]:

network.loads.p_set

[8]:

Load
My load    100.0
Name: p_set, dtype: float64

Fix the reactive power of the load

[9]:

network.loads.q_set = 100.0

Do a Newton-Raphson power flow

[10]:

network.pf()

INFO:pypsa.pf:Performing non-linear load-flow on AC sub-network SubNetwork 0 for snapshots Index(['now'], dtype='object', name='snapshot')

INFO:pypsa.pf:Newton-Raphson solved in 3 iterations with error of 0.000000 in 0.015694 seconds

[10]:

{'n_iter': SubNetwork  0
 snapshot
 now         3,
 'error': SubNetwork             0
 snapshot
 now         4.753531e-10,
 'converged': SubNetwork     0
 snapshot
 now         True}

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

[11]:

network.lines_t.p0

[11]:

	My line 0	My line 1	My line 2
snapshot
now	66.897487	-33.333333	-33.391038

…and what are the voltage angles on the buses?

[12]:

network.buses_t.v_ang * 180 / np.pi

[12]:

Bus	My bus 0	My bus 1	My bus 2
snapshot
now	0.0	-0.875939	-0.433813

…and their mangitudes?

[13]:

network.buses_t.v_mag_pu

[13]:

Bus	My bus 0	My bus 1	My bus 2
snapshot
now	1.0	0.981199	0.99057